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LI, TONGLEI. MATTEI ALESSANDRA - PHARMACEUTICAL CRYSTALS science and engineering. (2018, WILEY-BLACKWELL)

Pharmaceutical Crystals
Pharmaceutical Crystals
Science and Engineering
Edited by
Tonglei Li
Department of Industrial and Physical Pharmacy, Purdue University
West Lafayette, IN, USA
Alessandra Mattei
AbbVie Inc.
North Chicago, IL, USA
This edition first published 2019
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Library of Congress Cataloging-in-Publication Data
Names: Li, Tonglei, 1967– editor. | Mattei, Alessandra, 1977 June 18– editor.
Title: Pharmaceutical crystals : science and engineering / edited by Tonglei
Li, Alessandra Mattei.
Description: First edition. | Hoboken, NJ : John Wiley & Sons, 2018. |
Includes bibliographical references and index. |
Identifiers: LCCN 2018016966 (print) | LCCN 2018031765 (ebook) | ISBN
9781119046202 (Adobe PDF) | ISBN 9781119046349 (ePub) | ISBN 9781119046295
(hardcover)
Subjects: LCSH: Crystals–Structure. | Pharmaceutical chemistry. | Drug
development.
Classification: LCC QD921 (ebook) | LCC QD921 .P478 2018 (print) | DDC
548–dc23
LC record available at https://lccn.loc.gov/2018016966
Cover design by Wiley
Cover image: Courtesy of Tonglei Li
Set in 10/12pt Warnock by SPi Global, Pondicherry, India
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
v
Contents
List of Contributors
Preface xv
xiii
1
Crystallography 1
Susan M. Reutzel-Edens and Peter Müller
1.1
1.2
1.3
1.3.1
1.3.2
1.3.3
1.3.4
1.3.5
1.3.6
1.3.7
1.4
1.4.1
1.4.2
1.4.3
1.4.4
1.4.5
1.4.6
1.5
1.5.1
1.5.2
1.5.3
1.5.3.1
1.6
1.6.1
1.6.2
Introduction 1
History 6
Symmetry 7
Symmetry in Two Dimensions 7
Symmetry and Translation 11
Symmetry in Three Dimensions 12
Metric Symmetry of the Crystal Lattice 13
Conventions and Symbols 14
Fractional Coordinates 15
Symmetry in Reciprocal Space 15
Principles of X-ray Diffraction 17
Bragg’s Law 17
Diffraction Geometry 19
Ewald Construction 19
Structure Factors 21
Statistical Intensity Distribution 22
Data Collection 23
Structure Determination 24
Space Group Determination 24
Phase Problem and Structure Solution 25
Structure Refinement 28
Resonant Scattering and Absolute Structure 32
Powder Methods 33
Powder Diffraction 34
NMR Crystallography 35
vi
Contents
1.7
1.8
1.9
Crystal Structure Prediction 39
Crystallographic Databases 41
Conclusions 42
References 43
2
Nucleation 47
Junbo Gong and Weiwei Tang
2.1
2.2
2.2.1
2.2.2
2.2.3
2.2.4
2.2.5
2.3
2.3.1
2.3.2
2.4
2.4.1
2.4.2
2.5
2.5.1
2.5.2
2.5.3
2.5.4
2.5.5
2.5.6
2.6
Introduction 47
Classical Nucleation Theory 48
Thermodynamics 48
Kinetics of Nucleation 51
Metastable Zone 53
Induction Time 58
Heterogeneous Nucleation 60
Nonclassical Nucleation 63
Two-Step Mechanism 63
Prenucleation Cluster Pathway 66
Application of Primary Nucleation 66
Understanding and Control of Polymorphism 66
Liquid–Liquid Phase Separation 71
Secondary Nucleation 73
Origin from Solution 74
Origin from Crystals 75
Kinetics 76
Application to Continuous Crystallization 76
Crystal Size Distribution 79
Seeding 80
Summary 81
References 82
3
Solid-state Characterization Techniques
Ann Newman and Robert Wenslow
3.1
3.2
3.2.1
3.2.2
3.2.2.1
3.2.2.2
3.2.3
3.2.3.1
3.2.3.2
3.2.3.3
Introduction 89
Techniques 90
X-ray Powder Diffraction (XRPD) 90
Thermal Methods 94
Differential Scanning Calorimetry 94
Thermogravimetric Analysis (TGA) 95
Spectroscopy 97
Infrared (IR) 97
Raman Spectroscopy 99
Solid-state Nuclear Magnetic Resonance (SSNMR)
89
101
Contents
3.2.4
3.2.5
3.3
3.4
Water Sorption 105
Microscopy 106
Case Study LY334370 Hydrochloride (HCl)
Summary 114
References 114
4
Intermolecular Interactions and Computational Modeling
Alessandra Mattei and Tonglei Li
4.1
4.2
4.2.1
4.2.2
4.2.3
4.2.4
4.3
4.3.1
4.3.2
4.3.3
4.4
4.4.1
4.4.2
4.4.3
4.4.3.1
4.4.3.2
4.5
4.5.1
4.5.2
Introduction 123
Foundation of Intermolecular Interactions 124
Electrostatic Interactions 125
van der Waals Interactions 126
Hydrogen-bonding Interactions 127
π–π Interactions 129
Intermolecular Interactions in Organic Crystals 130
Approaches to Crystal Packing Description 130
Impact of Intermolecular Interactions on Crystal Packing 136
Impact of Intermolecular Interactions on Crystal Properties 138
Techniques for Intermolecular Interactions Evaluation 140
Crystallography 140
Spectroscopy 141
Computational Methods 142
Lattice Energy 144
Interaction Energy of Molecular Pairs from Crystal Structures 147
Advances in Understanding Intermolecular Interactions 149
Crystal Structure Prediction 150
Electronic Structural Analysis 152
References 160
5
Polymorphism and Phase Transitions
Haichen Nie and Stephen R. Byrn
5.1
5.2
5.2.1
5.2.2
5.2.3
5.2.4
5.2.4.1
5.2.4.2
5.2.4.3
5.2.4.4
5.2.4.5
Concepts and Overview 169
Thermodynamic Principles of Polymorphic Systems
Monotropy and Enantiotropy 176
Phase Rule 179
Phase Diagrams 179
Phase Stability Rule 182
Heat of Transition Rule 182
Heat of Fusion Rule 182
Entropy of Fusion Rule 183
Heat Capacity Rule 183
Density Rule 183
109
169
175
123
vii
viii
Contents
5.2.4.6
5.2.5
5.2.5.1
5.2.5.2
5.3
5.3.1
5.3.2
5.3.3
5.3.3.1
Infrared Rule 183
Crystallization of Polymorphs 184
Ostwald’s Rule of Stages 184
Nucleation 184
Stabilities and Phase Transition 189
Thermodynamic Stability 189
Chemical Stability 189
Polymorphic Interconversions of Pharmaceuticals 192
Effects of Heat, Compression, and Grinding on Polymorphic
Transformation 192
5.3.3.2 Solution-mediated Phase Transformation of Drugs 193
5.4
Impact on Bioavailability by Polymorphs 194
5.5
Regulatory Consideration of Polymorphism 196
5.6
Novel Approaches for Preparing Solid State Forms 199
5.6.1
High-throughput Crystallization Method 200
5.6.2
Capillary Growth Methods 200
5.6.3
Laser-induced Nucleation 201
5.6.4
Heteronucleation on Single Crystal Substrates 201
5.6.5
Polymer Heteronucleation 201
5.7
Hydrates and Solvates 202
5.7.1
Thermodynamics of Hydrates 203
5.7.2
Formation of Hydrates 204
5.7.3
Desolvation Reactions 205
5.7.4
Phase Transition of Solvates/Hydrates in Formulation and Process
Development 207
5.8
Summary 209
References 210
6
Measurement and Mathematical Relationships of Cocrystal
Thermodynamic Properties 223
Gislaine Kuminek, Katie L. Cavanagh, and Naír Rodríguez-Hornedo
6.1
6.2
6.2.1
6.2.2
6.2.2.1
6.2.2.2
6.2.2.3
6.2.3
6.3
Introduction 223
Structural and Thermodynamic Properties 224
Structural Properties 224
Thermodynamic Properties 226
Cocrystal Ksp and Solubility 226
Transition Points 229
Supersaturation Index Diagrams 231
A Word of Caution About Cmax Obtained from Kinetic Studies 232
Determination of Cocrystal Thermodynamic Stability and
Supersaturation Index 234
Keu Measurement and Relationships Between Ksp, SCC, and SA 234
Cocrystal Solubility and Ksp 241
6.3.1
6.3.2
Contents
6.3.3
6.4
6.5
6.5.1
6.5.2
6.6
6.6.1
6.6.2
6.6.3
6.7
Cocrystal Supersaturation Index and Drug Solubilization 243
What Phase Solubility Diagrams Reveal 246
Cocrystal Discovery and Formation 249
Molecular Interactions That Play an Important Role in Cocrystal
Discovery 249
Thermodynamics of Cocrystal Formation Provide Valuable Insight
into the Conditions Where Cocrystals May Form 251
Cocrystal Solubility Dependence on Ionization and Solubilization
of Cocrystal Components 253
Mathematical Forms of Cocrystal Solubility and Stability 253
General Solubility Expressions in Terms of the Sum of Equilibrium
Concentrations 257
Applications 258
Conclusions and Outlook 265
References 265
7
Mechanical Properties
Changquan Calvin Sun
7.1
7.1.1
Introduction 273
Importance of Mechanical Properties in Pharmaceutical
Manufacturing 273
Basic Concepts Related to Mechanical Properties 274
Stress, Strain, and Poisson’s Ratio 274
Elasticity, Plasticity, and Brittleness 276
Classification of Mechanical Response 277
Characterization of Mechanical Properties 278
Experimental Techniques 278
Single Crystals 278
Bulk Powders 281
Tablet Mechanical Properties 282
Structure–Property Relationship 284
Anisotropy of Organic Crystals 284
Crystal Plasticity, Elasticity, and Fracture 286
Role of Dislocation on Mechanical Properties 287
Effects of Crystal Size and Shape on Mechanical Behavior
Conclusion and Future Outlook 290
References 291
7.1.2
7.1.2.1
7.1.2.2
7.1.2.3
7.2
7.2.1
7.2.1.1
7.2.1.2
7.2.1.3
7.3
7.3.1
7.3.2
7.3.3
7.3.4
7.4
273
289
8
Primary Processing of Organic Crystals 297
Peter L.D. Wildfong, Rahul V. Haware, Ting Xu, and Kenneth R. Morris
8.1
8.1.1
8.1.2
Introduction 297
Solid Form 297
Morphology 298
ix
x
Contents
8.2
8.2.1
8.2.1.1
8.2.1.2
8.2.1.3
8.2.1.4
8.2.2
8.2.3
8.2.4
8.3
8.3.1
8.3.1.1
8.3.1.2
8.3.1.3
8.3.1.4
8.3.2
8.3.2.1
8.3.2.2
8.3.3
8.3.4
8.3.4.1
8.3.4.2
8.3.5
8.4
Primary Manufacturing: Processing Materials to Yield Drug
Substance 300
Crystallization (Solidification Processing) 301
Solvent Power 303
Solvent Classification 305
Batch Crystallization 307
Continuous Crystallization 308
Filtration and Washing 309
Drying (Removal of Crystallization Solvent) 313
Preliminary Particle Sizing 315
Challenges During Solidification Processing 319
Polymorphism 320
Cooling Crystallization 322
Solvent Selection 325
Antisolvent Crystallization 328
Selective Crystallization Using Additives 328
Hydrate and Organic Solvate Formation 329
Hydrate Formation 329
Organic Solvate Formation 335
Solvent-mediated Transformations (SMTs) 337
Morphology/Habit Control 342
Predicting Solvent Effects on Crystal Habit 343
Influence of Morphology on Surface Wetting 346
Crystallization Process Control 349
Summary and Concluding Remarks 350
References 351
9
Secondary Processing of Organic Crystals 361
Peter L.D. Wildfong, Rahul V. Haware, Ting Xu, and Kenneth R. Morris
9.1
9.1.1
9.1.2
9.2
Introduction 361
Structure and Symmetry 361
Process-induced Transformations (PITs) in 2 Manufacturing 362
Secondary Manufacturing–Processing Materials to Yield Drug
Products 365
Milling of Organic Crystals 366
Materials Properties Influencing Milling 366
Physical Transformations Associated with Milling 371
Chemical Transformations Associated with Milling 375
Pharmaceutical Blending 378
Granulation of Pharmaceutical Materials 382
Wet Granulation 384
Potential Transformations During Wet Granulation 385
9.2.1
9.2.1.1
9.2.1.2
9.2.1.3
9.2.2
9.2.3
9.2.3.1
9.2.3.2
Contents
9.2.3.3
9.2.3.4
9.2.3.5
9.2.3.6
9.2.3.7
9.2.3.8
9.2.4
9.2.4.1
9.2.4.2
9.2.4.3
9.2.4.4
9.2.4.5
9.2.5
9.3
9.3.1
9.3.2
Hydration and Dehydration 385
Solvent-mediated Transformations (SMT) 388
Polymorphic Transitions During Granulation 390
Salt Breaking 392
Formulation Considerations in Wet Granulation 392
Risk Assessment and Summary 394
Consolidation of Organic Crystals 395
Materials Properties Contributing to Effective Consolidation 397
Structural and Molecular Properties Contributing to Effective
Consolidation 402
Macroscopic Properties Affecting Effective Consolidation 403
Compaction-induced Material Transformations 404
Compression Temperature and Material Transformation 407
Data Management Approaches 408
Summary and Concluding Remarks 411
Development History 411
Risk Assessment 412
References 412
10
Chemical Stability and Reaction
Alessandra Mattei and Tonglei Li
10.1
10.2
10.2.1
10.2.2
10.2.3
10.2.4
10.2.5
10.3
10.3.1
10.3.2
Introduction 427
Overview of Organic Solid-state Reactions 429
Photochemical Reactions 431
Thermal Reactions 432
Mechanochemical Reactions 433
Hydrolysis Reactions 434
Oxidative Reactions 434
Mechanisms of Organic Solid-state Reactions 436
General Theoretical Concepts 436
Crystal Packing Effects on the Course of Organic Solid-state
Reactions 438
Perfect Crystals and Topochemical Control of Organic Solid-state
Reactions 438
Crystal Defects and Nontopochemical Control of Organic Solid-state
Reactions 440
Kinetics of Chemical Reactions: From Homogeneous to
Heterogeneous Systems 445
Fundamental Principles of Chemical Kinetics 445
Solid-state Reaction Kinetics 446
Factors Affecting Chemical Stability 448
Moisture 448
10.3.2.1
10.3.2.2
10.4
10.4.1
10.4.2
10.5
10.5.1
427
xi
xii
Contents
10.5.2
10.5.3
10.6
10.6.1
10.6.2
Temperature 448
Pharmaceutical Processing 450
Strategies to Prevent Chemical Reactions
Formulation-related Approaches 453
Prodrugs 454
References 455
11
Crystalline Nanoparticles 463
Yi Lu, Wei Wu, and Tonglei Li
11.1
11.2
11.2.1
11.2.2
11.3
11.3.1
11.3.1.1
11.3.1.2
11.3.1.3
11.3.2
11.3.2.1
11.3.2.2
11.3.3
11.3.3.1
11.3.3.2
11.4
11.5
11.5.1
11.5.2
11.5.3
11.5.4
11.5.5
11.6
11.6.1
11.6.2
11.6.3
11.6.4
11.6.5
Introduction 463
Top-down Technology 467
Media Milling (MM) 467
High-pressure Homogenization (HPH) 468
Bottom-up Technology 471
Precipitation by Solvent–Antisolvent Mixing 471
Sonoprecipitation 473
CIJP 473
HGCP 476
Supercritical Fluid Techniques 476
RESS 478
SAS 479
Precipitation by Removal of Solvent 479
SFL 479
CCDF 479
Nanoparticle Stabilization 480
Applications 482
Oral Drug Delivery 482
Parenteral Drug Delivery 484
Pulmonary Drug Delivery 485
Ocular Drug Delivery 486
Dermal Drug Delivery 486
Characterization of Crystalline Nanoparticles 487
Particle Size and Size Distribution 487
Surface Charge 487
Morphology 491
Crystallinity 491
Dissolution 491
References 492
Index
503
452
xiii
List of Contributors
Stephen R. Byrn
Department of Industrial and
Physical Pharmacy
Purdue University
West Lafayette, IN
USA
Katie L. Cavanagh
Department of Pharmaceutical
Sciences
Arnold and Marie Schwartz College of
Pharmacy
Long Island University
Brooklyn, NY
USA
Department of Pharmaceutical
Sciences
University of Michigan
Ann Arbor, MI
USA
Gislaine Kuminek
Junbo Gong
Tonglei Li
School of Chemical Engineering
and Technology
Tianjin University
Tianjin
P.R. China
Department of Pharmaceutical
Sciences
University of Michigan
Ann Arbor, MI
USA
Department of Industrial and
Physical Pharmacy
Purdue University
West Lafayette, IN
USA
Rahul V. Haware
Yi Lu
College of Pharmacy & Health
Sciences
Campbell University
Buies Creek, NC
USA
and
Key Laboratory of Smart Drug
Delivery of MOE and PLA,
School of Pharmacy
Fudan University
Shanghai
P.R. China
xiv
List of Contributors
Alessandra Mattei
Changquan Calvin Sun
AbbVie Inc.
North Chicago, IL
USA
Department of Pharmaceutics,
College of Pharmacy
University of Minnesota
Minneapolis, MN
USA
Kenneth R. Morris
Department of Pharmaceutical
Sciences, Arnold and Marie
Schwartz College of Pharmacy
Long Island University
Brooklyn, NY
USA
Peter Müller
X-Ray Diffraction Facility
MIT Department of Chemistry
Cambridge, MA
USA
Weiwei Tang
School of Chemical Engineering
and Technology
Tianjin University
Tianjin
P.R. China
Robert Wenslow
Crystal Pharmatech
New Brunswick, NJ
USA
Ann Newman
Seventh Street Development Group
Kure Beach, NC
USA
Haichen Nie
Department of Industrial and
Physical Pharmacy
Purdue University
West Lafayette, IN
USA
Susan M. Reutzel-Edens
Small Molecule Design &
Development, Eli Lilly & Company
Lilly Corporate Center
Indianapolis, IN
USA
Peter L.D. Wildfong
Graduate School of
Pharmaceutical Sciences, School
of Pharmacy
Duquesne University
Pittsburgh, PA
USA
Wei Wu
Key Laboratory of Smart Drug
Delivery of MOE and PLA,
School of Pharmacy
Fudan University
Shanghai
P.R. China
Ting Xu
Naír Rodríguez-Hornedo
Department of Pharmaceutical
Sciences
University of Michigan
Ann Arbor, MI
USA
Department of Pharmaceutical
Sciences, Arnold and Marie
Schwartz College of Pharmacy
Long Island University
Brooklyn, NY
USA
xv
Preface
Compiling this book has been a long journey. The idea started several years ago
when we were at the University of Kentucky, working together as a teacher–
student pair. While there were several books on solid-state organic chemistry,
including one favorite by the editors, Prof. Stephen Byrn’s Solid-State Chemistry
of Drugs, it was difficult to find a textbook that covers the fundamentals of
solid-state chemistry and solid-state materials processing and handling in
the pharmaceutical development process. When approaching Wiley, we were
encouraged by Jonathan Rose, and among the hectic transition to Purdue
University, we finally got the chapter contributors committed. Having everyone
finished on time however became a challenge. Needless to say, we managed to
accomplish the writing, and we are so grateful for the time and efforts by the
authors.
Majority of pharmaceutical solid-state materials are organic crystals. Dealing
with pharmaceutical crystals thereby defines the realm of small-molecule drug
development. Designing, understanding, producing, and analyzing organic
crystals have become an imperative skill set to master for those working in
the field. This book is thus aimed to offer an introductory yet comprehensive
description of organic crystals pertinent to the drug development and manufacturing. It is intended to bridge the fundamental knowledge and pharmaceutically relevant properties of crystalline materials. It may be used as a textbook
for teaching pharmaceutical solid-state materials, mainly organic crystals, at
the graduate and senior undergraduate student levels. This text may also serve
as a reference to pharmaceutical scientists and engineers.
The book starts by explaining fundamental aspects of organic crystals, including crystallography, intermolecular interactions, and crystallization. It further
covers topics of polymorphism and phase transition, form selection and crystal
engineering, and chemical stability. The book then extends to the characterization of solid-state materials, the fundamental understanding of mechanical
properties of organic crystals, the sensitivity of processing to material attributes,
and the influence of properties of pharmaceutically related solids on product
performance. The current state-of-the-art crystalline nanoparticles as drug
xvi
Preface
delivery approaches for poorly soluble compounds are also highlighted in this
book. With such a large span from chemistry to material processing, the volume
could not be possible without the contributions by the esteemed authors in their
respective research fields.
Admittedly, there are several interesting areas that we are not able to cover in
this edition. Crystal morphology plays an important role in affecting crystal
properties and often needs to be optimized in order to facilitate the manufacturing process. The ability to control and engineer crystal morphology is a desirable goal in the pharmaceutical industry. Surface properties, including surface
chemistry, surface topography, surface energy, and wettability, are also intrinsically related to crystal structure and can profoundly influence the formulation
and manufacture. Lastly, amorphization has become a key formulation strategy
for poorly soluble drugs.
We hope, through receiving feedback, that we will be able to continue revising
the volume. We also hope that readers find the topics valuable and can augment
their learning and experience. For these, we sincerely thank you for reading.
Tonglei Li, PhD
Alessandra Mattei, PhD
1
1
Crystallography
Susan M. Reutzel-Edens1 and Peter Müller 2
1
2
Small Molecule Design & Development, Eli Lilly & Company, Lilly Corporate Center, Indianapolis, IN, USA
X-Ray Diffraction Facility, MIT Department of Chemistry, Cambridge, MA, USA
1.1
Introduction
Functional organic solids, ranging from large-tonnage commodity materials to
high-value specialty chemicals, are commercialized for their unique physical
and chemical properties. However, unlike many substances of scientific,
technological, and commercial importance, drug molecules are almost always
chosen for development into drug products based solely on their biological
properties. The ability of a drug molecule to crystallize in solid forms with
optimal material properties is rarely a consideration. Still, with an estimated
90% of small-molecule drugs delivered to patients in a crystalline state [1],
the importance of crystals and crystal structure to pharmaceutical development
cannot be overstated. In fact, the first step in transforming a molecule to a medicine (Figure 1.1) is invariably identifying a stable crystalline form, one that:
•
••
•
Through its ability to exclude impurities during crystallization, can be used to
purify the drug substance coming out of the final step of the chemical
synthesis.
May impart stability to an otherwise chemically labile molecule.
Is suitable for downstream processing and long-term storage.
Not only meets the design requirements but also will ensure consistency in
the safety and efficacy profile of the drug product throughout its shelf life.
The mechanical, thermodynamic, and biopharmaceutical properties of a
drug substance will strongly depend on how a molecule packs in its
Pharmaceutical Crystals: Science and Engineering, First Edition.
Edited by Tonglei Li and Alessandra Mattei.
© 2019 John Wiley & Sons, Inc. Published 2019 by John Wiley & Sons, Inc.
2
1 Crystallography
Molecule
Crystal structure
Microscopic
crystals
Macroscopic
powder
Compressed
tablets
Figure 1.1 Materials science perspective of the steps involved in transforming a molecule to
a medicine.
three-dimensional (3D) crystal structure, yet it is not given that a drug candidate
entering into pharmaceutical development will crystallize, let alone in a form
that is amenable to processing, stable enough for long-term storage, or useful
for drug delivery. Because it is rarely possible to manipulate the chemical structure of the drug itself to improve material properties,1 pharmaceutical scientists
will typically explore multicomponent crystal forms, including salts, hydrates,
and more recently cocrystals, if needed, in the search for commercially viable
forms. A salt is an ionic solid formed between either a basic drug and a sufficiently acidic guest molecule or an acidic drug and basic guest. Cocrystals
are crystalline molecular complexes formed between the drug (or its salt)
and a neutral guest molecule. Hydrates, a subset of a larger class of crystalline
solids, termed solvates, are characterized by the inclusion of water in the crystal
structure of the compound. When multiple crystalline options are identified in
solid form screening, as is often the case for ever more complex new chemical
entities in current drug development pipelines, it is the connection between
internal crystal structure, particle properties, processing, and product performance, the components of the materials science tetrahedron, [3] that ultimately
determines which form is progressed in developing the drug product. Not surprisingly, crystallography, the science of shapes, structures, and properties of
crystals, is a key component of all studies relating the solid-state chemistry of
drugs to their ultimate use in medicinal products.
Crystallization is the process by which molecules (or ion pairs) self-assemble
in ordered, close-packed arrangements (crystal structures). It usually involves
two steps: crystal nucleation, the formation of stable molecular aggregates or
clusters (nuclei) capable of growing into macroscopic crystals; and crystal
growth, the subsequent development of the nuclei into visible dimensions.
Crystals that successfully nucleate and grow will, in many cases, form
1 There is good interest in using small-molecule crystallography to address the solubility limitations
of lead compounds by disrupting crystal packing through chemical modification, with some success
reported in the literature. See Ref. [2].
1.1 Introduction
distinctive, if not spectacular, shapes (habits) characterized by well-defined
faces or facets. Commonly observed habits, which are often described as
needles, rods, plates, tablets, or prisms, emerge because crystal growth does
not proceed at the same rate in all directions. The slowest-growing faces are
those that are morphologically dominant; however, as the external shape of
the crystal depends both on its internal crystal structure and the growth
conditions, crystals of the same internal structure (same crystal form) may have
different external habits. The low molecular symmetry common to many drug
molecules and anisotropic (directional) interactions within the crystal structure
often lead to acicular (needle shaped) or platy crystals with notoriously poor filtration and flow properties [4]. Since crystal size and shape can have a strong
impact on release characteristics (dissolution rate), material handling (filtration,
flow), and mechanical properties (plasticity, elasticity, density) relevant to tablet
formulation, crystallization processes targeting a specific crystal form are also
designed with exquisite control of crystal shape and size in mind.
Some compounds (their salts, hydrates, and cocrystals included) crystallize in
a single solid form, while others crystallize in possibly many different forms.
Polymorphism [Greek: poly = many, morph = form] is the ability of a molecule
to crystallize in multiple crystal forms (of identical composition) that differ in
molecular packing and, in some cases, conformation [5]. A compelling example
of a highly polymorphic molecule is 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile, also known as ROY, an intermediate in the synthesis of the
schizophrenia drug olanzapine. Polymorphs of ROY, mostly named for their
red-orange-yellow spectrum of colors and unique and distinguishable crystal
shapes, are shown in Figure 1.2 [6]. Multiple crystal forms of ROY were first
suggested by the varying brilliant colors and morphologies of individual crystals
in a single batch of the compound. Confirmation of polymorphism later came
with the determination of many of their crystal structures by X-ray diffraction
(Table 1.1) [7]. In this example, the color differences were traced to different
molecular conformations, characterized by θ, the torsion angle relating the rigid
o-nitroaniline and thiophene rings in the crystal structures of the different ROY
polymorphs [8].
The current understanding of structure in crystals would not be where it is
today without the discovery that crystals diffract X-rays and that this
phenomenon can be used to extract detailed structural information. Indeed,
it is primarily through their diffraction that crystals have been used to study
molecular structure and stereochemistry at an atomic level. Of course, detailed
evaluation of molecular conformation and intermolecular interactions in a
crystal can suggest important interactions that may drive binding to receptor
sites, and so crystallography is a vital component early in the drug discovery
process when molecules are optimized for their biological properties. Crystallography plays an equally important role in pharmaceutical development, where
material properties defined by 3D crystal packing lie at the heart of transforming
3
4
1 Crystallography
(a)
ON P21/c
mp 114.8 °C
θ = 52.6°
OP P21/c
mp 112.7 °C
θ = 46.1°
O
N
O
YN P–1
θ = 104.1°
N
H
C
N θ
S
ROY
CH3
Y P21/c
mp 109.8 °C
θ = 104.7°
R P–1
mp 106.2 °C
θ = 21.7°
ORP Pbca
θ = 39.4°
(b)
(c)
200 μm
50 μm
R
Y04
YT04
Figure 1.2 (a) Crystal polymorphs of ROY highlighting the diverse colors and shapes of crystals
grown from different solutions and (b) photomicrographs showing the concurrent cross
nucleation of the R polymorph on Y04 produced by melt crystallization and (c) single crystals of
YT04 grown by seeding a supersaturated solution. Source: Adapted with permission from Yu
et al. [6], copyright 2000, and from Chen et al. [7], copyright 2005, American Chemical Society.
a molecule to a medicine. Thus, this chapter considers small-molecule crystallography for the study of molecular and crystal structure. Following a brief history of crystallography, the basic elements of crystal structure, the principles of
X-ray diffraction, and the process of determining a crystal structure from
Table 1.1 Crystallographic data from X-ray structure determinations of seven ROY polymorphs.
Form
YT04
Y
ON
OP
R
YN
ORP
CSD refcode
QAXMEH12
QAXMEH01
QAXMEH
QAXMEH03
QAXMEH02
QAXMEH04
QAXMEH05
Crystal system
Monoclinic
Monoclinic
Monoclinic
Monoclinic
Triclinic
Triclinic
Orthorhombic
Space group
P21/n
P21/n
P21/c
P21/n
P-1
P-1
Pbca
Color
Yellow
Yellow
Orange
Orange
Red
Yellow
Orange-red
Habit
Prism
Prism
Needle
Plate
Prism
Needle
Plate
a, Å
8.2324(4)
8.5001(1)
3.9453(1)
7.9760(1)
7.4918(1)
4.5918(1)
13.177(3)
b, Å
11.8173(5)
16.413(2)
18.685(1)
13.319(2)
7.7902(1)
11.249(2)
8.0209(10)
c, Å
12.3121(6)
8.5371(1)
16.3948(1)
11.676(1)
11.9110(1)
12.315(2)
22.801(5)
α, deg
90
90
90
90
75.494(1)
71.194(1)
90
β, deg
102.505(1)
91.767(1)
93.830(1)
104.683(1)
77.806(1)
89.852(1)
90
γ, deg
90
90
90
90
63.617(1)
88.174(1)
90
Volume, Å3
1169.36(9)
1190.5
1205.9
1199.9
598.88
601.85
2409.8
Z
4
4
4
4
2
2
8
Dcalc, g cm−3
1.473
1.447
1.428
1.435
1.438
1.431
1.429
T, K
296
293
293
295
293
296
296
6
1 Crystallography
diffraction data are described. Complementary approaches to single-crystal diffraction, namely, structure determination from powder diffraction, solid-state
nuclear magnetic resonance (NMR) spectroscopy (NMR crystallography),
and emerging crystal structure prediction (CSP) methodology, are also highlighted. Finally, no small-molecule crystallography chapter would be complete
without mention of the Cambridge Structural Database (CSD), the repository of
all publicly disclosed small-molecule organic and organometallic crystal structures, and the solid form informatics tools that have been developed by the
Cambridge Crystallographic Data Centre (CCDC) for the worldwide crystallography community to efficiently and effectively mine the vast structural information warehoused in the CSD.
1.2 History
Admiration for and fascination by crystals is as old as humanity itself. Crystals
have been assigned mystic properties (for example, crystal balls for future
telling), healing powers (amethyst, for example, is said to have a positive effect
on digestion and hormones), and found uses as embellishments and jewelry
already thousands of years ago. Crystallography as a science is also comparatively old. In 1611, the German mathematician and astronomer Johannes Kepler
published the arguably first ever scientific crystallographic manuscript. In his
essay Strena seu de nive sexangula (a new year’s gift of the six-cornered snowflake), starting from the hexagonal shape of snowflakes, Kepler derived, among
other things, the cubic and hexagonal closest packings (now known as the
Kepler conjecture) and suggested a theory of crystal growth [9].
Later in history, when mineralogy became more relevant, Nicolaus Steno in
1669 published the law of constant interfacial angles,2 and in 1793 René Just
Haüy, often called the “father of modern crystallography,” discovered the periodicity of crystals and described that the relative orientations of crystal faces can
be expressed in terms of integer numbers.3 Those numbers describing the orientation of crystal faces and, generally, of any plane drawn through crystal lattice points are now known as Miller indices4 (introduced in 1839 by William
Hallowes Miller). Miller indices are one of the most important concepts in modern crystallography as we will see later in this chapter. In 1891, the Russian mineralogist and mathematician Evgraf Stepanovich Fedorov and the German
mathematician Arthur Moritz Schoenflies published independently a list of
all 3D space groups. Both their publications contained errors, which were
2 Published in his book De solido intra solidum naturaliter content (1669).
3 Published in the two essays De la structure considérée comme caractère distinctif des minéraux
and Exposition abrégé de la théorie de la structure des cristaux (both 1793).
4 Perhaps because Miller is easier to pronounce than Haüy.
1.3 Symmetry
discovered by the respective other author, and the correct list of the 230 3D
space groups was developed in collaboration by Fedorov and Schoenflies
in 1892.5
With the law of constant interfacial angles, the concept of Miller indices and
the complete list of space groups, the crystallographic world was ready for the
discovery of X-rays by Wilhelm Conrad Röntgen [11].6 Encouraged by Paul
Ewald and in spite of discouragement from Arnold Sommerfeld, the first successful diffraction experiment was undertaken in 1912 by Max Theodor Felix
von Laue, assisted by Paul Knipping and Walter Friedrich [12].7 Inspired by
von Laue’s results, William Lawrence Bragg, at the age of just 22, developed
what is now known as Bragg’s law [13], a simple relation between X-ray wavelength, incident angle, and distance between lattice planes. Together with his
father, William Henry Bragg, he determined the structure of several alkali
halides, zinc blende, and fluorite.8 In the following few years, many simple structures were determined based on X-ray diffraction, and as the method improved,
the structures became more and more complex. The first organic structure
determined by X-ray diffraction was that of hexamethylenetetramine [15]
and with the structures of penicillin9 [16] and vitamin B1210 [17], the relevance
of crystal structure determination for medical research became apparent. The
first crystal structure of a protein followed just a few years later11 [18], and since
then, crystal structure determination has become one of the most important
methods in chemistry, biology, and medicine.
1.3
Symmetry
1.3.1
Symmetry in Two Dimensions
Symmetry is at the heart of all crystallography. There is symmetry in the crystal
(also called real space) and symmetry in the diffraction pattern (also called
reciprocal space), and sometimes, there is symmetry in individual molecules,
which may or may not be reflected by the symmetry group of the crystal
structure. An excellent definition of the term symmetry was given by Lipson
and Cochran [19]: “A body is said to be symmetrical when it can be divided into
5 This is a wonderful example for constructive collaboration between scientific colleagues. There is
a long communication between Fedorov and Schoenflies, which eventually yielded the correct and
complete list of all space groups. For a history of the discovery of the 230 space groups. See Ref. [10].
6 In 1901 Röntgen received the Nobel Prize in Physics for this discovery.
7 Nobel Prize in Physics for von Laue in 1914.
8 Nobel Prize in Physics for father and son Bragg in 1915 [14].
9 Dorothy Hodgkin’s maiden name was Crowfoot.
10 Nobel Prize in Chemistry for Dorothy Hodgkin in 1964.
11 Nobel Prize in Chemistry for Max Perutz and John Kendrew in 1962.
7
8
1 Crystallography
Figure 1.3 Symmetry operations of mirror, threefold rotation, and glide are depicted on a
photograph of a hand. The symbol for a mirror is a solid line, for a threefold rotation a triangle
(▲), and for a glide a dashed line.
parts that are related to each other in certain ways. The operation of transferring
one part to the position of a symmetrically related part is termed a symmetry
operation, the result of which is to leave the final state of the body indistinguishable from its original state. In general, successive application of the symmetry
operation must ultimately bring the body actually into its original state again.”
In two dimensions, these are (besides identity) the following symmetry operations: mirror, rotation, and glide (Figure 1.3). Typically, the mirror is the easiest
operation to visualize, as most people are familiar with the effect of a mirror.
Rotation can be two-, three-, four-, or sixfold in crystallography.12 The glide
operation is somewhat more difficult to grasp. It consists of the combination
of two symmetry operations, mirror and translation. In crystallography, glide
operations shift one half of a unit cell length (except for the d-glide plane which
shifts 1/4 unit cell).
The above describes local symmetry of objects. When adding translation, the
following quotation from Lawrence Bragg [20] describes the situation perfectly:
“In a two-dimensional design, such as that of a wall-paper, a unit of pattern is
repeated at regular intervals. Let us choose some representative point in the unit
of pattern, and mark the position of similar points in all the other units. If these
points be considered alone, the pattern being for the moment disregarded, it will
be seen that they form a regular network. By drawing lines through them, the
area can be divided into a series of cells each of which contains a unit of the
pattern. It is immaterial which point of the design is chosen as representative,
for a similar network of points will always be obtained.” To illustrate this,
assume the two-dimensional (2D) pattern shown in Figure 1.4. Following the
instructions given by Bragg, we can select one point, say, the eye of the light/
white bird, and mark it in all light/white birds. The light/white bird’s eyes are
then the corner points of a 2D regular network, called a lattice. The design
12 That is, in conventional crystallography. Quasicrystals are a different story.
1.3 Symmetry
Figure 1.4 Wallpaper design by M. C. Escher. Lattice points are indicated by circles; the lattice
is drawn as lines. It does not matter which reference point is chosen; the same lattice is always
obtained. There is no symmetry besides translation. The lattice type is oblique and the plane
group is p1. Each unit cell contains two birds, one black and one white. Source: M.C. Escher’s
“Symmetry Drawing E47” © 2018 The M.C. Escher Company-The Netherlands. All rights
reserved. www.mcescher.com.
can now be shifted freely behind the lattice, and the lattice points will always mark
equivalent points in all birds, for example, into the eye of the black bird or, for that
matter, anywhere in the design. Those “cells” introduced by Bragg are commonly
called unit cells in crystallography. The entire design or crystal can be generated
by the unit cell and its content simply through translation. One can understand
the crystal as built up from unit cells like a wall may be built by bricks. All bricks
look the same, and all unit cells forming the crystal are the same.
The unit cell is the smallest motif from which the entire design can be built by
translation alone; however there often is an even smaller motif that suffices to
describe the entire design. This smallest motif is called the asymmetric unit, and
the symmetry operators of the plane group generate the unit cell from the asymmetric unit. In the design with the black and white birds, there is no symmetry in
the unit cell (plane group p1), and the asymmetric unit is identical with the unit
cell. More commonly, however, one can find symmetry elements in the cell, and
the asymmetric unit corresponds to only a fraction of the unit cell (for example,
½, ⅓, or, as in the example below, ⅛).
The design shown in Figure 1.5 contains several symmetry operators, which
are drawn in white. Most notably there is a fourfold axis, marked with the symbol ▀, but also several mirror planes (solid lines). In addition there are twofold
9
10
1 Crystallography
Figure 1.5 Wallpaper design by M. C. Escher. Assume the grey and white spiders are
equivalent and a symmetry operation transforming a grey spider into a white one or vice
versa is considered valid. Lattice points are indicated by black circles; the lattice is drawn as
black lines. Symmetry elements are drawn in white (fourfold axes, twofold axes, mirrors, and
glides). The lattice type is square and the plane group is p4gm. Each unit cell contains
4 spiders, the asymmetric unit ½ spider. Source: M.C. Escher’s “Symmetry Drawing E86”
© 2018 The M.C. Escher Company-The Netherlands. All rights reserved. www.mcescher.com.
axes (symbol ) and glides (dashed line). The crystal lattice is drawn in black; the
lattice type is square, the plane group p4gm. Each unit cell contains four bugs,
the asymmetric unit ½ bug. Careful examination of Figure 1.5 shows that there
are two different kinds of fourfold axes, those on the lattice corners and those in
the center of the unit cells. Although those two kinds of fourfold axes are crystallographically equivalent, they are, indeed, different, as one has the bugs
1.3 Symmetry
grouped around it in a clockwise arrangement, while the other one shows a
counterclockwise arrangement of the bugs.
1.3.2
Symmetry and Translation
Not all symmetry works in crystals or wallpapers. The 2- or 3D periodic object
must allow filling the 2- or 3D space without leaving voids. Just as one cannot
tile a bathroom with tiles that are shaped like a pentagon or octagon, one cannot
form a crystal with unit cells of pentagonal symmetry (Figure 1.6). This means
there are no fivefold or eightfold axes in crystallography.13 Compatible with
translation are mirror, glide, twofold, threefold, fourfold, and sixfold rotation.
Combination of all allowed symmetry operations with translation gives rise to
17 possible plane groups in 2D space and 230 possible space groups in 3D space.
Each symmetry group falls in one of the seven distinct lattice types (five for 2D
space): triclinic (oblique in 2D), monoclinic (rectangular or centered rectangular in 2D), orthorhombic (rectangular or centered rectangular in 2D), tetragonal
(square in 2D), trigonal (rhombic in 2D), hexagonal (rhombic in 2D), and cubic
(square in 2D).
Figure 1.6 In classical crystals (ignoring quasicrystals), only twofold, threefold, fourfold, and
sixfold rotation are compatible with translation. Attempts to tile a floor with, for example,
pentagons or heptagons will leave gaps.
13 Fivefold and other translational incompatible symmetry can occur within unit cells; however this
would always be local symmetry, and a fivefold symmetric object would be understood and treated as
asymmetric. Such a symmetry operation is called “pseudo symmetry” or “noncrystallographic
symmetry”.
11
12
1 Crystallography
1.3.3 Symmetry in Three Dimensions
In 3D space, there are additional symmetry operations to consider, namely,
screw axes and the inversion center. Screw axes are like spiral staircases. An
object (for example, a molecule) is rotated about an axis and then translated
in the direction of the axis. Screw axes are named with two numbers, nm.
The object rotates counterclockwise by an angle of 360 /n and shifts up
(positive direction) by m/n of a unit cell. For example, a 61 screw axis rotates
360 /6 = 60 counterclockwise and shifts up 1/6 of a unit cell, a 62 screw axis
also rotates 60 but shifts up 1/3 of a unit cell. Similarly, a 65 screw axis rotates
60 counterclockwise, yet it shifts up 5/6 of a unit cell. In a crystal, there always
is another unit cell above and below the current cell, and from any set of coordinates, one can always subtract 1 (or add 1) to any or all of the three coordinates
without changing anything. Therefore, shifting up 5/6 of a unit cell is equivalent
to shifting down by 1/6. This means that the 61 and 65 screw axes are mirror
images of one another; they form an enantiomeric pair or, in other words,
one is right handed, the other one left handed. The same is true for the 62
and 64 axes, which also form an enantiomeric pair. Figure 1.7 shows 3D models
of the five different sixfold screw axes.
Inversion centers can (and should) be understood as a combination of mirror
and twofold rotation. Whenever a twofold axis intersects a mirror plane, the
point of intersection is an inversion center. Intersection of twofold screw axes
with glide planes also creates inversion centers; however the inversion center is
not located at the point of intersection. Like all symmetry operations involving a
mirror operation, inversion centers change the hand of a chiral molecule.
Figure 1.7 Models of all five sixfold screw axes (built by Ellen and Peter Müller in 2010). From
left to right: 61, 65, 62, 64, 63. It can be seen that 61/65 and 62/64 are enantiomeric pairs, i.e.
mirror images of one another or, in other words, the right- and left-handed versions of the
same screw.
1.3 Symmetry
z
c
a
y
b
𝛽
𝛾
a
Unit cell
x
Crystal lattice
Figure 1.8 Unit cell, defined by lattice vectors (a, b, c) and angles (α, β, γ), the basic building
block used to construct the three-dimensional crystal lattice.
In addition, mirror and glide, which are mere lines in two dimensions, become
mirror planes and glide planes in 3D space. Glide planes are similar to the glide
operation in two dimensions. The only difference is that the glide can be in one
of several directions. Assume the mirror operation to take place on the a-cplane. The mirror image can now shift in the a- or the c-direction or even along
the diagonal in the a-c-plane. The first case is called an a-glide plane, the second
one a c-glide plane, and the third case is called an n-glide plane.
One possible definition of a crystal is this: A crystal is a 3D periodic14 discontinuum formed by atoms, ions, or molecules. It consists of identical “bricks”
called unit cells, which form a 3D lattice (Figure 1.8). The unit cell is defined
by axes a, b, c, and angles α, β, γ, which form a right-handed system. As
described above, the unit cell is the smallest motif that can generate the entire
crystal structure only by means of translation in three dimensions. Except for
space group P1, the unit cell can be broken down into several symmetry-related
copies of the asymmetric unit. The symmetry relating the individual asymmetric
units is described in the space group. Typically, the asymmetric unit contains
one molecule; however it is possible (and occurs regularly) for the asymmetric
unit to contain two or more crystallographically independent molecules or just a
fraction of a molecule.
1.3.4
Metric Symmetry of the Crystal Lattice
The metric symmetry is the symmetry of the crystal lattice without taking into
account the arrangement of the atoms in the unit cell. Each of the 230 space
groups is a member of one of the 7 crystal systems, which are defined by the
14 Again, this holds only for classical crystals. In quasicrystals strict periodicity is not observed.
13
14
1 Crystallography
β
β
Triclinic
a≠b≠c
α ≠ β ≠ γ ≠ 90°
β
Cubic
a =b =c
α = β = γ = 90°
β
Monoclinic
a≠b≠c
α = γ = 90° ≠ β
β
Trigonal/hexagonal
a=b≠c
α = β = 90°, γ = 120°
Orthorhombic
a≠b≠c
α = β = γ = 90°
β
Tetragonal
a=b≠c
α = β = γ = 90°
Figure 1.9 Seven crystal systems, defined by the shape of the unit cell. (Trigonal and
hexagonal have the same metric symmetry, but are separate crystal systems.)
shape of the unit cell (Figure 1.9). We distinguish the triclinic, monoclinic,
orthorhombic, tetragonal, trigonal, hexagonal, and cubic crystal systems.15
As will be shown below, the shape and size of the unit cell, its metric symmetry, in real space determines the location of the reflections in the diffraction
pattern in reciprocal space. Considering the metric symmetry of the unit cell
alone, ignoring the unit cell contents (that is, the atomic positions), is equivalent
to looking at the positions of the reflections alone without taking into account
their relative intensities. That means it is the relative intensities of the diffraction spots that hold the information about the atomic coordinates and, hence,
the actual crystal structure. More about that later.
1.3.5 Conventions and Symbols
As mentioned above, the unit cell forms a right-handed system a, b, c, α, β, γ. In
the triclinic system, the axes are chosen so that a ≤ b ≤ c. In the monoclinic system the one non-90 angle is β and the unit cell setting is chosen so that β ≥ 90 .
If there are two possible settings with β ≥ 90 , that setting is preferred where β is
closer to 90 . In the monoclinic system b is the unique axis, while in the
15 Some crystallographers count rhombohedral as a separate crystal system; however it usually is
understood as a special case of the trigonal system (R-centering). It should also be noted that trigonal
and hexagonal are considered different crystal systems even though they have the same metric
symmetry.
1.3 Symmetry
tetragonal, trigonal, and hexagonal systems, c is unique. If a structure is centrosymmetric, the origin of the unit cell is chosen so that it coincides with an inversion center. In noncentrosymmetric space groups, the origin conforms with
other symmetry elements (for details see Volume A of the International
Tables for Crystallography) [21].
1.3.6
Fractional Coordinates
In crystallography, atomic coordinates are given as fractions of the unit cell axes.
All atoms inside the unit cell have coordinates 0 ≤ x < 1, 0 ≤ y < 1, and 0 ≤ z < 1.
That means that, except for the cubic crystal system, the coordinate system in
which atomic positions are specified is not Cartesian. An atom in the origin of
the unit cell has coordinates 0, 0, 0, an atom located exactly in the center of the
unit cell has coordinates 0.5, 0.5, 0.5, and an atom in the center of the a-b-plane
has coordinates 0.5, 0.5, 0, etc. When calculating interatomic distances, one
must multiply the differences of atomic coordinates individually with the
lengths of the corresponding unit cell axes. Thus, the distance between two
atoms x1, y1, z1 and x2, y2, z2 is
d=
x2 −x1 a 2 + y2 − y1 b 2 + z2 − z1 c 2 =
Δxa 2 + Δyb 2 + Δzc
2
Note that this equation is valid only in orthogonal crystal systems (all three
angles 90 ), that is, orthorhombic, tetragonal, and cubic. For the triclinic case
the formula is
d=
Δxa 2 + Δyb 2 + Δzc 2 − 2ΔxΔyab cos γ − 2ΔxΔzac cos β − 2ΔyΔzbc cos α
The x, y, z notation is also used to describe symmetry operations. If there is an
atom at the site x, y, z, then x + 1, y, z is the equivalent atom in the next unit cell
in x-direction (a-cell axis), and coordinates −x, −y, −z are generated from x, y, z,
by an inversion center at the origin (that is, at coordinates 0, 0, 0). In the same
fashion, a twofold rotation axis coinciding with the unit cell’s b-axis (as, for
example, in space group P2) generates an atom −x, y, −z from every atom x,
y, z, and a twofold screw axis coinciding with b (say, in space group P21)
generates −x, y + ½, −z from x, y, z.
1.3.7
Symmetry in Reciprocal Space
The symmetry of the diffraction pattern (reciprocal space) is dictated by the
symmetry in the crystal (real space). The reciprocal symmetry groups are called
Laue groups. If there is, for example, a fourfold axis in real space, the diffraction
space will have fourfold symmetry as well. Lattice centering and other translational components of symmetry operators have no impact on the Laue group,
which means that symmetry in reciprocal space does not distinguish between,
15
16
1 Crystallography
Table 1.2 Laue and point groups of all crystal systems.
Crystal system
Laue group
Point group
Triclinic
1
1, 1
Monoclinic
2/m
2, m, 2/m
Orthorhombic
mmm
222, mm2, mmm
Tetragonal
4/m
4, 4, 4/m
4/mmm
422, 4mm, 42m, 4/mmm
Trigonal/rhombohedral
3
3, 3
3/m
32, 3m, 3m
Hexagonal
6/m
6, 6, 6/m
6/mmm
622, 6mm, 6m2, 6/mmm
Cubic
m3
23, m3
m3m
432, 43m, m3m
for example, a sixfold rotation and a 61-, 62-, or any other sixfold screw axis. In
addition, reciprocal space is, at least in good approximation, centrosymmetric,
which means that all Laue groups are centrosymmetric even if the corresponding space group is chiral.
The Laue group can be determined from the space group via the point group.16
The point group corresponds to the space group minus all translational aspects
(that is, glide planes become mirror planes, screw axes become regular rotational
axes, and the lattice symbol is lost). The Laue group is the point group plus an inversion center, as reciprocal space is centrosymmetric. If the point group is already
centrosymmetric, then Laue group and point group are the same. Take, for example, the three monoclinic space groups P21 (chiral), Pc (noncentrosymmetric), and
C2/c (centrosymmetric). While those three space groups have different point
groups, they all belong to the same (only) monoclinic Laue group (Table 1.2).
Space group
Point group
Laue group
P21
2
2/m
Pc
m
2/m
C2/c
2/m
2/m
It is important to note that the symmetry of the Laue group can be lower than
the metric symmetry of the crystal system but never higher. That means that, for
16 The point group is also called the crystal class (not to be confused with crystal system).
1.4 Principles of X-ray Diffraction
example, a monoclinic crystal could, by mere chance, have a β angle of exactly
90 and, thus, display orthorhombic metric symmetry. When considering the
unit cell contents, however, and when examining the symmetry of the diffraction pattern, the symmetry in both real and reciprocal space would still be
monoclinic, and, hence, the metric symmetry would be higher than the Laue
symmetry.17
1.4
Principles of X-ray Diffraction
In a diffraction experiment, the X-ray beam interacts with the crystal, giving rise
to the diffraction pattern. Diffraction can easily be demonstrated by shining a
beam of light through a fine mesh. For example, one can look through a layer
of sheer curtain fabric into the light of a streetlamp (Figure 1.10). The phenomenon is always observed when waves of any kind meet with an obstacle, for
example, a mesh or a crystal; however the effect is particularly strong when
the wavelength is comparable with the size of the obstacle (the mesh size or
the size of the unit cell in a crystal).
1.4.1
Bragg’s Law
One way of understanding diffraction is through a geometric construction that
describes the reflection of a beam of light on a set of parallel and equidistant
planes (Figure 1.11). The planes can be understood as the lattice planes in a
Figure 1.10 View of streetlamps from a hotel room in Chicago in 2010. The image on the
right side is the exact same view as the one on the left; only it was taken through the curtain
fabric. All strong and point-like light sources show significant diffraction.
17 This occurs occasionally and is prerequisite for merohedral and pseudo-merohedral twinning.
17
18
1 Crystallography
θ
d
½Δ
θ
θ
d
½Δ
½Δ
Set of parallel planes:
Bragg planes
Figure 1.11 Bragg’s law derived from partial reflection of two parallel planes.
crystal, the light as the X-ray beam. The beam travels into the crystal, is partially
reflected on the first plane, continues to travel until being partially reflected on
the second plane, and so forth. Only two planes are necessary to understand the
principle. Simple trigonometry leads to an equation that relates the wavelength
λ to the distance d between the lattice planes and the angle θ of diffraction:
sin θ =
1 2Δ Δ
=
d
2d
It is apparent that constructive interference is only observed if the path difference is the same as the wavelength of the diffracted light (or an integer multiple thereof ). That means Δ = nλ, and hence
nλ = 2d sin θ
This equation is also known as Bragg’s law, and the parallel planes of the
crystal lattice are called Bragg planes.
When Bragg’s law is resolved for d, one can easily calculate the maximum
resolution to which diffraction can be observed as a function of the wavelength
used:
d=
λ
2 sin θ
The maximum resolution corresponds to the smallest value for d, which
is achieved for the largest possible value of sin θ.18
18 The highest value the sin can ever have is 1. This corresponds to an angle of θ = 90 .
1.4 Principles of X-ray Diffraction
dmin =
λ
λ
=
2 sin θmax 2
Therefore the maximum theoretically observable resolution is half the wavelength of the radiation used. Practically, this resolution can never be observed,
as it would require the detector to coincide with the X-ray source; however
modern diffractometers get as close as ca. dmin = 0.52 λ. The two most commonly
used X-ray wavelengths are Cu Kα, (λ = 1.54178 Å) and Mo Kα, (λ = 0.71073 Å).
The respective practically achievable maximum resolutions are 0.80 Å for Cu
and 0.37 Å for Mo radiation. As will be seen below, most crystals do not diffract
to such high resolution as one could observe with Mo radiation, and some crystals
will not even diffract to the 0.84 Å resolution recommended as a minimum by the
International Union of Crystallography (IUCr).
1.4.2
Diffraction Geometry
Bragg planes can be drawn into the crystal lattice through the lattice points. The
planes are characterized by their angle relative to the unit cell and by their
spacing d, and each set of equidistant planes can be uniquely identified by a
set of three numbers describing at which point they intersect the three basis vectors of the crystal lattice (i.e. the unit cell axes) closest to the origin (Figure 1.12).
Those numbers are called the Miller indices h, k, and l and correspond to the
reciprocal values of the intersection with the unit cell. Each set of Bragg planes
gives rise to one pair of reflections in reciprocal space, which are uniquely identifiable by the corresponding Miller indices h, k, l and −h, −k, −l. Higher values
for h, k, l correspond to smaller distances between corresponding Bragg planes,
larger distances between lattice points on the planes, and higher resolution of
the corresponding reflection. For each interplanar distance vector dhkl, there is a
scattering vector shkl with s = 1/d.
1.4.3
Ewald Construction
Paul Ewald described Bragg’s law geometrically, and it is his construction
(Figure 1.13) that most crystallographers see in front of their inner eye when
they think about a diffraction experiment. The core of the construction is a
sphere with radius 1/λ, and the X-ray beam of wavelength λ intersects the sphere
along its diameter. The crystal and hence the origin of real space are located in
the center of the sphere (point C), while the origin of the reciprocal lattice (point
O) is located at the exit point of the X-ray beam. The scattering vector s is drawn
as footing in point O. For each set of Bragg planes with spacing d, there is one
s-vector with length 1/d and direction perpendicular to the planes. If the crystal
were represented by the s-vectors, it would be reminiscent of a sea urchin with
spines of different lengths, each spine corresponding to one s-vector. Rotation
19
c
b
1
cuts a at 1/1
is parallel to b
(1 0 /)
a
cuts a at 1/1
cuts b at 1/3
cuts c at 1/4
(1 3 4)
1
c
a 1
b
(1 3 4)
cuts a at 1/1
cuts b at 1/3
(1 3 /)
a
b
b
a
Figure 1.12 Between the points of a crystal lattice in real space, there are Bragg planes. Each
set of Bragg planes corresponds to one set of Miller indices. The Miller indices h, k, l
correspond to the reciprocal values of the points at which the planes cut the unit cell axes
closest to the origin. Each set of Bragg planes corresponds to one reflection. Each reflection is
identified by the corresponding Miller indices h, k, l. The positions of the reflections form
another lattice, the reciprocal lattice. There is a vector d perpendicular to each set of Bragg
planes; its length is equivalent to the distance between the corresponding Bragg planes. Each
reflection h, k, l marks the endpoint of the scattering vector s = 1/d. The length of s is inversely
related to the distance between the Bragg planes.
hkl reciprocal
lattice point
Diffracted beam
Detector
s
Q
θ
Incident
beam
θ
hkl lattice
planes
Ewald sphere with
radius r = 1/λ
C
hkl reflection
P
θ
s
d
O
Crystal
Reciprocal lattice
Figure 1.13 Ewald construction. The Ewald sphere has the radius 1/λ. Points C, O, P, and
Q mark the position of the crystal, the origin of the reciprocal lattice, the point where the
diffracted beam exits the Ewald sphere (corresponding to the endpoint of s on the surface of
the sphere), and the point where the primary beam enters the Ewald sphere, respectively.
Through rotation of the crystal, all s-vectors that are shorter than 2/λ can be brought into a
position in which they end on the surface of the Ewald sphere.
1.4 Principles of X-ray Diffraction
of the crystal corresponds to the rotation of the sea urchin located in point O.
Depending on crystal orientation, the various s-vectors will, at one time or
other, be ending on the surface of the Ewald sphere. It can be demonstrated that
Bragg’s law is fulfilled exactly for those s-vectors that end on the Ewald sphere.19
That means, for each crystal orientation, those and only those reflections can be
observed as projections onto a detector whose s-vectors end on the surface of
the Ewald sphere.
1.4.4
Structure Factors
With the help of Bragg’s law and the Ewald construction, we can calculate the
place of a reflection on the detector, provided we know the unit cell dimensions.
Indeed, the position of a spot is determined alone by the metric symmetry of the
unit cell (and the orientation of the crystal on the diffractometer). The relative
intensity20 of a reflection, however, depends on the contents of the unit cell, i.e.
on the population of the corresponding set of Bragg planes with electron density. If there are many atoms on a plane, the corresponding reflection is strong; if
the plane is empty, the reflection is weak or absent.21 Whether or not there are
many atoms on a specific set of Bragg planes in a given unit cell depends on the
shape, location, and orientation of the molecule(s) inside the unit cell. Every single atom in the unit cell is positioned in some specific way relative to every set of
Bragg planes. The closer an atom is to one of the planes of a specific set and the
more electrons this atom has, the more it contributes constructively to the corresponding reflection. Therefore, every single atom in a structure has a contribution to the intensity of every reflection depending on its chemical nature and
on its position in the unit cell.
Two other factors influencing the intensity of observed reflections are the
thermal motion of the atoms (temperature factor) and the atomic radius (form
factor). Only if atoms were mathematical points could they fully reside on a
side
19 Since the triangle OPQ is a right triangle and since sinα = adjacent
hypotenuse and the diameter of the
s
Ewald sphere is 2/λ, it follows that sin θ = 2λ. Since s = 1/d, it follows that 2d sin θ = λ, which is
Bragg’s law.
20 The absolute intensity also depends on many other factors such as exposure time, crystal size,
beam intensity, detector sensitivity, etc.
21 It is slightly more complicated than that, as “destructive interference” alone leads to observable
intensity as well (interference is only destructive if there is something to be destroyed…). That means
if the Bragg planes for a specific reflections are empty but many atoms can be found exactly halfway
between the Bragg planes, the reflection will be just as strong as if the atoms were all on the planes
instead of halfway in between. This can be understood when one realizes that the exact position (not
orientation or spacing!) of the Bragg planes depends on the origin of the unit cell, which is
established merely by conventions. If, in this example, the unit cell origin were to be shifted so that
the Bragg planes moved in such a fashion to coincide with the atoms, thus vacating the space
between the planes, all electron density would reside on the planes and not in between, yet the
structure would remain unchanged.
21
22
1 Crystallography
Bragg plane. Yet because they have an appreciable size and, in addition, vibration, an atom residing perfectly on a Bragg plane will have electron density also
above and below the plane. This density above and below will contribute somewhat destructively to the corresponding reflection, depending on the motion
and size of the atoms and on the resolution of the reflection in question. As
explained above, the distance d between Bragg planes is smaller for higher
resolution reflections. That means that at higher resolution, the electron density
above and below the Bragg planes will extend closer to the center between the
planes and, hence, weaken the corresponding reflection more strongly than it
would for a lower resolution reflection with a larger d. When d becomes small
enough that atomic motion will lead to so much electron density between the
planes and that perfect destructive interference is achieved, no reflections
beyond this resolution limit will be observed. This is a crystal-specific resolution
limit, and crystals in which the atoms move more than average will diffract to
lower resolution than crystals with atoms that move less. This circumstance also
explains why low-temperature data collection leads to higher resolution
datasets, as at lower temperatures atomic motion is significantly reduced.
Strictly speaking, “reflections” should be called “structure factor amplitudes.”
Every set of Bragg planes gives rise to a structure factor F , and the observed
reflection is the structure factor amplitude |F|2.22 The structure factor equation
describes the contribution of every atom in a structure to the intensity of every
reflection:
Fhkl =
fi cos 2π hxi + kyi + lzi + i sin 2π hxi + kyi + lzi
i
The structure factor F for the set of Bragg planes specified by Miller indices h,
k, l is the sum over the contributions of all atoms i with their respective atomic
scattering factors fi and their coordinates xi, yi, zi inside the unit cell. Note that
the i in i sin 2π is − 1 and not the same i as the one in fi or xi, yi, zi. Temperature
factor and form factor are, together with electron count, contained in the values
of fi for each atom.23
1.4.5 Statistical Intensity Distribution
In a diffraction experiment, we measure intensities. As described above, the
intensities correspond to the structure factor amplitudes (after application of
corrections, such as Lorenz and polarization correction and scaling and a few
other minor correction terms). It turns out that the variance of the intensity
22 Structure factors are vectors in a complex plane. They have intensity and a phase angle.
23 That means that the value of fi is a function of scattering angle θ and, hence, the resolution of the
reflection h,k,l.
1.4 Principles of X-ray Diffraction
distribution across the entire dataset is indicative of the presence or absence of
an inversion center in real space (remember: in good approximation reciprocal
space is always centrosymmetric). This variance is called the |E2 – 1|-statistic,
which is based on normalized structure factors E. To calculate this statistic, all
structure factors are normalized in individual thin resolution shells. In this
context, normalized means every squared structure factor F2 of a certain resolution shell is divided by the average value of all structure factors in this shell:
E2 = F2/<F2 > with E2, squared normalized structure factor; F2, squared structure factor; and <F2>, mean value of squared structure factors for reflections at
same resolution.
The average value of all squared normalized structure factors is one, <E2 > = 1;
however < | E2 – 1 | > = 0.736 for noncentrosymmetric structures and 0.968 for
centrosymmetric structures.
Heavy atoms on special positions and twinning tend to lower this value, and
pseudotranslational symmetry tends to increase it. Nevertheless, the value of
this statistic can help to distinguish between centrosymmetric and noncentrosymmetric space groups.
1.4.6
Data Collection
An excellent introduction to data collection strategy is given by Dauter [22]. In
general, there are at least five qualifiers describing the quality of a dataset:
(i) maximum resolution; (ii) completeness; (iii) multiplicity of observations
(MoO24, sometimes called redundancy); (iv) I/σ, i.e. the average intensity
divided by the noise; and (v) a variety of merging residual values, such as Rint
or Rsigma. A good dataset extends to high resolution the International Union
of Crystallography (IUCr) suggests at least 0.84 Å, but with modern equipment
0.70 Å or even better can usually be achieved without much effort)25 and is complete (at least 97% is recommended by the IUCr, yet in most cases 99% or even
100% completeness can and should be obtained). The MoO should be as high as
possible (a value of 5–7 should be considered a minimum), and “good data” have
I/σ values of at least 8–10 for all data. As usual with residual values, the merging
R-values should be as low as possible, and most small-molecule datasets have
Rint (also called Rmerge) and/or Rsigma values below 0.1 (corresponding to 10%)
24 “This term was defined at the SHELX Workshop in Göttingen in September 2003 to distinguish
the MoO from redundancy or multiplicity, with which the MoO has been frequently confused in the
past. In contrast to redundancy, which is repeated recording of the same reflection obtained from the
same crystal orientation (performing scans that rotate the crystal by more than 360 ), MoO,
sometimes also referred to as “true redundancy,” describes multiple measurements of the same (or a
symmetry equivalent) reflection obtained from different crystal orientations (i.e. measured at
different Ψ-angles)” [23].
25 Note that resolution describes the smallest distance that can be resolved. Therefore, smaller
numbers mean higher resolution, and 0.70 Å is a much higher resolution than 0.84 Å.
23
24
1 Crystallography
for the whole resolution range. In general, diffraction data should be collected at
low temperature (100 K is an established standard). Atomic movement is significantly reduced at low temperatures, which increases resolution and I/σ of the
diffraction data and increases order in the crystal.
1.5 Structure Determination
The final goal of the diffraction experiment is usually the determination of the
crystal structure, which means the establishment of a crystallographic model.
This model consists of x, y, and z coordinates and thermal parameters for every
atom in the asymmetric unit as well as a few other global parameters. After data
collection and data reduction, the steps described in the following paragraphs
lead to this model, which is commonly referred to as the crystal structure. In this
context it is worth pointing out that a crystal structure is not only the temporal
average, averaged over the entire data collection time, but also always the spatial
average over the whole crystal. That means the crystal structure shows what the
molecules making up the crystal look like on average. Crystal structure
determination is, therefore, not an ideal tool for looking at molecular dynamics
or single molecules. Real crystals are neither static nor perfect, and atoms can be
misplaced (packing defects or disorders) in some unit cells. On the other hand, it
is easy to derive information about interactions between the individual molecules in a crystal. Through application of space group symmetry and lattice
translation, packing diagrams reveal the positioning of all atoms within a
portion of the crystal larger than the asymmetric unit or unit cell, and interactions of neighboring molecules or ions become readily apparent.
1.5.1 Space Group Determination
The first step in crystal structure elucidation is typically the determination of
the space group. The metric symmetry is a good starting point; however,
considering that the true crystal symmetry could be lower than the metric
symmetry, it is important to determine the Laue group based on the actual
symmetry of the diffraction pattern, i.e. in reciprocal space. Having determined
the Laue symmetry, the number of possible space groups is significantly
reduced. The value of the |E2–1|-statistic allows reducing the number of space
group further by establishing at least a trend toward centrosymmetric or
noncentrosymmetric symmetry.
Finally, there are systematic absences that point out specific symmetry
elements present in the crystal. While, as described above, lattice type and other
translational components of the space group have no influence on the corresponding Laue group, those symmetry operations do leave their traces in
1.5 Structure Determination
Figure 1.14 Projection of a unit cell along the
crystallographic b-axis (i.e. in [h, 0, l] projection) in
presence of a c-glide plane coinciding with the a-cplane. In this projection the unit cell seems to be cut in
half which, in turn, doubles the volume of the
corresponding reciprocal unit cell. Reflections
corresponding to this projection will be according to
the larger reciprocal cell, which means that reflections
of the class h 0 l with l 2n are not observed, i.e.
systematically absent.
b
a
(x, y, z)
c′
(x, –y, ½+z)
c
reciprocal space in the form of systematic absences. Assume, for example, a
c-glide plane in the space group Pc. Figure 1.14 shows the unit cell in projection
along the b-axis, i.e. onto the a-c-plane. For every atom x, y, z, the c-glide plane
at y = 0 generates a symmetry-related atom x, −y, z + ½. In this specific 2D
projection, the molecule is repeated at c/2, and the unit cell seems to be half
the size (c = c/2) because one cannot distinguish the height of the atoms above
or below the a-c-plane when looking straight at that plane. This doubles the
apparent reciprocal cell in this specific projection h 0 l : c∗ = 2c∗. Therefore,
the reflections corresponding to this projection will be according to the larger
reciprocal cell, which means that reflections of the class h 0 l with l 2n (that is,
reflections with odd values for l) are not observed or, in other words, systematically absent. Similar considerations can be made for all screw axes and glide
planes as well as for lattice centering.
Combination of all these considerations can narrow the choice of space
groups down to just a few possibilities to be considered and sometimes even
to just one possible space group. Knowing the space group means knowing
all symmetry in real space. This knowledge can help to solve the phase problem.
1.5.2
Phase Problem and Structure Solution
Crystals are periodic objects, which means that each unit cell has the same
content in the same orientation as every other unit cell. Molecules inside the
unit cell consist of atoms, and atoms, simply put, consist of nuclei and electrons.
X-rays interact with the electrons of the atoms, not the nuclei, and – at least
from the perspective of an X-ray photon – an atom can be described as a more
or less localized cloud of electron density. Therefore, to the X-rays, the unit cell
looks like a 3D space of variable electron density, higher electron density at the
atom sites, and low electron density between atoms. Jean-Baptiste Joseph Fourier stated that any periodic function can be approximated through superposition of sufficiently many sine waves of appropriate wavelength, amplitude,
and phase. The example in Figure 1.15 is taken with permission from Kevin
25
26
1 Crystallography
FT
FT
0
1
2
3
4
5
6
7
8
Freq 2
Freq 3
Freq 5
Total
Figure 1.15 Electron density of a hypothetical one-dimensional crystal with a three-atomic
molecule in the unit cell (top right). This density function can be represented fairly well in
terms of just three sine waves: The first sine wave has a frequency of 2 (i.e. there are two
repeats of the wave across the unit cell); its phase is chosen that one maximum is aligned with
the two lighter atoms on the left of the unit cell and the other one is with the heavier atom on
the right. The second one has a frequency of 3; it has a different amplitude and also a
different phase (one maximum is aligned with the heavier atom on the right of the unit cell).
The third sine wave with a frequency of 5 also has a different amplitude, and its phase is
chosen so that two of this wave’s peaks are lined up with the two lighter atoms to the left of
the unit cell. Adding up the three sine waves results in the thick curve at the bottom left of the
figure. These sine waves are the “electron density waves” mentioned in the text above, and
the frequencies of 2, 3, or 5 correspond to the “electron density wavelengths.” The top left of
the figure shows the Fourier transformation of the unit cell, corresponding to the diffraction
pattern, together with the one-dimensional Miller indices. The three sine waves can be
identified as the three strongest reflections. The intensities of the reflections correspond to
the amplitudes of the sine waves in the right-hand side of the figure, and the frequencies of
the sine waves correspond to the respective Miller indices (2, 3, and 5). Unfortunately, the
phases are not encoded in the diffraction pattern. Source: Reproduced with permission of
Kevin Cowtan’s Book of Fourier. http://www.ysbl.york.ac.uk/~cowtan/fourier/fourier.html
Cowtan’s online Book of Fourier26 and illustrates how a one-dimensional (1D)
electron density function can be represented reasonably well by three sine
waves, assuming the amplitudes and phases are chosen correctly. The wavelengths of those sine waves used are all in integer fractions of the unit cell length
in accordance with the Miller indices of the corresponding reflections. These
26 http://www.ysbl.york.ac.uk/~cowtan/fourier/fourier.html
1.5 Structure Determination
wavelengths are referred to as “electron density wavelengths”27 and have nothing to do with the wavelength of the x-radiation used in the diffraction
experiment.
All reflections together form the diffraction pattern, which can be understood
as the Fourier transform of the 3D electron density function in the crystal. That
means that a Fourier transformation allows going from one space to the other
and back. Every independent reflection in the diffraction pattern is one Fourier
coefficient. As we saw above, structure factors F are vectors in the complex
plane28 with amplitude and phase angle. The amplitude of the reflection
corresponds to the amplitude of the electron density wave, its Miller indices
correspond to the electron density wavelength, and the reflection’s phase corresponds to the phase in the Fourier summation. In order to perform a Fourier
summation as in Figure 1.15, all three properties of the structure factors are
needed: amplitude, phase, and frequency (that is, the reciprocal of the electron
density wavelength). The structure factor amplitudes are measured as intensities in the diffraction experiment, the reflections’ Miller indices directly lead to
the frequencies, yet, unfortunately, the phase angles cannot be determined in a
standard diffraction experiment. This unlucky circumstance is typically referred
to as the “crystallographic phase problem,” and it has to be solved individually
for every crystal structure. Assigning a tentative and sometimes only approximate phase to the structure factors is called “solving the structure” or “phasing
the structure,” as together with amplitude and frequency, knowledge of the
phases (even if only approximate) affords an electron density map in which
atoms may be located. There are several methods for solving structures; two
of which will be described here, the Patterson function and direct methods.
The Patterson function goes back to Arthur Lindo Patterson who discovered
that a convolution of reciprocal space (that is, a Fourier transformation of the
measured intensities in the diffraction pattern without phases) gives rise to a
3D map, the Patterson map [24]. This map is not unlike an electron density
map; however the maxima in the Patterson map do not correspond directly to
atoms but rather they represent interatomic distances. The distance of a Patterson peak from the origin of the Patterson map corresponds to the distance
between two atoms in the crystal structure. Therefore, for every peak with coordinates u, v, w in the Patterson map, there is a pair of atoms in the unit cell that
reside on coordinates x1, y1, z1 and x2, y2, z2, such that u = x2-x1, v = y2-y1, and w =
z2-z1. The height of a Patterson peak corresponds to the number of electrons
involved in this interatomic distance. That means that distances between heavier
atoms (which have more electrons than light ones) will result in stronger Patterson peaks than distances between lighter atoms. The Patterson map is typically
fairly noisy, and Patterson peaks tend to be fuzzy and overlap with one another.
27 This term was introduced by Jenny Glusker.
28 Also called the Argand plane.
27
28
1 Crystallography
Therefore, it is difficult (though not impossible) to extract information about
light atoms from the Patterson map, and in the absence of any heavier atoms,
Patterson methods can fail. Knowledge of the symmetry in reciprocal space
(Laue group) and real space (space group) allows deriving coordinates for the
heaviest atom or atoms in a crystal structure. Based on those coordinates, phases
for all reflections can be calculated as if the structure consisted only of those
heavy atoms. In by far most cases, the structure has more atoms than just the
heavy ones located by the Patterson method, and, therefore, the first set of
phases is only approximate. Nevertheless, the phasing power of just a few heavy
atoms is usually sufficient to locate more atoms in the electron density map
calculated from the measured structure factor amplitudes and the
approximate phases. Including the newly found atoms into the crystallographic
model gives rise to better phases and, therefore, a clearer electron density map,
which will show more features than the one before. At this stage of structure
determination, we are no longer solving the structure but already refining it
(see below).
Direct methods are based on probabilistic relationships between specific
groups of structure factors and their phases. The foundations of classical
direct methods are a few simple and sensible assumptions, most importantly
(i) that electron density is never negative and (ii) that a structure consists of
discrete atoms resolved from one another. The first assumption gives rise to
a set of phase relationships, the Harker–Kasper inequalities, which allow
assigning phases to some select strong reflections. The second assumption
leads to the finding that the squared electron density function is similar to
the electron density itself times a scaling factor (Sayre equation). Derived
from the Sayre equation is the triplet phase relation, which states that the
sum of the three phases of three strong structure factors is approximately
zero if the three structure factors in question are related to one another
in such a fashion that three values for the h, the three values for k, and
the three values for l all add up to zero (h, k, and l are the Miller indices
of the reflections in question). An excellent introduction to direct methods
can be found in Chapter 8 of the book Crystal Structure Analysis
A Primer [25].
Since direct methods assume that atoms are discrete and resolved from one
another, comparatively high resolution of the diffraction data is required for
those methods to work (ca. 1.1 Å as a practical minimum requirement). Luckily,
most small-molecule crystals easily diffract to this limit.
1.5.3 Structure Refinement
“Refinement is the process of iterative alteration of the molecular model with
the goal to maximize its compliance with the diffraction data” [26]. The term
1.5 Structure Determination
structure refinement describes everything that leads from the initial structure
solution to the complete, publishable crystal structure. With the phase problem solved, a Fourier synthesis using all diffraction spots as Fourier coefficients and the freshly determined phases gives rise to a first electron
density map. This type of map is called the Fo-map, where Fo stands for the
observed structure factors. The Fo map gives the electron density at any given
point inside the unit cell, and it shows maxima where the atoms are located.
The height of the individual maxima is proportional to the number of electrons of the corresponding atom. Naively put, a high-electron density peak
is a heavy atom, a weaker peak is a light atom, and a very weak peak is usually
no atom at all but noise. The initial map is often noisy, and sometimes only the
heavier atoms can be located with confidence; however one can calculate a
new set of phases from the so-determined substructure. This new phase set
is usually better than the initial phases, and a new Fourier transformation gives
rise to a new and better Fo map. At this point, a second type of electron density
map is calculated, the so-called difference map or Fo–Fc map. Fc stands for the
structure factors calculated from the existing model, and, therefore, the Fc
map corresponds to the electron density distribution as described by the current model. The difference map is calculated by subtracting the Fc map from
the Fo map (hence the name Fo–Fc map). This map is essentially flat at places
where the molecular model is correct, as the difference between model and
crystal is small. In contrast, the Fo–Fc map has electron density maxima where
the model is still lacking atoms or where it contains an atom that is too light.
Similarly, the Fo–Fc map shows minima (negative electron density) where the
model accounts for too much electrons (if an atom in the model is heavier than
it should be or if the model contains an atom where there should not be one).
Based on the Fo–Fc map, the initial model can be improved, and phases calculated from the improved model lead to even better Fo and Fo–Fc maps.
The improved maps allow improving the model further, and another electron
density map can be calculated, which is better still. This iterative process continues until all nonhydrogen atoms are found and one has arrived at what is
called the complete isotropic nonhydrogen model.
Crystallographers distinguish between nonhydrogen atoms and hydrogen
atoms. Hydrogen atoms, which have only one electron and are more difficult
to detect in the electron density map, receive special treatment and are
introduced into the model toward the end of the refinement process. When
all nonhydrogen atoms are included in the model, the next step is to refine
the structure anisotropically. In an anisotropic model, the individual nonhydrogen atoms are allowed to move differently in different directions, and atoms are
no longer described as spheres but rather as ellipsoids (Figure 1.16). Expanding
the model to anisotropic atomic motion dramatically increases the number of
parameters to be refined. For an isotropic description, there are four parameters
29
30
1 Crystallography
C(8)
C(8)
C(3)
C(3)
C(9)
C(4)
C(2)
C(5)
C(7)
C(9)
C(1)
C(5)
C(6)
C(10)
C(2)
C(4)
C(10)
C(7)
C(1)
C(6)
Figure 1.16 Molecular model of a Cp∗ ring in a crystal structure refined with isotropic (left)
and anisotropic (right) displacement parameters.
per atom (atom coordinates x, y, z and the radius of the sphere), while an ellipsoid needs six parameters (a symmetric 3 × 3 matrix), in addition to the coordinates, for a total of nine parameters per atom. Therefore, anisotropic
refinement is only possible for datasets with sufficiently high resolution (the
cutoff is between 1.0 and 1.5 Å of resolution).
The IUCr recommends a data-to-parameter ratio of 10 : 1. For a fully anisotropic
model, this ratio is reached at a resolution of 0.84 Å. Many small-molecule datasets
extend to resolutions of 0.7 Å or even beyond; however, as mentioned above, not all
crystals diffract well enough to meet this IUCr standard. The use of restraints and
constraints can help improve the data-to-parameter ratio. Constraints are mathematical equations rigidly relating two or more parameters or assigning fixed
numerical values to certain parameters, thus reducing the number of independent
parameters to be refined. For example, two atoms could be constrained to have the
same thermal ellipsoid, or the coordinates of an atom located on a mirror plane
could be constrained to keep the atom from leaving the plane. Or, to give a third
example, the six atoms of a phenyl ring could be constrained to form a perfect hexagon. Restraints, in contrast, are treated as additional data and, just as data, have a
standard uncertainty. In the absence of restraints, the model is refined solely against
the measured diffraction data, and the minimization function M looks like this:
M=
w Fo2 −Fc2
2
In this equation w is a weighting factor applied to every structure factor
expressing the confidence in the corresponding observation29; Fo and Fc are
29 In good approximation, w = 1/σ, where σ is the standard uncertainty of the corresponding
reflection.
1.5 Structure Determination
the observed and calculated structure factors, respectively. Restraints allow
including additional information (for example, that aromatic systems are
approximately flat or that the three C–F bond distances in a CF3 group are
approximately equivalent). These additional bits of information can be added
to the diffraction data, and the function M in the presence of restraints
changes to
M=
w Fo2 − Fc2
2
+ 1 σ 2 Rt − Ro
2
In this equation σ is the standard uncertainty (also called elasticity) assigned
to a specific restraint, Rt is the target value the restraint assigns to a specific
quantity, and Ro is the actual value of the restrained quantity as observed in
the current model. Comparison of the two minimization functions above shows
that restraints are treated exactly like data in a structure refinement. Some
structures, perhaps even most, do not require any restraints at all; however
when the data-to-parameter ratio is low or disorders or twinning cause strong
correlations between certain parameters that should not be correlated,
restraints can be essential. “In general, restraints must be applied with great care
and only if justified. When appropriate however, they should be used without
hesitation, and having more restraints than parameters in a refinement is
nothing to be ashamed of” [27].
It is important to critically inspect a graphical representation of the anisotropic thermal parameters, as the shape, orientation, and relative size contain
important information about the quality of the model. Usually, those graphical
representations are called thermal ellipsoid representations or thermal ellipsoid
plots,30 and the word “thermal” implies that the ellipsoids represent the thermal
motion of the individual atoms. Most commonly, the volumes or boundaries of
the ellipsoids are chosen so that each ellipsoid contains 50% of the electron
density of the atom in question, and a typical description of such a plot would
be “thermal ellipsoid representation at the 50% probability level”. In a good
structure, all thermal ellipsoids should have approximately the same size,31
and their shapes should be relatively spherical. Strongly prolate or oblate
ellipsoids point to problems with the data or incorrect space group. Strongly
elongated ellipsoids usually indicate disorder that needs to be resolved, and
noticeable small or large ellipsoids suggest that the wrong element was assumed
for the atom in question.
30 Often, people call them “ORTEP plots”. ORTEP is the name of the first program that could
generate those graphical representations. The program was written by Carol Johnson, and ORTEP
stands for Oak Ridge Thermal Ellipsoid Plot. One should never call a thermal ellipsoid
representation an ORTEP plot unless the program ORTEP was actually used to generate them.
31 One should consider, however, that terminal atoms move more than central ones.
31
32
1 Crystallography
Once the complete anisotropic nonhydrogen model is established, the hydrogen atoms can be included. As hydrogen atoms have only one electron, which is
delocalized, they are difficult to place based on the difference density map.
Luckily, in most cases (especially with carbon-bound hydrogen atoms), it is
straightforward to calculate the positions of the hydrogen atoms and to include
them into their calculated positions.32 The hydrogen model derived in this
fashion is often better than it would be if the hydrogen positions were taken
from the difference map. An additional advantage of calculating hydrogen atom
positions is that no additional parameters need to be refined. In contrast, potentially acidic hydrogen atoms (for example, H bound to oxygen or nitrogen),
hydrogen atoms in metal hydrides, or other chemically unusual or special
hydrogen atoms should be included into the model from the difference map.33
When all hydrogen atoms are included into the model, the refinement is
essentially complete. Before the structure is published, however, a structure
validation step should be performed. Freely available software such as Platon
[28] or the online tool checkCIF34 analyze the final model for typical problems
(symmetry, thermal ellipsoid shape, data integrity, etc.) and create a list of alerts
that should be examined critically.
1.5.3.1 Resonant Scattering and Absolute Structure
It was mentioned above that reciprocal space is, in good approximation, centrosymmetric. This centrosymmetry of reciprocal space was described independently by Georges Friedel [29] and Johannes Martin Bijvoet [30], and the
equation |Fh,k,l|2 = |F−h, − k, − l|2 is called Friedel’s law or Bijvoet’s law. This law
only holds for strictly elastic interactions between photons and electrons, and
in the presence of resonant scattering (often also called “anomalous scattering”
or inelastic scattering), the centrosymmetry of reciprocal space is slightly disturbed in noncentrosymmetric space groups.35 The strength of resonant scattering depends on atom type and X-ray wavelength: Heavier atoms and longer
32 During the subsequent refinement cycles, the hydrogen positions are updated continuously as
the positions of the nonhydrogen atoms change. This treatment is called a riding model, as the
hydrogen atoms sit on the molecule as a rider on a horse and where the horse goes, the rider follows.
(The author of these lines made a different experience when attempting to ride a horse, but in
structure refinement this description of a riding model usually holds.)
33 Refinement of such hydrogen atoms is usually aided by application of X–H distance restraints
(X is any atom type) and by constraining the hydrogen atoms’ thermal parameter to, for example,
150% of the thermal motion of the atom X. Such a treatment is called a “semi-free refinement” of the
hydrogen atoms.
34 http://checkcif.iucr.org/
35 In centrosymmetric space groups where for every atom x, y, z there is another atom -x, −y, −z, the
effects of inelastic scattering for every such pair of atoms cancel each other out.
1.6 Powder Methods
wavelengths give rise to more inelastic scattering. To observe this effect with Mo
radiation, atoms heavier than Si should be present in the structure, while for Cu
radiation even oxygen gives enough resonant scattering to observe a slight violation of Friedel’s law. Those weak differences, often only a few percent of the
absolute intensity, allow determining the absolute structure of a crystal and,
thus, the absolute configuration of chiral molecules. During structure refinement, the model is treated mathematically as if it were a mixture of both hands,
and the ratio between the two hands is refined. This ratio is called the Flack x
parameter [31], and its value ranges from zero to one. A Flack parameter of zero
indicates that the hand of the molecule in the structure is correct, and a value of
one means that the structure should be inverted. Values between zero and one
indicate mixtures of both hands, and a value of 0.5 corresponds to a perfectly
racemic mixture. It must be noted that the Flack x comes with a standard uncertainty, which is as important as the value itself. For an absolute structure to be
considered determined correctly and confidently, the Flack x should be zero
within two to three standard uncertainties, and the standard uncertainty should
be smaller than 0.01. If it is known that a compound is enantiopure, racemic
twinning can be ruled out, and the Flack x can only be one or zero but not
in between. In this case, a higher standard uncertainty of, say, 0.1 can be
accepted [32].
1.6
Powder Methods
Single-crystal X-ray diffraction is unequivocally the most definitive technique
for determining crystal structures. All too often, however, the structures
of small-molecule crystal forms are elusive because of the single-crystal size/
quality requirements of the X-ray methods or the methods of preparation.
For example, solution methods of crystallization were used to produce single
crystals of seven of the ROY polymorphs (Figure 1.2). However, the four most
recently discovered polymorphs, YT04, Y04, RPL [33], and R05 [34], were not
initially crystallized from solution, having instead been discovered many years
later through melt crystallization, vapor deposition, and solid-state phase
transitions. None of these methods are conducive to generating single crystals,
and only by introducing YT04 seeds obtained by melt crystallization into a
supersaturated solution of ROY were single crystals of this polymorph ultimately produced for its structure determination. Fortunately, in cases where
single-crystal substrates are not available, powder methods may be used to solve
crystal structures. Two approaches, namely, structure solution from powder diffraction and NMR crystallography, are increasingly used for crystal structure
analysis in pharmaceutical development and will be briefly described in the following sections.
33
34
1 Crystallography
1.6.1 Powder Diffraction
Powder X-ray diffraction (PXRD) patterns provide 1D fingerprints of 3D crystal
packing arrangements dispersed among randomly oriented polycrystallites.
Owing to the ease with which powder patterns can be collected, PXRD is extensively used in pharmaceutical development to identify crystal forms based on
their unique diffraction peaks and intensities. PXRD patterns can also be used
for structure determination when suitable single crystals cannot be grown to
sufficient size (on the order of ~100 μm) or quality [35, 36]. Although singlecrystal and powder diffraction provide the same intrinsic information, when
3D diffraction in reciprocal space is compressed into a 1D powder pattern,
information is inevitably lost, particularly at shorter d-spacings (higher diffraction angles). The loss of intensity information for individual peaks in a powder
pattern due to peak overlap increases both the difficulty and uncertainty of
structure solution from powders. Therefore, to ensure that the structure model
is as accurate and precise as possible, measures must be taken to ensure that the
powder sample quality is high and that the PXRD data are properly collected. To
this end, PXRD data are usually collected in transmission mode for carefully
prepared, highly crystalline, and preferably phase-pure powders placed between
polymer films or packed in thin-walled capillaries. To minimize preferred
particle orientation effects and to give good powder averaging, the samples
are spun or rotated in the incident X-ray beam during data collection. For
the high accuracy needed for structure solution, the diffraction pattern is
typically collected over a wide 2θ range, usually up to 70 or 80 .
Structure determination from powder diffraction data involves three steps:
1) Indexing the peaks in the experimental pattern to determine the size and
shape of the unit cell, along with the space group symmetry.
2) Using the diffraction peak intensities to generate a good approximation to
the atomic positions in the crystal structure.
3) Refining (usually by the Rietveld method [37]) the trial structure to fit the
simulated PXRD pattern of the model to the full experimental PXRD
pattern.
Indexing programs that are widely used in the first step to determine the lattice parameters (a,b,c,α,β,γ) include X-Cell [38], DICVOL [39], and singular
value decomposition [40]. Sensible indexing solutions are generally identified
based on the molecular volume, cell volume, and number of unindexed reflections (checked using either Le Bail [41] or Pawley [42] fitting). Once the powder
pattern has been successfully indexed, the space group can be assigned by identifying systematically absent reflections. Here, it should be noted that of all of
the steps in the powder structure solution process, the first indexing step tends
to be the most problematic, and without a correct unit cell, structure solution is
impossible.
1.6 Powder Methods
In the second step of the structure determination process, trial crystal structures are generated in direct or real space independent of the experimental
PXRD data. Search algorithms, such as simulated annealing [43–45], Monte
Carlo [46, 47], or genetic algorithms [48–50], are used as implemented in commercially available programs (e.g. PowderSolve,36 DASH,37 and TOPAS38) to
generate trial structures with input of the chemical structure, the unit cell parameters, and space group. The positions, orientations, and internal degrees of
freedom of molecular fragments are stochastically varied within a unit cell until
a match between the simulated and experimental PXRD patterns is obtained.
The approximate structure solution(s) from the second step serves as a starting
point for the subsequent structure refinement in step 3.
At the third and final stage, the structure model, along with peak profile and
background parameters, temperature factors, zero-point error, preferred orientation, etc. are Rietveld refined to a more accurate, higher-quality description of
the structure, as shown for fexofenadine hydrochloride in Figure 1.17 [54]. The
correctness of a powder structure solution is assessed by comparing its calculated
powder pattern with the experimental pattern, the fit being qualitatively visualized by the difference curve (black curve at the bottom of Figure 1.17) and quantified by either a weighted powder profile R-factor (Rwp) or full profile χ 2. It is
generally recommended that the crystal structure solution be subsequently verified by dispersion-corrected density functional theory (DFT-D) energy minimization [55]. With this approach, a powder structure is judged correct when the
root mean square Cartesian displacement (RMSCD) value is 0.35 Å or less.
1.6.2
NMR Crystallography
NMR spectroscopy is universally recognized for its unparalleled ability to characterize molecular structure, conformation, and bonding in solution. A key to
the early and enormous success of solution NMR methods has been the ease
with which high-resolution spectra are acquired, made possible in part because
the orientation-dependent (anisotropic) interactions that affect NMR spectra
are normally averaged to single isotropic values by rapid molecular tumbling
in solutions.39 The molecular mobility in solids is, by contrast, highly restricted,
and therefore strong nuclear-spin interactions are not dynamically averaged.
This means that NMR spectra of solids acquired under the same (as solution)
36 PowderSolve – a complete package for crystal structure solution from powder diffraction
patterns [51].
37 DASH: a program for crystal structure determination from powder diffraction data [52].
38 TOPAS [53].
39 A single crystal would produce a comparably simple NMR spectrum, in this case not because of
Brownian motions but instead because only one crystal orientation is present with respect to the
direction of the external magnetic field.
35
1 Crystallography
14 000
12 000
a
10 000
Int./counts
36
b
8 000
6 000
c
4 000
2 000
0
10
20
30
40
50
60
70
80
2θ/°
Figure 1.17 Rietveld plot of racemic fexofenadine hydrochloride showing the fit of the
experimental PXRD pattern (dots) to the simulated pattern (solid line) for the powder
structure model [inset]. The vertical tick marks represent the theoretical peak positions.
Source: Adapted with permission from Brüning and Schmidt [54]. Reproduced with
permission of John Wiley & Sons.
conditions are poorly resolved, owing to the simultaneous observation of nuclei
in all possible orientations with respect to the external magnetic field. Not surprisingly, the widespread use of solid-state NMR spectroscopy would await the
development of methods to remove (and, in some cases, reintroduce on
demand) dipolar and scalar (J) spin–spin coupling interactions, as well as to
additionally overcome the poor sensitivity associated with the detection of
nuclei at low natural abundance.
Solid-state NMR methods were foreseen as a way to derive even more detailed
structural information for molecules in solution, based on the premise that they
would bridge solution-state NMR spectra and precisely determined molecular
structures and conformations derived from X-ray diffraction. However, molecular structure in solution can be rather different, and where material properties
are of interest, these attributes will be more relevant as they exist in the solid
state. Either way, from the time that cross polarization (CP), magic-angle spinning (MAS), and high-power 1H decoupling techniques were first combined to
produce high-sensitivity, high-resolution 13C spectra [56], solid-state NMR
1.6 Powder Methods
spectroscopy has become an indispensable technique for chemical analysis,
structure determination, and studying dynamic processes in the solid state.
The CP/MAS experiment with its variations and extensions allows local electronic environments of different NMR-active nuclei (1H, 13C, 31P, 15N, 17O,
19
F, etc.) that are common to pharmaceutical molecules and their formulations
to be uniquely probed over a large timescale without the requirement of single
crystals. Solid-state NMR spectroscopy therefore nicely complements X-ray
crystallography, rendering the combination of the two techniques highly powerful for providing a complete determination of structure and dynamics at an
atomistic level.
Advances in hardware and probe technology, higher magnetic field strengths,
and the development of a range of specialized multinuclear and multidimensional solid-state NMR experiments, along with quantum mechanical methods
for computing NMR parameters (e.g. shielding constants for chemical shift
prediction), have fueled interest within the pharmaceutical community in
applications of NMR crystallography, that is, the use of solid-state NMR
spectroscopy for determining or refining structural models [57, 58]. For the
fundamentals underpinning solid-state NMR spectroscopy, along with descriptions of the spectrometer hardware, pulse sequences, and operational aspects
involved, the reader is referred to comprehensive monographs on the subject
[59–61]. We focus herein on the practical application of solid-state NMR
spectroscopy for the structural characterization of pharmaceutical materials,
with particular attention to how this technique can be used to assist in crystal
structure determination from diffraction data.
Early pharmaceutical applications of solid-state NMR spectroscopy relied on
the basic CP/MAS experiment to fingerprint drug crystal forms (akin to PXRD),
mainly through their unique isotropic chemical shifts. In this capacity, not only
has NMR spectroscopy been invaluable for characterizing the solid-state form
landscapes of drug molecules en route to selecting the crystalline delivery
vehicle for a given drug product, but it also has secured its place as a research tool
in drug development, ensuring that crystallization processes deliver and preserve
the correct form and formulation processing and long-term storage preserve it.
Solid-state NMR spectroscopy has also been used to good advantage in claiming
drug crystal forms as intellectual property in patents, and in a number of cases, to
later prove patent infringement of those forms in generic drug products.
NMR crystallography has evolved from the fingerprinting applications
described above into what is now the derivation of precise bond lengths and
angles within a molecule, and the determination of intermolecular bond lengths
and angles associated with packing patterns. An impressive demonstration of
solid-state NMR spectroscopy for determining 3D structure at natural isotopic
abundance has been reported for simvastatin, the active ingredient in Zocor®
[62]. In this work, a combination of state-of-the-art through-bond and
through-space NMR correlation experiments was used to establish the
37
38
1 Crystallography
2.7 Å
3.4 Å
11
25
10
3.4 Å
12
3.8 Å
17
24
6
7
2.8 Å
14
15
2.7 Å
23 20
3.3 Å
2.9 Å
1
3.8 Å
13
2.7 Å
16
9
8
4.2 Å
2.2 Å
18
21
19
23’
22
22’
21’
5 4.6 Å
4
2
3.4 Å
3
2.1 Å
1.9 Å
Figure 1.18 Conformation of
a single molecule of
simvastatin (left) and
molecular packing in
crystalline simvastatin (right)
with interatomic 1H–13C
distances and intermolecular
contacts (marked by arrows)
established by solid-state
NMR spectroscopy. Disorder
of the terminal ester was
proposed by X-ray
diffraction. Source:
Reproduced from Brus and
Jegorov [62] with permission
of American Chemical
Society. (See insert for color
representation of the figure.)
15
11
16
10
molecular conformation of the drug molecule in its crystalline structure
and also to identify close contacts between near-neighbor molecules
(Figure 1.18). Such information, which nowadays is supported by first principles
density functional theory (DFT) computations of chemical shielding [63, 64],
may be used to validate structure solutions derived from PXRD; it may even
contribute to the crystal structure determination process, either by providing
restraints for structure refinement [65, 66], or in combination with CSP (vide
infra), and eliminate putative but incorrect structures [67].
A recent extension to chemical-shift-based NMR crystallography has combined MD simulations and DFT calculations to quantify the distribution of
1.7 Crystal Structure Prediction
atomic positions in a crystal [68]. With this approach, NMR parameters are
computed for a range of configurations taken from MD snapshots (simulating
thermal motions above 0 K), effectively allowing the dynamic contributions to
peak broadening in solid-state NMR spectra to be modeled and anisotropic
displacement parameters (depicted in thermal ellipsoid plots, cf. Figure 1.16)
to be derived to even greater accuracy than X-ray diffraction. Today, this application is neither trivial nor commonplace, but it shows the great promise that
extension of the computational methods of solid-state NMR spectroscopy, in
combination with experiment, has for extracting ever more detailed and accurate structural and dynamic information to reinforce or complement X-ray
crystallography.
1.7
Crystal Structure Prediction
Another route to molecular and crystal structure models that has emerged in
recent years is ab initio CSP, a computational methodology wherein 3D crystal
packing arrangements are calculated from first principles, starting with a chemical diagram of the molecule [69, 70]. Owing to the heavy demands of the computational methods involved, CSP is generally performed in two stages. The first
uses algorithms to generate trial structures that sample different crystal packing
possibilities, holding the molecular conformations rigid. At this stage, anywhere
from a 1000 to 1 000 000 or more plausible structures may be calculated,
depending on the size and flexibility of the molecule, how many space groups
and independent molecules (Z ) are included in the search, the chirality of the
molecule, and available computational resources and time. The low-energy
local minima among the computed crystal structures identified in the first stage
are then subjected in the second stage to more accurate (and computationally
expensive) lattice energy minimizations, this time refining the molecular conformation within the crystal structure (obeying space group symmetry) to identify those that are lowest in energy. All successful CSP methods use electronic
structure calculations, albeit in different ways. One approach involves first optimizing the geometry of the isolated molecule in a range of conformations and
then selecting input structures for the global structure search among the lowenergy conformational minima [71]. The computationally expensive but very
powerful method of Neumann and coworkers uses a molecule-specific force
field that is parameterized to reproduce DFT-D crystal structures, Monte Carlo
parallel tempering to generate structures, and solid-state DFT-D calculations
for the final energy minimization/ranking [72].
The output of a CSP is a crystal energy landscape, a collection of putative crystal structures, all at 0 K, which are usually ranked in order of their lattice energy
and separated in the second dimension by their crystal packing efficiency (or
density), as shown in Figure 1.19 [73]. In this example, one of the earliest
39
1 Crystallography
–180
–183
Intra H-bonds:
conf A
conf B
36
–186
Ecrys/kJ mol–1
40
–189
–192
3312
–195
1273
–198
Form II
62
64
43
25
41
74
214
133
39 26
2422
498
4
6
180
63
1
487
66
68
Form I
31
2060
Exptl.
Form I
Form II (297)
Form III (63 and 214)
2709
3420
297
Inter H-bonds:
C1 , 1(4)
C1 , 1(11)
C1 , 1(6)
R2 , 2(12)
R2 , 2(22)
R2 , 2(8)
Form III
798
70
72
74
Packing index/%
Figure 1.19 Crystal energy landscape of a model pharmaceutical. Each point represents a
mechanically stable 3D structure ranked in order of lattice energy and crystal packing
efficiency or packing index. Experimentally observed crystal structures found by solid form
screening are encircled. Source: Adapted from Braun et al. [73]. https://pubs.acs.org/doi/abs/
10.1021/cg500185h. Licensed under CC BY 4.0. Reproduced with permission of American
Chemical Society.
anticipated uses of CSP has been realized – to provide plausible structure
models for refinement in cases where crystal structure determination was
not possible from available experimental data. Unlike the Form I and II crystal
structures, which were solved from well-grown single crystals (but also found
on the crystal energy landscape), Form III is a metastable polymorph produced
exclusively by dehydration and thus was impossible to grow as a single crystal.
Using CSP-generated structures, a disordered structure model, giving a
promising match to both PXRD and solid-state NMR data, was proposed.
Progress in the development of CSP methods has been tracked over the last
18 years by blind test competitions hosted by the CCDC. Developers of the
methods are provided a series of target molecules (or salts), for which crystal
structures have not been published, and asked to predict the spatial arrangement of molecules in crystal structures given only the molecular structure diagram. Computed crystal structures are returned, usually ranked in order of their
0 K lattice energy, although most recently attempts have been made to provide a
Gibbs free energy ranking to compare stability at crystallization processrelevant temperatures. With each blind test, the complexity of the challenge
has increased in terms of the space groups considered, number of molecules
in the asymmetric unit (Z > 1), molecular size and flexibility, and inclusion
of less common elements and multicomponent and ionic (salt) targets, commensurate with the development of the algorithms. The results of the most
1.8 Crystallographic Databases
recent sixth blind test [74], which was published in late 2016, show that much
progress has been made in dealing with the challenges presented by flexible
molecules, salts, and hydrates. All of the targets, apart from one, were predicted
by at least one submission. However, this benchmark of CSP methodologies has
shown the need for further improvement of the structure search algorithms,
especially for large, flexible molecules. Furthermore, with the relative energy
differences between crystal polymorphs being small (typically less than 2 kJ
mol−1 [75]), it is clear that continued development of ab initio and DFT methods
will be required if lattice energies, let alone free energies, are ever to be calculated to the accuracy (and efficiency) needed for reliable ranking of the
structures.
The blind test benchmarks of CSP, along with early successes in predicting
crystal structures of “small” pharmaceuticals, have generated enormous interest
within the pharmaceutical community to develop CSP methods as a complement to experimental solid form screening and to increase access to crystallographic data [76]. The ability to reliably predict how a molecule will crystallize in
the solid state, in particular, the range of solid-state forms (polymorphism),
would not only confirm that the most stable form is known but could also help
design experiments to find new polymorphs, rationalize disorder, and estimate
the possible range of properties among different solid forms. These more ambitious goals of using computed crystal energy landscapes to aid solid form development are being realized to a limited extent today, with CSP not only
complementing pharmaceutical solid form screening but also helping to establish molecular-level understanding of the crystallization behaviors of active
pharmaceutical ingredients [77].
1.8
Crystallographic Databases
Any given crystal structure may hold the key to unlocking important details of
chemical structure, conformation, stereochemistry, or intermolecular interactions that improve our understanding of how structure underpins properties.
The crystallography community recognized long ago, however, that information gleaned from data collections would far exceed that derived from individual
experiments and set out to share their data through the creation of crystal structure databases for all researchers to use. A number of such compilations exist
today, including the Inorganic Crystal Structure Database,40 Protein Data
Bank,41 and Crystallography Open Database,42 the latter attempting to
combine all classes of compounds. However, for the discovery and development
40 Inorganic Crystal Structure Database (icsd.fiz-karlsruhe.de).
41 Protein Data Bank (rcsb.org/pdb/home/home.do).
42 Crystallography Open Database (www.crystallography.net/).
41
42
1 Crystallography
of small-molecule pharmaceuticals, there is no more important database than
the CSD,43 the world’s repository for small-molecule organic and metal–
organic crystal structures.
Curated and maintained by the CCDC, the CSD contains as of the time of this
writing over 900 000 entries from X-ray and neutron diffraction analyses, with
updates released to the public every six months. Each entry in the CSD is the
result of a structure determination from single-crystal or, in some cases, powder
diffraction data, and each is identified by its six-letter REFCODE, appended in
some cases by two numbers in reference to its publication history. The CSD has
grown exponentially over many (50+) years, as has the interest in using the database for structural research. This is due in part to the CCDC’s commitment to
develop tools to efficiently mine and analyze the structures. The CCDC now
offers a suite of CSD System software for searching the database (ConQuest);
visualizing and analyzing 3D structures (Mercury); comparing bond distances,
angles, and torsions against statistical distributions of those geometrical parameters within the CSD (Mogul); and interrogating noncovalent interactions in
the context of the CSD (Isostar). As a service to the worldwide crystallography
community, the CCDC has also made available programs for checking the syntax and format of crystallographic information files (CIF) (enCIFer), curating inhouse (proprietary) structure databases (PreQuest), and others.
In recent years, the CCDC, in partnership with pharmaceutical and agrochemical companies, has developed knowledge-based tools to aid solid form
development [78]. Two such structural informatics tools that are being increasingly applied in pharmaceutical development to assess the risk of polymorphism
(among other applications [79]) are the logit hydrogen-bond propensity (HBP)
tool [80] and full interaction maps (FIMs) [81]. The HBP tool computes the likelihood of H-bonds forming between specific donor and acceptor groups in a
target molecule, while FIMs are used to assess the geometries of noncovalent
interactions using various chemical probes, as shown for trimethoprim Forms
I and II in Figure 1.20. Collectively, these tools can be used to identify “weaknesses” in a crystal structure, such as statistically less favorable hydrogen bond
donor–acceptor pairings or unusual geometries that might warrant further
investigation, possibly extending the search for alternate polymorphs.
1.9 Conclusions
Crystallography is the cornerstone of all structure-based science. While singlecrystal X-ray diffraction remains the “gold standard” by which molecular and
crystal structures are established, powder methods, including X-ray diffraction
43 Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge, UK CB2 1EZ (www.ccdc.
cam.ac.uk).
References
(a)
(b)
Figure 1.20 Full interaction maps for trimethoprim polymorphs, (a) Form I (AMXBPM12) and
(b) Form II (AMXBPM13), showing hydrogen bond acceptor, hydrogen bond donor, and
hydrophobic CH “hot spots.” The solid-dashed circles highlight hydrogen bonding partners
just outside the hot spots, indicating that the interaction geometries are not well represented
in the CSD. The dashed circles point to where a hot spot near an NH donor is missing,
presumably due to steric hindrance within the crystal conformers.
and solid-state NMR spectroscopy (NMR crystallography) and more recently
crystal structure prediction, have provided unprecedented access to structural
information for a broad range of materials. Today, the experimental, computational, and informatics tools for crystal structure analysis are having an enormous impact on the design of molecules with optimal biological and
material properties. As the structure analysis toolbox continues to expand, so
too will the role of crystallography in discovering, developing, and delivering
safe and efficacious medicines.
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47
2
Nucleation
Junbo Gong and Weiwei Tang
School of Chemical Engineering and Technology, Tianjin University, Tianjin, P.R. China
2.1
Introduction
Crystallization from solution plays a fundamental role in various natural and
industrial processes such as formation of snow and ice, biomineralization of
bones and teeth, and industrial production of pharmaceuticals, agrochemicals,
and other fine chemicals. Nucleation, the first step of crystallization, determines
the crystal structure, crystal size and size distribution, and consequent solidstate properties of crystalline materials, as well as the kinetics of crystallization
process. Nucleation of a crystal is a first-order phase transition from a supersaturated state and has been investigated for more than one century. Nucleation
mechanisms generally can be divided into two categories: classical nucleation
theory (CNT) and nonclassical nucleation mechanisms. The latter is often seen
in inorganic and protein systems [1, 2].
The CNT was originally derived by the pioneering work of Fahrenheit on the
supercooling of water in the early 1700s; it was endowed with thermodynamic
underpinnings by Gibbs in the late 1800s on the studies of droplet formation
on a supersaturated vapor; in the early 1900s Volmer and Weber formulated
the kinetic aspects of CNT for vapor condensation; subsequently it was
addressed cases of nucleation in condensed phases by Turnbull and Fisher in
the 1950s [3]. CNT has been widely applied to explain the crystallization kinetics
from melts or solution. Recently, dense liquid-like clusters were experimentally
observed in the crystallization of protein systems [4, 5] and supported by
Pharmaceutical Crystals: Science and Engineering, First Edition.
Edited by Tonglei Li and Alessandra Mattei.
© 2019 John Wiley & Sons, Inc. Published 2019 by John Wiley & Sons, Inc.
48
2 Nucleation
computer simulations [6]. In addition, the growing evidence supports the existence of stable prenucleation clusters (PNCs) in the solution of inorganic systems
[1, 7]. Furthermore, the failure of several orders of magnitude in predicting nucleation kinetics brings the extra challenges of CNT [8]. The findings lead to the
nucleation studies move beyond CNT and suggest the much more complex
nucleation pathways. The two-step nucleation mechanism and PNC pathway
are the two main nonclassical nucleation mechanisms. The essential difference
between CNT and the two-step mechanism lies in the sequence of evolutions of
structure order and density during the formation of clusters and nuclei. To further clarify this point, recent progress has been made, including the examination
of structure link between solution chemistry and crystallography and the intensive studies on the liquid–liquid phase separation (LLPS) phenomenon.
In industrial crystallization, the primary nucleation is generally avoided due
to its uncertainties in control, but the secondary nucleation commonly exists.
The origin of secondary nucleation can be either from solution or from seeding crystals, which is mainly due to seeding-induced nucleation, breakage or
attritions under the mechanical stirring, and mixing conditions. The control
over secondary nucleation is critical to achieve the desire crystal size and size
distribution. The secondary nucleation needs to be either avoided to obtain
narrow crystal size distribution (CSD) typically in batch crystallization or
enhanced to improve the robustness and start-up efficiency of continuous
crystallization process.
Therefore, this chapter outlines the mechanisms, theoretical models and
applications of primary crystal nucleation and secondary nucleation in batch
or continuous crystallization process. Particular emphasis is placed on the control and optimization of organic polymorphs, crystal size and size distribution in
the frameworks of primary spontaneous nucleation mechanisms (CNT and
nonclassical mechanisms) and secondary nucleation mechanism.
2.2 Classical Nucleation Theory
2.2.1 Thermodynamics
Thermodynamic view provides the most fundamental way to describe nucleation phenomenon. Assuming the cluster is spherical with a diameter of L, the
total free energy change (△G) requiring for the formation of such cluster is
given by
ΔG = ΔGs + ΔGv
21
in which △Gs represents the free energy penalty due to the creation of a new
surface and hence is a positive quantity; △Gv, on the other hand, represents
the decreasing bulking energy because of the addition of monomer units and
2.2 Classical Nucleation Theory
thus is a negative quantity. The total free energy of dual processes determines
the growth or decay of a cluster.
△Gs is proportional to the size of the particle according to the equation:
ΔGs = Aγ = πL2 γ
22
where A is surface area of the cluster and γ is the interfacial tension between the
surface of the cluster and the surrounding solution.
At a given temperature and pressure, the value of △Gv can be computed by
ΔGv = − n μ− μb
23
where μ is the chemical potential of solute monomer in a supersaturated solution, μb represents the chemical potential of a cluster, and n denotes the number
of molecules in a cluster and is calculated by volume V of the cluster and molecular volume v0, for a spherical nucleus, according to the equation:
n=
V πL3
=
v0 6v0
24
The difference in chemical potential between monomer and a cluster can be
expressed as
μ − μb = kB T ln
C
= kB T ln S
C∗
25
where kB is Boltzmann constant and C∗ and C are concentrations of saturated
and supersaturated solutions, respectively.
Combining Eqs. (2.3)–(2.5) leads to
ΔGv = −
πL3
kB T ln S
6v0
26
and hence Eq. (2.1) can be rewritten as
ΔG = πL2 γ − πL3
kB T ln S
6v0
27
The total free energy goes through a maximum at a critical size Lc (see
Figure 2.1) in which the thermodynamically stable nucleus forms. At the
dΔG
= 0, the Eq. (2.7) is then expressed as
extreme point,
dL
2πLc γ − πL2c
kB T ln S
=0
2v0
28
Thus,
Lc =
4v0 γ
kB T ln S
29
49
2 Nucleation
+ ve
Free energy, ΔG
50
Figure 2.1 Free energy diagram of
nucleation involving the dual
processes of interfacial creation and
growth of clusters and the
appearance of critical clusters.
ΔGs
ΔGc
0
Lc
ΔG
– ve
ΔGv
Size of nucleus, L
0
From Eqs. (2.7) and (2.9), we obtain the critical free energy,
ΔGc =
16πγ 3 v20
3 kB T lnS 2
△Gc:
2 10
When the cluster size L > Lc, the total change in free energy, △G, decreases
continuously with L, indicating the growth of the cluster becomes energetically
favorable. If L < Lc, △G increases with L, suggesting the cluster tends to be dissolved. The critical number n∗ of solute molecules in a nucleus thus can be
derived as
n∗ =
32πγ 3 v20
3 kB T lnS 3
2 11
By the resemblance to kinetic theory of reaction, the steady-state rate of
nucleation (J) can be expressed in the form of the Arrhenius rate equation:
J = A exp −
ΔGc
kB T
2 12
in which A is the pre-exponential factor. Combining Eqs. (2.10) and (2.12)
results in
J = A exp −
B
ln2 S
2 13
2.2 Classical Nucleation Theory
B=
16πγ 3 v20
3 kB T
2 14
3
Here B is the thermodynamic parameter. The equation clearly shows the
effects of temperature, supersaturation ratio, and interfacial tension on the primary nucleation rate. Moreover, it provides an accessible way to predict the rate
of crystal nucleation.
2.2.2
Kinetics of Nucleation
The nucleation kinetics can be described in the framework of cluster approach by
assuming the existence of clusters of m (=2, 3, …) molecules (or atoms) in old
phase and transformations of m-sized clusters into n-sized ones via timedependent frequencies fmn(t) (s−1) [9]. It is possible the equally sized clusters have
different shapes, which make the mathematically described kinetic nucleation
equation much more complicated, and thus the clusters of a given size was generally postulated with only one shape. Note that such assumption leads to the size
being the sole parameter to describe clusters and thereof crystal nuclei.
Figure 2.2 illustrates the growth and decay of m-sized clusters. As can be seen,
a change of the cluster size may occur by attachment and detachment of monomers, dimers, trimers, or even higher aggregates. When the losing and gaining of
1
2
m–2
m–1
m
m+1
m+2
gn* fn* – 1
n* – 1
n*
fn*
gn* + 1
n* + 1
Figure 2.2 Schematic illustration of all possible changes in the size of a cluster of m molecules
(solid lines) and the change in the size of critical cluster n∗ by attachment and detachment
of monomers only according to the Szilard–Farkas model (dash lines). The diminishments
in concentration of m-sized clusters due to the m n∗ transitions (the arrows leaving size m)
and the increases because of n∗ m transitions (the arrows ending at size m).
51
52
2 Nucleation
clusters were assumed only by monomers, the above model is simplified to be
the Szilard–Farkas model. In this model, nucleation occurs by a successive
attachment and detachment of single molecules to and from the clusters of various sizes. This was considered as an acceptable approximation, because the
chance that the clusters lose dimers, trimers, etc. is rather low [9]. The cluster
and nucleus formation, thus, can be regarded as a series of chain “bimolecular
reactions” between monomers and n-mers (n = 1, 2, 3, …):
1⇄2⇄
⇄ n∗ − 1 ⇄ n∗ ⇄ n∗ + 1 ⇄
⇄M
where [M] denotes a cluster of M molecules. The nucleation kinetics are controlled by the frequencies fn∗ and gn∗ of monomer attachment and detachment
from an n∗-sized cluster, respectively. In a stationary state of nucleation process
with a constant concentration Xn of n-sized clusters, the nucleation rate was
defined as the difference between the transformation frequency fn∗ Xn∗ of the
nuclei (n∗) into the smallest supernuclei (n∗ + 1) and detachment frequency
gn∗ + 1 Xn∗ + 1 of the supernuclei n∗ + 1 into the nuclei n∗. Hence
J = fn∗ Xn∗ − gn∗ + 1 Xn∗ + 1 = ξfn∗ Xn∗
gn∗ + 1 Xn∗ + 1
ξ = 1−
fn ∗ X n ∗
2 15
2 16
With f ∗ ≡ fn∗ , X∗ ≡ Xn∗ , Eq. (2.15) can be expressed as the familiar form
J = zf ∗ C ∗
2 17
where z (=ξX ∗ Ca∗ = ln2 S 12πB) is the so-called Zeldovich factor accounting
for the use of Ca∗ instead of the actual nucleus concentration X∗ and for those
clusters larger than nuclei but eventually decay rather than growth into
macroscopic crystals. Ca∗ = C0exp(−ΔGc/kBT) is the equilibrium concentration
of crystal nuclei. C0 is the concentration of nucleation sites in the system and
is assumed equal to 1/v0 for homogenous nucleation (v0 is the volume of
single-solute molecule.)
Therefore, the nucleation rate was determined by not only nucleation barrier
ΔGc and the concentration of nucleation sites, C0, but also the attachment frequency f∗ of monomers to the nucleus. The nucleation, derived by attachment of
monomers, could be controlled either by volume diffusion process of monomers in solution toward the nucleus or by transfer of monomers across the
interface of nucleus and the surrounding solution.
When the monomer attachment is a diffusion-controlled process, f ∗ is the
product of the diffusion flux j∗ of monomers to the nucleus surface and the surface area A∗. By assumption of a spherical nucleus of a radius r∗ = (3v0n∗/4π)1/3,
j∗ can be expressed as DC/r∗ and A∗ = 4πr∗2, and hence f ∗ is given by
f ∗ = 48π2 v0
1 3
DCn∗1 3 = 48π2 v0
1 3
Dn∗1 3 C ∗ S
2 18
2.2 Classical Nucleation Theory
where D is the diffusion coefficient of monomers and C is the concentration of
monomers in the bulk solution.
If molecular attachment is controlled by interface transfer, the monomers can
be in immediate contact with the nucleus but need to make a random jump over
a distance d0 ≈ (6v0/π)1/3 before joining into the nucleus. Based upon the
assumption that such a jump is proportional to D and the sticking coefficient
λ of monomers, j∗ = DC/d0 and A∗ = 4πr∗2. Thus f ∗ is given by
f ∗ = λ 6π2 v0
1 3
DCn∗2 3 = λ 6π2 v0
1 3
Dn∗2 3 C ∗ S
2 19
The use of Eqs. (2.17)–(2.19) and Eq. (2.11) yields the 3D stationary rate of
crystal nucleation:
J = A0 S exp −
B
ln2 S
2 20
The dimensionless kinetic parameter A0 is given by
A0 =
kB T
v20 γ
1 2
DC ∗ ln S or A0 = λ
4π
3v0
1 3
γ
kB T
1 2
DC ∗
2 21
for volume diffusion and interface controlled, respectively. Note that the kinetic
parameter A in Eq. (2.13) is supersaturation dependent and thus different from A0.
2.2.3
Metastable Zone
The metastable zone describes the zone in the temperature–concentration
phase diagram where the concentration of a solution phase, beyond the solubility (i.e. supersaturated), is not yet a spontaneous nucleation within certain
period. Metastable zone width (MSZW) of a solution or melt system represents
the metastability of the supersaturated state, which may shed light on the nucleation behavior and determine the optimal operation zone of crystallization
process. MSZW can be determined by either isothermal or polythermal method
[10]. The isothermal method measures the elapsed time between the creation of
supersaturation and the formation of a crystalline phase, which is referred to as
induction time. By contrast, for polythermal method, the solution is cooled at a
constant cooling rate from arbitrary saturation temperature T0 to a temperature
at which nucleation occurs.
The limit of MSZW, nonetheless, is of dynamic characteristic and subjected
to the crystallization conditions such as cooling rate, the change in solvent composition, or impurities. Figure 2.3 demonstrated the dependence of MSZW on
crystallization pathways. The vertical line represents the crystallization by evaporating the solvent; the horizontal line is the pathway of cooling crystallization,
while the dash line denotes the crystallization via flashing evaporation approach.
Furthermore, the MSZW is also known to be affected by the utilized detection
53
2 Nucleation
Concentration
54
one n rate
ez
abl leatio
t
s
Un h nuc
Hig
e
zon tion
ble uclea
a
t
n
tas
Me rly no
a
e
N
e
zon ion
ble
at
Sta nucle
No
Temperature
Figure 2.3 Schematic representation of the MSZW (the regime between the bottom line and
top or dash line) along with different crystallization pathways represented by the arrowed
lines. The bottom line is the solubility curve, the top line is the limit of metastable zone with
instantaneous nucleation, and the dash line is the limit of metastable zone without
nucleation.
techniques of nucleation such as electrical conductivity, ultrasound velocity,
turbidity of the solution, and focused beam reflectance measurement (FBRM)
[11–14]. Recently, Jiang et al. [15] measured the MSZW by using a membrane
distillation-response (MDR) technology in which the transmembrane flux
sharply decreased upon the nucleation of crystals on the interface of pores of
the microporous membrane.
Following Nývlt [16], the absolute supersaturation Δc is related to the supercooling ΔT by
Δc =
dc0
dT
ΔT
2 22
T
and in the vicinity of metastability, the nucleation rate J is related with the maximum Δcmax by the empirical relation
J = k Δcmax
m
2 23
and with the cooling rate R = ΔT/Δt by
J=
dc0
dT
R
T
2 24
2.2 Classical Nucleation Theory
where k is the nucleation rate constant, m is the apparent nucleation order, and
(dc0/dT)T is the temperature coefficient of solubility at temperature T. Substituting the value of Δcmax from Eqs. (2.22) to (2.23) and equating the nucleation
rate J given by Eqs. (2.23) and (2.24), one obtains
dc0
ΔTmax =
dT
1−m
m
T
R
k
1
m
2 25
Taking logarithm on both sides of Eq. (2.25) and rearranging yields Eq. (2.26):
ln ΔTmax =
1 −m
dc0
ln
m
dT
−
T
1
1
lnk + lnR
m
m
2 26
The linear dependence of ln ΔTmax on ln R enables to calculate the values of
the apparent nucleation order, m, and the nucleation rate constant, k, as the
temperature coefficient can be determined from solubility data. However, several drawbacks of Nývlt’s approach exist as the following: Firstly, it cannot
describe the effect of saturation temperature on the maximum supercooling;
secondly, Nývlt’s equation is built on the assumption of the saturation
temperature-independent solubility coefficient, nonetheless, which is invalid
for solubility behaviors of most compounds; finally, the use of the empirical
power-raw relation results in the physical significance of nucleation constant
k, and nucleation order m remains obscure [17].
Kubota [18] proposed another model to explain the feature that even for the
same system, the value of the MSZW determined by different techniques is different. In Kubota’s model, the MSZW was assumed to correspond to a nucleation point at which the number density of accumulated crystals (grown nuclei)
had reached a fixed (but unknown) value in volume V and at some time t:
Ndet
=
V
t
J t dt
2 27
0
Assuming a linear solubility–temperature relationship, the nucleation rate is
given by
J t = k1 ΔT
q
2 28
in which k1 = [(dc0/dT)T]q and q is a constant. Combining the cooling rate R in
Nývlt’s equation with Eq. (2.27), one obtains
Ndet k1
=
V
R
ΔTmax
0
ΔT q dΔT =
k1
ΔTmax
q+1 R
q+1
2 29
Thus, taking logarithm on both sides of Eq. (2.29) and upon rearrangement,
one gets
ln ΔTmax =
1
Ndet
1
k1
1
ln
ln
lnR
−
+
q+1
q+1 q+1 q+1
V
2 30
55
56
2 Nucleation
When comparing Eq. (2.30) with Eq. (2.26), one can find that the nucleation
order in Kubota’s theory q = m + 1, where m is nucleation order in Nývlt’s theory. Furthermore, if the primary nucleation can be described by Eq. (2.28), then
the number density may be written as follows:
Ndet
=
V
tind
tind
J t dt =
0
k1 ΔT q dt
2 31
0
When the supercooling ΔT is constant, Eq. (2.31) becomes
Ndet
= k1 ΔT q tind
V
2 32
Hence the induction time can be described as a function of MSZW as
tind =
Ndet
ΔT
k1 V
−q
2 33
As given in the above equation, Kubota’s model provides an approach to evaluate the induction time by measuring MSZW and vice versa. The model also
gives a similarly linear relationship between ln ΔTmax and ln R, as given in
the Nývlt’s theory. Nonetheless, the nucleation constant k1 (Eq. 2.28) cannot
be determined because the fixed value of Ndet/V could not be measured [18].
Moreover, Kubota’s model has the same drawbacks as Nývlt’s theory
aforementioned.
Sangwal [19] assumes that the nucleation rate J is related with the rate of
change in solution supersaturation, and based on the theory of regular solutions,
the nucleation rate can be written by
J =f
Δc
Δc ΔT
ΔHS R
=f
=f
c1 Δt
c1 ΔT Δt
Rg T1 T2
2 34
where ΔT = (T2 – T1) so that T2 > T1 and c2 > c1, ΔHS is the heat of dissolution,
Rg is the gas constant, the cooling rate is R = ΔT/Δt, and the proportionality
constant f is defined as the number of entities (i.e. particles, ions, or clusters)
per unit volume, which is governed by aggregation and diffusion processes in
solution. Combining Eq. (2.34) with classical theory of 3D nucleation, and using
the notation T0 for T2 and considering T1 as the nucleation temperature, the
rate of formation of stable 3D spherical nuclei can be given by
exp
− 16πγ 3 v20
3 kB3 T1 3
Rg T1
ΔHS
2
T0
ΔTmax
2
=f
ΔHS R
Rg T1 AT 0
2 35
Taking logarithm on both sides of Eq. (2.35) and rearrangement gives
T0
ΔTmax
2
= F1 X+ ln T0− ln R = F −F1 ln R
2 36
2.2 Classical Nucleation Theory
with the constant F = F1(X + ln T0), where
F1 =
2
− 3 kB3 T1 3 ΔHS
16π γ 3 v20 Rg T1
X = ln
2 37
A Rg T1
f ΔHS
2 38
where the constant A is associated with the kinetics of formation of nuclei
in the growth medium lying between 1015 and 1042 m−3 s−1. Equation (2.36)
describes a linear relationship between the quantity (T0/ΔTmax)2 with ln R
with slope F1 and intercept F. It is noteworthy that Sangwal’s theory does
not depend on the linear relationship between saturation concentrations
and temperature. Moreover, the nucleation parameters are governed by
thermodynamics, kinetics and the solvation process of solutes, and their
transport in the solution based on the theory of regular solutions and
CNT. Nonetheless, it may be noted that the constants in Eq. (2.36) also
depend on the T0 and T1.
Taking logarithm on both sides, Eq. (2.35) can also be further simplified
by [20]
T0 ΔTmax 2
R
= M + N ln
2
T0 − ΔTmax
T0 −T0 ΔTmax
2 39
with the intercept of M and slope of N, where
N=
−3 kB3 ΔHS
16π γ 3 v20 Rg
M = N ln
f ΔHS
A Rg
2
2 40
2 41
Here the model parameters (M and N) do not depend on the T0 and T1.
Additionally, Eq. (2.41) predicts that there is a linear relationship between
(T0/ΔTmax)2/(T0 − ΔTmax) and ln[1/(T0(T0 − ΔTmax))] at a given cooling rate,
which can be applied to determine the kinetic parameter A and thermodynamic
parameter γ and shed light on the relationship between the nucleation kinetic
parameter and the cooling rates.
Considerable progress has been made in the last decades in understanding the physical basis of MSZW in solution. However, the main challenge
is that the nucleation mechanism still remains unclear, leading to the
accurate prediction of MSZW remaining unachievable. More specifically,
the structure and property of the cluster formation prior to nucleation
still remains elusive, hindering the development of the more realistic theoretical models.
57
58
2 Nucleation
2.2.4 Induction Time
The induction time is defined as the period between the generation of supersaturation and first nucleation events to be detected. The induction time is
constituted of several stages, including the relaxation time to achieve a
quasi-steady-state distribution in a system, tr, and the time required for the formation of a stable nucleus, tn, and for the growth of the nucleus to a detectable
size, tg. The induction time, tind, may therefore be expressed by
tind = tr + tn + tg
2 42
The induction time reflects the release rate of metastability of the system and
may be used to determine nucleation rates. But there exist some ambiguities in
physical aspects of nucleation. For example, the size of first appeared crystals is
not clear. Critical nuclei are of nanoscale size and generally cannot be detected.
In practical, the induction time is approximated by the time when the crystal is
first observed, and thus it may differ with the techniques used to detect the size
of observable crystals. As new crystals can be detected only after growing into a
certain size, the growth time, tg, should be taken into account, which indicates
both the rate of primary nucleation and crystal growth affect the induction time.
For the case of tr + tn tg, the growth time is negligible, and induction time will
be merely determined by crystal nucleation. Another ambiguous quantity is the
“detectable amount” of nucleated particles, which depends on the sensitivity of
the detection device.
Detection techniques can be divided into several categories, for example, by
the direct observation of crystals (such as optical microscopy) or by changes of
the solution or suspension properties (such as transmissivity, turbidity, refractive index, conductivity, spectroscopy), and each has its advantages and disadvantages. Optical microscopy has been proved to be a most sensitive method to
study nucleation events. The single nucleus mechanism has been visualized by
Kadam et al. [21] using in situ cameras. A single nucleus is formed in a supersaturated solution, grows to a particular size, and then undergoes secondary
nucleation. In this case, the latter category of detection instruments can only
detect nucleation events after the secondary nucleation. Generally, the detection time is delayed by monitoring the solution or suspension properties
because the properties will not change until the volume fraction of crystals in
suspension exceeds a specific threshold.
Induction time measurement remains a challenge due to the stochastic nature
of nucleation. Recent measurements are focused on small volume experiments
where crystallization conditions can be better controlled. The crystal 16™, a highthroughput setup, has been widely used to detect nucleation events as multiple
repetitions can be performed for the identical crystallization condition [22, 23].
Large variations in induction times have been observed in 1 ml scale solutions at a
constant supersaturation level. For the system of 4-hydroxy acetophenone in
2.2 Classical Nucleation Theory
ethyl acetate, the induction times measured in two vials of eight consecutive
experiments range from 156 to 3044 s and from 390 to 1673 s, respectively
[22]. This manifests the intrinsic stochasticity in the formation of critical nuclei,
as solution volume increases the distribution of induction time narrows and even
becomes deterministic for a large sample (e.g. > 0.1 l) [24].
According to Kubota’s theory, deterministic induction time model was given
above Eq. (2.33). A general expression taking the time of both primary nucleation and growth into account that is irrespective of whether one, several, or
many nuclei bring the breakdown of metastability of supersaturated phase is
expressed by [25]
1
α
+
JV
an JG n− 1
tind =
1 n
2 43
where J is the nucleation rate, G is the growth rate, V is the solution volume, α
represents the minimum detectable volume fraction of newly formed crystals
based on solution volume, an denotes a shape factor, and n = mv + 1 (m is
the dimensionality of growth, v is a number from 0.5 to 1).
If V α−1/4(G/J)3/4, the growth time is neglectable, and the induction time is
determined by primary nucleation, leading to the application of mononuclear
mechanism being appropriate. In the mononuclear mechanism, the loss of metastability of the supersaturated parent phase is triggered by the appearance of
the first nucleus, and the induction time for this mechanism is given by
tMN =
1
JV
2 44
On the opposite extreme, that is, V α−1/4(G/J)3/4, the polynuclear (PN)
mechanism holds where a statistically large number of nuclei formed and
resulted in the breakdown of the metastability equilibrium. The induction time
for the PN mechanism can be described as
tPN =
α
an JG n−1
1 n
2 45
The stochastic behavior of nucleation in smaller volume is consistent with
mononuclear mechanism and thus can be described by the Poisson distribution
[26]. The probability Pm of the formation of m nuclei at a constant supersaturation is given by
Pm =
N tJ
m
m
exp − N tJ
2 46
where N(tJ) = JVtJ represents the average number of primary nuclei formed with
the volume of the solution V, and the rate of nucleation J, at time tJ. The probability P0 representing that no nuclei are formed within the certain time interval
is therefore
59
60
2 Nucleation
P0 = exp −N tJ
2 47
The probability P(tJ) that one or more nuclei are formed in the time interval is
P tJ = 1 −P0 = 1− exp −JVt J
2 48
Considering there is a time delay tg, the growth time, between the time tJ of
appearance of a nucleus and the time t of detection of crystals, the probability
P(t) that crystals are detected can be
P t = 1− exp − JV t − tg
2 49
Enough experiments must be carried out so that the statistics can be captured
and the probability distribution function can be constructed. For M-independent
experiments, the probability P(t) can be written
P t =
M+ t
M
2 50
in which M+(t) is the number of experiments in which crystals are detected at
time t.
Recently, microfluidic technology offers an alternative approach to obtain
high-throughput data of induction times [27]. A microfluidic chip can store
hundreds of nanoliter droplets flowing in microchannels with 1–100 μm length
scales. During the flow, droplets are instantly cooled down to the desired temperature to generate a certain supersaturation, and subsequently nucleation
occurs. Coupled with optical microscopy, droplets containing crystals at different residence time are observed and counted. The experimental probability P(t)
of nucleated droplets is
P t =
N t
N0
2 51
where N(t) is the number of droplets containing crystals at different residence
time t and N0 is the total number of droplets that go through the observation
section. According to Eq. (2.49), the nucleation rate thus can be determined.
2.2.5 Heterogeneous Nucleation
It is well known that foreign particles affect the nucleation process, and the
nucleation taking place under the presence of a foreign particle is referred to
as the heterogeneous nucleation. The foreign particle can be of the same composition (i.e. seeding) or of the known different composition (for example, polymer template) as the nucleated phase, or even be an ill-defined dust. To
differentiate these three different sources of foreign particles, the heterogeneous
nucleation in this chapter refers to the primary nucleation in the presence of the
foreign particles from the last two situations. The nucleation with seeding of the
2.2 Classical Nucleation Theory
same composition as the crystalline phase is thus referred to as the secondary
nucleation, which will be introduced in detail in the below sections.
Homogenous nucleation assumes the nucleation occurs in solution without
the presence or influence of foreign particles. In practical, foreign particles,
for example, widely dispersed dust with the size of 0.005 ~ 10 μm always exist
in the real system [28]. Many reported cases of spontaneous (homogeneous)
nucleation are induced by some way, and the true homogeneous nucleation is
generally accepted not a common event. The atmospheric dust that may contain
“active” particles (heteronuclei) can be served as seeds to influence the nucleation
of a supercooled system. Aqueous solution as normally prepared in the laboratory may contain >106 solid particles per cm3 of sizes <1 μm [28]. The careful filtration of the solution can only reduce the numbers to <103 cm−3, and it is
virtually impossible to achieve a solution completely free of foreign particles.
The convinced evidence for foreign particle-induced spontaneous (heterogeneous) nucleation in real system is that the degree of supercooling of a given system
in large volumes was often found smaller than that in small volumes in many
cases. For example, based on the recent measurement on MSZW at different
scales from 10−3 to 1 L for spontaneous nucleation of paracetamol in water,
the small volume solution shows larger MSZW than that of large volume solution
[21]. A plausible explanation is that the larger samples stand a greater chance of
being contaminated with active heteronuclei. Further, the most active heteronuclei in liquid solutions were suggested to be in the range 0.1–1 μm [28].
In general, the presence of “sympathetic” surface of an active heteronuclei can
induce the nucleation at less degree of supersaturation than those for spontaneous (homogenous) nucleation, and thus the overall free energy barrier for the
formation of a critical nucleus under heterogeneous conditions ΔGc , will be less
than the corresponding free energy change, ΔGc, associated with homogeneous
nucleation:
ΔGc = ϕΔGc
2 52
where the factor ϕ is in the range 0 < ϕ < 1.
As aforementioned above (e.g. Eq. 2.13), the interfacial tension, γ, is one of the
important factors controlling the nucleation process. For the nucleation on the
surface of a foreign particle (Figure 2.4), the three interfacial tensions existed, and
they are, respectively, denoted as γ cl (between the crystalline phase, c, and the
liquid, l), γ sl (between the surface of foreign particle, s, and the liquid, l), and
γ cs (between the crystalline phase, c, and the foreign particle surface, s). Resolving
these forces in a horizontal direction gives
γ sl = γ cs + γ cl cos θ
2 53
or
cos θ =
γ sl −γ cs
γ cl
2 54
61
62
2 Nucleation
Figure 2.4 Interfacial tensions among
three phases (foreign particle and
crystalline deposit solid phases as well as
solution phase).
γcl
γcs
Crystalline
deposit (c)
Liquid (l)
θ
Solid surface (s)
γsl
The contact angle θ between the crystalline deposit and the foreign particle
surface corresponds to the angle of wetting in liquid–solid systems.
The factor ϕ in Eq. (2.52) can be expressed as [29]
2 + cos θ 1−cos θ 2
4
Thus, when θ = 0, and ϕ=0, Eq. (2.52) becomes
ϕ=
2 55
ΔGc = 0
2 56
The above equation means complete affinity (θ = 0), i.e. complete wetting
between solution and foreign particle, and hence the free energy of nucleation
is zero, corresponding to the crystal growth of seeds in a supersaturated
solution.
Where θ lies between 0 and 180 , ϕ < 1, and
ΔGc < ΔGc
2 57
This represents partial affinity (0 < θ < 180 ), i.e. the partial wetting of a solid
with a liquid, indicating that the required overall excess free energy is less than
that of homogeneous nucleation, and hence the spontaneous nucleation will be
easier to achieve.
When θ = 180 , ϕ=1, and
ΔGc = ΔGc
2 58
In this case, the crystalline phase is complete nonaffinity with the foreign particle surface (θ = 180 ), representing the complete nonwetting solid–liquid system, and the overall free energies for spontaneous nucleation in both
homogenous and heterogeneous systems are the same.
Additionally, the heterogeneous nucleation of a supersaturated solution may
also occur via seeding from embryos retained in cavities of foreign bodies, as
found and analyzed by Turnbull [30] in different types of cavity. The maximum
diameter of a cylindrical cavity retaining a stable embryo is given by
dmax =
4γ cl cos θ
ΔGv
2 59
2.3 Nonclassical Nucleation
where ΔGv is the bulk free energy of the nucleation. When the system is heated
for dissolution, only those embryos retained in cavities larger than dmax will be
eliminated, and in subsequent cooling crystallization, the embryos smaller than
dmax in the cavities may grow out from the mouth of the cavity. They will then
act as nuclei only if the cavity size dmax ≥ Lc, where Lc is the size of a critical
nucleus (Eq. 2.9).
2.3
Nonclassical Nucleation
The main criticism of CNT is the assumption of identical surface tension
between clusters formed in a solution and the resultant, macroscopic crystal.
It was suggested when a cluster or nucleus contains only 20–50 molecules,
its interface is sharply curved, differing from the macroscopic crystal [31].
Others found the surface tension is ill defined for clusters smaller than 100
molecules, and the shape of nucleus cannot be approximated with a sphere
[32]. Furthermore, the significant failure in the prediction of nucleation rate
of crystal from solution leads to the stage to move beyond CNT [2, 5]. The
experimental and computer simulation studies of ionic materials such as calcium carbonate [33, 34], proteins [32, 35], and some small organic molecular
crystals [7, 8] suggest much more complex crystallization pathways, mainly
including two-step mechanism [2, 8] and PNCs [7].
2.3.1
Two-Step Mechanism
The two-step mechanism was originally found by ten Wolde and Frenkel [6]
in a Monte Carlo simulation study on homogeneous nucleation with
Lennard-Jones intermolecular interactions. It was found that away from
the fluid–fluid critical point (T > Tc or T < Tc), fluctuations of density and
structure order occur simultaneously, similar to the scenario of CNT, but
around the critical point the formation of disordered liquid droplets prior
to the formation of crystal nucleus inside the droplet [8]. Additional support
has been provided from the various experimental studies. The nucleation
studies of lysozyme by dynamic and static light scattering showed that
the formation of fractal clusters through the aggregation of monomers in
the early stage of crystallization later on restructures into compact structures [36]. Another interesting experimental phenomenon, the so-called
nonphotochemical laser-induced nucleation (NPLIN) [37], on the formation
of glycine polymorphism in aqueous solution showed that depending on the
utilization of polarization state of the laser, the α-form can be obtained with
circular light, while γ-form can be crystallized using linear light. The reorganization of hypothetically pre-existed glycine clusters was suggested to
determine the formation of γ-glycine.
63
64
2 Nucleation
Classical nucleation
Two-step nucleation
Figure 2.5 The two alternative pathways leading from solution to solid crystal. Top: the
concomitant evolutions of density fluctuation with structure order of clusters, as proposed by
classical nucleation theory. Bottom: the density fluctuation prior to the development of
structure order of clusters so that the initial formed clusters are dense, liquid-like and
crystalline order appears later on, as postulated by two-step mechanism.
From a structure perspective, the essential difference of two-step mechanism
from CNT is that the development of structure order is considered to be
followed by density fluctuation [2], as illustrated in Figure 2.5. The two-step
nucleation mechanism holds that the nucleation process mainly comprises
two steps: solute molecules cluster into dense, liquid-like clusters, and crystal
nucleates by the reorganization of such disorderly packing ensembles. The
structural rearrangement was considered as the rate-determining step because
crystal nucleation was found to be 10 orders of magnitude slower than the
nucleation of dense liquid droplets [2].
A kinetic model was developed to describe the two-step nucleation mechanism. The main assumption is that the formation of intermediate, disordered
cluster has a temperature- and concentration-dependent rate, u0(C, T). The
cluster can be dissolved into the solution with rate u1(T) or transform into
an ordered crystal nucleus at rate u2(T). The above processes were illustrated
by energy landscape picture in Figure 2.6. A probability PΩ(t) was defined to find
the system in state Ω = 0, 1, or 2 at time t; then the mean time, τ, for the creation
of a crystal nucleus in a steady-state process is defined as
τ=
∞
t
0
dP2 t
dt
dt
2 60
Thus, the parameter represents a mean first passage time for the transition
from state 0 to state 2 and is given by
τ=
1
u1 T
1
+
+
u0 C,T
u2 T
u0 C, T u2 T
2 61
2.3 Nonclassical Nucleation
E2
ΔGL – L
Crystals
E1
Dense liquid
Solution
Free energy, G
E0
ΔGL – L
Nucleation reaction coordinate
Figure 2.6 Free energy G along with two possible pathways for nucleation of crystals
from solution. E1, E0, and E2 are the barriers for developing a dense liquid-like cluster, for
decay of the cluster, and for formation of an ordered cluster within cluster, respectively. ΔGL-L
represents the free energy of formation of the dense liquid phase [4]. Source: Reproduced
with permission of AIP Publishing LLC.
in which the rates uΩ = UΩ exp(−EΩ/RT) and the steady-state nucleation rate,
J, can be approximately calculated as J = 1/τ, and hence
J=
U0 U2 exp G0 + G2 RT
U0 exp − G0 RT + U1 exp − G1 RT + U2 exp − G2 RT
2 62
where U0, U1, and U2 are pre-exponential factors, accounting for formation and
decay of the transient cluster and formation of the ordered crystalline nucleus,
respectively. G0, G1, and G2 represent the energy barriers required for formation
of the disordered cluster, decay of the disordered cluster, and formation of an
ordered crystalline nucleus, respectively.
The two-step mechanism helps explain the nucleation kinetics of proteins. Its
applicability relies on the existence of disordered transient clusters in solution
prior to the formation of crystal nucleus. The main criticism of two-step mechanism is the physical meaning of the disordered, intermediate phase in which no
insight into the structure can be gained. Therefore the model could not help
explain the solvent-dependent polymorphism. In addition, the formation of
liquid-like, disorderly cluster was thought the essential step in the nucleation
process [38], which should not retain any ordered structure of prenucleation
aggregates in solution. Nevertheless, the direct structure correspondence or link
between solution chemistry and the resultant crystal structure was recently
65
66
2 Nucleation
revealed in many organic systems [39]. Experimentally, the two-step mechanism
is predominately seen in protein systems.
2.3.2 Prenucleation Cluster Pathway
The growing evidence of existing stable PNCs such as calcium carbonates [34]
and calcium phosphates [40, 41] was found in both under- and supersaturated
solutions. These clusters are stable and thus essentially different from a consequence of the assumption made by CNT that monomer associations lead to the
formation of unstable clusters. Nevertheless, the PNCs, resembled to unstable
clusters, can participate in the process of phase separation [1]. Figure 2.7
demonstrates the difference in nucleation pathways between PNCs and CNT.
The former suggests that the stochastic collisions among ions lead to the formation of stable precritical clusters and subsequent aggregation among the
clusters results in the creation of postcritical nucleus. The crystalline phase
nucleates within the amorphous phase and subsequently grows into macroscopic crystals (left). Such a crystallization pathway contradicts the paradigm
of CNT (right).
PNCs are actually thermodynamically stable associates in equilibrium with
solute monomers and thus different from two-step mechanism in which the
dense liquid-like clusters are metastable phase and have been nucleated [1].
Gebauer et al. [7] further give the five major characteristics of PNCs as follows:
1) PNCs comprise atoms, molecules, or ions of a forming solid and may contain
additional chemical species.
2) PNCs are small, thermodynamically stable solutes, and have no phase
boundary with the surrounding solution.
3) PNCs are the molecular precursors to the phase formed from solution and
participate in the process of phase separation.
4) PNCs are of dynamic entities and change configuration on timescales typical
for molecular rearrangements in solution.
5) PNCs bear resemblance or relate to one of the crystalline polymorphs.
Prenucleation cluster pathway, therefore, is promising in explaining solventdependent polymorphism [7]. However, these clusters are seen predominantly
in inorganic systems.
2.4 Application of Primary Nucleation
2.4.1 Understanding and Control of Polymorphism
Polymorphism in molecular crystals was defined by McCrone [42] as “the possibility of at least two different arrangements of the molecules of a compound in
the solid state.” It was first recognized in 1822 by Mitscherlich that different
2.4 Application of Primary Nucleation
Supersaturated solution
Addition of ions
to precritical
cluster
Stable precritical
clusters
Aggregation
Nucleation
Postcritical
aggregation
Postcritical
nucleus
Growth
Nucleation of
crystal phase
Crystal
Figure 2.7 Schematic representation of the difference in nucleation pathway between PNCs
(left) and CNT (right).
crystals of arsenates and phosphates exhibit the difference in physical and
chemical properties [43]. In 1832, Liebig and Wöhler investigated the earliest
example of polymorphs of organic compound, benzamide, but the observed,
fleeting metastable form was structurally determined in 170 years later [44].
Then, a wide range of attention on polymorphism was received, and numerous
substances were found existing more than two molecular arrangements. The
67
2 Nucleation
findings appear to support the statement by McCrone that the number of polymorphs discovered for each compound is proportional to the time and effort
spent in research on that compound [42].
Polymorphs of an organic substance have different free energies and thus thermal stabilities. At a given temperature and pressure, the polymorph having the
lowest free energy is the stable form, while the others are referred to as metastable forms. The high energy form can transfer to another one of less energy, and
such thermodynamic transformation is reversible at the transition point (or temperature), in which the two forms have the same stability. Temperature–energy
diagram is often applied to describe the thermodynamic behavior of polymorphs.
As seen in Figure 2.8, two polymorphs (I and II) of different intermolecular interactions in the lattice exhibit the difference in zero Kelvin enthalpy and the temperature dependence of the isobaric heat capacity. This may lead to the transition
temperature Tt below the melting point of both forms; in which case the system is
termed enantiotropic (solid lines). Below the transition point, Form II is stable
and has a lower enthalpy than Form I, and thus the phase transition from Forms
I to II is exothermic. Above the transition point, Form I becomes stable but still
has a high enthalpy, and hence the phase transition from Forms II to I is endothermic. When the phase transition occurs above the melting point of both
forms, the di-polymorphic system is termed as monotropic (dash lines).
HL
HL
HI
HII
Energy
68
GII
GI
GL
0
Tt
GL
Tm,II Tm,I
Temperature
Figure 2.8 Schematic representation of temperature–energy diagram for enantiotropic
(solid lines) and monotropic (dash lines) systems. The subscript I, II, and L denote polymorphs
I and II and the liquid, respectively; t represents the transition point, and m is the
melting point.
2.4 Application of Primary Nucleation
The high energy, metastable polymorph tends to transform into a stable one
via the pathway of a solid–solid physical transition, a solvent-mediated phase
transformation, or both. For the former pathway, a four-step mechanism has
been proposed: the molecular loosening in the initial phase and the formation
of an intermediate solid solution, as well as the nucleation and growth of the
new crystalline phase [45]. The phase transition by solid-state mechanism is
generally influenced by the characteristics of the crystal such as crystal habit,
size, presence of defects, the environment (e.g. temperature, pressure, and relative humidity), and the presence of impurities. The phase transition can also
take place in solution by dissolution and recrystallization, which is termed as
solvent-mediated phase transformation. Such transition driven by the difference in free energy between the metastable and stable phases is reflected as
the difference in solubility between the two phases. Thus, the phase transformation process involved three main steps: the dissolution of the metastable phase
and the nucleation and growth of the stable phase [46], which is encompassed by
Ostwald’s rule of stages that describes a stepwise transition from the metastable
polymorph to a more stable phase [47].
Polymorphs of organic compounds bear the difference in molecular arrangements and intermolecular interactions, and the study on its crystallization
mechanisms can shed light on the structure perspectives of crystal nucleation.
By examining the structural connection between solution chemistry and the ultimate crystal phase, Davey et al. [39] found that the prenucleation associates in solution bear resemblance to the structural synthons of crystal structures in a number
of organic systems. The significant similarity in structure correspondence was further revealed by solution spectroscopy and computer simulation studies [48–50].
Such a structural link suggests that at least at the dimer level, the nature of the associate and its intermolecular binding may be an important factor in the crystal
nucleation process. As seen in Figure 2.9, the self-association in two different solvents leads to the presence of two types of dimers in solution, eventually resulting
in the nucleation of two different polymorphic crystal structures. By virtue of
solvent-dependent self-association of solutes, the new crystalline form may be discovered such as isonicotinamide (INA) in chloroform and tetrolic acid in dioxane.
Another important implication of the finding of structure link between solute
associates and structural synthons implies the application of CNT is appropriate.
Nonetheless, in many other systems such as benzoic acid in methanol [51],
acetic acid in carbon tetrachloride [52], and tetrolic acid and tolfenamic acid
in ethanol [53, 54], the one-to-one structure correspondence was absent. We
found that the self-association of glycine displays pH dependence and correlates
well with the pH-dependent polymorphism [55]. Nevertheless, the configuration of open glycine dimer is different from the cyclic motifs of the resultant
α-form. Similarly, Gavezzotti [52] found by molecular dynamic simulation that
the acetic acid can form micelle-like aggregates of open hydrogen-bonding
configuration in solution, differing from the resultant crystal structure. The
69
70
2 Nucleation
Solvent I
Molecular
Solvent II
Building unit I
Building unit II
Nucleus form I
Nucleus form II
Form I
Form II
Figure 2.9 Schematic representation of solvent-dependent self-association leads to the
formation of two different building units (building unit I in solvent A, building unit II in
solvent B), which determine the crystal packing and thus the formation of the crystalline
phases Form I and Form II, respectively.
findings pointed to the involvement of supermolecular reorganization prior to
formation of crystal nucleus and thus suggested nonclassic nucleation mechanism may be involved. Despite the ambiguous view on the structural relationship
between clusters and crystal packing, the study on solution chemistry did shed
some light on the nucleation mechanism and advance our understandings on
the evolutions of structure and density during the formation of clusters and
crystal nuclei.
2.4 Application of Primary Nucleation
Some crystallization conditions (e.g. solvent, temperature, and supersaturations) may lead to two or more polymorphs crystallized in the same batch,
the so-called concomitant polymorphism [43]. These crystallization conditions
may lead to the overlap in occurrence domains of nucleation and growth of the
two polymorphs. Crystallization in a polymorphic system was well governed by
thermodynamic and kinetic factors [43]. As such, the appearance of concomitant polymorphs may arise either because specific thermodynamic conditions
prevail or because the kinetic processes have equivalent rates. In the latter case,
when two polymorphs have the similar or identical growth kinetics, the nucleation of the two forms may occur simultaneously. According to the nucleation
kinetic equations, Davey [56] found that by carefully controlling the supersaturation in solution, there may be conditions in which the two polymorphs
nucleate simultaneously. The concomitant formation of the two crystal structures under the identical crystallization conditions may provide an approach to
investigate the roles of structure order parameter in nucleation process and to
verify the validity of the lattice-energy programs, so-called polymorph predictor, due to their nearly energetically equivalent structures. On the other hand, a
proper understanding of the crystallization mechanism of concomitant polymorphs is necessary to develop the robust process to isolate a single, pure crystal
form.
2.4.2
Liquid–Liquid Phase Separation
LLPS, or termed as oiling out, refers to the appearance of a second liquid phase
during crystallization process. In general, the appearance of LLPS is due to a
miscibility gap in the phase behavior [57, 58].
Crystal nucleation in oiling-out systems follows a two-stage process: the initial formation of oil droplets and the occurrence of nucleation either in each
phase (i.e. the phase of solute lean or solute rich) or in the interface between
them. Figure 2.10 demonstrated this two-stage nucleation process, and the
nucleation appears in the solute-rich phase where the crystal nuclei grow into
large crystals, and the phase boundary of the two phases disappears finally.
Figure 2.10 Schematic diagram of the two-stage nucleation process. (1) Unsaturated
solution, (2) formation of oil droplets, (3) nucleation in oil droplets, and (4) final products.
71
2 Nucleation
The formation of oil droplets brings the nucleation and growth taking place in
two different crystallization environments, which differ from the overall composition. As expected, such change in crystallization conditions leads to a significant influence on the morphology of the resultant crystals. For example, in
the β-alanine–water–isopropanol system, the phase diagram of the three composition systems is shown in Figure 2.11; LLPS occurs under certain solvent
composition (regions 2 and 4).
The ternary phase diagram is vital to understand and control the crystallization of β-alanine in water–isopropanol system. Figure 2.12 shows the significant
changes in crystal morphology of β-alanine by manipulating the crystallization
in different ternary phase regions (Figure 2.11). In normal crystallization (point
1 point 1 ), tabular crystals can be obtained (Figure 2.12a). However, octahedron shape of crystals (Figure 2.12b) will be created in the crystallization of
LLPS system (point 2 point 2 ), in which the crystal nucleation occurs in
oil droplets (i.e. the solute-rich phase). The LLPS-dependent crystal morphology may be due to the relative higher supersaturation in oil droplets than that of
the solute-lean phase in which the crystal nucleates in the tiny spaces of oil droplets for crystal growth. Moreover, quasi-emulsion solvent diffusion method
[59] (point 3 point 3 ) can produce spherical shape of β-alanine crystals
0.00 1.00
0.75
Re
gio
n
1
0.50
ine
lan
n3
gio
Region 2
0.50
β-A
Re
pro
pa
no
l
0.25
Iso
72
0.75
2
4‘
Region 4
Region 5
2’
1.00
3(4)
0.00
3’
1
1‘
0.25
0.25
0.50
Water
0.75
0.00
1.00
Figure 2.11 The ternary phase diagram of β-alanine–water–isopropanol system at 25 C
(0.1 MPa). Region 1: solid–liquid equilibrium phase I. Region 2: solid–liquid–liquid equilibrium
phase. Region 3: solid–liquid equilibrium phase II. Region 4: liquid–liquid equilibrium phase.
Region 5: unsaturated liquid phase.
2.5 Secondary Nucleation
(a)
(c)
(b)
F
D6.3 x 80
1 mm
H
D5.5 x 60
1 mm
(d)
F
D6.3 x 30
2 mm
H
D5.5 x 100
1 mm
Figure 2.12 SEM images of morphology of β-alanine crystallization obtained under different
operation conditions: (a) normal crystallization (point 1 point 1 in Figure 2.11), (b)
crystallization with LLPS (point 2 point 2 in Figure 2.11), (c) quasi-emulsion solvent
diffusion crystallization (point 3 point 3 in Figure 2.11), and (d) quasi-emulsion solvent
diffusion crystallization with LLPS (point 4 point 4 in Figure 2.11).
(Figure 2.12c). Nevertheless, if the final operating point turned into phase region
2, LLPS will interrupt the formation of the spherocrystal, resulting in the
breakup of spherical crystals (Figure 2.12d) and the bimodal CSD.
2.5
Secondary Nucleation
In industrial crystallization, the primary spontaneous nucleation is often suppressed by seeding in a supersaturated solution due to its uncertainty in controlling CSD. The new crystal nuclei may be created in the presence of
external seeds at a given supersaturated solution, which is referred to as the secondary nucleation. The mechanism of secondary nucleation is very complicated
and has not yet been fully understood. Many mechanisms have been proposed
73
74
2 Nucleation
to interpret the secondary nucleation phenomenon, but they can be generally
classified into two groups [60]. The first group referred to the formation of crystal nuclei is origin from solution, and the other one is origin from crystals.
2.5.1 Origin from Solution
Seeding in a supersaturated solution may cause rapid nucleation, even in the quiescent solution with tethered crystal seeds [61]. The boundary layer in the solid–
solution interface was suggested to play an important role in the secondary
nucleation process. Miers [62] found that the concentration in this boundary
layer is higher than that in the bulk solution. Randolph and Larson [63] regarded
that the displacement of the adsorbed solution layer near the crystal surface was
an important source of formation of crystal nuclei. Qian and Botsaris [64] proposed the embryo coagulation secondary nucleation (ECSN) model to explain
the mechanism of secondary nucleation. In this model, the solution generates
many embryos at a certain supersaturation level, and these embryos were
attracted at the boundary layer by van der Waals forces. But the embryos in
the bulk solution would be dissolved because their size was smaller than the critical size of crystal nuclei. By the coagulation, the embryos at the boundary layer of
crystalline-solution interface became larger than the critical size and displace
away from the boundary layer likely by fluid dynamics or collision, which was
finally evolved to be secondary nuclei. The simulation presented by Anwar
et al. [65] reveals the similar mechanism for secondary nucleation. The clusters
after interacting with the crystal surface would become nuclei immediately, but
the new formed crystal nuclei are likely fallen off into the solution due to the
rather weak bound between the formed nuclei and crystalline surface. These
newly generated crystals in solution could be served as catalytic to induce further
crystal nucleation and hence result in a rapid nucleation rate.
The secondary crystal nuclei may be origin from solution, but the crystal surface was found playing a critical role in the properties of the resultant product.
A typical example is the crystallization of sodium chlorate. Under the agitated
conditions, when the supersaturation level exceeded certain limit but still lower
than the limit of spontaneous nucleation, the crystal nuclei of opposite chirality
relative to that of the seeds were formed [66]. The crystallization of glycine, presented by Cui and Myerson [67], indicated that contact force affects the polymorph of secondary nucleation. Using γ-form as seeds, at the lower contact
force, only the secondary nuclei of α-form were generated.
It is well known that there exists a threshold for the secondary nucleus created
originally from solution, referred to as the secondary nucleation threshold
(SNT). The nucleus was considered to be only generated by microattrition when
solution concentration is below this threshold [61]. SNT is not a deterministic
line because it moves with crystallization parameters, and the size of particles
and fluid dynamics likely affect the SNT.
2.5 Secondary Nucleation
2.5.2
Origin from Crystals
The creation of secondary nuclei can be origin from crystals by the microattrition when crystal contacts or collides with the surface of impeller or crystallizer,
or even another crystal. Thus the generated nuclei are of the identical polymorph and chirality with the seeds. Crystals colliding with solid surfaces, for
example, the stirrer, will generate a number of smaller fragments
(Figure 2.13). The strain induced by the impact will be released through the
fragmentation of the seeds, and a number of smaller particles are generated
and dispersed through the mechanistic stirring, finally grown into large particles. Energy−impact models describing such a process have been developed
based on attrition and breakage studies in agitated vessels using crystals
suspended in inert liquids [68, 69]. A generalized model based on Rittinger’s
(a)
(b)
Figure 2.13 Secondary nucleation induced by collisions of crystals with stirrer’s surfaces (b)
in comparation to the stand still stirrer (a).
75
76
2 Nucleation
law for the energy required to produce a new surface via crystal−crystal and
crystal−impeller collisions was proposed by Kuboi et al. [70] to quantify nucleation by mechanical attrition.
Crystal–crystal contacts are another type of source to produce the secondary
nuclei. It was found that at moderate levels of supersaturation, crystal–crystal
contacts readily caused the secondary nucleation of MgSO4 7H2O and produced
up to five times as many nuclei as that of collisions of crystals with the metal surface of stirrer [71]. Furthermore, the production of secondary nuclei may also be
induced by the dislocations, defects, or inclusions of growing crystals. Chernov
et al. [72] have shown that growing crystals containing dislocations, defects, or
inclusions are prone to secondary nucleation via the development of internal
stresses, leading to the crack formation and subsequently producing breakage
fragments. The crack propagation was suggested to be possibly due to the
adsorption of impurities on a defective crystal surface [73]. In addition, the generated fragments induced by collisions could be in a considerably disordered
state with many dislocations and mismatch surfaces, which were often found
growing slowly than macrocrystals. In some cases, these breakage fragments
were even found not growing at all [74, 75]. The observed growth rate dispersion
in attrition fragments was attributed to the formation of varying numbers of dislocations and the development of elastic strain in the new interface [76].
2.5.3 Kinetics
A power law (Eq. 2.63) is often employed to describe secondary nucleation
phenomenon. The model considers the rate of secondary nucleation B proportional to the suspension density mT, the input power ε, and the solution supersaturation S:
B
mTn ε r S l
2 63
in which typical values for the exponents are n = 1, r = 1/2, and l = 1–2. Note
that the main driving force supersaturation can be expressed in an either absolute or relative term. This model is simple and easy to be integrated in the modeling of CSD. As the growth rate typically depends linearly on supersaturation,
the dependence of the secondary nucleation rate on supersaturation can be
assessed from the slope of the nucleation rate versus the growth rate curve.
However, it is system specific and difficult to transfer into the unique environment in which they were developed.
2.5.4 Application to Continuous Crystallization
Secondary nucleation commonly exists in industry crystallization because breakage or attrition of crystals is often inevitable during crystal growth process under
the mechanical stirring and mixing conditions. As related to the degree of
2.5 Secondary Nucleation
mixing, operation profile (cooling–heating or solvent–antisolvent), magma density, geometry of crystallizer, operation method (batch–continuous), etc., the
secondary nucleation has already become an indicator to control and optimize
the crystallization process and the resultant crystal qualities. Thus the secondary
nucleation was widely studied regarding the crystallization kinetics, crystal
growth, and scale-up of crystallization process. With the advent of continuous
crystallization techniques, which require low energy consumption but have high
process robustness and efficiency, as well as good product quality, the secondary
nucleation played an important role in process evaluation and control.
Mixed suspension–mixed product removal (MSMPR) crystallizer is one of
the most widely used continuous crystallizers, and the secondary nucleation
is the key factor in the crystallization process to be optimized for improving
the crystal quality of big size and narrow CSD. The well-developed population
balance equation (PBE) can be used to describe the crystallization process
coupled with secondary nucleation [77]:
∂n ∂ Gn
+
= B −D −
∂t
∂L
k
nk Qk
V
2 64
where n is the volumetric number density of crystals, L is the characteristic crystal
size, G is the rate of crystal growth, and V is the magma volume. B and D represent
the birth (including secondary nucleation) and death functions of crystals due to
agglomeration or dissolution and breakage or attrition, respectively, and Qk is the
inlet or outlet flow rate of the system. Assumptions can be made to simplify the
model, for example, (i) agglomeration and breakage of crystals are ignored (B =
D = 0), and (ii) the crystal growth rate is independent of crystal size (G = (dL/dt),
G G(L)). At steady state, the Eq. (2.64) can be simplified as
∂n n
+ =0
2 65
∂L τ
where τ is the mean resident time, calculated by V/Q. The above equation can be
solved as
G
L
Gτ
n = n0 exp
2 66
where n0 is the initial number density of crystals. On the basis of Eq. (2.66), the
CSD can be derived and used to monitor and control the crystallization process.
The secondary nucleation dominating in MSMPR can be related to the supersaturation of solution and magma density. The magma density Mt can be calculated from the third moment of population density distribution, as given by
∞
Mt = ρc kv
L3 n L dL
0
2 67
77
78
2 Nucleation
where ρc, kv are crystal density and shape factor, respectively. Thus, the secondary nucleation rate will be calculated by
j
B = kb ΔS b Mt
2 68
in which kb is constant parameter of the secondary nucleation and ΔS is the
solution supersaturation. The secondary nucleation therefore is related to operation profile, including mixing and cooling–heating trajectory.
Recent progress is focused on the utilization of the secondary nucleation in
controlling continuous crystallization process. Instead of ignoring the secondary nucleation in crystallization process, the new developed techniques, such as
wet milling and contact secondary nucleation, make full use of the secondary
nucleation to generate seeds and hence to control crystallization process.
A commercial in situ wet unit was developed and coupled with the continuous
MSMPR crystallizers [78–81]. The miller has a rotor–stator-based unit with
high shear force and can achieve the control in secondary nucleation by the
operating conditions of the tip speed and turnover frequency. The rotor–stator
wet milling, served as a continuous seed generator through the in situ high shear
force, was proven to be effective in optimizing crystal size, CSD, yield, and process efficiency (start-up and residence duration). Wong et al. utilized a contact
secondary nucleation device to create continuous seeds for continuous tubular
crystallizer [67, 82, 83]. The device called nucleator is a “crossed” flow tube with
four channels, including inlet of solution, outlet of crystal slurry, and other two
channels for parent crystals transportation. By controlling the secondary nucleation in the nucleator, the nucleation and growth process was decoupled,
respectively, in nucleator and tubular, and thus the optimization of critical
product attributes in continuous crystallization process was achieved. Ni
et al. developed and commercialized oscillatory baffled crystallizer to enhance
the mixing performance in the flowing stream [84, 85]. The mass transfer and
secondary nucleation during crystallization process were strengthened to
improve process efficiency and narrow size distribution. An air-lift crystallizer
was found to suppress the secondary nucleation at a high supersaturation level
[86], which can potentially operate at higher supersaturation with a higher crystal growth rate. Apart from the mechanical design of secondary nucleation generation device, additive was also investigated to suppress secondary nucleation
in an MSMPR crystallizer [87]. The suppression of secondary nucleation can
effectively alleviate fouling and encrustation in continuous MSMPR process.
Secondary nucleation in continuous crystallization process can be potentially
utilized or avoided to enhance process robustness and efficiency and improve
product quality. While there is a competition between optimization of secondary nucleation and mixing performance (mass–heat transfer), the suppression
of secondary nucleation means decreasing the shearing force that will resist the
mass or heat transfer, especially for scale-up development. Quantitative control
2.5 Secondary Nucleation
of secondary nucleation without compromise mass–heat transfer and design of
conductive geometry and process strategy will lead to a producible continuous
crystallization process.
2.5.5
Crystal Size Distribution
CSD in the production of fine chemicals, particularly in high-value crystal product (e.g. pharmaceutical), plays an important role to evaluate chemical properties (purity, dissolution rate, etc.) and physical properties (flowability,
compactability, etc.). The latter produces the significant impact on product
quality and downstream processing. Failure in control of concentration or
supersaturation and uncertainties within crystallization process would lead to
out of control in CSD. Nucleation, as the first step of crystallization, is critical
to control product properties including CSD, crystal morphology, and
polymorphism.
Considering an ideal crystallization case, a certain number of nuclei or seeds
are presented at some time, consuming the supersaturation because of crystal
growth. The number of nuclei or seeds would be inversely proportional to crystal size given the same supersaturation. It is easy to build a relationship between
the number of nuclei and crystal size for an ideal model. This relationship provides a possibility to optimize crystal size and CSD via controlling the number
density of crystallization process; nonetheless, crystals’ breakage, attrition, and
agglomeration in practice affect the constructed model. In addition, uncertainties in the crystallization bring another difficulty in the control and modeling of
crystallization process, particularly in primary nucleation.
Primary nucleation is difficult to control essentially due to the unclear mechanism of nucleation. The involvements of various external factors such as the
surface of container and impeller, impurities, and unintentional seeding make
crystal nucleation even more complicated. The induction time required by primary nucleation affects the process efficiency, and the disturbance of this period
brings the significant impact on process performance and product quality. To
avoid the uncertainties of primary nucleation, CSD was often controlled by crystal growth. As shown in Figure 2.14, the initial nuclei are generated through
spontaneous nucleation using crash-cooling method; the suspension may contain a large amount of crystals with very small size. Then, by increasing the temperature most of the crystals will be dissolved until they reach the circle point,
which engineers a suitable number of crystals as seeds for the following crystal
growth. Such operation profile improves the robustness and efficiency of crystallization process, while the control of the number of crystals in solution is
highly dependent on individual experience.
An alternative approach, the so-called direct nucleation control (DNC), was
proposed by monitoring and controlling the number density of crystal nuclei
during crystallization process. The number density of crystals can be measured
79
2 Nucleation
Figure 2.14 Operation profile
of a typical crystallization
trajectory to control crystal
size distribution by avoiding
the uncertainties in the
primary nucleation.
MSZ limit
Solution concentration
80
Step 1
Step 2
Step 3
solubility curve
Temperature
by, for example, FBRM and controlled by heating–cooling and/or adding
solvent–antisolvent via advanced feedback control [88, 89]. Along the line of
sight toward optimization of crystal size and CSD, DNC has been coupled with
other techniques to improve performance, such as coupled with microwave to
shorten cycle time, integrated with wet milling to control the number density in
crystallization process [90]. Instead of model-free control strategy, the
model-based DNC strategies were developed recently such as bound DNC, predictive DNC, and reverse DNC, in which the analysis of crystal mass, count, and
qualities in the process can be achieved [91, 92]. In industrial crystallization,
seeding and secondary nucleation are the most widely used technology to control crystal size and CSD, while there is still enough room to study primary
nucleation to tune crystal properties such as crystal size, CSD, solubility, and
polymorphism.
2.5.6 Seeding
The utilization of seeding is a vital approach to control the crystallization process, and the importance of an appropriate seeding strategy cannot be overemphasized. The crystal seeds may be divided into two categories: the seeding
crystals being crystallized substance and isomorphous substances. The utilization of isomorphous substances to induce nucleated crystals could be attributed
to either the match in crystal lattice between them or other mechanisms [28]. In
addition, the seeding crystals of different sources such as dry-milled seeds, wetmilled seeds, and seeds from a previous batch may contain different amounts
2.6 Summary
and/or extent of defects, displaying different performance in their subsequent
crystal growth. Thus, the selection and optimization of seeding crystals of different sources are necessary step to obtain the best growth conditions of seeds.
The seed loading is another factor that affects the resultant crystal size and
size distribution. In general, in order to meet different requirements, the loading
of seeds can be classified into four levels: Trace addition (typically ~0.1%), to
avoid uncontrolled nucleation and/or oiling out in the laboratory, is rarely effective or reliable on scale-up; small addition (~1%), to aid in controllable nucleation but not adequate to achieve primarily crystal growth on scale-up; large
addition (~5–10%), to control mainly crystal growth and to avoid the bimodal
distribution of CSD; and massive addition, to maximize the crystal growth of
all seeds.
The rate of secondary nucleation was suggested to be proportional to the volumetric surface of seeds, which is related to the number, shape, size, and size
distribution of seeds. It is worth to point out that the seeds of large size may
promote the nucleation more readily than small size seeds do. This is because
the large seeds receive large contact and collision probabilities with other crystals, stirrer, or vessels in an agitated system. Additionally, the small size seeds of
some crystal fragments may not be capable of growing at all due to their dislocations and mismatch surfaces. The shape of seeds is an important factor for a
seeding crystallization but was often overlooked. Recent studies by using atomic
force microscopy (AFM) technology can provide a potential method of studying
seeding shape [93–95].
Overall, lots of factors affect the performance of seeding crystals in a crystallization system. Several key strategies are needed to obtain the best performance
of seeds. Firstly, the condition of the seeding surface is critical to be taken into
consideration, including the selection of using dried seed or making seed slurry
for activation of seeding surface. Secondly, the timing of seed addition plays
another key role in controlling nucleation and growth process. Nowadays, many
in situ analytical instruments such as attenuated total reflectance–Fourier
transform infrared (ATR-FTIR), Raman spectroscopy, and FBRM can provide
an effective way to aid the optimization of seeding time. Finally, the appropriate
aging of seeds is vital to suppress nucleation while promoting the further growth
of crystals and commonly applied in industrial crystallization.
2.6
Summary
In spite of numerous efforts, the general mechanism of crystal nucleation still
remains to be fully understood. The weaknesses of CNT are the utilization of
debatable assumption of capillary approximation between the nanosized nuclei
and macroscopic crystals and treating the size of clusters as a sole requirement
for crystal nucleus formation. The two-step mechanism, in contrast, is plausible
81
82
2 Nucleation
in some cases, for example, proteins, but the nature of disordered clusters is
unclear and arguable. Both mechanisms offer little insight into structure of
nucleated clusters and crystal nuclei. The PNCs are thermodynamic stable solution associates and could become precursors of crystal nuclei because they are
kinetically more favorable, nonetheless, predominantly seen in inorganic systems. The application of PNCs pathway in explaining the crystallization of crystalline polymorphs appears to be promising.
Secondary nucleation is critical in modeling, controlling, and optimizing crystal size and size distribution in both batch and continuous industrial crystallization process. The secondary nucleation can be either suppressed to obtain the
narrow size distribution or promoted to achieve the more robustness and higher
start-up efficiency of continuous crystallization.
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89
3
Solid-state Characterization Techniques
Ann Newman1 and Robert Wenslow 2
1
2
Seventh Street Development Group, Kure Beach, NC, USA
Crystal Pharmatech, New Brunswick, NJ, USA
3.1
Introduction
The ability of pharmaceutical materials to crystallize as different solid-state
forms has required a variety of techniques to identify the solid form as well
as its properties [1]. While single-crystal structure solution has provided
information about the bonding and orientation of the molecules in the structure, there has not been a routine technique that can be used to identify the crystalline form for large-scale batches, nor has information been provided on
properties such as melting point, hygroscopicity, stability, and solubility.
A variety of other techniques have been needed to obtain this information
on active pharmaceutical ingredients (APIs), excipients, and dosage forms.
This chapter discusses common analytical techniques used to characterize
pharmaceutical solids and identify the crystalline form. Methods include
powder diffraction for structure/form identification, thermal methods for phase
transitions upon heating and cooling, spectroscopy for bonding and information on the environment around the molecule, water sorption for potential
hygroscopicity and hydrate formation, and microscopy for visual assessment
and particle size estimates. Polymorphs (crystalline forms with the same
composition), hydrates, and solvates have been explored as the primary focus
of this chapter, but information on characterizing amorphous materials, especially amorphous solid dispersions, has also been included when relevant. The
techniques presented have been common to many pharmaceutical laboratories;
however, the list of new techniques to characterize solid forms has continued to
grow as molecules and dosage forms become more complex [2].
Pharmaceutical Crystals: Science and Engineering, First Edition.
Edited by Tonglei Li and Alessandra Mattei.
© 2019 John Wiley & Sons, Inc. Published 2019 by John Wiley & Sons, Inc.
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3 Solid-state Characterization Techniques
It is important to recognize that one analytical method cannot provide all the
information required for a solid material. A number of techniques have been
required for an overall picture of the crystalline form, properties of a material,
and whether it is acceptable for development. Each piece of data has been used
as a part of a puzzle whose pieces need to be combined to understand the whole
picture. The parameters used to collect the data hold potential to influence the
information obtained for many methods; therefore, it has been important to set
up the correct experiments to provide usable data. It has also been necessary to
understand how the samples were stored or prepared, since this can also alter
the sample being analyzed or the data collected.
While characterization of solids is the main focus of this chapter, quantitation
of different crystalline and amorphous forms present in a sample is also possible
with many of the techniques [3, 4]. These types of studies have been performed
on API [3], excipients [5], or drug products [4]. Specificity between forms (and
excipients in the case of drug product quantitation), linearity (range where
quantitation is possible), and sensitivity (how small an amount can be
measured) have also been necessary considerations for developing quantitative
methods. This aspect will be discussed briefly for many of the techniques, and
more detail can be found elsewhere [3, 4, 6].
3.2 Techniques
3.2.1 X-ray Powder Diffraction (XRPD)
As discussed in Chapter 1, molecules have been known to crystallize in a specific
orientation in a specific lattice to produce a crystal (Figure 3.1), and a single
crystal has then been used to solve the structure. For most pharmaceutical
processes, especially at large scale, materials are produced as bulk powders
rather than as single crystals. Powders are composed of imperfect crystals,
amorphous materials, or mixtures of forms. X-ray powder diffraction has been
used to analyze powder samples and provide a “fingerprint” for a crystalline
form. This pattern has also been compared with a “calculated” or “simulated”
powder pattern generated from single-crystal data in order to obtain information on form purity and identify planes that give rise to the peaks in the powder
pattern (Figure 3.2). XRPD patterns have also been indexed to obtain lattice
parameters of the form; a pattern that can be indexed has indicated a single
crystalline form, while a pattern that cannot be indexed has the potential to indicate a mixture of forms [7].
The diffraction of X-rays off the planes in the crystalline structure has been
recognized as XRPD7, which has been based on Bragg’s law [8]. A random orientation of powders has been necessary for researchers in finding a representative
distribution of peak positions and heights. Peak positions (x-axis in degrees 2θ)
3.2 Techniques
Unit cell
+ Symmetry
elements
Tra
nsla
tion
in a
, b,
and
c di
Asymmetric unit
rect
ions
Crystal
Powder
Figure 3.1 Steps leading to crystal/powder formation.
(a)
(b)
110 plane
200
1
1
0
1
2
0
Simulated
150
0
1
1
100
2
1
0
1
0 1
1 1
1
2
2
0
2
13
40
12
02 3
1
0 31
1
1
2
1
Experimental
50
0
Y
Zx
8
10
12
14
Diffraction Angle
16
Figure 3.2 (a) Packing diagram from a single-crystal structure determination showing the
100 plane in red and (b) simulated pattern from the single-crystal structure solution
compared with an experimental XRPD pattern.
91
92
3 Solid-state Characterization Techniques
are directly related to the diffraction angle, and peak heights (y-axis in counts
or counts per second) are related to the number of planes involved in the
diffraction. Different sample holders, such as low background or backfill
holders, have been made available for sample preparation, and care should
be used when preparing samples in order to ensure a random orientation of
particles can be obtained [7]. Particle size and morphology have also influenced
the peak heights for many systems [7]. When collecting XRPD on an unknown
sample, such as an early development compound that has been crystallized for
the first time, additional characterization methods have been needed to
determine if the powder pattern will represent a pure crystalline form or a
mixture of forms.
As research has shown, different forms of a compound will display different
powder patterns due to their structure, illustrated in Figure 3.3. The top pattern represents a crystalline material with sharp peaks and most peaks ending
at a mostly linear baseline. The middle pattern represents a poorly formed
crystalline material that has structure but may also contain defects or less crystalline regions, as shown by the broader peaks and raised baseline. These two
patterns represent two forms of an API, and the peaks can be used to identify
the form present in a sample. Mixtures of these forms could be readily
observed based on the specific peaks in the range 3–15 2θ. When water or
solvent is added to a lattice, different structures will result in a distinct pattern
in most cases [9].
XRPD can also be used to examine amorphous materials, which do not have
the long-range order observed with crystalline materials, but rather have shortrange order involving 8–10 molecules [10]. Amorphous materials will exhibit
up to three broad peaks called “halos” (Figure 3.3). When amorphous APIs have
been mixed with polymers to form amorphous solid dispersions [11], the halos
will change due to the interaction of the molecules and can be used with
computational studies [10] to determine if a physical mixture or a miscible
system can be observed [12, 13]. In many cases, small crystalline peaks will
be observed on top of an amorphous halo when a mixture of crystalline and
amorphous materials is present in a sample [14].
Variable temperature (VT) [15] and relative humidity (VRH) [16] attachments have been made available for investigating form changes in situ. These
experiments have been used to identify form changes without removing the
sample from the instrument; this information has been critical for some systems
where form changes have readily occurred upon exposure to ambient
conditions. Form transitions have been observed upon heating, through
instances such as temperatures related to drying processes, or upon exposure
to RH conditions when mimicking ambient or stability conditions, where
materials may hydrate or dehydrate. Understanding the regions where a form
is stable or may undergo a form change has been critical for researchers when
3.2 Techniques
4500
4000
Crystalline
3500
[counts]
3000
2500
2000
Low crystallinity
1500
1000
Amorphous
500
0.0
0
5
10
15
20
25
30
[2]
Figure 3.3 XRPD patterns of crystalline (top), poorly crystalline (middle), and amorphous
material (bottom).
selecting a suitable form for development, as well as in the development of API
manufacturing [17] or formulation processes [18].
XRPD has commonly been used for the quantitation of crystal forms or
crystalline/amorphous mixtures in API [19], excipients [20], and drug products
[21]. API quantitation necessitates distinct peaks for both forms to show
specificity. In drug product samples, overlap with excipients and low API
loadings have raised issues for researchers that need to be examined during
method development to determine if the technique can be used effectively.
Sample preparation [22], particle size [23], and morphology [24] are all variables
that need to be explored for all forms included in quantitative methods.
Linearity, detection levels, and robustness have also been necessary for other
considerations [6]. Processing of the data can include background subtraction,
data smoothing, and peak fitting. Data analysis methods that have been used
include univariate (one peak area or peak height) [25] and multivariate, whole
pattern, or chemometric methods [19, 25] (such as partial least square [PLS]
methods).
While XRPD data has helped identify the crystal form(s) in a sample, other
techniques have been needed in order to fully characterize physical properties
such as melting point, solvation state, and hygroscopicity.
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3 Solid-state Characterization Techniques
3.2.2 Thermal Methods
The most common thermal methods for analysis of pharmaceutical compounds
have been recognized as differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA), both of which will be discussed in this section.
Other thermal methods that have been used for pharmaceutical analysis outside
of this chapter’s focus include thermally stimulated current (TSC) [26], solution
calorimetry [27], dielectric analysis (DEA) [28], and thermal-mechanical
analysis (TMA) [29].
3.2.2.1 Differential Scanning Calorimetry
DSC analysis has been used to detect thermal transitions relative to a reference
pan (Figure 3.4). Transitions that absorb heat, such as melting or desolvation,
have produced peaks called “endotherms.” Transitions that release heat, such as
crystallization or decomposition, have produced peaks called “exotherms.”
Baseline shifts attributed to a glass transition (Tg) have been observed for amorphous materials. Other techniques, such as TGA, hot stage microscopy, or VT
techniques (XRPD or spectroscopic), have been required to identify the origin of
the transition [30, 31]. DSC has also been used to calculate heats of fusion for
crystalline materials, as well as heats of vaporization for hydrates and solvates.
A number of sample pans have been made available, including open, crimped,
hermetically sealed, aluminum, and platinum. The sample pan used for analysis
has been known to cause shifting in desolvation peaks; open pans have exhibited
–1.5
136.45 °C 172.90 °C
Heat flow (Wg–1)
94
–2.0
168.79 °C
–2.5
83.38 °C
–3.0
^ 0
exo
50
100
015020
150
200
250
300
Temperature (°C) Universal V1.7F TA instruments
Figure 3.4 DSC of a pharmaceutical compound showing endothermic (83.38, 168.79 C) and
exothermic (139.45 and 172.90 C) transitions.
3.2 Techniques
desolvation at lower temperatures, whereas pans that impede release of the
volatiles (such as crimped) have exhibited transitions at higher temperatures
due to partial pressures of the vapor in the pan [32, 33]. Scan rate has also
affected transitions, with the potential to result in transitions blending together
or becoming more distinct [34]. The peak maximum temperature will also move
with scan rate, with faster scan rates resulting in peaks at higher temperatures. It
has been important to recognize that the instrument can be calibrated for each
scan rate in order to ensure that the correct cell constant is used for calculations;
this ensures that the heat of fusion or desolvation values will be constant over
different heating rates [29]. When comparing different samples, it has been
critical for researchers that the same sample preparation and instrumental
conditions have been used for direct comparison of data.
Data obtained from DSC measurements (melting point and heat of fusion)
have been used to determine the thermodynamically stable form at ambient
temperature. In a monotropic system, the most stable form at low temperature
has been recognized as the most stable form up to the melting point. In an enantiotropic system, temperature dependence has been recognized as the stability
and has been defined by the transition temperature; below the transition temperature one form will be stable, but above the transition temperature, a different form will be stable [35]. Heat of fusion can be measured and calibration
curves constructed for quantitative measurements [36]. Other transitions, such
as crystallization or desolvation, can also be used. Quantitation can be performed in drug product when no overlap with the crystalline API forms and
the excipients has been observed [37].
Modulated DSC (mDSC) is a variation where a sinusoidal modulation is overlaid on a conventional linear temperature ramp. From this, researchers have
yielded a heating profile that continuously increases with time but in an alternating heating or cooling program [29]. The resulting data structures a composite of three curves. The first curve has conventional or deconvoluted qualities
similar to the curve obtained from a conventional DSC. The second curve holds
heating rate-dependent or reversing qualities related to the heat capacity, which
provides information on crystalline melting and amorphous Tg temperatures.
The third curve has nonheating rate-dependent or nonreversing qualities
related to kinetics, which includes desolvation, crystallization, and decomposition events. The advantages of this technique have been identified as
(i) separation of complex, overlapping transitions into individual components,
(ii) increased sensitivity for weak transitions (such as Tg), (iii) increased resolution without loss of sensitivity, and (iv) direct measurement of heat capacity.
3.2.2.2
Thermogravimetric Analysis (TGA)
TGA has been used to measure the amount of weight change in a material as a
function of temperature (Figure 3.5). It has been used to determine the volatile
content (water, solvent) in a solid sample; however, it has not been able to
95
3 Solid-state Characterization Techniques
101
6
99
4
2.779% (0.1555 mg)
98
97
2
0.4464% (0.02498 mg)
96
0
95
[—] Deriv. weight (% min–1)
100
Weight (%)
96
94
93
0
50
100
150
Temperature (°C)
200
250
–2
300
Universal V1.1F TA instruments
Figure 3.5 TGA curve (top) showing weight loss as a function of temperature (right axis) and
the derivative of the weight loss (left axis).
identify the volatiles unless it has been attached to an infrared spectrometer
(TG-IR) [38] or a mass spectrometer (TG-MS) [39]. Offline techniques, such
as gas chromatography, Karl Fischer (KF) titration, or solution NMR (organic
solvents only), have also been used to identify volatiles. The temperature at
which volatiles have been lost has been related to how tightly the molecules have
been held in the crystal lattice; low temperatures have indicated loosely held
molecules in the lattice, while higher temperatures have indicated more tightly
held molecules. Chemical decomposition at high temperatures has been identified by a large weight loss and the identification of degradants (carbon dioxide)
in the TG-IR. TGA data has been used to manage drying conditions by drying
above the weight loss temperature if volatiles need to be removed or below the
weight loss if volatiles need be retained (such as maintaining the water content
of a hydrate). In many cases, distinct steps have not been evident, and the derivative of the TGA curve can be used to identify temperatures related to various
weight losses.
TGA has also been commonly used to identify transitions in a DSC curve. By
overlaying the TGA and DSC curves, researchers have recognized which DSC
peaks have resulted from volatilization by comparing the temperatures of the
DSC endotherms and the TGA weight losses. For a direct comparison, DSC data
should be collected in an open pan similar to the TGA analysis. A DSC endotherm can be a combination of transitions; therefore, other methods, such as hot
stage microscopy, VT-XRPD, or VT spectroscopic methods, will be needed to
3.2 Techniques
fully characterize form changes upon heating. This information can then be
used to produce new forms or optimize drying processes for both API and drug
products.
3.2.3
Spectroscopy
Spectroscopic methods have been defined as key techniques when identifying
crystalline forms. Different polymorphs of a given molecule exist in distinct
structures, and the environments around the molecules result in peak shifts
when compared with another form. Peak shifts on the order 1–20 have been
observed for different forms and have been used for identification and quantitation. Common spectroscopic methods for solid samples that will be discussed
here include infrared (IR), Raman, and solid-state nuclear magnetic resonance
(SSNMR). Other methods, such as terahertz [40] and near-infrared (NIR) [41],
have also been made available.
3.2.3.1
Infrared (IR)
IR spectroscopy has been used to view the vibrational motions associated with
the molecule, including stretching, bending, and combination modes [42].
Research has shown that the frequency of the vibration corresponds to the
frequency of the incident radiation, indicating that absorption occurs to give
a peak. To be IR active, the dipole must change when the transition occurs
resulting in stronger signals for nonsymmetric polar groups such as OH,
NH, and carbonyl functionalities. The intensity of the absorption peak is
proportional to the magnitude of the dipole change, and the frequency
(wavenumber) is related to the strength of the molecular bond based on Hooke’s
law [43]. Frequency charts have been made available in order to highlight the
spectral regions for common signals [44]. In general, stretching frequencies
are higher than corresponding bending frequencies, and bonds to hydrogens
have higher stretching frequencies than those to heavier atoms. Mid-IR
occupies the spectral region between 4000 and 400 cm−1, which has been the
concentration in this section [45].
The two common types of spectrometers have been identified as Fourier
transform (FT) and dispersive [42], with FTIR being the most commonly used
method for routine analyses. A variety of sample holders have also been made
available for FTIR that include transmission, absorption, and reflection. The
most common methods have been recognized as the reflection methods of diffuse reflectance IR spectroscopy (DRIFTS) and attenuated total reflectance
(ATR). For DRIFTS, samples can be run neat or mixed with KBr in a special
sample holder [46]. This preparation allows for the possibilities of in situ VT
[47] and humidity. The absorption units for DRIFTS are Kubelka–Munk or
reflectance (log 1/R) [48]. The ATR method samples the surface of the material
using a crystal with no sample preparation needed [42]. Transmission methods
97
98
3 Solid-state Characterization Techniques
(a)
(b)
(c)
4000 3600 3200 2800 2400 2000 1600 1200 800
400
Energy (cm–1)
Figure 3.6 DRIFTS spectra for Fast-Flo (a), anhydrous (b), and hydrated (c) lactose. Source:
Brittain et al. [5]. Reproduced with permission of Springer Nature.
include alkali halide pellets (potassium bromide [KBr]) and Nujol mulls. These
methods have not been recommended for solid-form analysis because the KBR
preparation can change the form due to grinding/dehydration and the Nujol
mull adds peaks that may interfere with the sample [49]. Absorption methods
include microspectroscopy [49] and TG-IR [38].
Spectral differences for crystalline forms have been observed for APIs,
excipients, and drug products. DRIFTS spectra have been presented in
Figure 3.6 for lactose crystalline forms [5]. Differences in the spectra are due
to the different environments in the crystal structures. The crystalline water
present in the Fast-Flo and hydrated forms suggests a sharp peak around
3524 cm−1, in contrast to the surface and noncrystalline water band that
3.2 Techniques
suggests a broad peak around 3400 cm−1. The peak associated with crystalline
water can be used to monitor hydrate formation upon exposure to RH [47].
Drug product samples can also be analyzed to identify the crystalline form
present after manufacturing if minimal peak overlap with excipients has
occurred [50, 51]. IR microspectroscopy, a combination of IR spectroscopy
and microscopy, has been used to collect IR spectra on small areas of samples,
such as tablets. By choosing specific peaks for each component, researchers
have produced maps showing regions of high and low concentrations [50].
Higher sensitivity can be achieved using this technique due to the smaller analysis area; however, results may be skewed if the sample is not homogeneous.
Amorphous materials will show broad and less resolved IR peaks when
compared with crystalline materials. Peak positions will also shift due to the
environment around the functional groups in the amorphous material, such
as interactions between the API and polymer in amorphous solid dispersions
[52]. Peaks involved in H-bonding will shift to lower wavelengths, with larger
shifts corresponding to stronger bonding between components. These interactions have confirmed miscibility of the amorphous solid dispersions, which has
potential to change with water sorption in some systems [53].
Mid-IR spectroscopy is commonly used for form quantitation in drug
substance [54] and drug products [55] using DRIFTS or ATR. Overlapping
peaks, particle size, and homogenous sample preparation [23] must be
evaluated for method development. Multiple spectra have been needed to
obtain representative datasets. A number of data treatment and analysis options
have been made available, with chemometric whole pattern methods commonly
being used [41].
3.2.3.2
Raman Spectroscopy
Raman spectroscopy, complementary to IR spectroscopy, involves a change in
polarizability of symmetric nonpolar groups (aromatic rings, carbon double
bonds), which results in strong signals [49]. The absorption of energy results
in a high-energy state where a photon is emitted upon relaxation, resulting
in Raleigh scattering, Stokes Raman scattering, and anti-Stokes Raman scattering; Stokes Raman scattering has been used for routine Raman spectroscopy.
A typical spectral range for analysis has been recognized as 3600–3610 cm−1
[49]. Low wavenumber peaks (10–500 cm−1) have been attributed to lattice
vibrations, and significant spectral differences between different forms have
resulted from an inherent difference in the crystal structure [56]. These peaks
have been used to look at early crystallization in solution.
The use of Raman spectroscopy offers a number of advantages over IR when
characterizing solid forms. Samples can be analyzed through glass bottles or
capillary tubes without additional baseline in the spectrum, allowing easy analysis of neat samples in a container with no sample preparation. Solids in suspension can be readily analyzed without interference from many solvents, such as
99
100
3 Solid-state Characterization Techniques
water, which allows in situ measurements for formulation and crystallization
studies [56–58]. Issues necessary for consideration with Raman have been
identified as the small analysis area due to the size of the incident laser radiation;
therefore, multiple spectra in different areas of the sample need to be sampled
and combined. Particle size also needs to be controlled when performing
quantitative analysis.
The two main types of Raman instruments include dispersive and FT. The
dispersive Raman instrument typically uses a visible laser (diode 785 nm, HeNe
633 nm, or Ar+ 514 nm), which may lead to fluorescence, resulting in a broad
intense background signal that can interfere with the solid-form peaks.
Changing the laser wavelength has been recognized to decrease the fluorescence in some cases. Photodegradation has also been observed as a common
problem with dispersive systems. FT-Raman systems use an NIR laser (1064
nm), which results in less fluorescence, but thermal degradation is still possible.
Advantages of this instrument include high throughput, high precision, and
easier quantitation. Multiple-sampling holders have been made available,
including powder, capillary, pellet, and vial/bottle options. In situ measurements using heat and/or VRH have also been made possible to investigate form
changes [56]. Raman probes have been made available in order to monitor form
changes in crystallization or formulation processes by either insertion directly
into the equipment or by attachment to a window on the equipment [57].
Raman microspectroscopy has also been made available and has been used
to analyze drug substances and drug products [59].
The identification of crystalline forms is possible using Raman, as shown for
olanzapine Forms I and II in Figure 3.7 [60]. Significant differences have been
observed for the forms that can be used for identification or quantitation. Crystal form changes during wet granulation, such as hydrate formation, have been
monitored with Raman spectroscopy [58, 61]. Changes during drying have been
studied [57] as well as changes during stability, such as dissociation of a salt to
the free base [62]. A number of marketed drug products analyzed using Raman
have shown good specificity and sensitivity when identifying the form present at
both high and low doses [63].
Amorphous materials have exhibited broader peaks than crystalline materials
in a typical Raman spectrum, and mixtures of crystalline and amorphous materials have been analyzed using this technique [64]. Interactions between components, such as drug substances and polymers in amorphous solid dispersions,
have been investigated with shifts in wavelengths being correlated to miscibility
[65] and the amount of H-bonding present in the sample [66]. Imaging dispersions to monitor crystallization of amorphous drug substance in dispersions has
also been reported [67].
Quantitation of solid forms in drug substance [19, 62, 68] and drug product
[69] is commonly performed with Raman spectroscopy. As with other techniques, a variety of preprocessing and data analysis methods are available [70].
3.2 Techniques
Form (2)
Intensity (arb. units)
1.2
Form (1)
100
200
300
Wavenumber (cm–1)
400
Form (2)
0.6
Form (1)
0.0
400
600
800
1000
1200
1400
1600
Wavenumber (cm–1)
Figure 3.7 Raman spectra of olanzapine Forms 1 and 2. Source: Ayala et al. [60]. Reproduced
with permission of Elsevier.
One example involves three forms of mannitol (Forms I, II, and III) using
ternary mixtures, where various data preprocessing options (first derivative
and orthogonal signal correction [OSC]) and data analysis methods (PLS and
artificial neural networks (ANN)) were investigated, where researchers found
that preprocessing had improved the method [71]. The quantitation of free base
produced upon the dissociation of salts on stability has also been reported,
resulting in data that can be used to determine the rate of form change or dissociation, depending on the system [62]. The change in crystal form upon compression of neat drug substance was determined and subsequently used for
quantitation in a low-dose formulation [72].
3.2.3.3
Solid-state Nuclear Magnetic Resonance (SSNMR)
SSNMR spectroscopy of pharmaceutical materials has evolved from a sparingly
used technique into an important component of pharmaceutical solid-state
analysis activities over the past decade, largely due to its unique capabilities.
Continued innovation and application have been occurring in the field that
are likely to continue this trend. Several reviews have appeared in the past
few years about the application of solid-state NMR to pharmaceuticals
[73–80]. This section provides fundamentals of this technology and some key
applications to the pharmaceutical industry.
101
102
3 Solid-state Characterization Techniques
SSNMR has many unique benefits over other characterization tools used in the
pharmaceutical industry. Primarily, it is element selective, probing only the environment of the nucleus under investigation. Furthermore, it is interaction selective. By combining hardware and pulse programming, SSNMR experiments can
be tailored to extract specific information concerning the source nuclei being
probed. This includes dynamics (SSNMR relaxometry) and distance-dependent
interactions including dipole–dipole coupling [81]. This information is invaluable
in understanding structure property relationships in pharmaceutical materials.
In solution NMR, with rapid molecular tumbling of the liquid sample, quadrupolar and dipolar interactions are averaged away to zero, while the chemical shift
interaction is reduced to an isotropic value. In SSNMR, however, the absence of
rapid molecular tumbling results in all interactions retaining their full anisotropic
character having orientation dependence related to the direction of the applied
magnetic field. This anisotropy, for spin ½ nuclei (i.e. 1H, 13C, and 15N), is proportional to the second-order Legendre polynomial of cos θ. For chemical shift and
dipolar interactions, rapidly spinning the sample at an angle that is a root to the
equation will average away these interactions and yield high-resolution “liquidlike” spectra. This technique is known as “magic-angle” spinning (MAS) [82,
83]. When MAS is performed on quadrupolar nuclei, however, quadrupolar interaction still remains and results in nonisotropic spectra. Techniques for obtaining
high resolution for quadrupolar nuclei include MQ-MAS [84] and DOR [85].
Single resonance techniques in solid drugs often suffer from inadequate
signal/noise ratios and long experimental times due to low natural abundance
and long T1 relaxation times. The double resonance technique of crosspolarization MAS (CPMAS) permits low abundance nuclei (i.e. 13C, 15N) to take
advantage of the bath of surrounding abundant and relatively quick relaxing
nuclei (1H or 19F) for signal enhancement [86]. This technique employs a “contact time” where magnetization is transferred from the abundant to the insensitive nuclei. Variation of this contact time results in an initial growth, and
ultimate decay, of the observed CP signal. The initial growth of this CPMAS
curve is determined by the dipole–dipole coupling that is distance dependent.
A group of spin-1/2 nuclei placed in a magnetic field has been observed to
result in an equilibrium population distribution between upper and lower
energy states based on the Boltzmann distribution. The process of growth
toward this equilibrium state has been characterized by the spin–lattice or longitudinal relaxation (T1). Experiments for determining T1 include inversion and
saturation recovery.
Transverse relaxation (T2) is the loss of phase coherence among nuclei. T2 is
inherently less than or equal to T1, since return of magnetization to the zdirection inherently causes loss of magnetization in the x–y plane. In general,
the line width of an SSNMR signal is determined by T2, with a short T2 resulting
in broader peaks.
3.2 Techniques
Every two-dimensional (2D) SSNMR experiment involves preparation,
evolution, mixing, and detection periods. The ability of 2D SSNMR methods
to observe interactions between nuclei through the greater resolution and connectivity information in a 2D spectrum has allowed for more detailed structural
analysis of pharmaceutical materials.
The most common SSNMR method for polymorph characterization and
quantitation involves simple 1H/13C CPMAS [87]. If the API contains other
abundant NMR active nuclei (i.e. 31P, 19F, 23Na), simple MAS can often allow
for polymorph identification and/or quantitation [88, 89]. If using MAS,
quantitation is straightforward as long as at least 5X T1 of the slowest relaxing
component is used as a recycle delay between signal acquisitions. With this
criterion met, peak area is directly proportional to the amount of each phase.
For CPMAS spectra, quantitation has not been straightforward, and reference
spectra of each pure phase have been needed. Furthermore, each unique polymorph has been observed to possess different NMR relaxation values.
Depending on the differences in these values, spectral filtering can be implemented to identify the presence of multiple polymorphs and/or aid in quantitation [90].
In general, amorphous API will have the following SSNMR attributes compared with their crystalline counterparts: shorter T2 values – broader spectra;
exceedingly short T2 values above Tg – leading to “liquid-like” spectra; shorter
T1 values; and lower maximum CP contact time. The attributes listed above
allow for straightforward identification and potential quantification of amorphous components in either API or drug product samples from a variety of
SSNMR techniques. A T2 filter experiment could be used to determine the presence of amorphous components. A T1 filter, where amorphous component is
filtered out, can allow for crystalline quantitation in the sample. VT SSNMR
can readily identify, and even quantitate, the amorphous component when
the sample has been raised above Tg. These applications make SSNMR one
of the most powerful tools in the pharmaceutical industry in readily identifying,
characterizing, and quantitating amorphous content in API and drug product
samples.
One common challenge in the pharmaceutical industry has been the understanding as to whether solvent (including water) is bound or unbound to API
[91]. 13C CPMAS is a powerful tool in characterizing solvent sites in API samples (Figure 3.8). Since CPMAS is a “solids-only” technique based on the presence of unaveraged dipole coupling, the presence of a solvent peak in a CPMAS
specifically indicates that the mobility of the solvent has slowed down enough to
allow for CP to take place. The number of solvent peaks and chemical shifting
from solution-state values can provide secondary structural information
concerning number of different solvate sites and extent of hydrogen bonding.
Measuring 13C T1 values for specific solvent peaks can also provide insight into
103
3 Solid-state Characterization Techniques
H3C
O
H 3C
20
18
2
A
10
5
9
B
H
6
C
14
8
17
D
H
16
15
H
7
CH3CO
N
H
19
13
N
CH
CH3
CH2
CH2O
+CH2
O
3
1
12
25 CH
3
24
22 CH
3
23
70
CH3
11
H3C
60
C14 C22
50
C13
C23, C24
and C25
C8
C12
C7
C10
40
30
C11
C5 C17
C9
C6
C15
CH2O
104
C16
20
C18 C19
10
δC (ppm)
Figure 3.8 13C CP/MAS spectra of different solvate hydrates of finasteride (structure in inset).
From top to bottom: ethyl acetate, tetrahydrofuran, isopropanol, and dioxane solvate
hydrate, where the term solvate hydrate is used to indicate a 2 : 1 molecular ratio of
finasteride to both organic solvent and water. Source: Geppi et al. [79]. Reproduced with
permission of Taylor & Francis.
solvent mobility. 2D SSNMR can also provide information on solvent sites
within the crystal lattice [92]. This information is often invaluable when a
single-crystal structure is not available.
A recent trend to increase exposure for poorly soluble drugs has been to mix
the API with a polymer in order to render the entire mixture amorphous. The
resulting homogeneously mixed sample has been termed an “amorphous dispersion.” In order to maximize the increase in exposure and prevent recrystallization of the API, API and polymer must remain mixed on a molecular level.
SSNMR can provide quick screening experiments to determine the extent of
3.2 Techniques
mixing and identify any regions of inhomogeneity or phase separation. Since
13
C and 1H peaks for each component can be resolved in a SSNMR spectrum,
one can easily measure T1 values for each species in the mixture. Due to 1H spin
diffusion, when components have been mixed on a molecular level, the 1H for
both components will coalesce to a uniform value. When phase separation has
occurred, a break in the spin diffusion will result, and multiple 1H T1 values can
be witnessed. Additionally, 2D SSNMR has been recognized as a powerful technique for characterizing dispersions [93]. Since 1H and 13C from each component can be separated in the SSNMR spectra, 2D correlation experiments can
provide distance information and extend mixing between the multiple
components.
One of the greatest advantages of SSNMR is the ability to characterize the API
structure in drug product with minimal or no excipient interference in most
cases. When using 13C SSNMR on drug products, a spectrum of placebo and
pure API can be obtained. From this, researchers have easily determined spectral regions that will be excipient free or have limited interference from excipient, which allows for tracking of the API form in drug product at exceedingly
low drug loading. If analyzing 19F to determine API form in drug product, this
phenomenon will be intensified, since most excipients do not contain 19F nuclei,
hence no excipient interference [94].
3.2.4
Water Sorption
Water sorption is a general term used to describe the relationship between
the amount of water associated with a solid at a particular relative humidity.
Possibilities for water sorption include adsorption onto a surface or absorption
into the bulk. Solid samples have generally been equilibrated at different VRH
conditions and have then been analyzed by a variety of methods to determine if
there has been an uptake of water and subsequent transformation into another
form, such as a hydrate. Various salt solutions can be used to produce different
RH conditions, as shown in Table 3.1 [95]. These salt solutions can be placed at
the bottom of a desiccator and the solid placed above in an open container to
expose the solid to the RH condition. Weight gain can be monitored by KF
titration, TGA, or gravimetric methods to determine when equilibrium has
been established. Once equilibrium has been attained, the solids can be analyzed
by other methods, such as XRPD, DSC, and spectroscopy, in order to determine
hydrate formation. These types of experiments usually run long term over the
course of days, weeks, or months to achieve equilibrium.
Automated water sorption systems have also been made available and have
commonly been referred to as dynamic vapor sorption (DVS) systems. These
instruments monitor weight change at various RH conditions ranging from 2
to 98% RH using milligram quantities of material. The RH is produced by
105
106
3 Solid-state Characterization Techniques
Table 3.1 Saturated aqueous salt solutions and relative humidity values at 25 C [95].
Salt
Percent relative humidity
Lithium chloride monohydrate
11.3
Potassium acetate
22.5
Magnesium chloride hexahydrate
32.8
Potassium carbonate
43.2
Magnesium nitrate hexahydrate
52.9
Sodium chloride
75.3
Potassium chloride
84.3
Barium chloride dihydrate
90.0
Potassium nitrate
93.6
Potassium sulfate
97.3
Source: Data from ASTM [95].
internal mixing of gas and water within the instrument. Temperature can also
be varied in most systems, with a range of ambient to 60 C. Data from these
experiments have been acceptable for routine screening of materials, since
many analyses can be completed in a day, depending on the equilibration
conditions used, including a weight and time criteria. Tighter equilibrium conditions will result in more accurate data and longer collection times (Figure 3.9)
[96]. Information from the moisture sorption experiments can be used to target
specific RH condition for the chamber experiments described above. A variety
of sorption curves can be obtained, and several of these curves have been shown
in Figure 3.10 [97].
Water sorption can also be used to quantitate amorphous material in crystalline
forms. Amorphous materials will commonly sorb more water than crystalline
materials, resulting in values that can be used to produce a calibration curve
[96]. Amorphous standards made by different methods can result in varying sorption values, which can complicate method development. One example involves
the quantitation of amorphous in crystalline lactose [98].
3.2.5 Microscopy
Microscopic methods have been used to obtain a visual picture of the sample.
Information on particle morphology and size can be related to other properties,
such as flow and dissolution properties [99], and should be assessed for solidstate quantitative methods [20]. Identification of crystalline forms has been
limited in visual microscopic methods, unless the forms have been fully
characterized.
3.2 Techniques
1.4
Short equilibration
Medium equilibration
Long equilibration
% Weight change
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
20
40
60
80
100
% Relative humidity
Figure 3.9 Different equilibration conditions in an automated moisture sorption system.
Closed circles are sorption and open circles are desorption. Source: Newman et al. [96].
Reproduced with permission of Elsevier.
Light microscopy provides an image that produces information on particle morphology and size. Particle size can be estimated when a micron bar has been placed
on the image and individual particles have been observed. When viewed under
crossed polarizers, various colors have been observed in a crystalline particle due
to birefringence, which can be related to the thickness of the particles [100]. Refractive index can also be determined with optical microscopy using reference oils of
known values. The refractive index can be correlated to various solid forms [101].
Hot stage microscopy allows heating or cooling of the sample while being
viewed or recorded. A separate stage is used on an optical microscope, which
allows in situ heating or cooling. Hot stage microscopy has commonly been
used to identify transitions in the DSC curve and confirm melting points. Desolvation can be detected by immersing the sample in an oil and observing gas
formation [102]. Subambient microscopy has also been made available and can
be used to characterize lyophilization processes [103].
Scanning electron microscopy (SEM) has been used to view morphology for
micron-sized particles, in addition to viewing surfaces of particles at higher
magnifications than available with light microscopy [104]. SEM involves an
electron beam as a source and high vacuum for the sample chamber. Environmental SEMs allow vacuums closer to ambient, which allows various RH
conditions and heating options. Information from SEM photographs includes
particle morphology for small particles, estimation of particle size, and
mechanisms for cluster formation (bridges between particles or loosely held
particles). An attachment called energy dispersive X-ray (EDX) analysis allows
107
(a)
(b)
Sorption
Desorption
15
10
5
0
Sorption
60
20
40
30
20
10
0
20
40
60
80
0
100
0
20
40
(c)
(d)
Sorption
Desorption
0.8
% Weight change
% Weight change
1.0
0.6
0.4
0.2
0.0
0
20
40
60
80
100
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Sorption
0
20
% Relative humidity
80
100
80
100
80
100
80
100
Desorption
40
60
% Relative humidity
(e)
(f)
10
Sorption
10
Desorption
8
6
4
2
0
20
40
60
80
Desorption
6
4
2
0
0
Sorption
8
% Weight change
% Weight change
60
% Relative humidity
% Relative humidity
100
0
20
40
60
% Relative humidity
% Relative humidity
(g)
(h)
Sorption
14
Desorption
8
6
4
2
0
Sorption
12
% Weight change
10
% Weight change
Desorption
50
% Weight change
% Weight change
25
Desorption
10
8
6
4
2
0
20
40
60
% Relative humidity
80
100
0
0
20
40
60
% Relative humidity
Figure 3.10 Examples of moisture balance curve. (a) Amorphous, (b) deliquescence, (c),
highly crystalline, (d–g) hydrate formation, and (h) crystallization. Source: Reutzel-Edens and
Newman [97]. Reproduced with permission of John Wiley & Sons.
3.3 Case Study LY334370 Hydrochloride (HCl)
detection and quantitation of various elements in a sample. Mapping capabilities allow for a 2D display of the element in the area to be analyzed. EDX mapping can be used to investigate homogeneity and possible migration of API
molecules through tablet layers [104].
3.3
Case Study LY334370 Hydrochloride (HCl)
LY334370 hydrochloride (HCl) has been classified as a 5HT1f agonist investigated for the treatment of migraines. A polymorph screen was conducted in
early development to search for possible crystalline forms and solvates [105].
Five solid forms were found, including three anhydrous forms (Table 3.2).
Single-crystal structure solution was obtained only for Form I, which showed
a single molecule in the asymmetric unit, an orthorhombic crystal system, and a
space group of Fdd2 (#43). Researchers found that neighboring API molecules
were linked by hydrogen bonding into chains that propagated along the c-axis.
These chains were then cross-linked in three dimensions by two different bonding interactions. A high density of 1.375 g cm–3 was calculated for the structure,
indicating an efficiently packed structure. XRPD patterns were obtained for all
forms (Figure 3.11). Distinct patterns were observed for all forms except Form II
and the dihydrate. Researchers also found that Form II was an isomorphic desolvated form of the dihydrate, which indicated that the API molecules were in
similar positions in both forms, but water molecules were present in the dihydrate form. Slight shifts in the peak positions were observed in Form II due to a
slight contraction of the unit cell when water was removed. Optical micrographs
showed distinct morphologies for Form I (needles), the dihydrate (square
plates), and the acetic acid solvate (prisms). Forms II and III were opaque
Table 3.2 Summary of LY334370 HCl crystalline forms [105].
Form
Designation
Single
crystal
I
Anhydrous
Yes
Organic solvents, aqueous organic mixtures,
pure water with slow cooling
II
Anhydrous
No
Heat dihydrate to 150 C
Production
III
Anhydrous
No
Heat dihydrate to 210 C
Dihydrate
Dihydrate
No
Water with rapid cooling
Acetic acid
solvate
Solvate
No
Glacial acetic acid at 30 C
Source: Reproduced with permission of Elsevier.
109
110
3 Solid-state Characterization Techniques
(a)
Form I
Form II
Form III
Dihydrate
Acetic acid solvate
4
10
30
20
2-Theta - scale
(b)
Form I
Dihydrate
Needles
Square plates
Acetic acid solvate
Prisms
Scale: 10 microns/division
Figure 3.11 (a) XRPD patterns and (b) optical micrographs of LY334370 HCl crystalline forms,
with a scale of 10 μm/division. Source: Reutzel-Eden et al. [105]. Reproduced with permission
of Elsevier.)
but showed the same morphology as the dihydrate parent. The micron bar
allowed for an estimation of the particle size for each form.
Thermal data were also collected on the forms. The DSC curves (Figure 3.12)
showed a number of transitions. Form I exhibited a single melting endotherm at
274 C, and the anhydrous nature was confirmed with a TGA volatile content of
0.3%. Form II showed a melt endotherm of Form II at 190 C, a recrystallization
exotherm at 216 C, and a melt endotherm for Form III at 265 C; all transitions
were confirmed by hot stage microscopy. Form III was found to melt at 265 C.
3.3 Case Study LY334370 Hydrochloride (HCl)
1.0
0.5
Heat flow (W g–1)
0.0
–0.5
–1.0
–1.5
Form I
Form II
Form III
Dihydrate
Acetic acid solvate
–2.0
–2.5
0
Exo up
50
100
150
200
250
300
350
Temperature (°C)
Figure 3.12 DSC curves of LY334370 HCl crystalline forms, from top to bottom: Form I, Form
II, Form III, dihydrate, acetic acid solvate. Source: Reutzel-Eden et al. [105]. Reproduced with
permission of Elsevier.
Based on the DSC data, the thermodynamic stability was established for the
three anhydrous polymorphs. Using the heats of fusion and melting points,
researchers found that Form I was the thermodynamically stable form and that
Form II and Form III were monotropically related to Form I.
The dihydrate curve showed a desolvation endotherm around 100 C resulting in Form II, which melted at 190 C, a recrystallization exotherm to Form
I at 216 C, and the final melt of Form I at 265 C. The TGA water content of
8.0% was similar to the theoretical dihydrate. The acetic acid solvate curve displayed a desolvation endotherm around 30 C (sloping baseline, not an obvious endotherm as observed in the dihydrate), an endothermic conversion of
the solvate to Form I at 140 C, and the melt endotherm of Form I at
265 C. TGA data for the solvate resulted in a weight loss of 18.6% (approximate 3 : 4 drug: acetic acid ratio), and the amount of acetic was confirmed by
solution NMR.
13
C SSNMR studies were performed, and significant differences were
observed between the forms that could be used for identification
(Figure 3.13). The weak peaks have been identified as spinning sidebands or artifacts that have resulted from insufficient sample spinning. Factors such as conformational differences, crystal packing preferences, and hydrogen bonding
111
112
3 Solid-state Characterization Techniques
22
F
12
13
14
H CH3
20 N +
11
10
O
9
15
H
N 5
6
4
7
21 16
3a 3
7a N
18
17
–
Cl
2
C22, 16,
17, 21
H
C7a, 11, 15, 12, 14, 5,
10, 3a, 2, 6, 3, 4, 7
C18, 20
Form I
C9, 13
Form II
Form III
Dihydrate
Acetic acid solvate
180
160
140
120
Spinning sidebands
100
80
60
40
20
ppm
Acetic acid
Figure 3.13 SSNMR spectra of the LY334379 HCl crystalline forms, from top to bottom: Form
I, Form II, Form III, dihydrate, acetic acid solvate. Source: Reutzel-Eden et al. [105]. Reproduced
with permission of Elsevier.
3.3 Case Study LY334370 Hydrochloride (HCl)
impacted the chemical shifts of the forms resulting in different spectra for the
crystalline forms. The NMR data also confirmed the single molecule in the
asymmetric unit that was observed in the Form I single-crystal structure.
The acetic acid in the acetic acid solvate was evident in the spectrum. Even
though Raman and IR spectra were not collected in this study, they have been
known to show distinct spectra for the forms that could have been used for
identification.
The water sorption isotherms were collected on each form (Figure 3.14).
Form I sorbed minimal water (0.3%) at high RH and did not convert to the dihydrate, indicating that it was physically stable for storage and handling over the
course of development. Form III was found to transform to the dihydrate upon
exposure to high RH conditions. Around 80% RH, the material loses water,
transforms to the dihydrate, and remained as the dihydrate down to 10% RH.
Below 10% RH, it loses water and converts to an anhydrous form. The dihydrate
remained stable from 15 to 95% RH and lost water below 10–15% RH to form an
anhydrous material. The Form II isotherm was identical to its dihydrate parent.
Once the crystalline forms were characterized, transformations between the
forms were compiled (Figure 3.15). The next step was to select the best form for
development based on the properties required for development. Form I and the
dihydrate had acceptable properties for moving forward: easy to prepare, highly
14
% Weight change
12
10
8
6
4
2
0
0
20
40
60
80
100
% Relative humidity
Form I adsorption
Form I desorption
Form II adsorption
Form II desorption
Dihydrate adsorption
Dihydrate desorption
Figure 3.14 Water sorption isotherms for LY334370 HCl crystalline forms. Source: ReutzelEden et al. [105]. Reproduced with permission of Elsevier.
113
114
3 Solid-state Characterization Techniques
Dihydrate
50 °C or
<5% R.H.
H2O slurry
Form I seeds
>5% R.H.
Form II
>75% R.H.
190 °C
Form I
140 °C
Acetic acid
solvate
RT
solid state
Form III
Figure 3.15 Relationship between LY4334370 HCl forms. Source: Reutzel-Eden et al. [105].
Reproduced with permission of Elsevier.
crystalline, physically stable at room temperature over a wide RH range, and
could be crystallized in acceptable morphologies. Additional studies showed
that the dihydrate was more soluble and dissolved more rapidly but that Form
I was the thermodynamically stable form. Since Form I exhibited acceptable solubility and dissolution rate, Form I was chosen for further development.
3.4 Summary
Drug substances and excipients can crystallize and transform into a variety of
forms. A number of techniques have been made available in order to characterize solid samples and identify crystalline materials. XRPD can provide information on crystallinity, thermal methods will assess thermal transitions,
spectroscopy can distinguish environments and bonding patterns, and water
sorption will establish hygroscopicity/hydrate formation. Once the characterization information has been obtained, other data can be combined with this
information for selecting the best form for development. Relationships between
the forms can be used to help understand and prevent process-induced transformations during API and drug product processes, such as drying, milling, and
granulation.
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4
Intermolecular Interactions and Computational Modeling
Alessandra Mattei1 and Tonglei Li 2
1
2
AbbVie Inc., North Chicago, IL, USA
Department of Industrial and Physical Pharmacy, Purdue University, West Lafayette, IN, USA
4.1
Introduction
Intermolecular interactions are important in many branches of science. In its
more mathematical form, the topic is of great interest in physics and chemistry,
and its applications are significant in fields, such as molecular biology, crystallography, drug development, surface and colloid chemistry, polymer science,
and mineralogy.
Intermolecular forces are the molecular interactions that exist between molecules. They differ from the intramolecular bonding forces that hold individual
atoms within a molecule. Intermolecular forces exist for all states of matter and
are the forces that allow water, for instance, to exist as either gas, liquid, or solid,
depending upon temperature. In the absence of such interactions, nature would
consist solely of ideal gases. An understanding of real gases and of all condensed-phase matter and their thermodynamic as well as kinetic properties
must be rooted in the knowledge of intermolecular interactions. Intermolecular
interactions are involved in the formation of chemical complexes, such as
charge-transfer and hydrogen-bonded complexes. The study of the mechanism
of elementary chemical reactions is deeply related to understanding the energy
exchange processes, which depend on the interactions of particles under collision. Further, intermolecular interactions are of great importance in biology as
they account for the stability of biological macromolecules, such as DNA and
proteins.
Pharmaceutical Crystals: Science and Engineering, First Edition.
Edited by Tonglei Li and Alessandra Mattei.
© 2019 John Wiley & Sons, Inc. Published 2019 by John Wiley & Sons, Inc.
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4 Intermolecular Interactions and Computational Modeling
Our primary focus in this chapter will be the analysis of intermolecular interactions in crystalline solids in general and pharmaceutical molecules in particular. Intermolecular forces determine to a large extent the structure of
molecular organic crystals. Organic crystalline solids are held together by an
intricate mosaic of intermolecular interactions with varying strength, directionality, and distance dependence. Due to their diverse characteristic properties,
intermolecular interactions affect many of the physical and chemical properties
of crystalline materials (i.e. equilibrium geometry and lattice energy) and play an
important role in determining the most effective ways of packing molecules
together in the crystal. The concepts of geometry, directionality, and strength
of various intermolecular interactions within organic crystal structures have
been actively used in rationally designing molecular solids with specific structures and properties – the paradigm of crystal engineering.
To give a deservedly comprehensive and detailed review of all the aspects of the
subject would be a mammoth task. In this chapter, intermolecular interactions
are reviewed first. The nature of each intermolecular interaction and the context
in which it is important are emphasized. The discussion is qualitative in the sense
that the emphasis is more on fundamental theory than on specific strategies for
calculation. Various forms of intermolecular interactions in organic crystals and
their implications on the molecular packing as well as on the physicochemical
properties of pharmaceutical organic compounds are then discussed. Also given
are examples that show how experimental and computational methods are routinely used for calculating or estimating the strength of these interactions. The
last section of this chapter covers methodologies in crystal packing prediction,
with emphasis on the achieved progress and the current, inherent difficulties
in this area. Finally, concepts and advances in exploring the electronic origin
of intermolecular interactions in organic crystals are presented.
4.2 Foundation of Intermolecular Interactions
The foundation for a physical interpretation of intermolecular interactions was
laid toward the end of the nineteenth century and in the first decades of the
twentieth century. Electromagnetic forces are the forces that govern the interaction between atoms and molecules. They are the source of all intermolecular
interactions [1]. At the root of intermolecular interactions lies the electrostatic
(i.e. coulombic) interaction. Although all of the interactions between molecules
have essentially an electric origin, intermolecular interactions can be classified
in a variety of ways; to a certain extent the definition of various categories stems
from chemical convenience and is somewhat arbitrary.
Intermolecular forces can be ascribed to various atomic and molecular phenomena, which have electrostatics at their core, but all of these forces are
4.2 Foundation of Intermolecular Interactions
Table 4.1 Overview of intermolecular forces.
Interaction
type
Origin
Range
Directionality
Strength
Electrostatic
Coulomb attraction/repulsion
between charges
Long
None
Strong
Dispersion
Coulomb attraction between
mutually polarized electric
dipole moments
Long
Small
Weak but
increase with
increasing
molar mass
Induced
polarization
Coulomb attraction between
electric dipole of one molecule
and field-induced polarization
of the other
Long
Small/
medium
Moderate
Hydrogen
bonding
Attraction between X–H A
that includes electrostatic,
dispersion, polarization, and
covalent contributions
Short
High
Weak/strong
π–π
interaction
Attraction between π
electron-rich molecules
Long
Small/
medium
Weak
strongly dependent on the separation between molecules. Short-range interactions are repulsive and decay exponentially with the intermolecular separation,
while long-range interactions are attractive and vanish slowly at a certain power
of the intermolecular separation. At the fundamental level, repulsive interactions arise from the overlap of electron shells, which means that the nuclear
charges are no longer completely screened by electrons, thus they repel each
other. The classification in these two distinctive categories is often accompanied
by additional contributions to the total intermolecular potential into electrostatic, dispersion, induced polarization, hydrogen bonding, and π–π interactions. An overview of these intermolecular interactions and their most
important characteristics are provided in Table 4.1.
4.2.1
Electrostatic Interactions
Some interactions are purely electrostatic in origin, arising from the coulombic
forces between charges on atoms. If two atoms bear opposite charges, the electrostatic energy decreases as they approach each other, and the interaction is
favorable; if the two atoms bear charges of the same sign, there is repulsion
between them. The electrostatic forces between electroneutral molecules or
assemblies that are free to mutually orient are generally attractive. According
to Coulomb’s law, because the electrostatic interaction varies inversely with
the distance between the two atoms, it is effective over relatively large distances.
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4 Intermolecular Interactions and Computational Modeling
The electrostatic energy is first order in the coulombic interaction and as such
is pairwise additive. The electrostatic energy of a pair of molecules is the interaction energy between their permanent charge distributions. The interaction
modifies the charge distribution of each molecule, but this contributes to the
energy only at second or higher order. All electrostatic interactions in a solvent
medium involve polarization effects. The dielectric constant of a solvent
medium can have a large effect on the strength of particular electrostatic interactions. As the electrostatic interaction varies inversely with the dielectric constant of a medium, in media other than vacuum this interaction is always less
than that stated by Coulomb’s law. For example, two unit charges of opposite
sign, 5 Å apart in vacuum, have an electrostatic energy of about −280 kJ mol−1.
However, this may be reduced by almost two orders of magnitude in
polar media.
4.2.2 van der Waals Interactions
Three distinct types of forces, which are collectively known as the van der Waals
forces, contribute to the long-range, weak (physical) interactions between molecules. These include temporary fluctuating dipoles (London dispersion forces),
dipole–dipole interactions (Keesom forces), and dipole-induced dipole forces
(Debye forces) [1]. Each force has an interaction free energy that varies with
the inverse sixth power of the interatomic distance. As such, van der Waals
forces act between molecules at distances usually larger than the sum of their
electron clouds. They tend to be weak but their effects are additive; hence their
total collective contribution to molecular stability can be significant.
London dispersion forces arise from the fluctuations in the electric dipole
moments within molecules or atoms that become correlated as the molecules
come closer together, giving rise to an attractive force. The electron distributions of an atom orbit around the nucleus in a chaotic manner, causing random
fluctuations in the electron cloud density. As these electron distributions are not
completely uniform, they give rise to an electron-rich side of the atom. Such a
small negative charge of the atom, of course, results in the opposite side of the
atom being positively charged. The fleeting charge separation is called an
instantaneous dipole (or temporary dipole). This temporary dipole distorts
the electron charge in other nearby polar or nonpolar molecules, thereby inducing dipoles. Dispersion forces are present in all kinds of molecules; generally
their magnitude depends on how easily the electrons in the atom or molecule
can move or polarize in response to an instantaneous dipole, which in turn
depends on the size of the electron cloud. A larger electron cloud results in a
greater dispersion force because the electrons are held less tightly by the nucleus
and, thus, can polarize easily.
Polar molecules, although electrically neutral, may have permanent electric
dipoles. Generally, dipoles are associated with electronegative atoms, including
4.2 Foundation of Intermolecular Interactions
(but not limited to) oxygen, nitrogen, and fluorine. A permanent dipole on one
molecule produces an electric field that interacts with the permanent dipole on
a second molecule. The tendency of such permanent dipoles to align with each
other results in a net attractive force. The strength of this dipole–dipole interaction is inversely proportional to the temperature, as increased Brownian
motion can disrupt the alignment of the permanent dipoles and, therefore,
reduce the strength of this type of interaction.
The dipole-induced dipole force is an additional attractive force that results
from the interaction of a permanent electric dipole with a neighboring induced
dipole. Specifically, the electric field of a molecule with a permanent dipole
moment temporarily distorts the electron charge in other nearby polar or nonpolar molecules, thereby inducing further polarization. The induced dipole
tends to align with the permanent dipole of the molecule that induced it.
Since this is a transient effect, with interactions constantly forming, increasing
the temperature has little effect on the strength of dipole-induced dipole interactions. The key property in determining the strength of this type of interaction
is the molecular polarizability. The greater the polarizability, the larger the temporary induced dipole moment and, thus, the greater the strength of the Debye
interaction. Atoms with larger atomic radii are considered more polarizable
and, thus, experience greater attraction as a result of the Debye force.
4.2.3
Hydrogen-bonding Interactions
A hydrogen bonding is an attractive interaction, wherein a hydrogen atom
forms an electrostatic bond between two atoms. This attraction increases with
increasing the electronegativity of the two atoms or structural moieties. The
notion of hydrogen bonding as an electrostatic interaction goes back to Pauling
[2], who concluded that hydrogen bonding cannot be chemical (covalent) in
character and is formed only between the most electronegative atoms. Indeed,
the original examples of hydrogen bonding were found to involve the electronegative atoms of oxygen, nitrogen, or fluorine as hydrogen-bond acceptors.
The directional interaction between water molecules can be considered as
the prototype of hydrogen bonding. The large difference in electronegativity
between hydrogen and oxygen atoms makes the oxygen–hydrogen bond of a
water molecule inherently polar, with a partial positive atomic charge on the
hydrogen atom and a partial negative atomic charge on the oxygen atom. Neighboring water molecules orient themselves in such a way that local dipoles point
at negative partial charges; thus, the intermolecular distance is shortened by
around 1 Å compared with the sum of the van der Waals radii for hydrogen
and oxygen atoms [3]. Despite the significant charge transfer in the hydrogen
bonding between water molecules, the total interaction is predominantly electrostatic. Although many hydrogen bonds do fall within Pauling’s definition,
there is a substantial body of structural evidence that such definition is too
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4 Intermolecular Interactions and Computational Modeling
restrictive and precludes many examples of interactions that are now universally
accepted as hydrogen bonding.
The ever-increasing importance of hydrogen bonding has been acknowledged
by physicists, chemists, biologists, and materials scientists; however, there has
been a continual debate about what the term means. Even though Pimentel
and McClellan [4] recognized that weak donors (e.g. aliphatic methylene protons) and acceptors (e.g. alkenes, alkynes, aromatic π systems, and transition
metals) can be involved in this interaction, and although spectroscopic studies
had already been carried out in this regard, the classical dogma was in favor of a
strongly electrostatic interaction. The current International Union of Pure and
Applied Chemistry (IUPAC) definition given in the Gold Book still specifically
mentions the most electronegative atoms of oxygen, nitrogen, or fluorine, but
adds a caveat suggesting that the interaction is not limited to these atoms. The
elements of the hydrogen-bond donors have the effect of removing the electron
density from the hydrogen atom, leaving it with a significant partial positive
charge. This implies that the hydrogen-bond donor does not need to be a very
electronegative atom, but does at least need to be slightly polar. Similarly, the
acceptor atom should only supply a sterically accessible concentration of negative charge or be the center of high electron density.
Various criteria have been utilized to classify an interaction as hydrogen bonding. These criteria are geometrical, energetic, spectroscopic, or functional. None
of them is all-encompassing and exceptions are well known. A geometric criterion for hydrogen bonding stems from its peculiar directionality. Indeed, this
directionality is the hallmark of hydrogen bonding. The distance is not in all
hydrogen-bonding interactions shorter than the sum of the van der Waals radii.
This implies that the “cutoff distance” rule based on van der Waals radii for identifying hydrogen bonding is conservative and relegates almost all interactions to
the van der Waals realm [5, 6]. The energy of hydrogen-bonding interactions
ranges between 0.2 and 40 kcal mol−1 [7]. Thus, hydrogen bonding is classified
as weak, with energy less than 4 kcal mol−1; as moderate, with energy from 4
to 15 kcal mol−1; or as strong, with energy greater than 15 kcal mol−1 [8]. Such
classification reflects a transition from quasicovalent to pure van der Waals interactions. Some hydrogen bonds are so strong that they can resemble covalent
interactions; others are so weak that they cannot be distinguished from van
der Waals interactions. The electrostatic contribution of hydrogen bonding is
therefore dominant only for some configurations. Although the electrostatic
interaction does play a crucial role in hydrogen bonding, it cannot explain several
important experimental observations, including the lengthening of the proton
donor bond with a resultant redshift in the fundamental vibrational stretching
frequency. This is due to a significant electron density transfer from the lone pair
of a proton acceptor to the antibonding orbital of the proton donor bond.
Hydrogen bonding is a complex interaction composed of at least four
contributions, including electrostatics, polarization, dispersion arising from
4.2 Foundation of Intermolecular Interactions
instantaneous dipole-induced dipoles, and charge-transfer-inducing covalency.
The contribution from each force varies depending upon the particular donor–
acceptor combination and the environment, that is, the contact geometry.
Clearly, no single physical force can be attributed to hydrogen bonding. For
weak hydrogen bonds, dispersion may contribute as much as electrostatics to
the total bond energy. In contrast, for strong hydrogen bonds, their quasicovalent nature with a large charge-transfer contribution needs to be fully considered. In summary, hydrogen-bonding interactions are much stronger than
dipole–dipole interactions but are very directional in nature and operate over
much shorter distances.
4.2.4
π–π Interactions
Strong attractive interactions between aromatic and heteroaromatic rings are
known as π–π stacking or, more generally, π–π interactions. Such noncovalent
interactions are abundant in biological and chemical systems, spanning from
molecular recognition to self-assembly and to catalysis and transport. π–π interactions are major contributors to the tertiary structure of proteins [9], the protein–
ligand complexation, the stabilization of the double-helical structure of DNA, and
the intercalation of drugs into DNA [10]. In addition, interactions between π systems control the packing of aromatic molecules in crystals [11], the conformational preferences, and binding properties of polyaromatic macrocycles, and
thus they modulate the structure and function of supramolecular systems.
There are strong geometrical requirements for the interaction between aromatic rings. It has been suggested that π–π interactions are caused by intermolecular overlapping of p-orbitals in π-conjugated systems. Electrons in π bonds
of aromatic rings form a quadrupole moment (i.e. two dipoles aligned so that no
net dipole can be distinguished) due to the stronger electronegativity of carbon
compared with hydrogen atoms. In the prototypical benzene dimer, this quadrupole creates a partial negative charge on both faces of the π system and a partial positive charge around the aromatic ring. According to this description, a
parallel face-to-face stacking of π systems with the maximum overlap of aromatic rings would be energetically unfavorable and thus not stable, because
of a large electrostatic repulsion between negatively charged regions. Aromatic
rings can preferentially interact with each other through the edge-to-face stacking, known as T-shaped, or the parallel displaced orientation, referred to as parallel off-centered. These arrangements indeed lead to attraction. It is the
geometrical arrangement of molecules and not only the presence of π electrons
that determines the character of this type of intermolecular interaction.
The electrostatic contribution to the overall π–π interaction energy is usually
dominant [12]. Electrostatic concepts have been recast into more pragmatic
models to provide chemically intuitive pictures of how electronic factors can
influence aromatic π–π interactions. However, the major contribution of the
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4 Intermolecular Interactions and Computational Modeling
interaction energy arises from other factors. These contributing factors determine how the π systems interact and thus affect the strength of the π–π interaction based on the stacked geometry. van der Waals interactions can make an
appreciable contribution to the magnitude of π–π interactions. In large unsaturated systems with more than 10 carbon atoms that are in close proximity to
each other, π–π interactions are viewed as a particular type of dispersion effects,
such that electron correlations are significant. Nevertheless, they cannot override electrostatics, as face-to-face arrangements between aromatics, where π
overlap is maximized, would otherwise be prevalent. This means that the interactions between aromatic rings are generally far more complicated than can be
described by a simple π-orbital overlap or an electron donor–acceptor model.
Therefore, the term π–π stacking should be viewed as a convenient geometrical
descriptor for the interaction mode in unsaturated molecules.
4.3 Intermolecular Interactions in Organic Crystals
The majority of pharmaceutical compounds and a significant number of fine
chemicals are manufactured as crystalline solids. Organic crystals are periodic
supramolecular structures in which the component molecules arrange into a
highly regular fashion [13]. The molecular order extends in three dimensions
over short and long ranges. An organic molecular crystal is indeed viewed as
the supermolecule par excellence [14], that is, an assembly of molecular entities
held together by a variety of relatively weak intermolecular interactions. These
are the same forces that nature uses to bind its molecular assemblies (i.e. van der
Waals interactions, hydrogen bonding, aromatic interactions, and halogen
bonding). In most organic crystals more than one, and often all, of these interactions contribute to the ultimate stability of the crystal structure. In principle,
all occurring intermolecular interactions must be considered as determinants of
the molecular packing, some playing more prominent roles than others, but
none being completely insignificant. Since a crystal structure is the result of
a very fine balance between all the intermolecular interactions present in the
material, understanding of the structural influence of, and competition
between, several fundamental intermolecular forces is critical.
4.3.1 Approaches to Crystal Packing Description
The increasing recognition of the desire, indeed the need, to examine structural
data and crystal form space as thoroughly as possible has led to the development
of valuable methods for describing intermolecular geometries and packing patterns in a consistent and “user-friendly” way.
The packing of molecular organic crystals has been considered based on
geometry and molecular shape [15]. Ideas on shape-induced recognition
4.3 Intermolecular Interactions in Organic Crystals
between molecules became well established, implying that the high degree of
order in a crystal structure results from the complementary dispositions of
shape features and functional groups in the neighboring interacting molecules.
Molecules in a crystal can satisfy the need to have the highest possible density
just by letting the protrusions of one molecule fit efficiently into the hollows of
an adjacent molecule. Even though molecules are of complicated shapes, high
packing densities can be achieved by positioning molecules in interlocking patterns, thereby minimizing the empty space. The principle is illustrated by the
crystal structure of benzene, where adjacent layers are stacked one over the
other along the z axis so that the protrusions of one layer fit into the hollows
of the other. As a result of the complementarity of the molecular shapes in
building up crystal structures, molecules of a similar shape and size make similar crystal structures. Accordingly, the overall crystal packing of benzene and
thiophene, two structurally similar molecules, is largely unaltered, as depicted in
Figure 4.1a and b.
(a)
(b)
(c)
Figure 4.1 Molecular crystal packing of (a) benzene (refcode: BENZEN), (b) deuterothiophene
(refcode: ZZZUXA02), and (c) urea (refcode: UREAXX02).
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4 Intermolecular Interactions and Computational Modeling
The geometrical approach assumes that intermolecular interactions are weak
and lacking directionality. Thus, the model implies that molecules in a crystal
are held together by attractive forces that extend over long distances, but they
actually are clamped in their equilibrium positions by repulsive forces that
hinder any displacement and operate only at short range [16]. There is little
doubt that in crystals of aliphatic hydrocarbons, the dominant interactions
are dispersive in nature. The molecular packing in crystal structures, governed
by close packing, can be mainly explained in terms of the aforementioned simple geometrical model and the complementary recognition between molecules.
However, most crystal structures of organic compounds contain heteroatoms
and are dominated by hydrogen-bonding interactions, although long-range,
electrostatic forces significantly contribute to the bulk of the crystal energy.
In crystalline urea, for instance, hydrogen bonding hinders the densest possible
packing, as shown in Figure 4.1c. The particular arrangement adopted by urea
molecules maximizes hydrogen-bonding interactions. Hydrogen bonding is
undoubtedly the most critical force holding organic molecules in the solid state,
not only due to its strength but also to its highly directional nature [7, 17]. As
such, hydrogen-bonding interactions possess features that recommend them as
elements to rationalize and control the crystal structure of organic molecules.
Molecular crystals can alternatively be considered in terms of chemical factors and directional interactions formed by heteroatoms. The intermolecular
specificity of common organic functional groups in forming hydrogen bonding,
rather than the size or shape of molecules, is taken into account for directing
molecular assemblies. Crystal structures are thus understood based on how
donor and acceptor groups pair off in order of strength [18]. Relative to the conventional close-packing principle, the methodology includes a topological
approach, based upon graph theory, to analyze hydrogen-bonded patterns
where chemical structure and functionality are retained [19]. The need for
a general and simple method to be able to characterize and compare
hydrogen-bonded motifs in molecular crystals was recognized. By applying
graph theory to molecular assemblies, complex networks are broken down into
simpler constituent motifs, that is, into subsets of molecules joined by just one
type of hydrogen bonding.
All patterns of hydrogen bonding can be categorized into four simple motifs,
as shown in Figure 4.2. A notation – referred to as a graph set – is assigned to
each type of hydrogen bonding and provides a complete and accurate description of these motifs [20]. Empirical rules have been implemented for predicting
the connectivity of hydrogen bonding in molecular crystals, but because exceptions exist, they should be considered more as guidelines rather than as formal
rules. While the rigor in the graph set definition provides a precise topological
description, the same rigor can nevertheless obscure general similarities in
hydrogen-bonded patterns. Among other limitations of the graph set notation
are the definition of acceptors as single atoms and the inapplicability of the
4.3 Intermolecular Interactions in Organic Crystals
O
O
H
N
R
N
N
H
O
H
R2(8)
C(4)
H
O
O
O
H
N
D1(2)
S(6)
Figure 4.2 Examples of different hydrogen-bonding motifs with their corresponding
graph sets.
method to the many interactions that cannot be considered as being of the
donor–acceptor type. In fact, it deliberately excludes competing factors, including steric restraints and ionic and weak interactions. Further, this chemical
approach requires a real-space examination of molecular features to select a
packing direction.
The identification of appropriate intermolecular interactions for directing
and controlling the molecular assembly relies on a statistical analysis of determined crystal structures to search for motifs that are regularly generated. If a
particular motif is identified often enough, it can be correlated with a particular
molecular fragment, leading in turn to reliable strategies for the understanding
and design of molecular crystals. Notably, a variety of hydrogen-bonding interactions have been extensively utilized in crystal engineering and structural
chemistry for the design of reliable, structural motifs with the ultimate intent
of developing improved crystalline solids [21]. A full and rigorously accurate
knowledge of all the intermolecular interactions involved may not be of crucial
importance. What is important is the repetition of particular motifs. The concept of motifs or supramolecular synthons incorporates both geometrical and
chemical elements of molecular recognition. Such flexibility is advantageous
and permits to select crystal motifs not only on the basis of topological attributes but also through chemical intuition. Nevertheless, similar to the graph
set notation, the emphasis is on the hydrogen bonding and intermolecular interactions between functional groups, neglecting the molecular skeleton that is
deemed to be passive.
Supramolecular synthons are defined as structural units that can be formed
and/or assembled by known or conceivable intermolecular interactions [22].
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4 Intermolecular Interactions and Computational Modeling
They express the core features of a crystal structure; as such, they are considered
a reasonable approximation of the entire crystal. Such an approach hinges on
whether or not a particular simplification (i.e. structure to synthon) is substantial enough to allow an easy understanding of a crystal structure, but not so
excessive that essential attributes or features of the structure are lost in the
process of simplification. A few of supramolecular synthons that have been
employed in crystal engineering are shown in Figure 4.3.
A complementary method of analyzing molecular crystals is represented by
Hirshfeld surfaces. The Hirshfeld surface represents a measure of the space
occupied by a molecule in a crystal and is defined by the molecule and the proximity of its nearest neighbors. Hirshfeld surfaces reflect the interplay between
various intermolecular interactions, including close contacts in the crystal
[23, 24]. The concept is illustrated by the molecular Hirshfeld surface for Form
I of aspirin, which was evaluated with the CrystalExplorer 3.1 program [25], as
depicted in Figure 4.4a. The most interesting feature on the Hirshfeld surface of
the molecule is the pair of red spots on the hydrogen-bonding acceptor and the
adjacent hydrogen-bonding donor of the carboxyl group. The red spots arise
H
O
O
H
O
O
O
O
I
H
H
II
N
O
O
O
H
H
O
O
H
N
O
H
N
N
III
IV
O
O
N
H
O
H
H
O
N
O
H
O
N
H
H
VI
V
N
O
O
VII
O
N
O
CI
CI
O
VIII
O
N
C
O
H
N
N
C
H
H
O
IX
C
N
N
C
H
X
H
C
N
CI
CI
CI
N
Br
O
H
XI
XII
XIII
XIV
Figure 4.3 Supramolecular synthons employed in crystal engineering.
XV
4.3 Intermolecular Interactions in Organic Crystals
(a)
(b)
2.4
de
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
di
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Figure 4.4 (a) Hirshfeld surface and (b) two-dimensional fingerprint plot for Form I of aspirin
(refcode: ACSALA 02).
from close intermolecular contacts and, being adjacent to each other, are
distinctive of cyclic hydrogen-bonded dimers. This feature is reinforced in
the two-dimensional fingerprint plot, as shown in Figure 4.4b. The twodimensional fingerprint plot is derived from the Hirshfeld surface by plotting
the fraction of points on the surface as a function of the distance from the surface to the nearest atom exterior to the surface (de) and the distance from the
surface to the nearest atom interior to the surface (di). The two-dimensional
fingerprint plot uniquely identifies each type of interaction in the crystal structure. The hydrogen bonding appears as a pair of sharp spikes, pointing toward
the bottom left of the plot. The upper spike, where de is greater than di, corresponds to the hydrogen-bonding donor, while the lower spike corresponds to
the hydrogen-bonding acceptor. In addition to the dominant hydrogen bonding
between carboxyl groups of neighboring molecules, the fingerprint plot for aspirin displays two other patterns. The first is characteristic of H─H contacts,
superimposed on the pattern for hydrogen bonding. The second is due to weak
hydrogen-bonding interactions, C─H─π, which appear as “wings” in the plot.
The Hirshfeld surface gives a unique signature of a molecule in a crystal
because it strongly depends on its surroundings; thus, the same molecule in different crystal packing modes looks different. As such, Hirshfeld surfaces have
become highly useful for examining intermolecular interactions in crystal structures of polymorphs [26]. The caveat for this type of analysis is that the molecular crystal structure needs to be well characterized. All hydrogen atoms need to
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4 Intermolecular Interactions and Computational Modeling
be located accurately, and bond distances to hydrogen atoms need to be standardized to realistic values.
4.3.2 Impact of Intermolecular Interactions on Crystal Packing
Molecules tend to be involved in a synthon of several intermolecular interactions of comparable relative strength, and the structure of the resulting associated system is determined by the balanced cooperation of these interactions.
This is the case for molecules that can give rise to weak interactions only.
On the other hand, there are molecules that can form an organized network
with specific or functional features.
The common mode of association of carboxyl groups is via the centrosymmetric dimer homosynthon [27]. A Cambridge Structural Database study of
supramolecular synthons involving carboxylic acid revealed that 93% of crystal
structures feature the homosynthon in the absence of other competing
hydrogen-bond donors and/or acceptors. However, carboxylic acids tend to
form supramolecular heterosynthons in the presence of chemically different
but complementary functional groups (e.g. primary amides and aliphatic and
aromatic nitrogen moieties), which can attract adjacent molecules by hydrogen
bonding. Thus, while benzoic acid forms a centrosymmetric dimer homosynthon, pyrazine carboxylic acid forms a dimer heterosynthon in which a weak
hydrogen bonding between carboxyl groups is readily subjugated by the preferential formation of a strong hydrogen bonding between the carboxyl group and
the heterocyclic nitrogen atom [8]. Still, other carboxylic acids do not form
dimers at all; a handful of molecules bearing carboxyl groups arrange via the
hydrogen-bonded catemer motif.
The tessellation of organic molecules forming periodic structures in the solid
state is often dictated by intermolecular interactions that are responsible for
structural arrangements and by conformations that are adopted by molecules
in the crystal. The crystal packing in Forms I and II of aspirin exemplifies this
concept. Both crystal structures exhibit hydrogen-bonded dimers between carboxyl groups that are arranged into two-dimensional layers. The distinction
between the two crystal structures lies in whether the interlayer hydrogen bonding forms dimers (Form I) [28] or catemers (Form II) [29], as depicted in
Figure 4.5. The two interlayer arrangements are practically isoenergetic [30],
which explains why domains of both solid forms can occur in intergrowth structures [31]. The origin of polymorphism in aspirin crystals is, however, due to a
competition between intramolecular geometry relaxation and enhanced intermolecular interactions in the crystal [32].
Molecular conformations in the crystal structures of a simple diarylamine,
2-(phenylamino) nicotinic acid, also provide a fine probe to control the formation
of dimer homosynthons versus catemer heterosynthons. The molecule contains
both carboxyl and pyridyl functional groups, and its four different crystal
4.3 Intermolecular Interactions in Organic Crystals
(a)
0
c
b
a
(b)
0
a
b
c
Figure 4.5 Interlayer hydrogen bonding motifs in (a) Form I (refcode: ACSALA02) and
(b) Form II (refcode: ACSALA13) of aspirin. Hydrogen bonding is denoted as dashed line.
structures are characterized by hydrogen-bonded dimers between neighboring
carboxyl groups (i.e. homosynthons) and hydrogen-bonded chains between carboxyl and pyridyl groups (i.e. heterosynthons). The two crystal packing motifs in
Forms α and δ of 2-(phenylamino) nicotinic acid are shown in Figure 4.6.
(a)
(b)
Figure 4.6 Hydrogen-bonding motifs and crystal packing in (a) Form α (refcode: TOKSAO)
and (b) Form δ (refcode: TOKSAO03) of 2-(phenylamino) nicotinic acid.
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4 Intermolecular Interactions and Computational Modeling
Structural analysis and computational methods have demonstrated that the
capability of forming homosynthons or heterosynthons in the crystal structures
of 2-(phenylamino) nicotinic acid is associated with its molecular conformation
[33]. The molecule can either remain in its planar, more stable conformation
but form a weaker acid–acid homosynthon or take a twisted, less stable conformation and form a stronger acid–pyridine heterosynthon. This implies that
intermolecular hydrogen bonding can affect the molecular conformation such
that a molecule may have to adjust its spatial arrangement in order to interact
more strongly with its neighboring molecules.
A common deficiency of the graph set and the supramolecular synthon
approaches for the crystal structure description is that both methods represent
intermolecular interactions in a crystal without any indication as to the strength
and/or importance of these interactions in controlling crystal packing. In addition, the methodology based upon supramolecular synthons mainly amounts to
a knowledge of the strength and directional characteristics of hydrogen bonding
[34]. Yet, there is a plethora of other weak interactions, such as aromatic and
halogen interactions, that are known to have specific effects on crystal packing
leading to synthon control.
In the crystal structures of the isomeric ortho- and meta-aminophenol, the
hydroxyl group forms the common, dominant hydrogen bonding with the
amino group. The second atom of the amino group, however, participates in
an intermolecular interaction between the amino group and the π system
instead of forming another hydrogen bond with the hydroxyl group of a neighboring molecule similar to the crystal structure of para-aminophenol. In planar
aromatic compounds the nondirectional, aromatic interactions can alter the
structural arrangement, thus resulting in a characteristic T-shaped herringbone
synthon that, in specific instances, prevents the geometry and topology of even
the strong hydrogen-bonding motif. The driving force for the existence of the
weaker π interactions in the ortho- and meta-aminophenol stems from the need
to attain a herringbone structure that contains neighboring molecules related by
the inclined T-geometry of the phenyl rings. Such geometry renders the heteroatoms inaccessible for the formation of two conventional amino–hydroxyl
hydrogen bonds.
4.3.3 Impact of Intermolecular Interactions on Crystal Properties
Intermolecular interactions not only rule the assembly process, leading to the
formation of the ordered architecture, but also control the dynamic behavior
and properties of the final crystal. Most physical properties are indeed a function of the relative orientation of molecules and/or functional groups in a crystalline solid. In hydrocarbon aromatic systems, for instance, the phenyl groups
pack with specific geometries, leading to crystals characterized by high crystallinity and low solubility.
4.3 Intermolecular Interactions in Organic Crystals
Different crystal forms from the same organic molecule, known as polymorphs, show distinct X-ray diffraction patterns and have a specific melting
point, solubility, and mechanical strength in addition to other well-defined
physicochemical properties. As such, the arrangement or packing of the molecules in a crystal can and does lead to alteration in the physical, chemical, and
mechanical properties of the solid [13, 35]. Crystal polymorphism is particularly
relevant to pharmaceutical development. Two properties vital to the development of a quality drug product are bioavailability and solid-state stability.
Solubility and dissolution rate are physical characteristics directly related to bioavailability. Differences in solubility may have implications on the absorption of
the active pharmaceutical ingredient from its dosage form by affecting the dissolution rate and possibly the mass transport of molecules. Higher solubility and
faster dissolution rate can lead to measurable increases in bioavailability and,
presumably, therapeutic efficacy. However, a solid form with higher solubility
or faster dissolution rate is metastable and tends to convert to a thermodynamically more stable crystalline form over time.
A well-known example of the influence by intermolecular interactions on
physical properties and thus on controlling crystal packing is the antiretroviral
drug ritonavir, marketed as Norvir® [36]. A more stable and less soluble crystalline phase, referred to as Form II, appeared in the formulation that failed dissolution testing. Ultimately, the pharmaceutical product was withdrawn from
the market because the manufacturing process was no longer able to consistently and reliably produce the desired crystal form (Form I). The product
was then reformulated using the most stable polymorph (Form II). Differences
in solubility and dissolution rate between the two crystalline forms are related
to their hydrogen-bonding motifs, thus resulting in the stabilization of their
respective crystal lattices to a differing extent. In the crystal structure of
Form I, ritonavir molecules stack to form a β-sheet structure, which is comprised of amide–amide and hydroxy–thiazole hydrogen bonding. On the
contrary, in the crystal structure of Form II, ritonavir molecules form hydrogen-bonded one-dimensional stacks, in which each molecule is hydrogen
bonded to two other molecules through amide–amide, amide–hydroxy, and
hydroxyl–amide hydrogen bonding. A hydrogen-bonding propensity study
showed that Form I entails statistically improbable intermolecular interactions
between hydroxyl–thiazoyl and ureido–ureido groups. On the other hand,
Form II forms hydrogen-bonded patterns such that all of the strong hydrogen-bond donors and acceptors are satisfied. Therefore, the faster dissolution
rate of Form I is ascribed to the hydrogen-bond donors and acceptors that
are exposed at the surface of the crystal, giving rise to stronger, attractive interactions with hydrogen-bonding solvents [37].
Another well-documented case of the influence of intermolecular interactions on crystal properties is that of the Parkinson drug rotigotine [38], which
has been recalled due to the occurrence of a new crystalline form, in the form of
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4 Intermolecular Interactions and Computational Modeling
“snow-like crystals” in Neupro® patches. The new polymorph, referred to as
Form II, shows a greatly enhanced thermodynamic stability. The two polymorphs, Forms I and II, exhibit similar hydrogen-bonding motifs, that is,
one-dimensional zigzag chain. The example highlights the consistency of primary structural motifs, governed by relatively strong interactions; however,
weaker interactions can dramatically alter the three-dimensional arrangement
of the dominating structural motifs.
4.4 Techniques for Intermolecular
Interactions Evaluation
Intermolecular interactions can be evaluated either analytically or computationally. However, direct measurements of intermolecular interactions are
not feasible experimentally. The experimental methods, such as crystallography
and spectroscopy, are to a greater or lesser extent indirect. While the experimental measurements can provide evidence of the existence of intermolecular
interactions, particularly hydrogen bonding, the experiments alone may not
give conclusive information on their chemical and/or structural origins. Intermolecular interaction energies are not directly measured by any experimental
method; rather relative energies are indirectly inferred by some thermophysical
properties or spectral parameters, which are functionally correlated with intermolecular interactions. Theoretical and computational methods complement
the experimental measurements by allowing for the accurate calculation of
the intermolecular interaction energy and by providing insights into the physical origin of the intermolecular interaction effects on a chemical system. The
following represents a summary of the nature of experimental methods and
quantum chemical calculations and is intended to provide the framework necessary to comprehend the purpose of each method and evaluate the quality and
reliability of a given calculation.
4.4.1 Crystallography
Studying crystal structures of organic molecules by X-ray diffraction and neutron scattering provides valuable insights into the spatial arrangement of the
atoms and the molecular packing in the crystal lattice. A crystal structure determination by X-ray diffraction consists of measuring the electron density.
A crystal is subjected to a narrow beam of intense X-rays. The amplitude
and the positions of the scattered X-ray waves from the crystal are measured
experimentally. The result is a map of the crystal that shows the electron density
distribution, which may be interpreted to find the coordinates for each atom
in the molecule. Crystallography allows the determination of molecular
4.4 Techniques for Intermolecular Interactions Evaluation
geometrical parameters, including the distances between the atoms involved in
the intermolecular bond, the angles between the vectors connecting the atoms
in the intermolecular bond, and deviations of a functional group involved in an
intermolecular interaction from planarity. The resulting crystallographic data
can be used to compare the geometrical properties (i.e. bond lengths, bond
angles, and torsion angles) and make inferences about bond strengths and, ultimately, the relative crystal structure stability for a set of organic compounds.
The positions of atoms in the unit cell of a crystal can be determined by X-ray
diffraction methods with an accuracy that increases with the number of electrons in the atom. This means that the location of hydrogen atoms by the conventional X-ray technique of crystal structure analysis shows considerable
difficulties, owing to their very small scattering power for X-rays. Moreover,
in a hydrogen atom the electron is not generally located near the atomic
nucleus, but rather is involved in a covalent bond to a neighboring atom. As
such, the positions of hydrogen atoms located using X-rays are systematically
displaced toward the atom to which the hydrogen is bound; consequently bond
lengths from hydrogen to other elements are consistently shorter than their
“true” values even in a high-precision experiment. The problem worsens at
higher temperatures because the bonded electrons are subject to increased thermal motion, resulting in shortened average position apparent from the X-ray
data. Thus, the position of all protons in a crystal structure determined by
X-ray diffraction must be adjusted by using average neutron values or
ab initio (first principles) optimization.
Because the scattering power of an atom is not dependent on atomic numbers, neutron diffraction is able to describe all atoms in organic crystal structures, as well as detect hydrogen atoms at the same level of precision. It is
important to note that neutrons are scattered by the nucleus rather than the
electrons, so that a neutron scattering density distribution gives the positions
of the nucleus. Although in some cases refined techniques have enabled hydrogen atoms to be directly located by X-ray diffraction, and although in a few other
instances their positions have been found by neutron scattering, in the majority
of organic crystal structures, the location of hydrogen atoms is determined only
by inference.
4.4.2
Spectroscopy
Spectroscopic methods, including infrared, Raman, and nuclear magnetic resonance (NMR), are used to investigate intermolecular interactions, specifically
hydrogen bonding, in the solid state [6]. Both infrared and Raman spectroscopies probe the fundamental vibrational frequencies of organic molecules. The
formation of a hydrogen bond affects the vibrational modes of the functional
groups involved. Thus, band shifts or width changes can provide information
on the local environment of the functional groups. The stretching vibration
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4 Intermolecular Interactions and Computational Modeling
of the bond between the hydrogen and acceptor atoms is generally observed to
shift to lower frequency as a consequence of the weakening of that bond. In
principle, the shift in the frequency of the hydrogen-acceptor stretch is often
used as the simplest and most direct spectroscopic criterion for a hydrogenbonding formation [7]. For relatively simple systems, intermolecular effects
in the solid state can be also studied quantitatively by infrared or Raman spectroscopies. Nevertheless, in complex systems overlapping bands may prevent
the deduction of molecular details necessary for deriving structure and interaction information.
Solid-state NMR spectroscopy is a versatile technique for the description of
hydrogen-bonding interactions due to the sensitivity of the magnetic shielding
parameter to the local electronic environment. Specifically, 1H-NMR is well
suited for studying both structural and dynamic aspects of hydrogen bonding
in solids by directly probing the hydrogen atoms involved in hydrogen bonds.
The most direct information can be derived from spectra of magnetically active
nuclei of atoms participating in hydrogen bonding, such as 1H, 2H, 13C, 15N, 19F,
and 31P. The main measurable NMR parameters are chemical shifts and scalar
spin–spin couplings between adjacent and closely located nuclei. The chemical
shift is a specific characteristic of magnetic shielding of a nucleus by the electron
shell of a given atom in a molecule. The scalar spin–spin coupling constant is a
characteristic of indirect interaction energy of magnetic moments of nonequivalent nuclei through the electron shell and determines the multiplet structure
of signals. The formation of a hydrogen bond leads to a downfield shift of the
proton signal of the donor group due to a decrease in the electron magnetic
shielding, which increases with the increase of hydrogen-bond strength. Further, scalar spin–spin couplings between nuclei of proton donors and proton
acceptors give valuable information about the overlapping of electron clouds
of partner groups upon formation of a hydrogen bond. Various studies [39] have
shown that qualitative and/or semiquantitative correlations can be drawn
between NMR parameters, related to chemical shift and scalar spin–spin
coupling, for various types of nuclei in the vicinity of hydrogen bonds and
parameters describing the hydrogen-bond geometry. In comparison with measurements of stretching vibration frequencies, the advantage of using NMR
parameters is that the experimental errors of NMR measurements are usually
lower than those of infrared measurements, since hydrogen-bonding interactions considerably broaden vibration bands.
4.4.3 Computational Methods
A proper quantitative evaluation of intermolecular interaction energies is a prerequisite for the understanding, control, and, ultimately, prediction of structural, thermodynamic, and physical properties of molecular organic crystals.
The levels of computational calculations to evaluate intermolecular interaction
4.4 Techniques for Intermolecular Interactions Evaluation
energies of organic crystals include (i) ab initio quantum mechanical calculations, which use the Hartree–Fock (HF) self-consistent field theory with
one-electron molecular orbitals or the density functional theory (DFT);
(ii) semiempirical molecular orbital calculations, which are based on the same
or related quantum mechanical principles as ab initio methods but make
approximations or assumptions to simplify the computations and include semiempirical parameters based on experimental data; and (iii) molecular mechanical calculations, which are based on classical Newtonian mechanics but use
quantum mechanical concepts to formulate empirical equations.
Quantum mechanics (QM) provides the fundamental laws for calculating the
properties of individual molecules and their intermolecular interactions. The
fundamental postulate of QM is that a wave function exists for any chemical
system and that appropriate operators return the observable properties of the
system. Quantum mechanical computations are based on solving the Schrödinger equation:
ΗΨ = EΨ
41
where Ĥ is the Hamiltonian operator, used to describe the total energy of the
system, and Ψ is an amplitude function, which is the eigenfunction with E as
the eigenvalue. Computations derived directly from theoretical principles
(e.g. Schrödinger equation) are named ab initio calculations. The most common
type of ab initio calculation is the HF calculation, which does not include
coulombic electron–electron repulsion. In essence, HF calculations use oneelectron orbitals; thus they cannot account for the simultaneous behavior of
several electrons (i.e. electron correlation). The HF theory, which as the alternative name self-consistent field indicates, only allows each electron to respond
to the average field of all the other electrons. Not only does the electron correlation lower the energy of a system, it also affects the overall electron density of
the system. An alternative ab initio method is DFT, in which the total energy is
expressed in terms of total electron density rather than wave function. In general, ab initio calculations give good qualitative results and increasingly quantitative results, as the given molecule is smaller. A detailed perspective of the
DFT approach is provided in the next section.
Semiempirical calculations of molecular orbital theory are applied to molecules that exceed the size of those practically accessible by ab initio methods.
Semiempirical methods involve developing empirical parameters by fitting
experimentally observable features to a set of potential functions in order to
reproduce experimental data to the highest degree possible. The underlying
assumption is that there is transferability of the empirical potential functions
between similar molecules. Although semiempirical calculations are much faster than ab initio calculations, the results can be slightly defective, especially if
the molecule being computed is different from molecules used to parameterize
the method.
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4 Intermolecular Interactions and Computational Modeling
Molecular mechanics (MM) is a purely empirical method that neglects
explicit treatment of electrons, relying instead on the laws of classical physics
to predict the chemical properties of molecules. In the mechanical representation, the total potential energy is computed based on the positions of those
nuclei that are the centers of mass joined together by harmonic forces. The
energy is expressed by simple classical equations, such as the harmonic oscillator and Morse potential, in order to describe the energy associated with bond
stretching, bending, rotation, and nonbonded atom–atom interactions. As a
result, MM calculations cannot treat bond formation or breakage phenomena,
where electronic or quantum effects dominate. Because the zero or reference
value depends upon the number and type of atoms and their connectivity, energies are not calculated in an accurate manner by MM and tend to be meaningless as absolute quantities. Thus, they are generally useful only for comparative
studies.
4.4.3.1 Lattice Energy
Intermolecular interactions within a crystal structure can be described by a
potential energy function, known as force field. The basic assumption of the
force field, or atom–atom, method is that the interaction between two molecules can be approximated by the sum of the interactions between the constituent atom pairs. As such, the atom–atom interactions only depend upon the
separation of the two atoms.
The lattice energy represents a global measure of intermolecular interactions
in organic crystals. The lattice energy of a crystal (Elatt) is defined as the energy
of formation of a crystal from the isolated, gas-phase molecules and is typically
evaluated as the difference between the energy of the crystal (Ecryst) and that of
its single molecule in the gas phase (Emol), according to the equation:
Elatt = Ecryst − Emol
42
The energy differences among various crystal structures of a molecular compound can be a few kJ mol−1. As such, an accurate evaluation of intermolecular
interaction energies or lattice energies of organic crystals is required in order to
predict the relative stabilities of different polymorphs and identify competing
low-energy crystal structures, which might complicate the selection of a pharmaceutical solid form and the production of pharmaceutical products.
Because the lattice energy is an energy change accompanying a transformation between gas and crystal states, corresponding most closely to sublimation,
the enthalpy of sublimation represents a direct measure of the lattice energy.
The sublimation enthalpy can be measured fairly readily from vapor
pressure measurements [40]. By assuming that the gas phase is ideal and that
gas and crystal phases have similar energy contributions from intramolecular
vibrations, the lattice energy of the selected molecular crystal can be derived
4.4 Techniques for Intermolecular Interactions Evaluation
from experimental sublimation enthalpy at a finite temperature, according to
the equation:
Hsub T = − Elatt − 2RT
43
where Hsub(T) is the sublimation enthalpy, T is the temperature at which the
sublimation enthalpy is measured, and R is the gas constant.
Quantum mechanical force field models may provide a better reliability for
the determination of lattice energies, especially of small molecular systems.
The application of higher-level quantum mechanical theories, such as the second-order Møller–Plesset perturbation (MP2) theory, remains limited to small
molecular systems due to the requirement for computational resources, namely,
processing time and memory [41]. As such, ab initio methods have primarily
been focused on HF and DFT, which do not always give qualitatively similar
results for the lattice parameters and bond distances of crystals when compared
with experimental values. The main reason is the difficulty in fully considering
and/or adequately describing van der Waals energies at large interatomic distances. The HF theory completely lacks such dispersive interactions because
it neglects electron correlation. DFT calculations, which incorporate currently
accepted exchange-correlation functionals [42–44], give the exact description
of the ground-state energy, including the van der Waals energy. Still, they fail
to capture the attractive dispersion interaction between weakly bound systems.
Since the dispersion energy is believed to be the most significant component
in the lattice energy of organic crystals, various strategies have been proposed to
improve current ab initio approaches. One strategy consists of introducing an
empirical correction to the HF or DFT method that takes into account dispersive forces. In practice, the approach augments the quantum mechanical methods for the dispersion energy with analytical atom–atom pairwise models,
which are based on interatomic distances and empirical parameters (i.e. van
der Waals radii and atomic coefficients). The empirical correction assumes
the form of a dumping function that preserves the appropriate long-range
behavior of the dispersion energy, but it tunes down at short-range interatomic
distances where HF or DFT produces reliable energy values, according to the
equation [45–48]:
Edisp R = − fd R C6 R −6
44
where Edisp is the empirical dispersion energy, R is the interatomic distance, C6
is the dispersion coefficient, and –fd(R) is the damping function, which equals
one at large values of R and zero at small values. In other words, the procedure
includes the dispersion contribution only in the regions where the HF or DFT
method does not contribute well to the intermolecular interactions. The
method has been demonstrated to produce satisfactory results among selected
molecular crystals [45, 49, 50].
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4 Intermolecular Interactions and Computational Modeling
Three forms of damping functions have been studied, with one dropping to
zero at short interatomic distances faster than the others. For crystals where the
DFT energy, including intermolecular hydrogen bonding, accounts for approximately 20–25% of the lattice energy, a stronger damping function is more
appropriate. Conversely, a weaker damping function should be used for computing the lattice energy of crystals where the dispersion energy constitutes
the most significant contribution. Crystal systems, such as aspirin and ibuprofen, illustrate the principle [50]. The lattice energy of aspirin has been calculated
as −108.3 kJ mol−1 at a suitable ab initio level of theory, DFT-B3LYP/6-31G
(d,p), and with a stronger damping function for evaluating the van der Waals
energies. The reliability of the computed lattice energy can be tested by comparing theoretical lattice energies to experimental estimates for the heat of sublimation, but corrections must be included to account for the enthalpy change of
the crystal from 0 K (the temperature at which calculations are conducted) to
the measurement temperature of the sublimation enthalpy as well as the
zero-point vibrational energy, which considers the lattice mode vibrations of
the crystal. After allowance for thermal effects and zero-point vibrational
energy, corresponding to the 2RT factor in Equation (4.3), the calculated lattice
energy of aspirin is compared with the experimental estimate of −114.7 kJ mol−1.
The lattice energy of S(+)-ibuprofen crystals, where the nature of intermolecular
interactions is mainly dispersive, has been computed to be −114.7 kJ mol−1 at the
same ab initio theory as for aspirin. By utilizing a weaker damping function, the
calculated value agrees well with the estimated lattice energy of −112.8 kJ mol−1.
Overall, by correcting with an empirically parameterized dispersion term, the
DFT method yields lattice energies that are in fairly good agreement with experimental data.
Another semiempirical force field approach for the calculation of lattice energies of organic crystals is semiclassical density sums (SCDS), usually known as
the PIXEL method [51, 52]. The PIXEL hybrid approach is based on the numerical integration of classical formulas over quantum chemical determination of
molecular electron densities, which are used to compute different physical contributions (i.e. electrostatic, polarization, dispersion, and repulsion) to the intermolecular interaction energies. Thus, the PIXEL method yields a nonempirical
coulombic energy together with semiempirical polarization, overlap repulsion,
and dispersion terms. As far as accuracy is concerned, the PIXEL method reproduces the sublimation enthalpies of organic crystals and mimics the results of
ab initio calculations with considerable accuracy at a quite modest computational cost [53]. Lattice energy results of 60 organic crystals computed by the
PIXEL approach have been compared with first principles electronic structure
calculations, which include the empirical dispersion correction to the DFT
method, referred to as DFT-D [54]. The employed methods show excellent
agreement. Both DFT-D and PIXEL approaches can provide reliable estimates
of sublimation enthalpies and in turn are robust predictive tools for computing
4.4 Techniques for Intermolecular Interactions Evaluation
intermolecular interaction energies of molecular crystals. However, the comparison between computational and experimental data shows few cases of discrepancies between theory and experiment. In particular, lattice energies of
carboxylic acids and amides computed by the PIXEL approach are systematically underestimated. It is important to note that the considered compounds
are characterized by hydrogen-bonding interactions. The discrepancy may be
due to the lack of taking into account relaxation effects, which would influence
more strongly the molecule than the crystals, thus reducing the computed lattice energy. Another general reason for the difference between lattice energies
and sublimation enthalpies stems from the inaccuracies in experiments and
uncertainties in the dependence of heats of sublimation from temperature in
connection with the temperature of the X-ray determination.
4.4.3.2
Interaction Energy of Molecular Pairs from Crystal Structures
The intermolecular interaction energy of a pair of molecules in a supramolecular structure (as in molecular crystals) is usually calculated as the difference
between the total energy of the system and the energies of the individual molecules. In the calculation of the energy of the molecular complex, each molecule
uses not only its own basis functions but also the basis set of the other molecule
to improve its own wave function, thus providing an artificially lower energy of
the complex. This effect, which is purely mathematical in origin, has no physical
meaning and is referred to as basis set superposition error [55]. One method to
correct this phenomenon is the so-called counterpoise correction [56]. The procedure corrects the atomic energies by computing the atoms in the full molecular basis set. The energy of each molecule is then calculated by using the
complete basis set of the complex, including the “ghost” functions of the other
molecule. Since these ghost functions slightly lower the energies of each monomer, the overall interaction energy is less than if they were not used.
Intermolecular interaction energies of molecular synthons extracted from the
crystal structure of benzoic acid were calculated by the counterpoise-corrected
DFT-D and MP2 methods with 6-311G(d,p) basis set [57]. The MP2 level of
theory is known to be capable of better considering the van der Waals interactions at the price of greatly increased computing resources. Benzoic acid is a
small, slightly flexible molecule, yet embodies almost all of the major types of
intermolecular interactions encountered in organic crystals. Electronic structure analysis of the optimized crystal structure of benzoic acid identified eight
pairs of intermolecular contacts. Note that the crystal structure optimization
was performed with the lattice parameters held constant while allowing fractional coordinates of all atoms to adjust, in order to correct minor structural
artifacts induced by hydrogen positions that were assigned by single X-ray
structure determination. The hydrogen-bonded dimer between carboxyl groups
(Figure 4.7a) shows the strongest intermolecular interaction of −76.19 or
−93.72 kJ mol−1 (for two hydrogen bonds in a dimer) by the MP2 or DFT-D
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4 Intermolecular Interactions and Computational Modeling
(a)
(e)
(b)
(f)
(c)
(g)
(d)
(h)
Figure 4.7 Packing motifs of molecular pairs extracted from the crystal structure of benzoic
acid (refcode: BENZAC12), featuring (a) carboxyl dimer; (b, d, and e) π–π stacking; (c)
hydrogen bonding between the carbonyl oxygen and the phenyl ring; and (f–h) close
contacts between phenyl rings.
approach, respectively. A weak hydrogen bonding between the carbonyl oxygen
and a hydrogen atom of the phenyl group (Figure 4.7c) yielded an interaction
energy of −11.97 or −16.19 kJ mol−1 by the MP2 or DFT-D method, respectively.
Three pairs of contacts featured π–π stacking, involving the carboxyl group and
phenyl, the phenyl groups, or the carboxyl groups of neighboring molecules
(Figure 4.7b, d, and e, respectively). Intermolecular interaction energies of these
contacts calculated by the MP2 method were −11.97, −9.20, and −8.83 kJ mol−1,
respectively, while those computed by the DFT-D method were −11.13, −9.73,
and −10.50 kJ mol−1, respectively. A close contact occurred between the paracarbon atom and a hydrogen atom of the phenyl ring with energy values of −5.27
or −5.15 kJ mol−1 by the MP2 or DFT-D level of theory, respectively
(Figure 4.7f ). Moreover, the interaction energies of two edge–edge contacts
between phenyl rings (Figure 4.7g and h), which are characterized by van der
Waals interactions, were −4.23 and −2.30 kJ mol−1, as calculated by the MP2
theory, or −4.14 and −3.51 kJ mol−1, as calculated by the DFT-D method.
A comparison of the interaction energies for each type of nearest neighbor pairs,
using the methods tested, is depicted in Figure 4.8. Despite the discrepancy
between MP2 and DFT-D methods when calculating the hydrogen-bonding
energy between carboxyl groups, the energy results by the two levels of theory
are in very good agreement for molecular pairs that are dominated by dispersion
interactions, highlighting the appropriate treatment of dispersion energy by
the DFT-D method augmented with the empirical dispersion correction. The
intermolecular hydrogen bonding of benzoic acid dimer is a more relevant
contribution compared with other types of intermolecular interactions, including π–π stacking arrangements, C─H─O hydrogen bonding, dispersion
4.5 Advances in Understanding Intermolecular Interactions
Molecular pair label
0
A
B
C
D
E
F
G
H
–10
Interaction energy (kJ mol−1)
–20
–30
–40
–50
MP2
DFT-D
–60
–70
–80
–90
–100
Figure 4.8 Intermolecular interaction energy computed by MP2 and DFT-D levels of theory
for molecular pairs extracted from the crystal structure of benzoic acid.
interactions, and C─H─π contacts. As such, the crystal structure of benzoic acid
is dictated by a greater dominance of centrosymmetric hydrogen-bonded
dimers, rather than by a C─H─π attraction, characteristic of aromatic
hydrocarbons.
4.5 Advances in Understanding Intermolecular
Interactions
The strength and directionality of intermolecular interactions control the
crystal packing of organic molecules and thus polymorphism. Given the strong
interest in and importance of multiple crystal structures, considerable
efforts have been made to both predict the possible existence of polymorphs
and understand the crystal packing of the molecule of interest at the electronic
level.
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4 Intermolecular Interactions and Computational Modeling
4.5.1 Crystal Structure Prediction
The ability to accurately predict the number of crystalline forms that can be
expected in a given case does not yet exist, although not for lack of effort
[58]. Though the last two decades have seen enough of an increase in computer
power to make the computational prediction of organic crystal structures a
practical possibility, polymorph prediction is still a long-term goal [59]. Much
of the relevant background on crystal structure prediction is readily available
elsewhere [60]. Herein, our focus is to provide a basic, coherent overview of
a crystal structure prediction methodology, together with illustrative examples
aimed to highlight the progress in this field.
The most commonly applied method of crystal structure prediction is based
upon a search of the global minimum in the lattice energy, that is, the structure
for which the sum of the intermolecular potential energies between all molecules in the lattice is the most favorable. By ignoring molecular vibrations
and zero-point energies, this method seeks the static, perfectly ordered infinite
crystal structure at 0 K that gives the most energetically favorable crystal packing. This classical, thermodynamic approach has been successfully applied to
the blind tests of crystal structure prediction [61–65]. Although the results from
the blind tests represent considerable progress in the prediction of the most stable form, there is still a debate as to whether all crystal structures are predictable.
In general, the methodology for crystal structure prediction involves
three steps:
1) Construct a three-dimensional molecular structure from the chemical
diagrams.
2) Search for possible molecular crystal packing arrangements.
3) Rank the relative stabilities of the generated crystal structures.
The limitations on the type of crystals that can be studied are, namely, related to
the model for the molecule, the model for intermolecular forces, and the
method for searching for the low-energy structures. Many crystal structure prediction programs are restricted to treat the molecular structure as rigid, assuming that the crystal packing forces are too small to significantly distort the
molecular geometry (i.e. bond lengths, bond angles, and torsion angles). The
molecular structure is expected to be the same in the gas and crystalline states.
As such, it is determined by an ab initio calculation of the isolated molecule.
Many methods for searching the vastness of the energy space of possible crystal structures have been used. A few are more extensive search methods, such as
CrystalPredictor [66], where millions of structures are considered in random
fashion, as a function of unit cell dimensions and molecular positions and orientations, based on a simulated dynamics process, but many new structures are
rejected from the full lattice energy optimization at an early stage. Other methods use physical insights into the basis of a crystal packing arrangements search.
4.5 Advances in Understanding Intermolecular Interactions
For instance, the MOLPAK [67] approach performs a systematic grid search
using a pseudo-hard-sphere model of molecules in common packing types
and generates a few thousands of densely packed structures for a rigid molecule.
Another approach is the PROMET [68] procedure that systematically builds up
clusters (i.e. dimers, chains, and layers) of molecules by adding crystallographic
symmetry elements. One shortcoming of this method is the lack of periodic
boundaries in generating the cluster, thus limiting its use for compounds with
heteroatoms, because the distance over which electrostatic interactions are
important are typically greater than those explored in the small clusters.
The final ranking of crystal structures, based on the minimized lattice energy,
depends upon the choice of the model for the intramolecular and intermolecular energies. The reliable prediction of the relative lattice energy requires accurate models for the intramolecular forces and the intermolecular interactions
that dominate the lattice energy of typical, hydrogen-bonded systems.
One of the main challenges associated with the crystal structure prediction is
related to the molecular flexibility. Conformational polymorphism has long
been known [69] and has often been observed in pharmaceuticals [70]. When
the molecular structure and resulting crystal packing influence one another
implicitly, predicting the crystal packing of a molecule becomes extremely
difficult. Molecular conformation and crystal packing cannot be varied simultaneously during the crystal structure prediction methodology; therefore,
assumptions are required. During the prediction of the second solid form of
aspirin, which was later experimentally found as a metastable polymorph
[29], the molecular conformation was assumed to be similar to the one in
the known Form I crystal structure [30]. This assumption turned out to be correct, even though the molecule in the experimental crystal structure does not
adopt the most stable conformation.
The fifth blind test [61] highlights that crystal structures of small and slightly
flexible molecules can be fairly easy and reliably predicted, while those of larger
and more flexible molecules and complex systems, such as salts and hydrates,
are still challenging to predict. Despite the development of methods for more
accurate crystal energies, coupled with the increasing computer power, molecular conformational diversity still represents a bottleneck in fully exploring the
structural space for large, flexible molecules. In this regard, crystal structure
prediction might not offer any breakthrough. At the time of this writing, a sixth
blind text is taking place [71]. Efforts should be devoted to address simpler questions, such as whether the tendency toward polymorphism exists and how multiple crystal forms differ in hydrogen-bonding arrangements.
Overall, the ease of crystal structure prediction depends on the molecule
itself. It is the molecular structure itself that determines whether there is a
unique intermolecular interaction synthon for the molecule to pack with itself
or whether there are many possible packing motifs that are very similar in
energy. The ultimate purpose of performing a crystal structure prediction study
151
152
4 Intermolecular Interactions and Computational Modeling
is to evaluate the types of molecular packing that are competitive in energy with
those that are experimentally known. In some cases, all of the low-energy structures may contain the same expected supramolecular synthon, such as a
hydrogen-bonded dimer, and different modes of packing the same motif are
predicted. In other cases, an unexpected hydrogen-bonding motif, which differs
from that found in the experimental crystal structures, can be predicted.
The most explicit example is provided by carbamazepine [72, 73], where a
hydrogen-bonded catemer-based crystal structure was predicted to be energetically competitive with the known solid forms containing hydrogen-bonded
dimer motifs. Although extensive crystallization screening [74] did not yield
the polymorph with the predicted hydrogen-bonding catemer motif, the new
solid form was eventually found in a solid solution with isostructural dihydrocarbamazepine [72]. Nevertheless, different hydrogen-bonding patterns do
not necessarily lead to newly discovered polymorphs. The unsuccessful, extensive search for an alternative hydrogen-bonding motif of the rigid molecule
3-azabicyclo[3.3.1]nonane-2,4-dione [75] is particularly noteworthy. Overall,
a crystal structure prediction study can either reduce or expand the amount
of experimental work needed to determine the complexity of the solid form
landscape of a molecule by either confirming that all practically important
polymorphs are known or suggesting that additional structures should be
targeted. In other words, crystal structure prediction may prove helpful as a
warning for hidden crystalline polymorphs.
4.5.2 Electronic Structural Analysis
DFT offers an alternative computational method from the traditional ab initio
wave function techniques for calculating molecular energies and properties [76].
It can provide fairly accurate estimates of molecular energies at much lower
computational cost. Based on the notion that the electron density is the fundamental quantity for describing atomic and molecular ground states [76, 77],
many electronic concepts have been developed for studying chemical reactivity
and molecular interaction. The framework and development of these concepts
constitute the so-called conceptual DFT [78–80]. By calculating and examining
how the electronic structure of a molecular system responds to electronic perturbation (e.g. change in the number of electrons in the system), the intrinsic
behavior of the molecule interacting with other systems, physically and chemically, can be uncovered. This theory bridges the gap between physicochemical
properties and underlying structural causes and allows studies of chemical reactivity and molecular interaction from the viewpoint of electron density and its
derivatives. The conceptual DFT is being actively developed and embraced for
studying chemical reactivity [81–85]. More importantly, the conceptual DFT
has been utilized to characterize intermolecular interactions of organic crystals
[32, 86–90], demonstrating great potential for studying molecular packing.
4.5 Advances in Understanding Intermolecular Interactions
The theoretical framework for evaluating intermolecular interactions and
understanding the molecular assembly in organic crystals stems from the principle of hard and soft acids and bases (HSAB) by Pearson [91], in terms of the
generalized acid–base reaction of Lewis:
A + •• B
A −B
45
The Lewis acid, A, is an electron acceptor, or electrophile, while the base, B, is an
electron donor, or a nucleophile. In general terms, acids and bases can be classified as (i) soft acid, when the acceptor atom is of low positive charge, large size,
and has polarized electrons; (ii) hard acid, when the acceptor atom is of high
positive charge, small size, and has no easily polarized electrons; (iii) soft base,
when the donor atom is of low electronegativity and high polarizability; and
(iv) hard base, when the donor atom is of high electronegativity and low polarizability. Pearson’s principle asserts that hard acids prefer to interact with hard
bases and soft acids with soft bases from the thermodynamic and kinetic standpoints. The principle has successfully rationalized most of the acid–base reactions at a qualitative level but does not allow for the quantification of hardness
and softness.
The advent of conceptual DFT was crucial for interpreting the HSAB principle quantitatively through the electronic softness and hardness concepts. As
such, the HSAB principle has been extensively applied to probe the locality
and regioselectivity of intermolecular interactions in organic crystals. In principle, when two molecules interact, their spatial orientation is determined by
local softness and hardness. These functions are called local descriptors because
they refer to the molecular site at which a given reaction occurs; however, they
do not describe the properties of the molecule as a whole [92]. Both local softness and hardness can be applied to hard and soft systems. In this framework,
larger values of local softness and hardness do not necessarily correspond to the
softest and hardest regions of the molecule, respectively. In a soft system, both
functions describe the soft site of a molecule [93]. Further, a soft region or functional group of a molecule prefers to coordinate with a soft region of another
molecule.
Within the DFT framework, the total energy of a system is a function of the
system’s electron density and is dependent upon the electronic structure and
the nuclear–nuclear coulomb repulsion energy:
W ρ, ν = E ρ, ν + Vnn ν
46
where E is the electronic energy, Vnn is the nuclear–nuclear repulsion energy,
ρ(r) is the electron density at point r in space, and v(r) is the external potential
defined by nuclear positions and charges. As a molecular system changes from a
ground state to another because of the perturbation in the number of electrons,
153
154
4 Intermolecular Interactions and Computational Modeling
N, as well as the external potential, ν(r), the system energy change to second
order can be expressed as
∂E
∂N
dE =
dN +
νr
μ
δ2 E
δv r δN
+
δE
δv r
dv r dr +
N
ρr
dv r drdN +
N
f r
1 δ2 E
2 δN 2
1
δ2 E
2 δν r δν r
dN
2
vr
η
dν r drdν r dr
N
χ r, r
47
where μ is the electronic chemical potential (i.e. the negative of the electronegativity of an atom) that characterizes the tendency of electrons to escape from
equilibrium, η is the hardness, f(r) is the Fukui function, and χ(r, r ) is the linear
response function. The differentiability of E with respect to N and ν(r) gives rise
to a series of response functions that are summarized in Scheme 4.1 and which
will be discussed in this section.
The Fukui function, derived by conceptual DFT, was introduced to quantitatively describe local softness as it pertains to electronic structural analysis. The
electronic Fukui function, f(r), is defined either as the change in electron density,
ρ(r), with the change in the total number of electrons, N, at constant external
potential, v(r), or as the sensitivity of a system’s chemical potential, μ, to an
external potential [79, 94]:
f r =
∂ρ r
∂N
μ = –χ =
=
vr
δμ
δν r
48
N
∂E
∂N ν(r)
ρ (r) =
Electronic chemical potential
(= −Electronegativity)
η=
∂2E
∂χ
=−
∂N2 ν(r)
∂N
Chemical hardness
f (2) (r) =
f (r) =
δE
δν (r) N
Electron density
∂2E
∂ρ (r)
δμ
=
=
∂N δν (r)
∂N ν(r) δν (r)
χ (r, r′) =
N
Electronic Fukui function
∂3E
∂2ρ (r)
∂f (r)
=
=
∂N ν(r)
∂N2 δν (r)
∂N2 ν(r)
Fukui function derivative
(dual descriptor)
Scheme 4.1 Energy derivatives and response functions.
∂2E
∂ρ (r)
=
δν (r) δν (r′) N δν (r′)
Linear response function
N
4.5 Advances in Understanding Intermolecular Interactions
The external potential is defined by nuclear charges and positions of a given
molecular system. Because of the discontinuity of the number of electrons [95,
96], the Fukui function can be evaluated by finite difference. As such, the nucleophilic Fukui function, f +(r), and the electrophilic Fukui function, f –(r), are
introduced as
r = ρ + r − ρ0 r ≈ ρLUMO r ; f − r = ρ0 r − ρ − r ≈ρHOMO r
+
f
−
49
In these equations, ρ (r), ρ (r), and ρ (r) represent the electron densities of anionic, cationic, and neutral species of a given molecular system, respectively [79].
The Fukui functions can be approximated as the electron densities of frontier
orbitals (LUMO, the lowest unoccupied molecular orbital, and HOMO, the
highest occupied molecular orbital), because the depletion of electrons generally occurs at the HOMO while the addition of electrons occurs at the LUMO.
The difference between f +(r) and f –(r) yields the dual descriptor or secondorder Fukui function, f (2)(r) [79, 97, 98], which is defined as the second derivative of the electron density with respect to the number of electrons, at constant
external potential:
+
f
2
r =
∂2 ρ r
∂N 2
0
=f
νr
+
r − f − r ≈ ρLUMO r − ρHOMO r
4 10
The sign of the dual descriptor is very important to characterize the reactivity
of a site within a molecule toward a nucleophilic or an electrophilic attack. It is
shown that f (2)(r) is positive at electrophilic regions that prefer to accept
electrons and f (2)(r) is negative at nucleophilic regions that prefer to donate
electrons. Consequently, the dual descriptor can be regarded as the electron
distribution between the LUMO and the HOMO.
These DFT-based concepts are illustrated in Figure 4.9 for the Form I conformer of tolfenamic acid, whose crystal and electronic structures have been
extensively studied [90]. The similarity between the HOMO and f –(r)
(Figures 4.9a and c, respectively) or between the LUMO and f +(r)
(Figures 4.9b and d, respectively) is clearly shown. Regions that have large Fukui
functions are susceptible to electronic perturbation, which is defined as either
an increase or decrease in electron density, and bear large polarizability. The
dual descriptor isosurface, depicted in Figure 4.9e, illustrates both electrophilic
and nucleophilic regions of the conformer in Form I of tolfenamic acid. On the
other hand, electron density (Figure 4.9f ) seems to be just indicative of the
molecular shape, which represents the repulsive region of electron density preventing other regions of electron density from occupying the same space.
The Fukui functions and dual descriptor, being local functions at every point
(r) in space, cannot characterize the ability of a particular functional group of a
molecule to interact. As such, a convenient yet effective approach to quantify
the local electronic properties pertinent to the locality of intermolecular
155
156
4 Intermolecular Interactions and Computational Modeling
(a)
(b)
(c)
(d)
(e)
(f)
Figure 4.9 Isosurfaces of the single molecule of tolfenamic acid Form I : (a) highest occupied
molecular orbital, (b) lowest occupied molecular orbital, (c) electrophilic Fukui function,
(d) nucleophilic Fukui function, (e) dual descriptor, and (f ) electron density. The values of
isosurfaces are 0.02 a.u. for the frontier orbitals and electron density and 0.002 a.u. for the
Fukui functions and dual descriptor, respectively. Source: Adapted from Mattei and Li [90].
Reproduced with permission of Elsevier.
4.5 Advances in Understanding Intermolecular Interactions
interactions is the so-called condensed Fukui functions [99, 100]. The approach
consists of integrating the Fukui functions over atomic regions and using atomic
charges for partitioning the electron density, in analogy with the population
analysis procedure. This can be thought of as a rigorous method of assigning
partial charges on the atoms. Combined with the finite difference approximation, similar to Equations (4.9) and (4.10), condensed Fukui functions and dual
descriptor can be calculated from the atomic charges of anionic, natural, and
cationic species of a molecule. Obviously, the atomic charge values will be sensitive to both the partitioning scheme and the level of calculation of the electron
density function. Because there is no observable property associated with the
partial atomic charges, there is not a reference value to which computed values
can be compared; thus, the accuracy cannot be evaluated.
Various population analysis schemes, including Mulliken [101], Hirshfeld
[102], Bader’s atoms in molecules (AIM) [103], and natural bond orbital
(NBO) [104, 105], can be employed to partition or condense electron density
into individual atoms. Mulliken and NBO analyses are based on molecular orbitals calculations, while the Hirshfeld procedure and the AIM method are based
on the electron density distribution. Each of these methods has its own merits
and disadvantages that are briefly discussed below.
The historically first scheme of the Mulliken population analysis is based on
the linear combination of atomic orbitals and thus the wave function of the molecule. Conceptually, the electrons are distributed among the atomic orbitals,
depending upon the degree to which atomic orbital basis functions contribute
to the overall wave function. This means that shared electrons may be partitioned equally between the atoms on which the basis functions reside. This
still-popular electron partitioning scheme has a disadvantage in that the results
are sensitive to the basis set, so comparison of atomic charges from different
levels of theory is not possible. Moreover, the calculated population can have
unphysical negative numbers. To alleviate these shortcomings, in the NBO population analysis, the atomic orbitals are orthogonalized. The NBO method has
been designed to give a quantitative interpretation of the electronic structure of
a molecule in terms of Lewis structure. NBO charges prove to be robust in electron population analysis against changing the basis set [106]. In comparison to
other methods, however, NBO charges tend to be among the largest in magnitude. Bader’s AIM approach, with a quantum mechanical basis, relies on properties of the electron density and not on basis sets. The method uses physical
space partitioning; that is, it divides the space of a molecular system into atomic
“basins” separated by the so-called “zero-flux” surfaces in the gradient of the
molecular electron density, on which the flow of electrons between subsystems
vanishes. As a result, the AIM method represents discrete, nonoverlapping
atomic fragments associated with each nucleus. Within the AIM theory, partial
atomic charges are defined as nuclear charges less the total number of electrons
residing within the atomic basin. As such, the density contained within a basin is
157
158
4 Intermolecular Interactions and Computational Modeling
summed (or integrated) to determine the net atomic charge. Yet in the Hirshfeld
partitioning of the electron density, the molecular electron density is decomposed into atomic contributions according to a weight function, such that
the atomic fragment electron density, ρa(r), is given by [24]
ρa r = ωa r ρ mol r
4 11
where ωa(r) is the weight function for each atom in a molecule and ρmol(r) is the
molecular electron density. Unlike the Bader’s AIM method, the Hirshfeld partition scheme yields overlapping, nonspatially confined atomic fragments. For
our purposes, we have restricted ourselves to computing partial atomic charges
in terms of NBO and Hirshfeld methods.
Alongside the body of preceding work, condensed Fukui functions and dual
descriptor calculations have been applied to evaluate the root cause of the difference in hydrogen-bonding strength between the packing motifs in known
crystal structures of conformational polymorphs – either between carboxyl
dimers or between carboxyl dimer and carboxyl–pyridyl catemer. The 2-(phenylamino)nicotinic acid system, which bears both carboxyl and pyridyl moieties,
serves well as an illustrative application of the conceptual Fukui function in the
enumeration of potential hydrogen-bonding donors or acceptors [107]. Such a
molecule can adopt either a planar conformation in the dimer crystal packing or
a more twisted conformation in the catemer heterosynthon. The DFT properties were calculated based on the NBO partitioning scheme. The calculated condensed Fukui functions and dual descriptor for selected atoms of the molecule
in both conformations are gathered in Table 4.2. In the planar molecular conformation, the oxygen atom of the carboxyl group has a high positive value of
Table 4.2 Condensed Fukui functions and dual descriptors of the carbonyl oxygen and the
pyridyl nitrogen of the 2-(phenylamino)nicotinic acid single molecule in its planar (a) and
twisted (b) conformations, computed by B3LYP/6-311G++(2d,p) in gas phase.
Electronic property
Carbonyl oxygen
Pyridyl nitrogen
(a)
f+
f
−
f (2)
0.126
0.049
0.030
0.050
0.096
−0.001
0.128
0.054
(b)
f+
f
−
f (2)
0.034
0.058
0.094
−0.014
Source: Adapted from Li et al. [107].
4.5 Advances in Understanding Intermolecular Interactions
dual descriptor, making it electrophilic and thus a poor hydrogen-bonding
acceptor compared with the pyridyl nitrogen, which has a negative dual descriptor. As such, the pyridyl nitrogen, being nucleophilic, offers greater ability to
donate electrons to an electron-deprived hydrogen forming a stronger hydrogen bonding. Conversely, the carbonyl oxygen is reluctant to share electrons
in spite of its two lone pairs of electrons. The positive value of the dual descriptor of the carbonyl oxygen stems from the local dominance of the LUMO over
the HOMO. The local dominance of the LUMO is indicated by the larger value
of the nucleophilic Fukui function, 0.126 e, compared with the lower value of the
electrophilic Fukui function, 0.030 e. In the twisted molecular conformation, the
pyridyl nitrogen becomes more nucleophilic as compared with that in the planar
conformation with a dual descriptor value of −0.014 e. This further corroborates
that the pyridyl nitrogen is a better hydrogen-bonding acceptor than the carbonyl oxygen. A significant conformational change can occur if there is any perturbation in the electron density, influencing the electronic structure of the
molecule and, in turn, intermolecular interactions.
Condensed properties, including Fukui functions and dual descriptor, were
also computed according to the Hirshfeld partition scheme of the electron density. A major advantage of the Hirshfeld surface, by virtue of its definition, is that
surfaces of adjacent molecules in a crystal are in contact with each other, partitioning out the maximum space occupied by a molecule without overlapping
with surfaces of neighboring molecules. The application of the DFT-based concepts mapped on Hirshfeld surfaces has been demonstrated for benzoic acid
[57]. The Fukui function, being the correct, local electronic property for predicting the regioselectivity of soft-type interactions, was mapped on Hirshfeld surfaces of hydrogen-bonded dimers and π–π stacking packing motifs, as shown in
Figure 4.10. Fukui functions calculated from the crystal were mapped to the
Hirshfeld surfaces and compared with the results from the single molecule in
order to gain further understanding of crystal packing. The Fukui functions
obtained from the crystal and the molecule of benzoic acid show the largest
values on the Hirshfeld surface between the carboxyl groups; specifically, the
electrophilic Fukui function is predominant near the carbonyl oxygen, while
the nucleophilic Fukui function seems to be larger near the hydroxyl group.
The hydrogen-bonded dimer between neighboring carboxyl groups matches
with regions of relatively large electrophilic and nucleophilic Fukui functions,
while the π–π stacking between neighboring carboxyl groups matches with
regions of large nucleophilic Fukui functions. This means that matching these
electronic properties can decide the intermolecular interaction strength. The
Hirshfeld surface has proven to be a useful visualization tool for identifying
the dominant intermolecular interaction in benzoic acid. The similarity
between crystal- and molecule-based Fukui functions suggests that the intermolecular interactions in the crystal are governed by the electronic properties
computed from the single molecule. As such, the chemical information
159
160
4 Intermolecular Interactions and Computational Modeling
(a)
(b)
0.008
0.005
0.006
0.004
0.003
(c)
0.002
0.001
0.004
(d)
0.000
0.002
0.000
Figure 4.10 Hirshfeld surfaces of the hydrogen-bonded dimer mapped with crystal-based
(top of each motif ) and molecule-based (bottom of each motif ) (a) nucleophilic and
(b) electrophilic Fukui functions. Hirshfeld surfaces of the π–π stacking mapped with crystalbased (top of each motif ) and molecule-based (bottom of each motif ) (c) nucleophilic and
(d) electrophilic Fukui functions. Source: Adapted from Zhang and Li [57]. Reproduced with
permission of Royal Society of Chemistry.
embodied in the molecule can be used to rationalize the type of intermolecular
interactions experienced by molecules in organic crystals.
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167
169
5
Polymorphism and Phase Transitions
Haichen Nie and Stephen R. Byrn
Department of Industrial and Physical Pharmacy, Purdue University, West Lafayette, IN, USA
5.1
Concepts and Overview
Polymorph, a terminology originated from the Greeks (poly for “much/many”
and morph for “shapes/forms”), is employed in crystallography to describe crystals with same chemical compositions but different molecular arrangements
and/or different conformations [1]. Perhaps, most common examples of polymorphism (actually allomorphism) are graphite and diamond. As we know,
both graphite (polyaromatic sheets) and diamond (tetrahedral lattice) are composed of carbon atoms, but they have significant different properties and
appearance due to different internal structures (Figure 5.1). In chocolate industry, cocoa butter has six polymorphs with different stability and melting temperature. Hence, the chocolate manufacturers need to delicately select the
appropriate crystalline form of cocoa butter to ensure the suitable melting point
and good stability during storage [2].
For pharmaceutical compounds, different internal structures can also lead to
polymorphic modifications. Typically, there are two mechanisms, nominated as
packing polymorphism and conformational polymorphism, used to categorize
the crystalline lattice of polymorphs. For packing polymorphism, molecules
with same chemical structure and rigid conformational structures are packed
into various three-dimensional unit cells. On the other hand, for conformational polymorphism, molecules with flexible conformational structures are
typically folded in different shapes in the crystal lattice and thus form different
three-dimensional structures [3]. Spiperone, for instance, can exist as different
Pharmaceutical Crystals: Science and Engineering, First Edition.
Edited by Tonglei Li and Alessandra Mattei.
© 2019 John Wiley & Sons, Inc. Published 2019 by John Wiley & Sons, Inc.
170
5 Polymorphism and Phase Transitions
Graphite
Diamond
Figure 5.1 Examples of polymorph: diamond and graphite.
molecular conformations due to the presence of a flexible carbon chain [4].
Hence, the two different molecular conformations contribute the formation
of two different conformational polymorphs, displayed in Figure 5.2, which have
different unit cells and densities [4, 5]. Some pharmaceutical solids may exist as
amorphous form, which can be considered as a special polymorph. However,
amorphous solids, unlike the crystalline polymorphs, lack long-range order
and therefore possess neither crystal lattice nor unit cell. These distinctive
characteristics of the amorphous solids result in higher molecular mobility,
which results in higher reactivity and lower stability.
Generally, the different unit cells of polymorphs result in the different physicochemical and mechanical properties of polymorphic solids including various
thermodynamic characteristics, different spectroscopic performances, or even
different interfacial phenomena [6–8]. For pharmaceutical solids, the properties
of a given drug with different polymorphs demand careful attention to meet regulatory requirements. Table 5.1 demonstrates that the key physicochemical
5.1 Concepts and Overview
(a)
Form I
(b)
Form II
(c)
Unit cell of
form I
(d)
Unit cell of
form II
Figure 5.2 Molecular conformations of the spiperone molecule in polymorphic form I (a) and
II (b) and its corresponding unit cell (c) and (d). Source: Adapted from Koch [5].
Table 5.1 Properties of a drug substances that affected by the internal structures.
Density
Hardness
Solubility
Cleavage
Hygroscopicity
Optical properties
Spectroscopic properties
Thermodynamic behavior
Solid-state reactivity
Physical stability
Chemical stability of electrical
properties
properties of a drug can be altered when the internal structures of the drug substance are changed [9].
In some cases, polychromism (different colors) could be observed among
polymorphs. For instance, dimethyl-3,6-dichloro-2,5-dihydroxyterephthalate
has been reported to crystallize as yellow, light yellow, and white polymorphs
due to the oriental differences of the carboxylate group on the aromatic ring
and the different intra- and/or intermolecular hydrogen bonding [10–14]. Perhaps the most dramatic case of polychromism is 5-methyl-2-[(2-nitrophenyl)
amino]-3-thiophenecarbonitrile, which is also aliased as ROY for having red,
orange, and yellow forms (Figure 5.3) [16, 17]. To be specific, crystallizing this
compound from ethanol yields a mixture of yellow and red prisms. On the other
171
172
5 Polymorphism and Phase Transitions
(a)
N
C
N
H
CH3
S
NO2
5-Methyl-2-2[(2-nitrophenyl) amino]-3-thiophenecarbonitrile
Figure 5.3 Chemical
structure of 5-methyl-2-[(2nitrophenyl)amino]-3thiophenecarbonitrile (ROY)
(a); red, orange, and yellow
crystal of 5-methyl-2-[(2nitrophenyl)amino]-3thiophenecarbonitrile (b)
conformations of ROY (c).
Source: Adapted from Yu [15].
Chemical structure of ROY
(b)
Red prisms
Orange needles
Yellow needles
Light red plates
(c)
Light red
Orange
Yellow
Red
hand, orange needle-shaped crystals could be produced by crystallization from
methanol. ROY, having seven polymorphs with known structure and three polymorphs with unsolved structure, was currently reported as the most polymorphic case according to the Cambridge Structural Database (CSD) [18–22].
5.1 Concepts and Overview
Interestingly, in polarized illumination, the red form of the ROY compound has
pleochroic characteristic by showing red and orange color.
From a thermodynamic perspective, the melting points of red, orange, and
yellow crystals are 106.2, 114.8, and 109.8 C, respectively, which are very similar. Moreover, the three polymorphs with striking different colors are free of
solvent and stable at ambient temperature [15]. The primary reason for the different colors is attributed to the different conformations of each form. Specifically, single-crystal X-ray diffraction shows that the nitro groups of the yellow
and orange forms are coplanar with the phenyl ring. However, for the red form,
the angle between the nitro group and the phenyl ring is twisted 18 out of the
plane (Figure 5.3c). Moreover, the angle between thiophene moieties and the
phenyl group varies significantly in each form (red 46 , orange 54 , yellow
106 ) [15, 22, 23]. These conformational differences of the structure lead to
the changes of electron distribution/degree of electron delocalization, which
result in the change of colors [24]. Similar color change phenomenon could
be observed in salt formation whereby the electron density of the chromophore
was influenced by forming ionic interactions [25]. Hence, polychromism is treated as a particular case of conformational polymorphisms.
Noteworthy, polymorphs should be differentiated with crystal habits. Crystal
habits are crystalline materials that have same chemical composition and same
crystalline structure but different morphologies [9]. For some pharmaceutical
operations, such as filtration or lyophilization, particle morphology and size distribution can be largely influenced by crystal habits even when the crystal structure and chemical compositions are fixed.
Apart from the single entity polymorphs discussed above, polymorphs can
also be crystallized out together with solvent molecules as molecular adducts.
The molecular adducts can be further categorized into nonstoichiometric
and stoichiometric adducts. Nonstoichiometric adducts, generally aliased as
inclusion compound, contain both guest and host molecules. By definition,
the host molecules are packed as a crystalline structure with a cavity whereby
the guest molecule resides. These inclusion crystals can be further classified as
channel, layer, or clathrates [26, 27]. Such nonstoichiometric adducts are
beyond the scope of this chapter, and more details of these compounds could
be found from an informative review written by Haleblian in 1975 [7]. On the
other hand, stoichiometric adducts are generally referred to as hydrates or solvates. Solvates can be crystallized by incorporating solvent molecules into their
lattice. Similarly, when the incorporated solvent molecule is water, the molecular structure formed is termed as hydrate. Typically, the term pseudopolymorphic system is frequently used to describe solvates and hydrates. In this
chapter, a detailed example of the pseudopolymorphism and the loss of solvent
for hydrates and solvates is further discussed at the end of this chapter. The
interrelationship between single entity polymorphism, crystal habit, molecular
adducts, and amorphous forms is summarized in a flowchart (Figure 5.4).
173
174
5 Polymorphism and Phase Transitions
Chemical compound
Crystal habits
Polymorphism
(internal structure)
Crystalline
Single entity polymorphs
Pack polymorphisms
Amorphous
Molecular adducts
Conformational
polymorphisms
Polychromism
Nonstoichiometric adducts
Stoichiometric adducts
Solvent
Channel
Layer
Water
Cage (clathrate)
Solvates
Figure 5.4 Flowchart of the polymorphic system.
Hydrates
5.2 Thermodynamic Principles of Polymorphic Systems
5.2 Thermodynamic Principles
of Polymorphic Systems
As discussed earlier, each polymorph has its own packing pattern/conformations, which leads to different intermolecular interactions to variations of heat
dissipation within the crystalline lattice [28]. Therefore, each polymorph
demonstrates its own molar heat capacity, which can be generally considered
as the required energy of overcoming molecular frictions and symbolized as
Cm [29]. Typically, Cm is measured under either constant pressure (P) or constant volume (V). Hence, the corresponding molar heat capacity could be
expressed as CP,m or CV,m and quantified by Equation (5.1), where T is the absolute temperature, H stands for enthalpy, and U symbolizes the internal energy.
Based on the definition of CP,m, for a polymorphic system with form I (assume
to be more thermodynamically stable) and form II, the differences of enthalpy
(ΔHIIT I = HIT − HIIT ) and the differences in entropy (ΔSIIT I = SIT −SIIT ) between
the two polymorphs at T can be expressed as Equations (5.2) and (5.3) [30].
Under the assumption that the entropy differences between two perfect crystals
of polymorphs can be ignored at absolute zero temperature, we apply
Equations (5.2) and (5.3) to the differences of Gibbs free energy
(Equation 5.4) to get the relation between free energy and molar heat capacity
(Equation 5.5). It is important to point out that Equation (5.5) is derived under
the assumption that no phase transition occurs between the temperatures ranging from 0 to T. An extra term needs to be added for the scenario with the
phase transitions. According to the above discussion, we notice that the heat
capacity difference between the two polymorphs is a critical thermodynamic
property that enables the quantification of difference of Gibbs free energy
between the two polymorphs. It has been reported that CV,m could be estimated
by Equation (5.6) for monatomic crystals where n symbolizes the number of
moles in the crystal, v represents the frequency of oscillation, and k and h
are Boltzmann’s constant and Planck’s constant, respectively. For most crystalline solids, CP,m could be treated as CV,m for an approximation [31]:
∂H
∂T
CP , m =
P
T
ΔHIIT
ΔSIIT
; CV , m =
I
=
T
I
ΔCP, m II
I
0
=
0
ΔCP, m II
T
I
∂U
∂T
51
P
dT + ΔHII0
dT + ΔSII0
I
I
52
53
175
5 Polymorphism and Phase Transitions
ΔGIIT
I
= ΔHIIT
ΔGIIT
I
= ΔHIIT
CV , m =
k
n
T
I − T ΔSII I
T
I
+
T
I
dT −T
0
hv kT
v
54
ΔCP, m II
0
2
ΔCP, m II
T
I
dT
exp hv kT
55
56
exp hv kT −1 2
5.2.1 Monotropy and Enantiotropy
In 1888, the concepts of enantiotropy and monotropy were first introduced to
describe two different polymorphic systems [31]. For monotropes, one polymorph is stable at any temperature below the melting point, while the other polymorph is always unstable regardless of temperature. To be specific, an energy–
temperature diagram can be applied to describe such systems (Figure 5.5) [32].
The unstable polymorph would demonstrate higher free energy curve and solubility at any given temperature. The free energy curves of the two forms do not
ΔHf, form I
Liquid
Form II Enthalpies
ΔHf, form II
Form I
Energy (G or H)
176
Liquid
Form II
Monotropic system
Temperature
Free energies
Form I
Tm, form II Tm, form I
Figure 5.5 Energy–temperature plots for a monotropic system. H is enthalpy, G is free
energy, T is temperature, subscript f refers to fusion, and subscript m indicates melting point.
Source: Adapted from Brittain [1].
5.2 Thermodynamic Principles of Polymorphic Systems
cross, indicating there is no transitional point below the melting temperature.
Hence, the phase transitions between the two polymorphs are irreversible [30].
Chloramphenicol palmitate was demonstrated as a typical example of a monotropic system [33].
The other type of polymorphic system is named as enantiotropic system,
which could also be described by energy–temperature diagram (Figure 5.6).
According to Figure 5.6, we observe that both form I and form II are the stable
polymorphs over a certain temperature range. The free energy curves of two
forms cross over at a definite temperature below the melting point, which is
named as the transition temperature. At the transition temperature, a reversible
transition between two polymorphs can occur. In such a scenario, the two polymorphs are termed enantiotropes. For instance, carbamazepine, tolbutamide,
and acetazolamide were reported to have such thermodynamic behavior and
treated as enantiotropic systems [33, 34].
Energy–temperature diagrams (H-T plot or G-T) are commonly used to evaluate thermodynamic behavior of pharmaceutical polymorphs by applying modern thermal analytical techniques, such as differential scanning calorimetry
(DSC) [35]. According to Figures 5.5 and 5.6, we observe that the enthalpy
increases with the increment of temperature. On the basis of mathematical definition of CP,m (Equation 5.1), the slope of the curvature can be expressed as CP,m.
Energy (G or H)
ΔHf, form I
ΔHf, form II
Enthalpies
ΔHt, II→I = Hform I – Hform II
Liquid
Form I
Enantiotropic system
Temperature
Free energies
Form II
Ttransition
Tm, form I
Tm, form II
Figure 5.6 Energy–temperature plots for an enantiotropic system. H is enthalpy, G is free
energy, T is temperature, subscript f refers to fusion, subscript m indicates melting point, and
subscript t symbolizes the transition point. Source: Adapted from Brittain [1].
177
178
5 Polymorphism and Phase Transitions
On the other hand, based on the third law of thermodynamics, the entropy term
(TS) and temperature should be positively correlated due to the positive value of
the entropy. Hence, as we see from Figures 5.5 and 5.6, the Gibbs free energy
decreases with the temperature, since the slope of curvature is equal to the negative value of the entropy.
Returning to the monotropic systems, the energy–temperature diagram
(Figure 5.5) illustrates that the Gibbs free energy of form I is always lower than
that of form II in solid state, indicating that form I is more thermodynamically
stable. As the enthalpy of form II is higher than form I, the conversion from form
II to form I would be a spontaneous exothermic transformation. Importantly, in
such cases, although this conversion is thermodynamically favorable at all temperatures, sufficient energy is required to overcome the activation energy barrier for the solid-state transformation from a kinetic perspective [36].
On the other hand, for enantiotropic systems, the transition temperature is
considered an equilibration point whereby the two polymorphs have equal
Gibbs free energy. On the basis of Figure 5.6, below the Tt, form I exists as
the more thermodynamically stable solids due to the lower Gibbs free energy.
Moreover, the ΔHfusion of form I is higher than that of form II. Hence, the
conversion from form II to form I would be a spontaneous exothermic transformation. Furthermore, when the temperature is higher than the Tt, form II
is the stable solid phase since its free energy is lower than that of form I. Consequently, form I would undergo a spontaneous endothermic transformation to
form II.
According to the above thermodynamic discussion about polymorphs, we
notice that the Gibbs free energy difference is a critical thermodynamic parameter to evaluate the stability of each polymorph and their interconversions. The
value of ΔGII I could be estimated by calculating the ratio of fugacities ( f ),
vapor pressures (p), thermodynamic activities (a), solubilities (s), dissolution
per unit area ( J ) under sink conditions, and the rate of chemical reactions
(r) (Equations 5.7–5.10). Based on these equations, we can claim that high
energy (less stable) polymorph will have higher fugacity, vapor pressure, thermodynamic activity, solubility, dissolution rate per unit area, and rate of reactions [1, 31]:
ΔGII
I
= RT ln
fI
PI
≈ RT ln
fII
PII
57
ΔGII
I
= RT ln
aI
sI
≈ RT ln
aII
sII
58
ΔGII
I
= RT ln
JI
JII
59
5.2 Thermodynamic Principles of Polymorphic Systems
ΔGII
5.2.2
I
= RT ln
rI
rII
5 10
Phase Rule
In order to further describe the relationship between different solid phases, the
Gibbs phase rule needs to be introduced. According to Equation (5.11), C represents the number of components, and the integer is noted as the two variables
not associated with the relative amount of components (i.e. temperature and
pressure). A component is defined as chemically independent constituent of
a system [37]. For polymorphic system, the drug substance would be considered
as single component. It is worth pointing out that the number of components
would be more complicated for hydrates or solvents due to the presence of solvent molecules, which would be discussed in later sections. P symbolizes the
number of phases that exist in the equilibrium. Theoretically, a single phase
is defined as a chemically or physically homogeneous single substances/mixture. In terms of polymorphism, each polymorph would be considered as a separate phase. Moreover, F indicates the number of degrees of freedom in the
system. By definition, the number of degrees of freedom is the number of variables required to be fixed to completely specify a system at the equilibrium.
Taking a single-component system (only 1 chemical structure, C = 1) with
two different crystal packing patterns (P = 2) as an example, the degree of freedom equals 1, which simply means at the chosen pressure, the temperature is
fixed as the transition temperature:
P+F =C +2
5 11
Hence, we can summarize that only one phase can be present at the given
temperature or pressure unless at the transition temperature, where the two
phases/polymorphs can coexist.
5.2.3
Phase Diagrams
On the basis of the Gibbs phase rule, two types of phase diagram for singlecomponent monotropic (Figure 5.7) and enantiotropic systems (Figure 5.8)
can be generated accordingly. For Figures 5.7 and 5.8, SI–V and SII–V are the
vapor pressure–temperature curve for polymorph I and polymorph II, respectively. SI–L curve represents the melting curve of polymorph I, while SII–L
stands for that of B. Based on the melting curve, we can easily figure out the
melting point of each polymorph under atmospheric pressure, which was
denoted as Tm, I and Tm, II (the brackets indicating the unstable form). L–V
curve is the vapor pressure–temperature curve for the liquid phase. As polymorphs have the same chemical composition, the differences between
179
L
S
II)
PHigher
II –
–S
(S I – L)
(S I
Monotropic system
(2)
(S I
(S
(S II –
II –
SI–L
Liquid
II)
(Solid II)
Patm
–S
Pressure, P
Solid I
L)
(1)
L–V
Vapor
V)
SI
–V
Tm, form I
(Tm, form II)
(Ttransition)
Temperature, T
II)
S
(S
I–
PHigher
–L
Enantiotropic system
SI
(S II – L)
Figure 5.7 Phase diagram of pressure vs. temperature for single-component monotropic
system. Source: Adapted from Lohani and Grant [31] and McCrone [38].
S
S II – L
Patm
I–
L)
(S
I–
Solid I
(S
Pressure, P
2
II)
Liquid
1
SI
–V
lid
So
II
L–V
S II – V
Vapor
Ttransition
(Tm, form I)
Tm, form II
Temperature, T
Figure 5.8 Phase diagram of pressure vs. temperature for single-component enantiotropic
system. Source: Adapted from Lohani and Grant [31] and McCrone [38].
5.2 Thermodynamic Principles of Polymorphic Systems
polymorph will vanish in liquid or vapor phase. Therefore, only one liquid–
vapor phase is presented for both polymorphs [38].
The curve of SI–SII represents the equilibrium curve between the two forms,
and the dash line indicates the metastable phases. Point 1 (bracket indicates the
metastable phase) represents the three-phase transition point between solid
form I, solid form II, and the vapor. Below point 1, form I demonstrates the
lower vapor pressure, indicating the solid phase of form I is stable in equilibrium
with the vapor phase. One the other hand, above point 1, form I demonstrates
the higher vapor pressure, illustrating its solid phase is less stable in equilibrium
with vapor than that of form II. Furthermore, point 2 refers to the triple-phase
point between solid form I, solid form II, and the liquid. It could also be named
as condensed transition point, whereby form II undergoes a stable equilibrium
with the liquid phase. On the other hand, form I is in the stable equilibrium with
the liquid phase above the condensed transition point [39].
For a monotropic system (Figure 5.7), the transition point demonstrated on the
curve of SI–SII at atmospheric pressure is a virtual transition point because it is
higher than the melting point of each polymorph. This observation on the pressure–temperature diagrams matches well with the results of energy–
temperature diagrams. In contrast, for an enantiotropic system, the transition
point of the two polymorphs, which is located at the intersection of the SI–SII
curve and the Patm, is the real transition point due to the fact that it is lower than
the melting temperature of each form. Noteworthy, the impact of the pressure on
the transition temperature could be quantified by Clapeyron’s equation
(Equation 5.12), where the ΔHII I represents the heat of transition between
form I and II and the Vm, I/II symbolizes the molecular volume for polymorphs
I and II, respectively [40]. On the basis of Figures 5.7 and 5.8, we can see that the
slope of the SI–SII is sharp, while the molecular volume difference between each
form is relatively small. Hence, we could claim that the impact on the transition
point attributed by changing the pressure is negligible:
dP
ΔHII I
=
dT T VI, m − VII, m
5 12
However, for Figure 5.7, we observe at higher pressure (Phigher) that transition
point of the two polymorphs is lower than the melting point of each polymorph,
which shows enantiotropic behavior in a monotropic system. Similarly, in the
enantiotropic system, monotropic behavior will be observed at higher pressure.
Hence, the pressure and temperatures need to be specified before describing the
monotropic and enantiotropic system [41]. A more strict thermodynamic definition of monotropic system is the system with a metastable three-phase transition point among form I, form II, and the vapor. Similarly, restricted definition
for enantiotropic system could be stated as the system with a stable triple point
among form I, form II, and the vapor.
181
182
5 Polymorphism and Phase Transitions
5.2.4 Phase Stability Rule
Several thermodynamic rules have been introduced and applied since 1926 to
predict whether the relationships between polymorphs belong to enantiotropic
or monotropic systems. These rules include heat of transition rule, heat of
fusion rule, entropy of fusion rule, heat capacity rule, density rule, and infrared
rule. The details of these rules and their applications are discussed as follows.
5.2.4.1 Heat of Transition Rule
Heat of transition rule is considered as the rule of thumb to predict the relationship between the polymorphs. It has been reported that this rule can accurately
predict 99% of the polymorphic cases except for some special cases of conformational polymorphism [42]. To be specific, we observe an exothermic phase
transition occurring at a certain temperature, and there are no thermodynamic
transitions below this point. We could conclude that this system is a monotropic
system. Likewise, two polymorphs are enantiotropically related when we
observe an endothermic phase transition point, and the thermodynamic transitions occur below this specific point. Figure 5.6 illustrates the heat of transition
rule as an example. The enthalpy difference from form I to form II is a positive
value (ΔHI II = HII – HI > 0), indicating an endothermic phase transition at the
transition temperature. Below this point, form II could spontaneously transit to
form I. Hence, we claim that the two polymorphs demonstrated in Figure 5.6 are
enantiotropically related.
Although the heat of transition rule can be satisfactorily applied in most cases, it
is important to point out the two underlying assumptions of this rule. First, there
are no intersections between the two curves of the enthalpy. Second, the free
energy isobars should intersect with each other. It has been reported that the
polymorphs with a significant difference of molecular conformations would demonstrate obvious discrepancies with the first assumption. Thus, this rule might
not be suitable for some special cases with conformational polymorphism [43].
5.2.4.2 Heat of Fusion Rule
We can consider that two polymorphs are enantiotropically related when we
observe that the polymorph with higher melting point has the lower heat of
fusion. Otherwise, the two polymorphs are monotropically related. The above
statement is the heat of fusion rule. To be specific, we can use Figure 5.6 as an
example again to illustrate this rule. Form II has the higher melting point in the
diagram. However, the ΔHfusion of form II is obviously lower than that of form I.
Thus, an enantiotropic system is suggested.
Noteworthy, this rule is under the hypothesis that the heat of fusion differences (ΔHfusion) between the two polymorphs is approximately equal to the heat
of transition. However, as the polymorphic transition between the two forms is a
slow process, the ΔHfusion between two polymorphs cannot accurately reflect
5.2 Thermodynamic Principles of Polymorphic Systems
the heat of transition. Therefore, a correctional term with difference in heat
capacity (CP) is introduced to the ΔHfusion, II I to more accurately predict
the heat of transition (Equation 5.13).The correctional term might also contribute to the error of predictions when the enthalpy isobars of the two polymorphs
diverge or the difference of the melting temperature between two forms is larger
than 30 K [30]. These exceptions of the heat of fusion rule should be noticed
before the application of the rule:
ΔHII
I
= ΔHf , I − ΔHf , II +
Tf , II
Cp, liquid − CP, I dT
5 13
Tf , I
5.2.4.3
Entropy of Fusion Rule
For the entropy of fusion rule, an enantiotropic system can be identified as the
polymorph with higher melting point but with lower entropy of fusion. The
entropy of fusion of each form can be calculated by Equation (5.14). In contrast,
monotropically related polymorphs can be identified as a polymorphic system
where with the higher melting point form has higher entropy of fusion:
ΔSf =
5.2.4.4
ΔHf
Tf
5 14
Heat Capacity Rule
The heat capacity rule is limited in application due to the difficulty of measuring
the small differences of heat capacity between polymorphs. Theoretically, the
heat capacity rule states that if a polymorph has higher melting point and a
higher heat capacity, then the polymorphic system has an enantiotropic relationship. Conversely, if a polymorph has higher melting temperature but lower
heat capacity, the system is identified as a monotropic system.
5.2.4.5
Density Rule
Density rule applies to a non-hydrogen-bonded system at absolute zero. This
rule states that the most stable form has the largest density due to the strong
intermolecular van der Waals interactions. In other words, crystal structures
with the most efficient packing will show the lowest free energy. However, in
some cases, the hydrogen bonds in the crystalline lattice will give the metastable
polymorph closer molecular packing and higher density. However, the stable
polymorph of acetaminophen is shown to have a lower density than that of
the metastable form, which is an exception of the density rule.
5.2.4.6
Infrared Rule
In contrast to the density rule, the infrared rule is mainly applied to hydrogenbonded polymorphs. It states that the polymorph with the higher bond
183
184
5 Polymorphism and Phase Transitions
stretching frequency would demonstrate higher entropy. The underlying
assumption of this rule is that the bond stretching vibrations are correlated with
the rest of the molecule.
5.2.5 Crystallization of Polymorphs
5.2.5.1 Ostwald’s Rule of Stages
In pharmaceutical industry, polymorphs can generally be crystallized from the
supersaturated solution by using solvent evaporation, cooling the solution from
supersaturation, or adding antisolvent [39]. However, it has been observed that
the unstable form is generally obtained first and then transits into the stable form
during the crystallization process. This phenomenon is well explained by Ostwald’s rule of stages with satisfactory. The details of the Ostwald’s rule of stages
will be introduced as follows [44, 45]. Ostwald’s step rule states that during the
crystallization process, the least stable state lying closest in the free energy to the
original state will be initially formed instead of forming the most stable state with
the lowest Gibbs free energy [45]. To be specific, this rule is illustrated in a monotropic system or enantiotropic system (Figure 5.9). For two monotropically
related polymorphs (Figure 5.9a), point A represents the initial state, which is
a metastable supersaturated solution. As the solution is cooling (temperature
decreases), the Gibbs free energy of the system is decreasing accordingly (following the arrow). As a result of applying Ostwald’s step rule, form II tends to crystallize first due to its closeness to the initial state. Similarly, for enantiotropic
systems (Figure 5.9b), as the cooling process goes through from the original state,
form II tends to be formed instead of form I. Again, Ostwald’s step rule would
provide a satisfactory explanation: Isobar of form II is closer to the original state.
It is necessary to point out that this rule is an empirical rule for the kinetics of
crystallization rather than an invariable thermodynamic law.
5.2.5.2 Nucleation
Before we go through the details of the nucleation of polymorphs, it is necessary
to briefly introduce the kinetics of the crystallization process. Generally, nucleation is the first step of crystallization, in which the nuclei are formed from the
supersaturated solution. The next step is crystal growth, in which molecules
progressively attach to the nuclei to form larger crystals. With the decreasing
concentration of the supersaturated solution, the saturated equilibrium is
achieved. At this time point, according to the Thomson equation, smaller crystals tend to dissolve into the saturated solution due to their slightly higher solubility. At the same time, larger crystals with higher solubilities tend to grow.
This process can also be summarized as Ostwald ripening [44]. As we have seen
from the crystallization process, the nucleation is the most significant step since
it determines the production of various polymorphs, which will be discussed as
follows.
5.2 Thermodynamic Principles of Polymorphic Systems
(a)
A
Energy (G)
Form II
B
C
Liquid
Form I
Monotropic system
Tm, form II Tm, form I
Temperature
(b)
A
Energy (G)
Form II
C
B
Liquid
Form I
Enantiotropic system
Temperature
Ttransition
Tm, form I
Tm, form II
Figure 5.9 Gibbs free energy–temperature plots for a monotropic system (a) and an
enantiotropic system (b) in which the system is cooled from point A, the arrows indicating the
changing direction in the diagram.
185
186
5 Polymorphism and Phase Transitions
The nucleation can be categorized into primary and secondary nucleation. In
primary nucleation, the nuclei of substances crystallized from the supersaturated solution do not involve the induction of the crystals. On the other hand,
secondary nucleation is a process that requires the preexisting seeds to begin.
The primary nucleation can be further classified into homogeneous nucleation
(spontaneous crystallization in the bulk supersaturated solution) and heterogeneous nucleation (crystallized on the contaminated particles).
It is also critical to review the fundamental principles of thermodynamics of
nucleation. The driving force of the nucleation process is the reduction of the
free energy. In the classic nucleation model, the total Gibbs free energy (ΔGTotal)
of a cluster is algebraically governed by the volume term (ΔGvolume – favors the
accretion of molecule from a supersaturated medium) and the surface term
(ΔGsurface – favors the dissolution of molecular clusters). The above nucleation
model can be summarized into Equation (5.15), where the k is Boltzmann’s constant, γ symbolizes the interfacial free energy between the supersaturated
medium and the nuclei, v is the molecular volume, and the T is the absolute
temperature. The supersaturation ratio, termed σ, is mathematically defined
as the concentration of the solute in the saturated solution divided by the concentration of solute in the supersaturated solution. Noteworthy, the critical
cluster size (mean radius is rc) is an important factor, since its Gibbs free energy
(ΔGc∗ ) represents the free energy barrier of nucleation (Equation 5.16) and
determines the rate of the nucleation (J) by Equation (5.17):
ΔGTotal = ΔGsurface + ΔGvolume = 4πr 2 γ +
ΔGc∗ =
16πv2
3 kT ln σ
J = An exp
−ΔGc∗
kT
2
− 4πr 3 kT ln σ
3v
5 15
5 16
5 17
Furthermore, the nucleation model expressed by Equation (5.15) can be
demonstrated as a Gibbs free energy vs. radius of cluster plot (Figure 5.10)
[31, 44]. According to Figure 5.10, we observe that the surface term is the dominating factor during the early period of nucleation (r < rc), which indicates that
small nuclei formed in the initial stage tend to dissolve. As the nuclei grow to the
critical size (r = rc), the two terms balanced with each other and lead to the maximum Gibbs free energy of the critical cluster. The maximum free energy indicates the free energy barrier/activation free energy of nucleation. After the
critical point (r > rc), the cluster is termed as nucleus and could eventually grow
to a crystal.
The thermodynamic theory of nucleation discussed above can be applied to polymorphic nuclei. A polymorphic system with form I (stable) and form II
5.2 Thermodynamic Principles of Polymorphic Systems
Free energy of cluster (G)
ΔGSurface
ΔG*c
rc
ΔGVolume
Radius of cluster (r)
ΔGtotal
Figure 5.10 Plot of Gibbs free energy vs. the radius of cluster, where ΔG∗c is the activation
free energy of the cluster and rc represents the mean radius of the critical clusters.
Source: Adapted from Lohani and Grant [31] and Mullin [44].
(metastable), for instance, will undergo drastic competition of forming different
clusters during the nucleation process (Figure 5.11a) [46]. Generally, polymorphs
with lower activation free energy of nucleation (ΔGc∗ ) would have the priority to
crystallize. In this case (Figure 5.11b), the metastable polymorph II will exhibit
higher nucleation rate due to its lower free energy barrier (ΔGc∗, II < ΔGc∗, I ). The
metastable polymorph II will eventually transform into stable form I under
some thermodynamic conditions. In the solution or vapor phases, the rate of
the conversion is relatively rapid. However, in the solid phase, the rate of conversion between the polymorphs is slower. The interconversion mechanism can
be summarized into the following three steps. First, the noncovalent intermolecular forces are interrupted in the metastable form II. Second, a disordered
solid, similar to amorphous solid, is formed as the intermediate form. Last,
new intermolecular forces are formed attributed to the crystallization of the stable polymorph. The details and examples of the polymorphic interconversion
will be further discussed in the later sections.
It has been reported the rate of interconversion between polymorphs could be
affected by temperature (Figure 5.12) [34]. According to Figure 5.12, we observe
the rate of interconversion reaches the minimum at the transition temperature,
since two polymorphs coexisted in an equilibrated state. However, the conversion rate of form I to form II increases dramatically with temperature, indicating
that form II is stable form at high temperature. On the other hand, below the
transition temperature, as the temperature decreases, the conversion rate from
187
(a)
Cluster I
Nucleus I
Polymorph I
Cluster II
Nucleus II
Polymorph II
Molecule
(b)
Free energy (G)
ΔG*c, form I
ΔG*c, form II
Ginitial
Gform II
Gform I
Reaction coordinate
Rate
Figure 5.11 Competing crystallization of form I and form II (a); activation free energy of
nucleation for form I and form II (ΔG∗c ). Ginitial represents the partial free energy in the
supersaturated solution, and Gform I or II symbolizes the partial free energy of form I or
form II (b). Source: Adapted from Lohani and Grant [31] and Etter [46].
Form I ⇋ form II
Form I → form II
Form II → form I
Temperature
Ttransition
Figure 5.12 Enantiotropic system which has a temperature-dependent rate of
transformation between form II and form I.
5.3 Stabilities and Phase Transition
form II to form I reaches the maximum, indicating that form II is the unstable
form. With the further decrement of the temperature, the conversion rate from
form II to form I becomes negligible, indicating that at sufficient low temperature, form II could exist as the metastable form.
Hence, based on the above discussion related to the thermodynamic principles of nucleation, we can conclude that numerous factors can impact the products of nucleation including temperature, supersaturation, impurities, surface
of crystallization vessels, seed crystals, etc.
5.3
Stabilities and Phase Transition
5.3.1
Thermodynamic Stability
On the basis of the above thermodynamic theories, we notice that the Gibbs free
energy of the polymorphs shows various dependences on pressure and/or temperature. According to a study of the CSD, for the most cases, it has been summarized that enthalpy difference between polymorphs has the same sign with
the difference of Gibbs free energy between them at room temperature [47].
Typically, the Gibbs free energy between polymorphs is lower than 10 kJ mol−1,
which has the same scale as the kinetic energy of a molecule at room temperature
(2.5 kJ mol−1) [48]. Hence, modification of pressure and/or temperature might
able to change the thermodynamic stability of each polymorph and therefore
attribute to the form transformation. It has been reported that numerous manufacturing process with high shear mechanical stress or elevated temperatures
might result in such thermodynamic transformations. The transformation of
polymorphs during these processes would be discussed in the polymorphic interconversion section.
5.3.2
Chemical Stability
The differences between the crystal structure and conformations of polymorphs
lead to various chemical reactivities and in some cases different chemical products of reactions. The dimerization of cinnamic acid can be illustrated as a classic example of polymorphs with different chemical stability. To be specific, in
solution, trans isomerization of cinnamic acid will convert to cis-cinnamic acid
after irradiation (Figure 5.13). Three different polymorphs of cinnamic acid
(α, β, and γ) can be crystallized in different solvent systems. For instance,
cinnamic acid yields α-form in acetone; the β-form can be obtained in benzene;
γ-form can be produced in the aqueous ethanol system. Furthermore, exposing
the α-polymorph to strong ultraviolet light will form a centrosymmetric dimer.
On the other hand, the irradiation of the β-polymorph will produce a dimer with
mirror-symmetric structure. However, the γ-polymorph of cinnamic acid is not
189
OC2H5 COOH
Solution state
Solid state
Acetone
α form
Centro-symmetric
Irradiation
HOOC C2H5O
OC2H5
OC2H5
Irradiation
HOOC
COOH
Benzene
β form
Irradiation
C2H5O
OC2H5
Mirror symmetric
COOH
cis-2-Ethoxycinnamic acid
COOH
trans-2-Ethoxycinnamic acid
Aqueous
ethanol
γ form
Irradiation
No reaction
Figure 5.13 Scheme of the reactivity of the α-, β-, and γ-crystalline forms of trans-2-ethoxycinnamic acid upon
exposure to ultraviolet light.
5.3 Stabilities and Phase Transition
affected by irradiation (Figure 5.13) [49]. Carbamazepine can be considered as
another example. It has been observed that the photodecay rate of carbamazepine form II demonstrates 5- and 1.5-fold faster than that of form I [50].
Many other pharmaceutical compounds also have the polymorphic-related
chemical stability issues. For instance, methylprednisolone is a dimorphic compound. One form is stable, while the other has high reactivity when exposed
under conditions of high temperature, strong ultraviolet light, or high relative
humidity (RH) [51]. Based on the density rule, we know that higher crystal packing density will be more thermodynamically favored. Generally, it has been considered that the polymorph with more efficient crystal packing (higher density)
will be more chemically stable. However, this statement has many exceptions
due to the interference of other variables involved in the crystal lattice including
hydrogen bond, van der Waals forces, and molecular orientations. Indomethacin, for instance, exists as both α-form (the metastable form) and γ-form (the
thermodynamic favorable form). Diverging from the density rule, the density
of the α-form (1.42 g ml−1) is higher than that of the γ-form (1.37 g ml−1), indicating α-form has more efficient crystal packing. However, it has been reported
that the drastic reaction occurs between solid in α-form and ammonia vapor,
while the γ-form is almost inert to ammonia. This poor correlation between
the density and chemical reactivity can be explained by the different crystal
packing and the existence of hydrogen bond in the crystal lattice. For one thing,
the higher density of the α-form is due to the existence of one extra hydrogen
bond. For another, the α-form shows two centrosymmetric molecules in the lattice, while the γ-form demonstrates asymmetric molecules in its crystal lattice.
Hence, the α-form has a layer motif exposing its carboxylic acid group to the
surface of the crystal, which leads to the higher reactivity with ammonia gas.
On the other hand, the carboxylic acid group in the γ-form is buried inside
the lattice, which leads to the lower reactivity of the γ-form crystals [52, 53].
Thus, the chemical stability differences between polymorphs can be influenced
by various factors.
It is also important to point out that the amorphous forms of pharmaceutical
compounds are more reactive than their crystalline form due to higher free volume and molecular mobility. Early in 1965, Macek observed the differences in
the ability to withstand heating between the crystalline form and amorphous
form of potassium penicillin G. He also concluded that the amorphous forms
of potassium and sodium penicillin G show further decreased chemical stability
than their crystalline form [54]. Similar differences between crystalline and
amorphous form of cephalosporins were reported in 1976 by Pfeiffer et al.
[55]. Furthermore, the crystalline form and the amorphous form of the same
drug substances follow different paths of degradation, indicating different
underlying mechanisms. For instance, the prime degradation path of tetraglycine methyl ester (TGME) in crystalline form is the methyl transfer. However,
for the amorphous TGME, the major reaction path switches from the methyl
191
192
5 Polymorphism and Phase Transitions
transfer to polycondensation. A reasonable explanation is that the amorphous
state has higher free volume, which enables the reaction requiring higher
changes in orientation – polycondensation to occur [56]. Moreover, the supercooled liquid state (T > Tg) of the amorphous form is typically less chemically
stable than its glass state (T < Tg) due to the great molecular mobility of the
supercooled liquid state. For instance, the supercooled liquid state of Asnhexapeptide has been reported 10–100 times folds less stable than its glassy
state [57, 58].
Based on the above discussions, we notice that controlling the polymorph is a
prerequisite for addressing the chemical stability issues. In addition, selection of
excipients and choosing the appropriate manufacturing processes is also critical
to avoid chemical instability issues especially for formulating metastable polymorphs or amorphous compounds [59–63].
5.3.3 Polymorphic Interconversions of Pharmaceuticals
Based on the previous discussion, various physical properties such as solubility
or bioavailability will be altered when drugs undergo polymorphic transitions.
Hence, understanding of polymorphic transitions for drugs induced by changing temperature or pressure during manufacturing is very important, because
it is important to understand the physical stability of the selected solid-state
dosage forms [64]. In this section, several examples of polymorphic transformations of drugs are reviewed and discussed. In addition, the solution-mediated
phase transformations of drugs will be briefly introduced.
Phenylbutazone provides a classic example of polymorphic interconversions
under different pressure, temperature, or even RH. Four polymorphs of
phenylbutazone can be prepared by crystallization from different solvents
(polymorph I, from tert-butyl alcohol; polymorph II, from cyclohexane;
polymorph III, from heptane; polymorph IV, from 2-propanol/water) [65].
When pressing polymorph III into disks, it will convert to polymorph IV,
indicating that the high pressure can induce the polymorphic interconversions.
Moreover, it has been reported that temperature and RH can also attribute to
the polymorphic transmission of phenylbutazone. For instance, spray-dried
phenylbutazone prepared by applying different drying temperatures will result
in different polymorphs. Matsuda et al. also demonstrated that these transformations have a remarkable impact on the dissolution rate and intrinsic
solubility of phenylbutazone [66, 67].
5.3.3.1 Effects of Heat, Compression, and Grinding on Polymorphic
Transformation
High temperature is another factor that can induce polymorphic transformation. For instance, quantitative DSC analysis of tolbutamide shows that the rate
of polymorphic transmission increases with the increase of temperature [68].
5.3 Stabilities and Phase Transition
As most of the manufacturing processes can generate heat (i.e. compaction,
grinding, or drying), close attention needs to be paid to manufacturing of specific compounds. Several concrete cases are discussed as follows.
For example, the polymorphic transformation of chlorpropamide was investigated during compression. The results suggested that the heat generated by
the compaction process would accelerate the transformation process [69]. Sulfamathoxydiazine, for instance, has six solid-state forms (5 polymorphs and
1 amorphous form). These six forms undergo interconversions during heating
or grinding. To be specific, heat can convert all forms of sulfamathoxydiazine
into polymorph I. On the other hand, all forms can convert to polymorph III
when grinding or suspending in aqueous solution [70, 71]. The suspension reaction is a solution-mediated interconversion, which will be discussed later in this
section. The effects of grinding on the form transformation for 29 drugs were
investigated by Chan et al. 10 out of 29 drug molecules show polymorphic transformation after grinding. Moreover, their study also demonstrated the form
transformation of maprotiline hydrochloride during compression [72]. These
interesting results strongly suggested that mechanical forces during manufacturing have remarkable impacts on the interconversion between different forms.
Chloramphenicol palmitate, a monotropic system discussed in Section 5.2,
will also undergo a polymorphic transformation during ball milling. It has been
demonstrated that the required milling time for transforming polymorph B to
polymorph A was more than 150 min. However, for the sample with seed crystals of form A, the polymorphic transformation time is only 40 min [73]. This
was the first time seeds crystals were shown to influence the rate of polymorphic
interconversion. This interesting finding indicates that the presence of the stable form of crystals can accelerate the transformation of the metastable form to
the stable one. Hence the transformation kinetics for an unstable form should
be investigated adequately before it comes to the market. In addition, using the
DSC and X-ray powder diffraction, researchers also found that heating and
grinding could induce the form transformation of chloramphenicol palmitate.
To be specific, form B and form C of chloramphenicol palmitate could transfer
to form A upon heating at 82 C for 1600 min [74].
5.3.3.2
Solution-mediated Phase Transformation of Drugs
Solution-mediated phase transformations widely occur in pharmaceutical
systems such as solid or semisolid dosage forms (suspension/slurries). For
instance, salt disproportionation, a conversion from the ionized form to neutral
form, is a solution-mediated reaction. In addition, amorphous forms tend to
crystallize out as crystalline form. Such phase transformation could also be
observed in granulation process or dissolution testing. For instance, Lin et al.
observed a hypertension drug transfer from the metastable/more soluble form
(hexagonal crystal) to its stable/less soluble form (rod-shaped crystal) within
193
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5 Polymorphism and Phase Transitions
30 min during dissolution [75]. Theoretically, the solution-mediated phase
transformation can be divided into three steps. First, the metastable/more soluble form dissolves into the media to reach a supersaturated state. Second, the
stable form starts to nucleate in the solution. Last, the crystal of the stable form
starts to grow, while the metastable form continues to disappear [76–78]. This
process can be easily affected by numerous factors, which was summarized well
by Zhang et al. [79]. On the other hand, polymorphic transformation has significant influence on creams or suspensions. For instance, phase transformation in
a cream can lead to the crystal growth of a new phase, which could result in a
gritty cream product. Similarly, the solution-mediated phase transformation
can lead to a caking problem of the suspension. Hence, selection of the appropriate polymorphs with desired stability and solubility is very critical for such
pharmaceutical systems.
5.4 Impact on Bioavailability by Polymorphs
It has been reported that bioavailability and/or absorption rate can be polymorph dependent in many cases [80–85]. To be specific, by studying the intrinsic dissolution rate and kinetic solubility over four to six hours, researchers
found that the obvious solubility differences (generally two to threefolds)
between polymorphs result in different oral absorption rates and therefore
demonstrate a significant differences in Cmax but minor changes in AUC
[52, 86–88]. In this section, the impact of polymorphism on dissolution
and/or oral absorptions will be discussed in detail.
The rate of oral absorption for a drug is often associated with dissolution rate.
The dissolution rate is influenced by the presence of polymorph. In most cases,
the most stable polymorph generally has slowest dissolution rate and lowest solubility, while the metastable polymorph typically has higher dissolution rate.
Hence, ignorance of the existence of polymorphism can attribute to significant
dose-to-dose variations [8].
Chloramphenicol palmitate, for instance, prepared in a suspension formulation with different ratios of form A and form B shows significant differences in
bioavailability [89]. The blood serum levels of chloramphenicol suspension with
different ratios of form A and form B are demonstrated in Figure 5.14. Obviously, the maximum blood level of 100% form B is higher than that of 0% form
B by a factor of 7, indicating that bioavailability is significantly influenced by the
type and concentration of polymorphs. Furthermore, the presence of the amorphous form will have impact on the bioavailability. In vivo studies of the serum
levels of the amorphous form and form A of chloramphenicol palmitate have
been performed both in rhesus monkeys and children. Based on the result tabulated in Table 5.2, we can conclude that the bioavailability of the amorphous
5.4 Impact on Bioavailability by Polymorphs
24
100% Form B
22
Chloramphenicol (μg ml−1)
20
75% Form B
18
16
50% Form B
14
12
10
25% Form B
8
6
4
0% Form B
2
0
0
1
2
3
4
5 6 7 8 9
Time after dosing (h)
10 11 12 13
Figure 5.14 The mean blood serum levels obtained with chloramphenicol palmitate
suspension containing various percentages of form B and form A (ranging from 100%
form B to 0% form B). Source: Adapted from Aguiar et al. [89].
Table 5.2 Blood levels (μg/100 ml) for different suspensions of chloramphenicol palmitate.
Time after feeding (h)
Suspension used
2
4
6
8
Blood levels in children
Amorphous
Form A
102
60
42
26
34
35
57
23
NA
Blood levels in rhesus monkeys
Amorphous
68
39
18
Form A
22
17
17
form is much great than that of form A [90]. The aforementioned bioavailability
differences between form A and form B of chloramphenicol palmitate can be
explained by the polymorph-dependent hydrolysis of this prodrug [91]. The
higher rate and the extent of hydrolysis of form B lead to its higher solubility
and faster dissolution rate in in vitro studies.
Another example is the polymorphism of oxytetracycline. In 1969, a report
summarized 16 batches of the oxytetracycline capsules, coming from
195
196
5 Polymorphism and Phase Transitions
13 different suppliers, showing significant lower blood levels than the products
from innovator. Moreover, seven out the 16 batches showed blood levels even
lower than the lower limit of the therapeutic window. Scientists reported similar
observations in the in vitro dissolution studies suspecting the presence of an
oxytetracycline polymorph [92, 93]. The studies conducted on the six batches
of bulk oxytetracycline materials show more evidence of the impact of polymorphism on dissolution variations. Although all the samples met USP specifications, two of the six batches contain different forms (polymorph A). When
using the tablets prepared by polymorph A to do the dissolution studies in
the 0.1 M HCl media, the dissolution rate of tablets containing polymorph
A is significantly slower than the others by a factor of 0.57 in the first 30 min
[92]. All these examples discussed in this section have demonstrated that the
presence of the polymorphs in the different dosage forms can significantly affect
bioavailability of drugs and have the potential to lead to batch-to-batch variations of dissolution and/or bioavailability of pharmaceutical products. Hence,
the existence of unexpected polymorphs in dosage forms might lead to some
severe consequences such as batch failure or withdraw of drug product from
the market.
5.5 Regulatory Consideration of Polymorphism
Numerous activities in pharmaceutical industry, ranging from drug discovery to
manufacturing, require the consideration of polymorphism. In this section, the
regulatory aspects of the polymorphism are reviewed with several examples.
Moreover, traditional and innovative analytical techniques to detect and identify the existence of polymorphs in drug products will be briefly introduced.
The presence of polymorphs could influence tableting behavior. Simmons
et al. reported that polymorph B of tolbutamide has severe powder flow issues
due to the platelike shape of the crystals. In contrast, polymorph A is not platelike crystals and has better powder flow. Hence, the existence of polymorph B in
the bulk powder materials might lead to powder bridging in the hopper and tablet capping [94]. For semisolid dosage forms, the influences of polymorphism
should also be taken into account. The behavior of a suspension, for example,
would be significantly changed if the inappropriate polymorphs are present. It
has been reported that the solvent-mediated form transformation from the metastable polymorph to the stable one might lead to undesirable change of crystal
size or even cause serious caking issues. All these severe consequences might
significantly affect the syringeability of the suspension. Suspension of oxyclozanide was reported to undergo an obvious particle size increase even without disturbing due to this solvent-mediated phase transition [95].
Based on the above discussion, it is pivotal and advantageous to select and
control the polymorphs for each specific pharmaceutical application. The Food
5.5 Regulatory Consideration of Polymorphism
and Drug Administration (FDA) guideline for drug substance further highlighted the significance of controlling the crystal form: The applicants have
the responsibility to control the crystal form of the drug substance, and the suitability of the crystal form needs to be demonstrated if bioavailability is affected.
Thus, Abbreviated New Drug Applications (ANDAs) should include the information of solid-state properties, especially when bioavailability is affected [96].
“How to scientifically gather the information of solid-state properties?” is a
favorable topic in pharmaceutical industry, because each individual compound
generally has its own characteristics and displays a wide range of unpredictable
properties. Rather than restate the list of guidelines or regulations, in this section, a decision tree is introduced for efficiently gathering information on drug
substances that will address the specific questions about solid-state characteristics in a logical order [97]. Applying this decision tree will not only provide a
conceptual framework to understand how the justification for the different crystal forms might be presented but also used as strategic tool to organize the solidstate specifications of the drug substance.
The decision tree/flowchart for polymorphs is demonstrated in Figure 5.15.
This decision tree addresses the crystallization conditions to obtain a polymorph, analytical approaches to identify polymorphs, physical properties of
the polymorph, and confirmation of the integrity of a drug substance. Specifically, “Is the formation of polymorph possible?” is the first question that needs
to be addressed in the polymorph decision tree. In order to answer this question,
conditions of crystallization need to be modified to do the polymorph screening.
During sample preparation, the effects of preparation procedure (e.g. drying or
grinding) need to be addressed. Combining powder X-ray diffraction (PXRD)
and at least one of the other methods listed in the flowchart may be used as
the analytical approach to identify the existence of the polymorph. If the crystals
we obtained at various crystallization conditions are identical, then the answer
to the first question is “No.” If we observe the existence of polymorphs, the study
is then moved to the second step of the decision tree.
The second step of the decision tree is to characterize the physical properties
of the polymorphs that might have impact on the dosage forms or drug products
(e.g. bioavailability, stability, manufacturability, etc.) As we discussed above, solubility and dissolution rate perhaps are the most significant properties that need
to be characterized, since they might be directly associated with bioavailability.
Hence intrinsic dissolution rate experiments and equilibrium solubility studies
need to be conducted. Moreover, the stability (both chemical and physical),
morphology of crystal (size and shape), and calorimetric behavior need to be
investigated as well, because the manufacturability, shelf life of drug product,
and reproducibility are strongly associated with these characteristics. If there
are no obvious differences between these physical properties, the answer to
the second step is “No.” Noteworthy, if there are significant physical property
differences between polymorphs, the characteristics of the drug products might
197
Physical properties
Stability (chemical or physical)
Solubility profile
Morphology of crystals
Calorimetric behavior
Relative humidity (%RH) profile
Change crystallization conditions
Solvent polarity
Temperature
Concentration
Agitation and pH
Polymorphs
discovered?
Test for polymorphs
X-ray powder diffraction (XRPD)
DSC, TGA, thermomicroscopy
Vibrational spectroscopy
Solid-state NMR
NO
Figure 5.15 Decision tree/flowchart for polymorph.
YES
Different
physical or
chemical
properties?
NO
Single polymorph
Qualitative control
(e.g. DSC or PXRD)
YES
Drug
substance
composition?
Mixture of forms
Quantitative control
(e.g. DSC or PXRD)
5.6 Novel Approaches for Preparing Solid State Forms
be altered under certain circumstances. Hence, from a regulatory perspective, it
is necessary to establish a series of specifications or tests to confirm the proper
polymorph is reproducibly obtained.
Sometimes the isolation of the specific polymorph is difficult to achieve.
When obtaining a mixture of forms, quantitative analytical approaches are
required. Moreover, the quantitative method needs to be validated properly
according to the International Conference on Harmonisation (ICH) guidelines.
Typically, PXRD is used as analytical tool to determine the percentage of the
specific form in the powder mixture. The limits of detection (LOD) can be varied from case to case. It has been reported that the LOD of PXRD can be varied
from 0.5 to 15% [98, 99]. Solid-state nuclear magnetic resonance (ssNMR) is
another powerful tool to detect the polymorph in solid dosage forms due to
its sensitivity of detecting the existence of low-level polymorph presented in
the drug product [100, 101]. However, there many cases involving low-level
content of active pharmaceutical ingredient (API) or multicomponent mixture,
whereby ssNMR will not be sensitive enough to detect the existence of polymorphs in the drug products.
It has been reported that a minor amount of a polymorph, as low as
0.025% w/w, in a tablet matrix was detectable by an innovative method that
combined Raman mapping with statistically optimized sampling [102, 103].
Nevertheless, application of this analytical strategy is limited due to its long
analytical period and the requirement of significant spectral differences
between the targeted species and other components. Nowadays, with the
development of the nonlinear spectroscopy, nonlinear optical methods
can be employed to rapidly image pharmaceutical systems with superior
spatial resolution [104]. Hartshorn et al. demonstrated an example of using
broadband coherent anti-Stokes Raman scattering (BCARS) microscopy to
detect the presence of indomethacin polymorphs [105]. In their study, α-, γ-,
and amorphous forms of indomethacin could be clearly discerned in a multicomponent tablet matrix with high spatial resolution. In addition, BCARS
microscope also shows significant advantages over traditional Raman mapping methods based on data acquisition time. The results suggest that a reasonable signal-to-noise ratio can still be obtained even when increasing the
analytical speed of BCARS to 100 ms per pixel. The aforementioned advantages of the modern analytical technologies enable pharmaceutical scientists
to better identify and characterize the polymorphs of drugs.
5.6
Novel Approaches for Preparing Solid State Forms
Nowadays, a very challenging task in the field of polymorphism is to find as
many forms of the API as possible. Hence, developing a universal approach
to produce all possible polymorphs of an API severs as a common goal of
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5 Polymorphism and Phase Transitions
pharmaceutical companies. Although there are no specific methods to control
the polymorphs, several methods have been investigated with varying degrees of
success. Five approaches of polymorph screening are discussed in this section.
Theoretically, the first two approaches (high-throughput crystallization method
and capillary growth method) are improved based on the standard crystallization methods. For the other three methods (laser-induced nucleation, heteronucleation on single crystalline or on polymer surface) were developed in
order to influence the nucleation process [106]. In general, each of these methods has worked for specific cases but, to date, no universal method for finding all
polymorphs has been developed.
5.6.1 High-throughput Crystallization Method
By combing numerous possible conditions (possible temperature, concentrations, and solvent), the high-throughput crystallization method is employed
to probe the new polymorphs. Robotic liquid handling system was utilized to
prepare thousands of crystallization solutions with different concentrations
and solvent. This automatic technique enables efficient crystallization at various conditions, which significantly exceeds the conventional benchtop
screening process [107]. Advanced analytical techniques, such as Raman
microscopy or optical imaging, are required to analyze and screen the
products. Polymorphs of acetaminophen were investigated and screened
by using this technique. It was demonstrated that polymorph I and
polymorph II could be selectively produced by using different solvent
mixtures [108–111].
5.6.2 Capillary Growth Methods
As we know, the ratio of supersaturation is a dominating factor related to the
production of the desired polymorph from solution. For example, generating
the metastable form of an API molecule requires a high supersaturated ratio.
Having a small volume of solution, crystallization from capillaries not only
has the advantage of isolating heterogeneous nucleates but also has less turbulence. All these advantages enable this method to produce an ideal highly supersaturated environment [112, 113]. Furthermore, crystals produced by this
approach could be directly subjected to PXRD or single-crystal X-ray diffraction
for further analysis even without further extraction or isolation. Capillary
growth method has been successfully applied in pharmaceutical industry to crystallize metastable polymorph from highly supersaturated solution. For instance,
by evaporating the solvent mixture (water/acetone = 1 : 3) in a 1.00 mm capillary
at ambient condition, scientists successfully isolated the metastable form of
nabumetone [114, 115].
5.6 Novel Approaches for Preparing Solid State Forms
5.6.3
Laser-induced Nucleation
Nonphotochemical laser-induced nucleation (NPLIN) technique was first
introduced to modify the nucleation rate. It has been reported that NPLIN
can induce critical nucleus formation by forming clusters to reduce the corresponding entropic barrier [116]. Furthermore, scientists also found that this
method could be employed for polymorph selection. For instance, in the presence of NPLIN, γ-glycine could be produced. Without this technique, the supersaturated solution only yielded the α-form of glycine. Unfortunately, this
method has not been applied in pharmaceutical industry yet. Still, it can be
developed as a possible tool for polymorph screening [117].
5.6.4
Heteronucleation on Single Crystal Substrates
Based on the epitaxial mechanism, controlling the crystallization on specific
surface of organic or inorganic crystals could provide polymorph selectivity
[117, 118]. From a molecular perspective, alignment of the lattice parameters
attributes to the oriented crystal growth on the surface as a substrate. Polymorph selection of ROY compound, as we discussed before, is a classic example
of using this approach. Subliming of ROY on the (101) face of pimelic acid crystal can yield the yellow needle crystal. However, the orange needle and red plates
could be produced by sublimation of ROY on (010) face of succinic acid single
crystal [119]. Red plate crystal was reported as the seventh polymorph of the
ROY compound. Furthermore, scientists are trying to employ a combinatorial
library of surfaces to utilize the “heteronucleation on crystal surface” as a tool
for polymorph selection [21, 120].
5.6.5
Polymer Heteronucleation
Polymer heteronucleation involves crystallizing a compound on polymer heteronuclei using sublimation, solvent evaporation, or even cooling. When using polymer
heteronucleation, the nucleation of the compound is significantly influenced by the
chemical diversity of each polymer. Hence, by changing the polymer, scientists are
not only able to control the formation of an established form but also to discover
unreported new polymorphs even without knowing the solid-state structure. This
technique was employed to isolate the orthorhombic form of acetaminophen from
aqueous solution. Moreover, a successful example of applying polymer heteronucleation is the polymorph screening of carbamazepine. To be specific, carbamazepine was only reported to have three polymorphs in the past 30 years. However,
Lang et al. successfully discovered the fourth polymorph of carbamazepine by crystallizing the carbamazepine on hydroxypropyl cellulose. Furthermore, the fourth
polymorph of carbamazepine, which was reported as platelike crystals, was demonstrated to have better stability than that of trigonal form [121, 122].
201
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5 Polymorphism and Phase Transitions
Unfortunately none of these four methods work all of the time, and it is still
necessary to utilize common crystallization techniques as well as various other
methods to conduct a comprehensive polymorph screen.
5.7 Hydrates and Solvates
Solvates are defined as molecular complexes that have incorporated solvent
molecule in the regular position of their crystal lattice. Typically, based on
the Kuhnert-Brandstätter’s previous studies, solvate formation is independent
of polymorphism [123–125]. Solvates can be produced during the crystallization of many classes of pharmaceutical compound. For instance, it has been
reported that certain classes of drugs (including steroid, antibiotics, and
sulfonamides) have the propensity to form solvates during the crystallization
[126, 127]. To be specific, estradiol was reported to be capable of forming
solvates with 30 tested solvents [125]. Moreover, many antibacterials (e.g. gramicidin, ampicillin, erythromycin, griseofulvin, etc.) have also been reported to
form solvates [126, 128–130]. In addition, some other miscellaneous
compound, like caffeine or ouabain, can also form solvates according to previous studies [131, 132].
For solvates, the guest molecule/solvent molecule is an important component
of the crystal structure. Based on previous publications, Table 5.3 summarizes
Table 5.3 Possible solvents to form solvates with drugs and organic compounds.
Water
Methanol, ethanol, 1-propanol, isopropanol, 1-butanol, sec-butanol, isobutanol,
tert-butanol
Acetone, methyl ethyl ketone
Acetonitrile
Diethyl ether, tetrahydrofuran, dioxane
Acetic acid, butyric acid, phosphoric acids
Hexane, cyclohexane
Benzene, toluene, xylene
Ethyl acetate
Ethylene glycol
Dichloromethane, chloroform, carbon tetrachloride, 1,2-dichloroethane
N-Methylformamide and N,N-dimethylformamide, N-methylacetamide
Pyridine
Dimethyl sulfoxide
5.7 Hydrates and Solvates
many possible solvents involved in solvate formation. For some specific solvates,
two or even three solvent molecules can be incorporated into the crystalline lattice. For some special cases, the solvents may have different ratios in the crystalline structures when forming solvates [133].
Among these solvent molecules, water can easily fill structural voids due to
its small size and multidirectional hydrogen bonding capacities. When the
incorporated solvent molecule is water molecule, the molecular complex is
termed hydrate. It has been suggested that hydrogen bonding is the dominating force holding the structure of hydrates together. Scientists found that
hydrogen bonds are not only formed between water molecules but also to
the other functional groups (such as carbonyl or amines). The presence of
these intra-/intermolecular interactions within the crystalline lattice leads
to the unique physical properties of solvates or hydrates including the value
of Gibbs free energy, internal energy, entropy, etc. These unique physical
properties can result in variations of solubility or bioavailability. For instance,
Shefter and Higuchi reported that the solvated form and unsolvated form of
theophylline show significant differences in the dissolution tests [131].
Hence, understanding the physical properties from a thermodynamic
perspective is important to further understand solvates. Hydrates, a special
case of solvates, are more commonly observed than other organic solvates
[134]. Therefore, the thermodynamics of hydrates is addressed in detail as
follows.
5.7.1
Thermodynamics of Hydrates
Hydrate formation is not merely dependent on the presence of water, but determined by water activity. Noteworthy, water activity could be easily correlated
with RH by multiplying water activity by 100. RH is defined as the ratio of vapor
pressure of water to the saturated vapor pressure of pure water at the given temperature. Based on the water uptake capacities of the crystal at water activity or
different RH, hydrates can be further classified as either stoichiometric hydrates
or nonstoichiometric hydrates [135]. Specifically, crystal structures having a
constant ratio of water to host are termed stoichiometric hydrates. For instance,
both ampicillin trihydrate and theophylline monohydrate are reported as stoichiometric hydrates [136, 137]. In contrast, nonstoichiometric hydrates are
characterized as crystal structures having a changing water–host ratio at different RH. A classic example of a nonstoichiometric hydrate is cromolyn sodium.
Based on the crystal structure of cromolyn sodium, it has been reported that one
sodium ion was fixed and the other one is disordered as water molecules enter
the crystals when the water activity is increased. Hence, continuous changes of
the crystal structure were monitored by employing PXRD [138, 139]. In a
hydrate system, suppose there are m moles of water. Then Equation (5.18)
203
204
5 Polymorphism and Phase Transitions
expresses an equilibrium to describe the transition from anhydrous phase to a
m-hydrate [140]:
Bsolid + mH2 O
Kh , m
B mHs2 O
5 18
solid
On the basis of the law of mass action, Kh,m is denoted as the equilibrium constant for the above equilibrium and could be expressed as follows [131]
Kh, m =
a B mH2 O
a Bsolid
eq
solid eq
5 19
a H2 O eq m
The a[B mH2O]eq, a[Bsolid]eq, and a[H2O]eq are denoted as the thermodynamic activities for each species at equilibrium. Assuming the crystalline phases
have very high purity with few crystal defects, we can treat the solid crystalline
phases as a constant. Hence, the Gibbs free energy of forming B mH2O from an
anhydrate from B can be expressed as Equation (5.20) (standard) and
Equation (5.21) (general condition) [141]. Based on Equation (5.21), we can
conclude that the m-hydrate form would be more thermodynamically stable
than the anhydrate when the water activity is higher than (Kh,m)−1/m. On the
other hand, when a[H2O] is lower than (Kh,m)−1/m, the anhydrate would be
the stable thermodynamic species. Similarly, the transformation from B mH2O
to B nH2O can be derived accordingly, and the details could be found in a book
chapter composed by Lohani and Grant [31]. On the basis of the discussion
about the relationship of a[H2O]eq and (Kh,m)−1/m, we can estimate the range
of RH values, at which the hydrate form would be more thermodynamically
stable:
ΔGBΘ
B mH2 O
= −RT lnKh, m = −RT ln a H2 O eq
ΔGB
B mH2 O
= ΔGBΘ
B mH2 O
+ RT ln a H2 O
= − RT lnKh, m + RT ln a H2 O
−m
5 20
−m
−m
5 21
5.7.2 Formation of Hydrates
Formation of hydrates can be carried out by reducing the solubility (e.g. cooling
or evaporating) of an aqueous drug solution. For instance, Figure 5.16 demonstrates an idealistic example of producing different hydrates by varying the temperature of evaporation. Hydrates could also be formed in mixture of water and
organic solvent. For the water-immiscible solvent mixtures, the water content
needs to be rigorously controlled to avoid forming multiple hydrates especially
in large-scale operations [133].
As hydrates can be formed at different RH, the stability of hydrates needs to be
further discussed. An understanding of the stability of hydrates and the
5.7 Hydrates and Solvates
Evaporation T1
Anhydrate
Temperature
T2
Monohydrate
T3
Dihydrate
Concentration
Figure 5.16 Hydrates and anhydrate produced by evaporations under different
temperatures. Source: Adapted from Byrn et al. [133].
conditions of their formation is critical because it will help pharmaceutical
scientists to decide the appropriate storage conditions and design ways to avoid
the crystallization of the undesired form. Perhaps the most promising approach
to describe moisture uptake or loss behavior is to make a water content versus
RH plot after the equilibration of the solid at different RH. This can be readily
carried out using the dynamic vapor sorption (DVS) technique. Figure 5.17
shows an idealized moisture uptake profile of a compound that can exist as
anhydrate, monohydrate, or dihydrate at ambient temperature. Specifically, at
0% RH, the compound would exist as anhydrate. When increasing the RH to
point I, the anhydrate form would transform to monohydrate. With the further
increment of RH, the monohydrate can convert the dihydrate at point II. Finally,
when the RH reaches the critical relative humidity (RH0), the sample will begin
deliquescence starting at point III.
It is important to briefly introduce the concept of deliquescence because it can
be commonly observed for pharmaceutical solids, especially for salts and certain
excipients [142, 143]. When the RH of the environment is higher than the RH0,
water-soluble crystalline solids undergo dissolution in the aqueous layer on the
solid surface formed by condensed water. This process is called deliquescence
(Figure 5.18) [144].
5.7.3
Desolvation Reactions
Desolvation of solvates or hydrates is a widespread phenomenon in pharmaceutical systems. Crystal losses of solvent molecule during crystallization can dramatically affect stability, dissolution rate, and even bioavailability [145]. Hence,
205
5 Polymorphism and Phase Transitions
Water content (moles)
206
Deliquescence
Dihydrate
2
Theoretical transition
from monohydrate
to dihydrate
RH0
Monohydrate
1
Theoretical
transition from
anhydrate to
monohydrate
Anhydrate
I
II
III
% RH
Figure 5.17 Idealized moisture uptake profile for a compound has anhydrate, monohydrate,
and dihydrate. Source: Adapted from Byrn et al. [133].
Water vapor at
RH1 condenses
Drug
RH0<RH1
Drug
dissolves
Drug
Figure 5.18 Deliquescence process. Source: Adapted from van Campen et al. [144].
in order to probe the underlying mechanisms of desolvation reactions, numerous analytical techniques have been involved including PXRD, DSC, and
thermomicroscopy. For instance, by using thermomicroscopy, Kuhnert-Brandstätter et al. found that most of the hydrates dehydrate before melting. The
dehydration reactions not only yield opaque crystal at the end but also associated with some “jumping behavior” of the crystal due to generation of gaseous
products [123–125]. The desolvated products could be categorized into the
following three types. Firstly, the crystal structure undergoes a significant
change after the desolvation by showing a different PXRD pattern. Secondly,
desolvation results in only a slight change in crystal structure by creating
crystals with voids or cavities (e.g. cephaloglycin and cephalexin) [146, 147].
Lastly, the crystalline solids transfer to its amorphous form after the solvent
5.7 Hydrates and Solvates
evaporation due to the collapse of the crystal lattice (either partially or
wholly) [148].
It is worth pointing out that the mechanisms of desolvation can be affected by
many factors including atmospheric environment, crystal packing, crystal
defects, or even intra-/intermolecular hydrogen bonding [149]. The details of
the mechanisms of the desolvation reaction can be found in the literature
but are beyond the scope of this section [150]. In this section, several examples
of desolvation for hydrates or solvates will be reviewed as follows.
Solvates/hydrates of caffeine are reported to be desolvated at various conditions. For instance, it has been reported that caffeine∙2HOAc lost the acetic acid
after exposed to air. The loss of the HCl and water has been observed for
caffeine∙HCl 2H2O stressed at 80–100 C early in the eighteenth century
[151, 152]. Moreover, it has been reported that caffeine hydrates could effloresce, give off water vapor, and easily dehydrate even at room temperature
[153]. Dehydration of thymine hydrates has also been observed upon exposure
at 40 C, which yields the anhydrous form (Figure 5.19a). Similarly, cytosine
monohydrate can be dehydrated into anhydrate form within 115 hours
(Figure 5.19b) [149]. These experiments show that completion of desolvation
for single crystals can take several days. Apart from hydrates, many papers
reported that other organic solvates, like acetone or chloroform, can also
undergo desolvation at certain conditions [154–156].
5.7.4 Phase Transition of Solvates/Hydrates in Formulation
and Process Development
As we discussed in Section 5.3.3, different unit operations can result in polymorphic transformation. Phase transitions of solvates and hydrates can also be
induced during the process development. Hence, possibility of phase changes
needs to be carefully considered when formulating API in hydrate or solvate
form. Several relative examples will be reviewed as follows.
Darunavir, a protease inhibitor for treating human immunodeficiency virus
(HIV), was marketed as darunavir ethanolate (Prezista™). However, it has been
reported that darunavir can exist as anhydrous/amorphous form, hydrate, and
ethanolate [157–159]. Van Gyseghem et al. reported the interconversions
between different solid-state forms of darunavir at different conditions. Specifically, in the presence of water, ethanolate crystalline and the amorphous form
of darunavir have high possibility of converting to its hydrate crystalline. Heating can lead to both desolvation and dehydration of darunavir ethanolate and
hydrate, resulting in the formation of its amorphous form [148]. Moreover,
the interconversion between ethanolate and hydrate can be affected by peroxide
and form some oxidized impurities, which can be characterized by solution
nuclear magnetic resonance (NMR) spectroscopy (unpublished data of our
lab). All the aforementioned information should be taken into account to select
appropriate unit operations and storage conditions.
207
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5 Polymorphism and Phase Transitions
(a)
Thymine hydrate
O
Heating to 40 °C
CH
HN
.H O
O
N
H
After 24 h
At start
O
CH
HN
O
After 48 h
After 5 days
N
H
Thymine anhydrate
(b)
NH
N
Heating to 40 °C
.H O
O
N
H
Cytosine hydrate
At start
After 54 min
After 115 h
After 97 min
NH
N
O
N
H
Cytosine anhydrate
Figure 5.19 Behavior of hydrate crystals upon heating to 40 C A (thymine) B (cytosine).
Source: Adapted from Perrier and Byrn [149].
When a stable hydrate of a pharmaceutical compound can be formed under
ambient conditions, wet granulation of the anhydrous form of such compound
may induce the solution-mediated phase transition and yield its hydrate form
[160]. On the other hand, the subsequent drying process of wet granulation also
has the possibility of producing anhydrous crystals or even amorphous materials via desolvation [161]. Thiamine hydrochloride is a classic example to illustrate the hydration and dehydration in granulation process. It has been reported
5.8 Summary
that monohydrate is formed during spray granulations and the subsequent drying process dehydrated the hydrates to yield the anhydrous crystals [162]. Interestingly, during storage, the monohydrate of thiamine hydrochloride can
convert to the hemihydrate at ambient temperature. These interconversions
are reported to result in the change of tablet hardness and disintegration time.
Phase changes of hydrates can also be observed in lyophilization process. The
kinetics of the phase transition was complex in a freeze-drying process due to
the complexity of nucleation and growth rate of different hydrates during freezing. Pentamidine isethionate, for instance, has trihydrate and several anhydrous
forms. Lyophilization can yield form A (stable form) and form B (metastable
form) upon different conditions. To be specific, high concentration and slow
freezing rate will yield form B, while low concentration and fast freezing rate
produced form A. Interestingly, it was demonstrated that nucleation of trihydrates is the critical process to determine the final product. Form B, as the dehydration product of the trihydrate, favors higher concentration to nucleate
pentamidine isethionate trihydrate and longer time of the crystal growth [163].
From a formulation perspective, selecting different pharmaceutical excipients, such as surfactant or polymeric materials, can also significantly affect
the kinetics of solution-mediated phase transitions [164–166]. For wet granulation, impacts of excipients on the rate of form transformation can also be
expected. For instance, granulating theophylline with silicified microcrystalline
cellulose or α-lactose demonstrates different extent of phase transition. Specifically, with 3% of water addition, monohydrates were not discerned in the blend
of theophylline anhydrate and silicified microcrystalline cellulose. In contrast,
when formulating theophylline anhydrate with α-lactose, its monohydrate
was detected in various levels of water addition (3–20% w/w) [167]. For theophylline granules, drug loading, granulation liquid, amount of water addition,
and water activity were reported to further influence the formation of its
hydrates [137, 168, 169]. Hence, pharmaceutical scientists need to pay close
attention to select the formulation and unit operation for such API. More details
and further theoretical illustrations can be found in some informative reviews
[160, 170].
5.8
Summary
In this chapter the fundamental concepts of polymorphism, amorphous forms,
crystal habits, and molecular adducts have been described. Thermodynamic
theory for both polymorphism and pseudopolymorphism was introduced.
These fundamentals will help us better understand and predict the differences
of physicochemical properties between polymorphs including their stability,
reactivity, and bioavailability. The unique characteristics of each polymorph will
lead to different performances of its drug products, which will require extra
209
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5 Polymorphism and Phase Transitions
regulatory consideration. Moreover, in this chapter, polymorphic interconversion and phase transitions were also reviewed with concrete examples. Understanding the factors influencing polymorphic transformations can be helpful for
formulation design or selecting the appropriate manufacturing operations. All
of this information should lead to better understanding of the polymorphic
behaviors of pharmaceutical compounds.
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221
223
6
Measurement and Mathematical Relationships
of Cocrystal Thermodynamic Properties
Gislaine Kuminek, Katie L. Cavanagh, and Naír Rodríguez-Hornedo
Department of Pharmaceutical Sciences, University of Michigan, Ann Arbor, MI, USA
6.1
Introduction
One of the most important properties of cocrystals is their ability to enhance
and fine-tune solubility. This property enables cocrystals to solve absorption
and bioavailability problems of poorly water-soluble drugs. Cocrystals are a
class of multicomponent solids containing two or more neutral molecular components in a single homogenous crystalline phase with well-defined stoichiometry [1–5]. They are distinguished from solvates in that cocrystal components
are solids at room temperature.
A pharmaceutical cocrystal is generally composed of an active pharmaceutical
ingredient (API) and benign molecules or other APIs as coformers that form
hydrogen-bonded molecular assemblies or complexes in the crystalline state.
These molecular interactions occur between neutral and nonionized molecules,
providing an opportunity to modify properties by cocrystal formation with
drugs that cannot form salts. Coformers are commonly selected from
substances appearing on the generally regarded as safe (GRAS) status list or
from those that have been demonstrated to be nontoxic and have regulatory
approval [6, 7].
Over the last decades cocrystals have received significant attention from
the pharmaceutical industry, and numerous pharmaceutical cocrystals
have been reported [1, 8–20]. In contrast with the science-based solid-state
characterization of cocrystals, there is a wide gap between the principles
that explain their solution behavior and their application to cocrystal
development.
Pharmaceutical Crystals: Science and Engineering, First Edition.
Edited by Tonglei Li and Alessandra Mattei.
© 2019 John Wiley & Sons, Inc. Published 2019 by John Wiley & Sons, Inc.
224
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
A property that differentiates cocrystals from other supersaturating drug
forms is their fine-tunable solubility. The stoichiometric nature of cocrystals
predisposes them to huge, yet predictable, changes in solubility and thermodynamic stability as solution conditions change (drug solubilizing agents or pH,
for instance). Cocrystal solubility is a result of a delicate interplay between
the cocrystal constituents in solution, their speciation, and molecular interactions. Therefore, an important first step in understanding cocrystal solution
behavior is to determine the relationships between cocrystal and its constituents
in solution by identifying the underlying equilibrium reactions. Without this
knowledge, selecting and developing cocrystals becomes an empirical exercise
based on trial and error.
The aims of this chapter are to present basic concepts and mathematical relationships that predict how cocrystal solubility and thermodynamic stability
change with solution conditions and to describe key thermodynamic parameters that explain kinetic properties, which are essential to streamline cocrystal discovery and development.
6.2 Structural and Thermodynamic Properties
6.2.1 Structural Properties
Multicomponent solids include crystalline and amorphous systems. Polymorphs, solvates, and salts are common crystalline forms employed for product development. In contrast with salts, cocrystals do not rely on ionic
interactions and can be made with nonionizable drug (A) and coformer (B).
Salt forms, on the other hand, comprise the ionized forms of drug and counterion A− and B+. Cocrystals and salts can both exhibit polymorphism and
solvate formation. Salt forms can be crystalline or amorphous, whereas
cocrystals are crystalline molecular complexes. Cocrystalline salts are crystalline systems that include both the nonionized, AB, and ionized, A−B+, interactions. Cocrystals and salts have been described as the extremes of a
continuum depending on the location of the acidic proton in the crystal structure [21]. A schematic representation of the different classes of multicomponent solids is shown in Figure 6.1.
Pharmaceutical cocrystals are generally characterized by hydrogen-bonded
assemblies between drug and coformer molecules, as shown for the carbamazepine (CBZ) cocrystals in Figure 6.2. Some CBZ cocrystals maintain the CBZ
homomeric carboxamide dimer such as the carbamazepine–saccharin cocrystal
(CBZ-SAC) where coformer interacts with the exterior hydrogen bond donors
and acceptors. Other CBZ cocrystals disrupt the carboxamide homodimer by
forming a carboxamide–carboxylic acid dimer. An example of this is the carbamazepine–succinic acid cocrystal (CBZ-SUC).
6.2 Structural and Thermodynamic Properties
= API
+
= Counterion
1. Homomeric
2. Hydrate/solvate
+
–
+
+ –
–
+ –
+ –
+ –
–
–
– + – +
+ –
+
–
– + – +
+
+
6. Salt hydrate
5. Salt
= Water/
solvent
3. Cocrystal
–
–
–
+
+
+
+
–
+
–
+
–
7. Salt cocrystal
= Neutral
guest
4. Hydrated cocrystal
– +
– +
– +
– +
– +
– +
8. Salt hydrate cocrystal
Figure 6.1 Multicomponent crystalline forms that can be used to alter the physicochemical
properties of an active pharmaceutical ingredient (API) or drug without changing molecular
structure [22]. Source: Reproduced with permission of ACS Publications. http://pubs.acs.org/
doi/abs/10.1021%2Fcg900129f. Further permissions related to the material excerpted should
be directed to the ACS.
(a)
(b)
Figure 6.2 Examples of two strategies used to form cocrystals of carbamazepine: (a)
carbamazepine–saccharin, which maintains cyclic carboxamide homosynthon, and (b)
carbamazepine–succinic acid, which disrupts carboxamide homosynthon in favor of a
heterosynthon between carboxamide and dicarboxylic acid [12]. Source: Adapted from
Fleischman et al. [12], reproduced with permission of American Chemical Society, and from
Kuminek et al. [23], reproduced with permission of Elsevier.
The structural properties of a cocrystal and/or salt can be determined by crystallographic and spectroscopic techniques. Single-crystal X-ray diffraction and
solid-state NMR spectroscopy provide molecular and crystal structure information that is invaluable in identifying the nature of molecular assemblies in
225
226
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
cocrystals and salts. X-ray powder diffraction provides useful information about
crystal structure, which, combined with other techniques, may identify cocrystals and salts, their polymorphs, and solvates. Raman and IR spectroscopy can
characterize proton transfer in the solid state and has been extensively used in
the identification of salts and cocrystals. Methods of cocrystal or salt form characterization are beyond the scope of this chapter. The reader is referred to excellent reviews and articles on the subject [21, 22, 24–28].
6.2.2 Thermodynamic Properties
Answers to questions such as whether a cocrystal is stable or how unstable it is,
how fast it can convert to a less soluble form, or how its solubility compares with
that of the drug are obtained from experimentally determined thermodynamic
properties.
Despite thermodynamic properties being associated with equilibrium conditions, the departure from such equilibrium states provides information about
the kinetics of a process. The condition for equilibrium is that the Gibbs free
energy change for the process, ΔG, is equal to 0. For a spontaneous process,
ΔG is negative. ΔG is proportional to the logarithmic ratio between the actual
and thermodynamic variable driving the process. For a phase conversion
between a cocrystal and its constituent drug,
ΔGCC
D
= −RT ln
SCC
SD
61
where S is solubility and subscripts CC and D refer to cocrystal and drug, respectively. In this equation SCC is expressed in terms of moles of drug. The phase
conversion from cocrystal to drug is favored when SCC > SD. The rate of nucleation is proportional to ΔG.
In this chapter we are concerned with solution-mediated conversions, where
the more soluble form dissolves and generates supersaturation with respect to a
less soluble form. Supersaturation can be as high as the solubility ratio of cocrystal and drug or lower, depending on the actual and the equilibrium concentration values, Cactual/Ceq.
6.2.2.1 Cocrystal Ksp and Solubility
Cocrystal solubility product, Ksp, and solubility, SCC, are both key thermodynamic parameters. Cocrystal solubility is a conditional constant, while Ksp is
not. Cocrystal solubility varies with pH, solubilization, and concentration of
cocrystal components in solution. In theory, Ksp has a constant value as long
as deviations from ideality are accounted for. Ksp is the product of the molar concentrations or activities of cocrystal constituents. Both SCC and Ksp are dependent on temperature.
6.2 Structural and Thermodynamic Properties
The relationship between cocrystal Ksp and solubility is derived by considering the equilibrium between a cocrystal (AyBz) and the solution phase:
Ksp
Ay Bz, solid
yAsoln + zBsoln
62
where A and B represent cocrystal constituents and y and z are the stoichiometric coefficients. The forward reaction is dissociation and represents dissolution,
while the reverse reaction is association and represents precipitation. The thermodynamic equilibrium constant for this reaction is Ksp:
y
Ksp =
aA aBz
aAy Bz
63
where a represents activities and subscripts represent cocrystal constituents and
cocrystal. Since the activity of the cocrystal is assumed to be constant and equal
to 1, Ksp becomes an activity product. Under ideal conditions activities are
approximated by concentrations, and Ksp becomes
Ksp = A y B z
64
The terms in brackets represent molar concentrations of cocrystal constituents
in equilibrium with cocrystal. The relationship between cocrystal solubility and
Ksp is
SCC =
y+z
Ksp
yyz z
65
It is important to note that Ksp is the product of only the cocrystal constituents in
the same molecular state as in the cocrystal. The solubility calculated from
Equation (6.5) is an intrinsic cocrystal solubility. It does not include any other
species in solution.
The reader should be cautious of incorrect Ksp values calculated from
total analytical concentrations of salt or cocrystal components that do not
correspond to the Ksp definition according to the equilibrium in
Equation (6.4). Ksp = [A] [B] for cocrystal AB, or [A+] [B−] for salt A+B−.
Ksp [A]T [B]T when there are molecular species in solution different from
those in the corresponding solid phase.
Cocrystal Ksp values in aqueous media are presented in Table 6.1 in terms of
pKsp = −log Ksp. Higher pKsp values refer to lower Ksp values. The range of
values is similar to those reported for pharmaceutical salts [29–31]. pKsp values
for CBZ cocrystals are in the range of 2–6, indicating order of magnitude
increases in Ksp. When solubility is determined by solvation and not by solidstate lattice energy [5, 23], cocrystal solubility is dependent on the solubility
of its components. Nicotinamide and glutaric acids are among the most
soluble coformers in Table 6.1 and generally correspond to cocrystals with
227
228
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
Table 6.1 Cocrystal pKsp values.
Cocrystal (drug-coformer)
Cocrystal stoichiometry
(drug : coformer)
pKsp
Reference
Caffeine–salicylic acid
1:1
3.1
[5]
Carbamazepine–saccharin
1:1
6.0
[33]
Carbamazepine-salicylic acid
1:1
5.9
[34]
Carbamazepine-4-aminobenzoic acid
hydrate
2:1
8.9
[34]
Carbamazepine–succinic acid
2:1
8.2
[35]
Carbamazepine-malonic acid
a
b
2:1
6.1
[5]
Carbamazepine-glutaric acid
1:1
2.5
[5]
Carbamazepine-nicotinamide
1:1
2.3
[5]
Carbamazepine-oxalic acid
2 : 1b
8.0
[5]
Danazol-hydroxybenzoic acid
1:1
8.0
[36]
Danazol–vanillin
1:1
8.5
[36]
Gabapentin lactam-4-hydroxybenzoic
acid
1:1
3.7
[18]
Gabapentin lactam-4-aminobenzoic acid
1:1
3.1
[18]
Gabapentin lactam-benzoic acid
1:1
3.5
[18]
Gabapentin lactam-gentisic acid
1:1
3.9
[18]
Gabapentin lactam-fumaric acid
2:1
3.4
[18]
Indomethacin–saccharin
1:1
8.9
[33]
Ketoconazole-adipic acid
1:1
7.5
[37]
Ketoconazole-fumaric acid
1:1
8.8
[37]
Ketoconazole-succinic acid
1:1
7.6
[37]
Nevirapine-maleic acid
1:1
4.7
[38]
Nevirapine–saccharin
2:1
10.0
[38]
Nevirapine-salicylic acid
2:1
10.4
[38]
Pterostilbene–caffeine
1:1
5.3
[17]
Pterostilbene–piperazine
2:1
6.3
[39]
Piroxicam–saccharin
1:1
7.1
[36]
Theophylline–nicotinamide
1:1
0.7
[5]
Theophylline–salicylic acid
1:1
3.8
[5]
Source: Adapted from Cavanagh et al. [32]. Copyright 2018 with permission from Elsevier.
a
Form B (hydrated cocrystal) [40].
b
Disordered crystal structure that does not provide definitive stoichiometry [41].
6.2 Structural and Thermodynamic Properties
Table 6.2 Cocrystal and salt pKsp values of lamotrigine.
Solid-state forms
Stoichiometry
pKsp
Reference
Lamotrigine-methylparaben cocrystal
1:1
6.3a
[32]
Lamotrigine-nicotinamide hydrate cocrystal
1:1
3.9
[32]
Lamotrigine-phenobarbital cocrystal
1:1
7.9
Lamotrigine-hydrochloride salt
1:1
4.2
Lamotrigine-saccharin salt
1:1
5.0
[42]
b
[32]
[32]
Source: Adapted from Cavanagh et al. [32]. Copyright 2018 with permission from Elsevier.
a
Calculated from steady-state concentration during cocrystal dissolution reported in [43].
b
Ksp of lamotrigine-hydrochloride (LTG-HCl) salt was calculated from reported solubility of
0.46 mg ml−1 at 37 C (pH 1.2) from Floyd and Jain [44]. Ksp of the salt was estimated at 25 C
from [LTGH+] and [Cl−] concentrations calculated from the dissolved salt and HCl concentrations,
using a heat of solution value of 30 kJ mol−1.
higher Ksp values for a given drug. The highest 1 : 1 cocrystal Ksp corresponds to
theophylline–nicotinamide with a pKsp of 0.7, among the most soluble combination of cocrystal constituents.
Comparing the pKsp values of salts and cocrystals of the same drug, lamotrigine (LTG), Table 6.2 shows that some cocrystals are more soluble than salts or
less soluble depending on the coformers and counterions. Lamotrigine nicotinamide cocrystal has a higher Ksp than salts of saccharin or HCl. The cocrystal
with methylparaben has the lowest Ksp among these forms [32].
6.2.2.2
Transition Points
Knowledge of transition points early in development is important to obtain and
maintain a cocrystal. Transition points establish conditions under which
cocrystals are thermodynamically stable or unstable, or more or less soluble
than drug. One may wish to protect cocrystals from conversion during processing and storage (thermodynamically stable) and have a cocrystal solubility
advantage during dissolution (thermodynamically unstable). Kinetic stabilization is always an option but not desirable as a first option due to its inherent risks.
Figure 6.3 illustrates that cocrystal and drug solubilities are deeply influenced
by solution conditions such as ionization, solubilization, and solution stoichiometry. Furthermore, the variation in solubility for cocrystal and drug is not
equal. A defining feature of these plots is the existence of a transition point,
at which the cocrystal and drug have equal solubilities. This means that cocrystals that are more soluble than drug can become less soluble than drug by changing pH or by adding solubilizing agents or coformer. Without knowledge of
cocrystal transition points, cocrystal development will be risky as cocrystal
229
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
(a)
(b)
8
Solubility (mM)
100
Solubility (mM)
10
1
0.1
0
2
4
6
6
4
2
0
8
pH
8
16
24
32
40
48
Solubilizing agent (mM)
(c)
25
[Drug] (mM)
230
Scocrystal
20
Sdrug
15
10
5
0
0
50
100
150
200
[Coformer] (mM)
Figure 6.3 Solubilities and regions of thermodynamic stability for cocrystal and crystalline
drug are not fixed but vary with solution conditions such as (a) pH, (b) drug solubilizing
agents, and (c) coformer concentration. The intersection of the cocrystal and drug solubility
curves represents a transition point, where Scocrystal = Sdrug. The thermodynamic stability of
the cocrystal relative to drug can be determined from their solubility ratios >1, = 1 or <1,
where SA = 1 is the transition point. Source: Adapted from Kuminek et al. [23]. Reproduced
with permission of Elsevier.
solubility and stability can profoundly change with small variations in commonly encountered conditions.
Transition points are characterized by two solid phases in equilibrium with a
liquid phase, and the solution is doubly saturated with both phases. This point is
also referred to as eutectic point. Transition points between cocrystals and other
phases can exist, such as cocrystal and coformer, cocrystals of different stoichiometries, polymorphs, or solvates. This chapter considers the transition point
between cocrystal and drug solid phases, since pharmaceutical cocrystals are
generally more soluble than drug and it is their conversion to drug that one
is most concerned with.
Table 6.3 summarizes key stability indicators that are well recognized for the
characterization of pharmaceutical solids that can undergo conversions, such as
polymorphic, solvation/desolvation, salt/drug, cocrystal/drug, and amorphous/
crystalline systems. Determining the regions of thermodynamic stability and
6.2 Structural and Thermodynamic Properties
Table 6.3 Key stability indicators of solid-state forms.
Solid-state forms
Stability indicating parameters
Polymorphs
Transition temperature
Hydrates/anhydrous
Critical water activity or critical relative humidity
Salts/nonionized form
pHmax
Amorphous
Glass transition temperature (Tg)
Cocrystals/drug
Keu = [coformer]eu/[drug]eu, pHmax, SR∗D , CSC, S∗
Cocrystal transition points are eutectic points, where cocrystal and drug phases are in equilibrium
with solution. Eutectic constant is defined as Keu = [CF]eu/[D]eu. A transition point induced by pH is
a pHmax. A transition point induced by drug solubilizing agents is characterized by equal drug and
cocrystal solubilities (S∗) at a given drug solubilization ratio SR∗D or a critical stabilization
concentration of solubilizing agents (CSC).
Source: Adapted from Kuminek et al. [23]. Copyright 2016, with permission from Elsevier.
instability is essential for the development of such materials. For instance, in the
case of hydrate/anhydrous forms of a drug, the critical relative humidity is a key
indicator of the regions of stability of each form. Similarly, other indicators such
as pHmax for salts, transition temperature for enantiotropic polymorphs, and
glass transition temperature for amorphous solids are used. For amorphous/
crystalline conversions, there is no transition point per se or equilibrium state.
The potential for conversion to a crystalline state is based on assessment of
molecular mobility and kinetic behavior.
For cocrystals, the eutectic point expressed as the eutectic constant Keu is a key
stability and solubility indicator. Keu is the ratio of coformer to drug molar concentrations at the eutectic point. A cocrystal is at a transition point when its Keu
value is equal to that of its stoichiometry (coformer and drug ratio in the cocrystal). Cocrystal transition points can be induced by pH or drug solubilizing agents
and are expressed in terms of pH (pHmax) or in terms of solubilizing agents (S∗,
SR∗D , and CSC). These terms and their application to assess cocrystal stability
and supersaturation index (SA) are described in Sections 6.3.3 and 6.6.3.
6.2.2.3
Supersaturation Index Diagrams
Solubilizing agents such as polymers, surfactants, and complexing agents can
alter the thermodynamic relationship between cocrystal and drug and change
the driving force for conversions from cocrystal to drug. The solubility relationship between cocrystal and drug can change from a cocrystal that is more soluble
than drug to one that is less soluble and vice versa. The SA (SA = SCC/SD)
expresses the cocrystal solubility advantage over drug and is the driving force
for conversions from cocrystal to drug as described by Equation (6.1). SA is readily obtained from cocrystal eutectic constants at transition points as described in
Section 6.3.1.
231
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
1
100
SA = (Scocrystal /Sdrug)
232
10
log(SA) = log(SAaq) – –
log(SRdrug)
2
SAaq = 100
SAaq = 10
Supersaturated
SAaq = 2
1
Undersaturated
0.10
1
10
100
1000
104
SRdrug = (ST /Saq)drug
Figure 6.4 SA–SR diagram of (1 : 1) cocrystals with three different aqueous solubilities.
Cocrystal solubility advantage over drug or supersaturation index (SA) decreases in a
predictable way with increasing drug solubilization (SRdrug), according to the equation in the
plot. The dashed line indicates SA = 1. Intersections of cocrystal SA and SA = 1 lines represent
the SRdrug at which Scocrystal = Sdrug and identify transition points. In this example transition
points are at SR∗drug values of 4, 100, and 10 000 for the corresponding cocrystals. Cocrystal is
more soluble than drug below SR∗drug and becomes less soluble than drug above this SR∗drug
value. Source: Adapted from Kuminek et al. [23]. Reproduced with permission of Elsevier.
A remarkable property of cocrystals is that their SA dependence on solution
chemistry is quantifiable. We recently discovered a simple mathematical
expression between cocrystal SA and drug solubilization ratio (SRD) that is
the basis for SA–SR diagrams (Figure 6.4) [23]. A schematic SA–SR diagram
shows transition points and supersaturation and undersaturation regions as a
function of SRD. The slope of a log–log plot of SA and SRD is determined by
the cocrystal stoichiometry and is not dependent on solution conditions. For
a 1 : 1 cocrystal the slope is −1/2 (under the assumption that coformer solubilization is negligible). Therefore, cocrystal SA can be dialed to a desired value
from knowledge of cocrystal solubility in aqueous media by selecting additives
that achieve the corresponding SRD value.
6.2.3 A Word of Caution About Cmax Obtained from Kinetic Studies
Measurements of Cmax (maximum drug concentration) during cocrystal dissolution and conversion to less soluble forms abound in the literature. Cmax being
6.2 Structural and Thermodynamic Properties
a kinetic parameter is incorrectly interpreted as a thermodynamic solubility
(Figure 6.5). It is a result of two opposing kinetic processes, cocrystal dissolution
and drug precipitation. Dissolved drug concentrations are determined by these
two competing processes. As cocrystal SA increases, the expected higher
cocrystal dissolution may be dampened by a faster precipitation to the less soluble drug. Thus, the ranking of Cmax values may not correspond with that of
solubility values. In fact, Cmax may elude detection for cocrystals with high solubility advantage over drug or high SA. The term solubility in this chapter refers
to thermodynamic solubility.
Cmax values are variables in different works due not only to their kinetic
nature but also to differences in experimental conditions, pH, and composition of the solutions studied. Attempted relationships between Cmax and
crystal composition or structural properties should therefore be interpreted
with caution. In spite of the uncertainties about interpretations, Cmax
values are useful as long as they are taken as kinetic values with all their
implications.
Cmax ≠ Scocrystal
[Drug]
Moderately soluble cocrystal
Highly soluble cocrystal
Drug
Time
Figure 6.5 Cmax is a kinetic parameter determined by the rates of cocrystal dissolution and
drug precipitation. Cmax is not proportional to cocrystal SA as the relation between
dissolution and precipitation rates shifts with SA. Cmax will decrease and may elude detection
as precipitation rates become much higher than dissolution. Source: Reproduced from Roy
et al. [45] with permission of The Royal Society of Chemistry.
233
234
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
6.3 Determination of Cocrystal Thermodynamic
Stability and Supersaturation Index
6.3.1 Keu Measurement and Relationships Between Ksp, SCC, and SA
The cocrystal eutectic constant Keu describes cocrystal solubility and phase
behavior as a function of solution conditions. Its importance has been demonstrated for numerous cocrystals in a wide range of solvents, ionization, complexation, and solubilization conditions [33, 38, 46].
Keu is defined as the ratio of solution concentrations of cocrystal components
at the eutectic point (equilibrium of two solid phases with solution). Evaluation
of Keu is central to cocrystal characterization and determines:
••
••
•
Cocrystal to drug solubility ratio or SA.
Cocrystal thermodynamic stability relative to drug.
Transition points.
Ksp.
Cocrystal solubility and phase behavior as a function of ionization (pH) and
solubilization (additives that solubilize cocrystal components, such as complexing agents, surfactants, lipids, polymers, etc.).
The important implication of this analysis is that one only needs to measure
the point of mutual equilibrium of two solid phases of interest, for instance,
cocrystal and drug solid phases, in order to determine cocrystal solubility
and establish the cocrystal stability regions. Measurement of other thermodynamic data to generate a full phase diagram is not necessary for this purpose.
The diagram in Figure 6.6 summarizes the relationships between eutectic
points and cocrystal properties. Knowledge of Keu guides cocrystal selection,
formation, and formulation without the large materials and time requirements
of traditional methods. One can simply utilize the measured Keu to (i) evaluate
cocrystal Ksp and solubility under the experimental conditions studied or
(ii) predict cocrystal solubilities and transition points at other conditions of
interest without directly measuring them.
The procedure is as follows:
1) Measure the drug and coformer solution concentrations in equilibrium with
cocrystal and drug phases, [D]eu,T and [CF]euT, at a particular temperature,
pH, solution composition, etc. Concentrations and solubilities in this
section represent total values (with or without subscript T) unless otherwise
specified.
CF eu
2) Calculate Keu from Keu =
.
D eu
3) Compare Keu with the cocrystal stoichiometric molar ratio to determine
cocrystal solubility and stability relative to drug phase. Cocrystal is more
6.3 Determination of Cocrystal Thermodynamic Stability and Supersaturation Index
Cocrystal solubility
Solubility product
Ksp = [drug]eu,u [coformer]eu,u
Ksp = (Scc,u)2
Scc,T = [drug]eu,T[coformer]eu,T
Eutectic point
Supersaturation index
S
SA = cc,T
Sdrug,T
[drug]eu,T and [coformer]eu,T
in equilibrium with drug
and cocrystal phases
SA = Keu
Eutectic constant
[coformer]eu,T
[drug]eu,T
Keu =
Keu =
Scc,T
Sdrug,T
2
Transition point
[drug]eu,T = [coformer]eu,T
Keu = 1
Figure 6.6 Diagram illustrating how cocrystal solubility (SCC), cocrystal supersaturation
index (SA), and transition points can be obtained from eutectic point measurements. The
eutectic point here refers to 1 : 1 cocrystal and drug solid phases in equilibrium with a
solution at given pH, additive concentrations, and temperature. The terms are described
in the text. Source: Adapted from Kuminek et al. [23]. Reproduced with permission of
Elsevier.
soluble than drug under stoichiometric conditions when the value of Keu is
greater than cocrystal stoichiometric molar ratio. For the case of a 1 : 1
cocrystal, this means that when
CF eu
= 1 SCC = SD
D eu
CF eu
< 1 SCC < SD
D eu
CF eu
> 1 SCC > SD
D eu
The term SCC refers to the stoichiometric solubility of the cocrystal, that is,
the cocrystal solubility under solution molar ratios equal to those of the
cocrystal.
4) SA can be evaluated from the relationship of Keu and (SCC/SD). For a 1 : 1
cocrystal
Keu =
SCC
SD
2
= SA
2
66
235
236
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
5) SCC can be evaluated from knowledge of Keu and SD from the above relationship or from SCC = CF eu D eu for a 1 : 1 cocrystal. It is important to note
that this solubility refers to the specific conditions (pH, solution composition, temperature, etc.) under which it is measured.
Equations for Keu and SCC for other cocrystal stoichiometries are presented later
in this chapter.
The experimental methods to measure eutectic points are well established [5,
46, 47] and are summarized in the flowchart in Figure 6.7. It requires the suspension of the two solid phases of interest such as drug and cocrystal in a solution under desired conditions (pH, additives, temperature, etc.) until saturation
or equilibrium is reached. At this point solid phases are qualitatively analyzed
(since the ratio of solid phases at eutectic point does not affect the solution concentrations), and solution compositions of [D]eu and [CF]eu are quantitatively
measured. It is also essential to record the solution pH and temperature at
equilibrium.
Once a cocrystal is discovered, Keu can be evaluated according to the methods
described above. This Keu can then be used to calculate cocrystal transition
points, phase stability, SA, Ksp, and solubility, under conditions of interest.
Add cocrystal
and drug to
saturated drug
solution
Slurry until saturation or
equilibrium
Analyze solid phases by
XRPD or another solid state
technique. Are the two solid
phases present?
No
Only drug
Add cocrystal and
slurry until
saturation or
equilibrium
Yes
Measure [drug]eu,T
and [coformer]eu,T
at this equilibrium
in solution
No
Only cocrystal
Add drug and
slurry until
saturation or
equilibrium
Figure 6.7 Flowchart of representative method to determine equilibrium solution eutectic
concentrations of cocrystal components. In this case, the solid phases at equilibrium are
cocrystal and drug. Source: Reproduced from Kuminek et al. [23] with permission of Elsevier.
6.3 Determination of Cocrystal Thermodynamic Stability and Supersaturation Index
The importance of Keu for meaningful cocrystal characterization is described
below for the purpose of determining the influence of solubilizing agents
and pH.
The influence of a solubilizing agent on cocrystal stability and solubility
is shown in Figure 6.8 for the 1 : 1 cocrystal of carbamazepine-salicylic acid
(CBZ-SLC) in pH 3 aqueous solution [48]. Eutectic concentration measurements show that Keu for this cocrystal decreases from 4.8 in aqueous media
to 0.6 in 1% sodium lauryl sulfate (SLS). This simple experiment reveals very
important information with regard to cocrystal and drug solubilities and their
thermodynamic stabilities:
1) Cocrystal is more soluble (less stable) than drug (Keu > 1) in aqueous media
at pH 3.
2) Cocrystal is less soluble (more stable) than drug (Keu < 1) in 1% SLS.
3) Cocrystal exhibits a transition point at SLS < 1% where SCC = SD; both phases
are in equilibrium, Keu = 1.
Concentration at eutectic point (mM)
10
CBZ
SLC
Keu = 0.6
8
Keu =
[coformer]eu
[drug]eu
6
4
Keu = 4.8
2
0
Scocrystal
0% SLS
1% SLS
2.3 Sdrug
0.8 Sdrug
Figure 6.8 Concentrations of drug (carbamazepine, CBZ) and coformer (salicylic acid, SLC) at
the eutectic point for the 1 : 1 CBZ-SLC cocrystal and CBZ dihydrate system in pH 3.0 aqueous
solutions with and without surfactant (sodium lauryl sulfate, SLS). In the absence of
surfactant, [SLC]eu > [CBZ]eu, and Keu > 1, indicating that the cocrystal is more soluble than
the drug. This situation is inverted in 1% SLS, where [CBZ]eu > [SLC]eu and Keu < 1, indicating
that the cocrystal is less soluble than the drug. The solid phases at the eutectic point are the
cocrystal and CBZ dihydrate, which is the drug solid form in equilibrium with cocrystal in
aqueous media. The evaluation of Keu and SA = Scocrystal/Sdrug is described in the text. Source:
Reproduced from Kuminek et al. [23] with permission of Elsevier.
237
238
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
4) Cocrystal SA is 2.3 in aqueous media and 0.8 in 1% SLS at pH 3. This means
that cocrystal is 2.3 times more soluble than drug in the aqueous media,
whereas it is only 0.8 times as soluble as the drug in 1% SLS. Cocrystal
SA is calculated from SA = Keu as described by Equation (6.6) for a 1 : 1
cocrystal.
SA values represent (i) the driving force for conversion to the less soluble drug
and (ii) the highest possible drug levels that a cocrystal can achieve. Therefore,
knowledge of SA will guide the selection of additives and conditions required to
protect cocrystals from conversions and to achieve higher levels of drug exposure during dissolution. Cocrystal stability and dissolution studies without
knowledge of Keu provide interesting but not necessarily meaningful
information.
A similar characterization of 1 : 1 and 2 : 1 cocrystals and the influence of pH is
shown in Figure 6.9 for nevirapine (NVP) cocrystals [38]. For 1 : 1 nevirapinemaleic acid cocrystal (NVP-MLE), Keu > 1 at all pH values studied, indicating
that the cocrystal is more soluble than drug and that its solubility increases with
pH (Keu increases with pH). The pH value where drug and cocrystal solubilities
are equal is the pHmax, [D]eu = [CF]eu, for a 1 : 1 cocrystal or Keu = 1. For a 2 : 1
cocrystal at pHmax, [D]eu = 2[CF]eu or Keu = 0.5. Cocrystals are less soluble than
the drug below pHmax but become more soluble above pHmax [38]. The 2 : 1
nevirapine–saccharin (NVP-SAC) and 2 : 1 nevirapine-salicylic acid (NVPSLC) cocrystals are characterized by Keu < 0.5 at pH 1.2 and Keu > 0.5 at higher
pH values. This means that NVP-SAC and NVP-SLC cocrystals exhibit pHmax.
Therefore, whether the cocrystal has lower, equal, or higher solubility than the
drug is dependent on the solution pH.
A common mistake in cocrystal solubility and stability studies is that solution
conditions are not considered, and the solubilities or stabilities are incorrectly
applied. Even when initial pH conditions are known, in aqueous or buffered
solutions, the pH during cocrystal dissolution can change dramatically, causing
huge errors in interpretations.
Keu values for several cocrystals in aqueous solutions under specific pH and
additive conditions are shown in Table 6.4. The strong influence of ionization
and solubilization of cocrystal components is evident from the range of Keu
values.
The eutectic constant is related to the cocrystal SA [5, 46] by the expression
11
=
Keu
CF eu
SCC
=
D eu
SD
2
= SA
2
67
for 1 : 1 cocrystal and
21
=
Keu
CF eu
SCC
=0 5
D eu
SD
3
= 0 5 SA
3
68
6.3 Determination of Cocrystal Thermodynamic Stability and Supersaturation Index
(b)
(a)
200
Keu = 17
Keu = 50
Keu = 83
150
100
15
10
5
0
1.0
Nevirapine
Maleic acid
1.3
pH
Eutectic concentration (mM)
Eutectic concentration (mM)
250
Nevirapine
Keu = 102
50
25
10
Keu = 0.4
Keu = 8
5
0
1.5
Saccharin
1.2
2.4
pH
2.7
(c)
Eutectic concentration (mM)
30
Nevirapine
Salicylic acid
Keu = 240
25
8
Keu = 0.3
6
4
Keu = 6
2
0
1.2
3.2
pH
4.0
Figure 6.9 Drug and coformer eutectic concentrations at different pH values for (a) NVP-MLE,
(b) NVP-SAC, and (c) NVP-SLC. For the NVP-MLE cocrystal, [MLE]eu > [NVP]eu at all pH values,
indicating that the cocrystal is more soluble than the drug. SAC and SLC cocrystals have
[NVP]eu < or > than 2[SAC]eu and 2[SLC]eu. This behavior indicates that these cocrystals
exhibit a pHmax. For NVP-SAC pHmax is between pH 1.2 and 2.4. For NVP-SLC, pHmax is
between pH 1.2 and 3.2. Therefore, cocrystal solubilities are lower, equal, or higher than drug
depending on pH. The solid phases at the eutectic points are cocrystal and NVP hemihydrate,
which is the drug solid form in equilibrium with cocrystal in aqueous media. Source:
Reproduced from Kuminek et al. [38] with permission of The Royal Society of Chemistry.
239
240
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
Table 6.4 Influence of pH and solubilizing agents on Keu values.
pHeqa
Solid phases
at equilibrium
—
3.0
CBZ-SLC and CBZH
1% SLS
3.0
Cocrystal
Stoichiometry
Surfactant
CBZ-SLCb
1:1
CBZ-SACb
CBZ-SUC
1:1
b
2:1
b
CBZ-4-ABA-H
DNZ-HBA
c
DNZ-VANc
NVP-MLEd
2:1
1:1
1:1
1:1
—
2.2
1% SLS
2.2
—
3.1
1% SLS
3.1
CBZ-SAC and CBZH
CBZ-SUC and CBZH
4.0
CBZ-4-ABA-H and
1% SLS
4.0
CBZH
—
4.5
DNZ-HBA and DNZ
Tween
150 mM
4.4
—
5.0
Tween
150 mM
5.0
—
1.0
NVP-SLCd
2:1
—
1.2
31.2
2.2
—
—
14.7
1.5
10.8
1.0
400 000
56.0
DNZ-VAN and DNZ
76 000
27.0
NVP-MLE and NVPH
17.4
49.6
1.5
2:1
4.8
0.6
1.3
NVP-SACd
Keu
83.2
NVP-SAC and NVPH
0.4
2.4
8.1
2.7
101.9
1.2
NVP-SLC and NVPH
0.3
3.2
5.7
4.0
239.5
CBZH, carbamazepine dihydrate; CBZ-SAC, carbamazepine–saccharin cocrystal; CBZ-SLC, carbamazepinesalicylic acid cocrystal; CBZ-SUC, carbamazepine–succinic acid cocrystal; CBZ-4-ABA-H, carbamazepine-4aminobenzoic acid hydrate cocrystal; DNZ, danazol; DNZ-HBA, danazol-hydroxybenzoic acid cocrystal;
DNZ-VAN, danazol–vanillin cocrystal; NVPH, nevirapine hemihydrate; NVP-MLE, nevirapine-maleic acid
cocrystal; NVP-SAC, nevirapine–saccharin cocrystal; and NVP-SLC, nevirapine-salicylic acid cocrystal.
a
pH at equilibrium.
b
From reference [47].
c
Calculated from experimentally measured eutectic concentrations in reference [38] according to
Equation (6.6).
d
From Ref. [38].
6.3 Determination of Cocrystal Thermodynamic Stability and Supersaturation Index
1000
K 2:1
eu = 0.5
Scocrystal
Sdrug
3
K 1:1
eu =
4.0
2.7
100
Scocrystal
Sdrug
2
1.5
Keu
1.3
10
1
2.4
3.2
pH 1:1
max
2:1
pH max
0.1
0.1
1.0
NVP-MLE (1 : 1)
1.2
NVP-SAC (2 : 1)
1.2
NVP-SLC (2 : 1)
pHmax
1
10
100
Scocrystal /Sdrug
Figure 6.10 Predicted and experimental Keu and SA (Scocrystal/Sdrug) values for 1 : 1 (full line)
NVP-MLE and 2 : 1(dashed line) NVP-SAC and NVP-SLC cocrystals. Keu is a key indicator of SA.
Keu dependence on pH reveals the cocrystal pHmax and the cocrystal increase in solubility
over drug as pH increases. At pHmax, Keu = 1 for 1 : 1 cocrystals and Keu = 0.5 for 2 : 1 cocrystals.
Log axes are used due to the large range of values. Symbols represent experimental values.
The numbers next to data points indicate pH at eutectic point or equilibrium pH. The lines
were not fitted to the data but were calculated from the logarithmic forms of Equations (6.7)
and (6.8). Source: Reproduced from Kuminek et al. [38] with permission of The Royal Society of
Chemistry.
for 2 : 1 cocrystals where cocrystal solubility is expressed in terms of moles of
drug. Concentrations and solubilities refer to the analytical concentrations and
total solubilities.
These equations describe the dependence of Keu on SA as shown for 1 : 1 and
2 : 1 cocrystals of NVP in Figure 6.10. NVP is a weakly basic drug and its cocrystals
include weakly acidic coformers. Both SA and Keu are found to be dependent on
pH, and there is a pHmax at SA = 1 and Keu = 1 for 1 : 1 cocrystals and Keu = 0.5
for 2 : 1 cocrystals.
6.3.2
Cocrystal Solubility and Ksp
The stoichiometric cocrystal solubility (cocrystal at equilibrium with solution
concentrations of constituents equal to their molar ratio) is often difficult to
measure directly because of conversion to less soluble forms. In these cases,
241
242
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
the stoichiometric solubility of cocrystals (AyBz) can be obtained from equilibrium concentrations with cocrystal phase or at eutectic:
SCC =
y+z
ATBT
yyz z
69
where the total concentrations A and B correspond to the analytical equilibrium
concentrations of each component. For 1 : 1 and 2 : 1 cocrystals in terms of drug
and coformer [CF] molar concentrations, Equation (6.9) becomes
11
=
SCC
D T CF T
6 10
D T 2 CF T
4
6 11
and
21
SCC
=
3
Subscript T refers to the total concentration (or analytical concentration) at
equilibrium and is given by the sum of all the drug and coformer species in solution. This may include ionized and nonionized as well as aqueous and solubilized species. Equation (6.11) refers to SCC in terms of moles of cocrystal. The
value of [D]T corresponds to the drug solubility at the eutectic point or to the
drug concentration in equilibrium with cocrystal when cocrystal is the only
solid phase.
Ksp can be evaluated from (i) the product of concentrations of free and nonionized drug and coformer according to the definition of Ksp in Equation (6.2)
[34, 35] or (ii) the appropriate solubility equations under ionizing and solubilizing conditions, presented in Section 6.6. These two approaches are shown for
the 1 : 1 cocrystal of a weakly basic drug (NVP) and an acidic diprotic coformer
(MLE). First, Ksp was calculated from the product of concentrations of nonionized eutectic concentrations (eu,n) cocrystal components according to
Ksp = B eu, n H2 A eu, n
6 12
Applying nonionized eutectic concentrations of drug and coformer ([NVP]eu,n
and [MLE]eu,n) presented in Table 6.5 gives
Ksp = 0 00012 × 0 1423 = 1 7 × 10 −5 M2
A second method to evaluate Ksp relies on determining SCC solubility and solving for Ksp from the appropriate equation. The cocrystal solubility under stoichiometric conditions is calculated from measured total eutectic concentrations
of drug and coformer presented in Table 6.5 according to Equation (6.10):
11
SCC
= 0 0036 × 0 1806 = 0 0255 M
6.3 Determination of Cocrystal Thermodynamic Stability and Supersaturation Index
243
Table 6.5 Eutectic point concentrations and solid phases for NVP-MLE/ NVP system measured in
water at 25 C [38].
[NVP]eu,T (M)
[MLE]eu,T (M)
[NVP]eu,n (M)a
[MLE]eu,n (M)a
pHeu
Solid phases at
equilibrium
0.0036
0.1806
0.00012
0.1423
1.3
NVPHb and NVP-MLE
a
Calculated from measured eutectic concentrations and pKa values shown in the text using Henderson–
Hasselbalch equations.
b
Nevirapine hemihydrate (NVPH).
The cocrystal Ksp can be then calculated by solving the cocrystal solubility
equation for Ksp, which for a 1 : 1 cocrystal of a diprotic acid (H2A) and a basic
drug (B) is
Ksp =
SBH2 A
2
1 + 10 pKa, B− pH 1 + 10 pH −pKa1, H2 A + 102pH −pKa1, H2 A − pKa2, H2 A
6 13
with SCC = 0.0255 M and pKa values for NVP and MLE reported in the literature
(pKa1,MLE = 1.9, pKa2,MLE = 6.6 [49], and pKa,NVP = 2.8 [50]). The Ksp value
obtained is equal to that from Equation (6.12).
The eutectic concentrations presented in Table 6.5 are the average of measurements at a single pH value. Ksp can also be obtained by fitting
Equations (6.12) and (6.13) by regression as described elsewhere [34]. Small
deviations in Ksp values have been observed for cocrystals [34, 38, 51] and salts
[29, 31] with changing pH and ionic strength.
6.3.3
Cocrystal Supersaturation Index and Drug Solubilization
Drug solubilizing agents are often encountered in formulations as well as
in vitro and in vivo dissolution. Since solubilizing agents can lead to changes
in cocrystal SA, it is of practical importance to be able to predict such behavior.
This section describes how to select solubilizing agents to achieve desired SA
and to predict cocrystal transition points from knowledge of only cocrystal solubility in aqueous media.
While cocrystal solubility is described by considering the solution-phase
chemistry, reaction equilibria, and equilibrium constants, we first present
a simplified version of this analysis in terms of commonly measured drug
solubilization parameters. Coformer solubilization is assumed to be
negligible in this analysis. It is a first good approximation since solubilizing
agents preferentially solubilize hydrophobic drugs and not hydrophilic
coformers.
244
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
For a 1 : 1 cocrystal, the SA varies with drug solubilization ratio SRD according to
SCC SD aq
SCC
=
SD
ST Saq D
6 14
or
SA =
SAaq
SRD
6 15
SA is the cocrystal solubility advantage at drug solubilization SRD, and SAaq is
the aqueous cocrystal solubility advantage in the absence of drug solubilization.
SR is the ratio of total solubility in drug solubilizing media (ST) and aqueous
solubility (Saq). ST represents the sum of concentrations of all dissolved species
(ST = Saqueous + Ssolubilizing agent). Saq represents the cocrystal aqueous solubility
at a given pH in the absence of solubilizing agent (Saq = Snonionized,aq + Sionized,
aq) and is the sum of the nonionized and ionized contributions to the aqueous
solubility. When SRD = 1, SA = SAaq. The above expression clearly suggests a
way of fine-tuning cocrystal supersaturation by changing drug solubilization
through addition of polymers, surfactants, lipids, or additives that preferentially
solubilize drug over coformer.
The logarithmic form of Equation (6.15)
1
log SA = log SAaq − log SRD
2
6 16
is of practical importance as the dependence of SA on SRD is simply predicted
from knowledge of SAaq. As described in Section 6.2.2.3, SA diagrams, log (SA)
versus log (SRD) (Figures 6.4 and 6.11), are characterized by (i) lines with slope
of −1/2 where the position of each line is determined by the cocrystal SA value,
(ii) the drug solubilization associated with a given cocrystal SA, and (iii) the
regions of drug solubilization over which the cocrystal is more soluble, equally
soluble, or less soluble than drug, SA > 1, = 1 or < 1.
The intersection of a cocrystal SA line with the SA = 1 line establishes the SRD
value below which cocrystal can generate supersaturation with respect to
drug or transition point. Consequently, the level of supersaturation or
undersaturation with respect to drug (SA) can be selected from knowledge of
the additive influence on SRD. Therefore, rather than developing a cocrystal
under its highest SA, the SA can be modulated to a lower value that meets
the required exposure levels of drug with or without addition of crystallization
inhibitors [23].
6.3 Determination of Cocrystal Thermodynamic Stability and Supersaturation Index
1 000
DNZ-HBA Tween 80 pH 4.5
PTB-CAF Lipid
CBZ-SAC SLS pH 2.2
SAaq = 770
100
SA = Scocrystal/Sdrug
SAaq = 26
10
SAaq = 4
1
0.1
0.01
0.001
0.1
1
10
100
1 000
SRdrug
10 000 100 000 1 000 000
Figure 6.11 Predicted (full lines) and observed (symbols) behavior of cocrystal solubility
advantage (SA) as a function of drug solubilization ratio (SRdrug) for danazol-hydroxybenzoic
acid (DNZ-HBA), pterostilbene–caffeine (PTB-CAF), and carbamazepine–saccharin (CBZ-SAC)
cocrystals. Cocrystal SA predicted from equations using only experimentally determined
cocrystal SAaq. The dotted line at SA = 1 indicates the line of equal cocrystal and drug
solubilities, SA = 1. Source: Adapted from Kuminek et al. [23]. Reproduced with permission
of Elsevier.
Figure 6.11 shows the SA–SR diagram for cocrystals of CBZ, danazol (DNZ),
and pterostilbene (PTB) in different surfactant systems as indicated in the plot.
Both cocrystal SA and SRD are well predicted according to Equation (6.15),
using only the SAaq experimental value for each cocrystal. The results also anticipate the observed lower solubility of PTB cocrystal compared with drug at SRD
in a lipid formulation [52]. SRD for PTB in this formulation was measured to be
12 200. This value is above the SRD at the transition point, and therefore SCC is
lower than SD. A similar analysis for the DNZ cocrystals indicated that for these
cocrystals, the SA values decreased with SRD, but the cocrystal solubility still
exceeded drug solubility. It is noted that these calculations are based on the
assumption of negligible coformer solubilization.
An important insight from this analysis is that the smaller SAaq is, the lower is
the drug solubilization ratio at the transition point, SR∗D This means that
cocrystals with modest SAaq values are more susceptible to inversion of SA
at low extents of drug solubilization. Therefore, it is essential to know what
the SR∗D is before formulating cocrystals so that inadvertent inversion in cocrystal SA does not occur.
245
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
6.4 What Phase Solubility Diagrams Reveal
Figure 6.12 illustrates the phase solubility diagram (PSD) of a 1 : 1 cocrystal and
its constituents (drug (A) and coformer (B)). In this case, the cocrystal is more
soluble than the drug under stoichiometric conditions. This plot shows that
cocrystal solubility is a function of solution composition. Cocrystal solubility
decreases with increasing coformer concentration as a result of the cocrystal Ksp.
Another important feature of the cocrystal is that its solubility curve intersects the drug, and the coformer solubility curves at c1 and c2. These intersections represent eutectic points: c1 where drug and cocrystal are in equilibrium
and c2 where coformer and cocrystal are in equilibrium. Knowledge of the
eutectic points defines the solution concentrations of A and B at which cocrystal
is the thermodynamically stable phase. As pharmaceutical cocrystals are generally more soluble than drug and less soluble than coformer under stoichiometric
conditions, the cocrystal/drug eutectic point is the most relevant to determine
cocrystal to drug transformations and vice versa. Cocrystal is the equilibrium
phase in the range of compositions of the liquid phase in Domain III. Depending
on the liquid phase composition, drug phase can transform to cocrystal
(Domain III) or vice versa (Domain I).
SAB
II
I
SA
C1
[A]T
246
III
IV
C2
[B]T
SB
Figure 6.12 Phase solubility diagram showing the dependence of solid-phase equilibria on
solution composition. Drug, coformer, and cocrystal are represented by A, B, and AB.
Cocrystal solubility, line SAB, decreases with increasing coformer concentration and intersects
the coformer and drug solubility curves, SA and SB, at eutectic points represented by c1 and c2.
The solution is saturated with both A and AB at c1 and with B and AB at c2. The filled circle
refers to a cocrystal solubility in a solution of 1 : 1 molar ratio of cocrystal components.
Solubilities of pure components are represented by lines SA and SB. Source: Adapted from
Nehm et al. [53]. Reproduced with permission of ACS Publications.
6.4 What Phase Solubility Diagrams Reveal
The important implication of this analysis is that one only needs to measure
the eutectic point corresponding to the two solid phases of interest, for instance,
cocrystal and drug, in order to determine cocrystal solubility and establish the
cocrystal stability regions. Measurement of other thermodynamic data to generate a full phase diagram is not necessary for this purpose.
Phase diagrams also reveal the stability and conversions of cocrystals with different stoichiometries. Figure 6.13 shows the phase diagram for the 1 : 1 and 2 : 1
cocrystals of carbamazepine-4-aminobenzoic acid (CBZ-4ABA). In this case,
there are three eutectic points corresponding to the following pairs of solid
phases in equilibrium: c1 – drug and 2 : 1 cocrystal, c2 – 2 : 1 cocrystal and
1 : 1 cocrystal, and c3 – 1 : 1 cocrystal and coformer. The 2 : 1 cocrystal is stable
in solutions of 1 : 1 ratio of CBZ and 4ABA and between c1 and c2. The 1 : 1
cocrystal is thermodynamically unstable in these solutions except for conditions
between c2 and c3. One would expect that in pure ethanol, 2 : 1 converts to drug,
and 1 : 1 converts to drug and to 2 : 1. One can see that attempts to form the 1 : 1
or the 2 : 1 cocrystals under conditions where the drug and the coformer have
the same molar ratio as the cocrystal are not necessarily appropriate or successful [51].
0.30
2:1
1:1
0.25
1 : 1 cocrystal
[CBZ]T (m)
0.20
0.15
a
0.10
c1
c2
Drug
c3
2 : 1 cocrystal
0.05
0.00
0.00
Coformer
b
0.20
0.40
0.60
0.80
1.00
1.20
1.40
[4ABA]T (m)
Figure 6.13 CBZ-4ABA phase solubility diagram in ethanol demonstrates the influence of
coformer concentration on the solubilities of drug (open diamond), coformer (filled
diamond), 2 : 1 cocrystal (open circles), and 1 : 1 cocrystal (open square). Source: Reprinted
with permission from Jayasankar et al. [51]. Reproduced with permission of American
Chemical Society.
247
248
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
A graphical representation in a triangular phase diagram (TPD) of the data in
Figure 6.13 provides information about the composition of the solid and solution phases in equilibrium (Figure 6.14).
These two types of graphical representations are useful for different applications. The PSD (Figure 6.13) shows the liquid phase composition in equilibrium
with solid phases, whereas the TPD (Figure 6.14) shows the total composition of
solid and liquid phases at equilibrium. That is, when there is more than one solid
phase in equilibrium with solution, the fraction of each phase can be obtained
from a TPD but not from a PSD. The PSD shows the solubility of three solid
phases (A, B, and cocrystal AB) as a function of solution concentrations of
A and B. Concentrations are generally expressed in terms of molarity or molality. PSDs are useful to determine solution phenomena and evaluate equilibrium
constants such as complexation. The TPD shows both the solubilities of the
three solid phases and the composition of solid phases when two solid phases
are in equilibrium with solution (fraction of A or B and cocrystal AB in the solid
Ethanol
0.0
a
1
1.0
c1
b
c2
0.2
c3
0.8
0.4
4
0.6
2
3
0.6
0.4
0.2
0.8
5
1.0
CBZ
0.0
6
2:1
0.2
1:1
7
0.0
0.4
0.6
0.8
1.0
4ABA
Figure 6.14 Triangular phase diagram of the CBZ, 4ABA, ethanol system shows the stability
domains and corresponding solution-/solid-phase compositions. In this solvent and at the
temperature studied, the domain of existence (2) of the pure 2 : 1 cocrystal. By comparison,
the domain of existence (3) of the pure 1 : 1 cocrystal is quite narrow and may be found at
high coformer to drug ratios (greater than 12). Source: Reprinted with permission from
Jayasankar et al. [51]. Reproduced with permission of American Chemical Society.
6.5 Cocrystal Discovery and Formation
phase). The units in the TPD are not solution concentrations but total composition in terms of mole fraction or weight fraction of each component, such as
(A/(A + B + C)).
6.5
Cocrystal Discovery and Formation
6.5.1 Molecular Interactions That Play an Important
Role in Cocrystal Discovery
Crystal engineering has provided a rational basis to design new crystals with
desired physicochemical and pharmaceutical properties [54]. Favorable intermolecular interactions and geometries during self-assembly are responsible
for the generation of supramolecular networks that may lead to crystalline
phases [55–60]. These solid-state supermolecules are assembled from specific
noncovalent interactions between molecules, including hydrogen bonds, ionic,
van der Waals, and π–π interactions.
Common spatial arrangements of noncovalent intermolecular interactions
with specified geometries and bonding motifs are referred to as synthons
[54]. Some examples of synthons are shown in Figure 6.15. The coformer selection for cocrystallization can be identified based on molecular recognition interactions using synthon theory. Complementarity of hydrogen bonds between
coformers and drugs is one of the criteria for coformer selection.
The Cambridge Structural Database (CSD) is often used to perform supramolecular retrosynthetic analysis, which involves identifying intermolecular units
O
H
O
O
H
H
O
O
H N
N H
O
N
H
H
O
O
H
N
N
N
H
H
H
O
O H
H N
O
O
H
N
O H
N
N
H
H
O
O
Figure 6.15 Common supramolecular synthons formed with carboxylic acids, amides,
pyridines, and other aromatic nitrogens. Source: Reproduced from Kuminek et al. [23] with
permission of Elsevier.
249
250
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
for a target cocrystal structure. There are two distinct categories of synthons:
(i) homosynthons, which are formed between identical functional moieties,
as exemplified by carboxylic acid and amide dimers in Figures 6.15, and (ii) heterosynthons, composed of different but complementary functional moieties,
including carboxylic acid-amide, carboxylic acid-pyridine, and carboxylic
acid-aromatic nitrogen synthons [61]. Cocrystal structures may contain different combinations of homosynthons and heterosynthons [54, 56]. Additionally,
these intermolecular interactions may be homomeric, between the same molecule, or heteromeric, between different molecules [62].
CBZ is a primary amide drug, and a synthon-based strategy was applied to
form 1 : 1 and 2 : 1 stoichiometric cocrystals with 4ABA. As described earlier
for other CBZ cocrystals, homomeric or heteromeric synthons can form as
shown in Figure 6.16 [10, 51]. It is interesting to note that in the case of 2 : 1
cocrystal hydrate, the water molecule is inserted into the amide-acid heterosynthon to form an amide-acid-H2O heterosynthon (Figure 6.16c).
Hydrogen bonds most strongly influence molecular recognition due to their
directional interactions. Donohue and Etter developed general guidelines for
preferred hydrogen bond patterns in crystals based on rigorous analysis of
hydrogen bonds and packing motifs, these include: (i) the hydrogen bonding
in the crystal structure will include all acidic hydrogen atoms, (ii) all good
hydrogen bond acceptors will participate in hydrogen bonding if there is an
(a)
(b)
(c)
Figure 6.16 Different synthons in carbamazepine: 4-aminobenzoic acid cocrystals (CBZ4ABA): (a) carboxamide homosynthon of the 1 : 1 CBZ-4ABA, (b) tetrameric amide-acid
heterosynthon of the 2 : 1 CBZ-4ABA, and (c) amide-acid-H2O heterosynthon of the 2 : 1 CBZ4ABA-H. Source: Adapted with permission from Jayasankar et al. [51]. Copyright 2009,
American Chemical Society.
6.5 Cocrystal Discovery and Formation
adequate supply of hydrogen bond donors, (iii) hydrogen bonds will preferentially form between the best proton donor and acceptor, and (iv) intramolecular
hydrogen bonds in a six-membered ring form in preference to intermolecular
hydrogen bonds [63–65].
In addition to these rules, the stereochemistry and competing interactions
between molecules may need to be considered in cocrystal design. Other considerations in designing stable crystal structures include minimizing electrostatic energies and the free volume within the crystal [66]. Beyond the
synthon-based complementarity, the factors that influence cocrystal formation
need to be considered and are discussed below.
6.5.2 Thermodynamics of Cocrystal Formation Provide Valuable
Insight into the Conditions Where Cocrystals May Form
Cocrystal screening has been performed using a variety of solution and solidstate-based methods such as slow solvent evaporation [9, 12, 13, 67, 68], slurry
conversion [69], neat (dry) grinding [70, 71]), solvent-drop grinding [72–74],
melt [75, 76], and sublimation. When using these methods, it is possible that
only one of the components crystallizes, and often a very large number of solvents and experimental conditions need to be tested. This section will not discuss all these methods in depth but summarizes the main principles that guide
cocrystal formation. In order to avoid the obtainment of just individual component crystals, basic concepts of crystallization can be applied to understand and
control the nucleation and growth of cocrystals.
Cocrystal formation requires that two or more different molecular components crystallize in a single homogeneous phase in well-defined stoichiometry
as described by the reaction in Equation (6.2). The thermodynamic equilibrium
constant for this reaction is the solubility product Ksp (Equation (6.4)). The concept of Ksp is well recognized in salt formation (salting out), and it also applies
for cocrystal formation as described below.
The driving force for nucleation and crystal growth is the supersaturation (σ),
which is dependent on solution composition, and for a 1 : 1 cocrystal RHA, it is
expressed by
σ=
aR aHA
Ksp, a
1 2
R HA
Ksp
1 2
6 17
where [R] is the drug concentration and [HA] is the coformer concentration.
This equation shows that supersaturation with respect to cocrystal increases
by increasing the concentration product above Ksp.
The reaction crystallization method (RCM) for cocrystal formation is based
on these concepts. The advantage of RCM over other screening methods is that
the solution is supersaturated with respect to cocrystal, while it is saturated or
251
252
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
undersaturated with respect to individual components [77]. Under these conditions, crystallization of pure components does not occur. Cocrystals are prepared by simply dissolving cocrystal components without the need of
subsequent evaporation or cooling. RCM is also the process by which moisture/vapor sorption and solvent-drop grinding lead to cocrystal formation.
Cocrystal screening by RCM has been successfully applied for cocrystal
discovery using 96-well plates [40]. First, several solvents are presaturated
with the coformers of interest. Second, the solid drug (above its solubility)
is added to these solutions and slurried. Solid-phase changes are then monitored by in situ methods such as by Raman microscopy (Figure 6.17) or
other appropriate method [40]. Since crystallization, if it occurs, is a result
of drug dissolution into a highly concentrated coformer solution, a new solid
phase is likely to be a solvate, salt, or cocrystal, or combinations of these.
RCM is useful for both screening and synthesis and is transferable to large
and small scales.
Other solution-based methods to form cocrystals involve temperature change
(solvothermal) [9, 12, 13, 68, 78], slurrying reactants with or without ultrasound
Raman microscope
Raman Shift indicates cocrystal formation
Cocrystals
CBZ
240 260 280 300 320 340
Raman shift (1 cm–1)
370 380 390 400 410 420
Raman shift (1 cm–1)
760 765 770 775 780 785 790 795 800 805 810
Raman shift (1 cm–1)
Figure 6.17 Rapid in situ cocrystal screening by RCM in microliter (96-well plates) by Raman
microscopy, indicating spectral changes between drug crystals (carbamazepine) and its
cocrystals [23, 40]. Source: Reproduced from Kuminek et al. [23]. Copyright 2016, with
permission from Elsevier.
6.6 Cocrystal Solubility Dependence on Ionization and Solubilization of Cocrystal Components
pulses (sonic slurry) [79, 80], vapor sorption of solid reactants (moisture/vapor
sorption) [81–83], changing concentration (evaporation), [9, 12, 13, 68], and
changing cocrystal solubility through pH or antisolvent addition [84].
Cocrystal formation by solid-state-mediated processes is based on molecular mobility and molecular complementarity. Cogrinding cocrystal
components has been commonly used in the search for cocrystals [9, 64,
65, 70–74, 79]. Cocrystallization in some of these cases has been shown
to be mediated by amorphous phases. Cogrinding reactants with addition
of solvent drops (solvent-drop grinding or liquid-assisted grinding) can lead
to cocrystal formation through solution and/or solid-phase-mediated processes [72–74].
Cocrystal formation in melts has also been used in cocrystal screening [75, 76]
and large-scale processes. The application of hot melt extrusion appears to be a
promising alternative to formation of cocrystals where chemical instability is
not an issue [85].
6.6 Cocrystal Solubility Dependence on Ionization
and Solubilization of Cocrystal Components
6.6.1
Mathematical Forms of Cocrystal Solubility and Stability
Previous sections of this chapter provide most of the general concepts and
quantitative relationships that are needed for characterization and prediction of cocrystal behavior. In this section we will consider the phase and
chemical equilibria that give rise to cocrystal solubility and stability equations. We will first present the general form of the cocrystal solubility equations obtained by considering ionization and solubilization equilibria. We
will then consider cocrystal ionization and solubilization behavior for
1 : 1 cocrystals.
Although solubility is often reported as a single value, in reality it varies with
changing solution conditions such as pH and presence of solubilizing agents.
Total solubility of a binary cocrystal AyBz may be expressed as a function of
equilibrium constants and relevant concentrations as
SCC, T = f Ksp , Ka , Ks , Kc , H + , M y z
6 18
where Ksp, Ka, Ks, and Kc are the dissociation, ionization, solubilization by additives, and complexation equilibrium constants, respectively, [H+] represents
hydrogen ion concentration as determined by pH, [M] represents total solubilizing agent concentration or micellar concentration, and y and z represent the
stoichiometric coefficients of the drug and coformer, respectively. For simplicity, complexation will not be considered in this section.
253
254
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
The total influence of both ionization and solubilization on cocrystal solubility may be summarized for both the drug and coformer using the representative
terms δD,T and δCF,T, where
δD, T = δD, I + δD, S
6 19
δCF, T = δCF, I + δCF, S
6 20
and
where subscripts I and S refer to ionization and solubilization. The ionization
parameters δD,I and δCF,I are a function of Ka and [H+], and the solubilization
parameters δD,S and δCF,S are a function of Ks and [M]. Thus, Equation (6.18)
may be simplified as
SCC, T = f Ksp , δD, T , δCF, T y z
6 21
Cocrystal solubility can be calculated from the general equation
SCC, T =
y+z
Ksp y
δ δCF, T z
y y z z D, T
6 22
This equation can be used to calculate solubility for a cocrystal of given
stoichiometry and under specific ionization and solubilization conditions by
substituting δI and δS expressions in terms of the appropriate equilibrium constants (Table 6.6) [46].
When cocrystal solubility is only influenced by dissociation (δD,T = 1 and
δCF,T = 1), Equation (6.22) becomes
SCC, T =
y+z
Ksp
yyz z
This equation was described earlier in this chapter (Equation 6.5).
For a 1 : 1 cocrystal, y = z = 1 and Equation (6.22) becomes
SCC, T =
Ksp δD, T δCF, T
6 23
The equations associated with the expressions in Table 6.6 are mathematically derived from equilibrium and mass balance equations of a particular system. The equilibrium reactions corresponding to the δ terms in Table 6.6 are
presented in Table 6.7.
The mass balance equation for the case of a 1 : 1 cocrystal RHA composed of
nonionizable drug (R) and ionizable coformer (HA) is based upon the phase and
chemical equilibria presented in Figure 6.18 [23].
Table 6.6 Ionization (δI) and solubilization (δS) terms used to calculate cocrystal solubility
according to Equations (6.19), (6.20), and (6.22).a
Ionization of cocrystal component
δI
δS
Nonionizable (R)
1
KsR M
Monoprotic acidic (HA)
1+
KaHA
H+
Diprotic acidic (H2A)
1+
KaH2 A KaH2 A KaHA
+
H+
H+ 2
Monoprotic basic (BH+)
1+
H+
+
KaBH
KsBH M
Amphoteric (HAB)
1+
KaHAB
H+
+ H AB +
H+
Ka 2
KsHAB M
Zwitterionic (−ABH+)
1+
Ka− ABH
H+
+ HABH +
+
H
Ka
KsHA M
−
KsH2 A M
+
+
Ks− ABH + M
The expressions for cocrystal solubilities were previously derived and experimentally confirmed
[34, 46].
a
It should be noted that these expressions for δS have excluded the Ks term(s) for all charged species.
In many cases when Kneutral
>> Kcharged
, the solubilization of charged species will have a negligible
s
s
effect on total cocrystal solubility [35, 86–88].
Table 6.7 Homogeneous equilibrium reactions and associated constants corresponding to
ionization and micellar solubilization of cocrystal components.
Ionization of cocrystal
component
Equilibrium expression
Equilibrium
constant
Nonionizable (R)
Raq
KsR
Monoprotic acidic
(HA)
Diprotic acidic (H2A)
Monoprotic basic
(BH+)
Amphoteric (HAB)
Rm
−
aq + A aq
HAaq
H
HAaq
HAm
KaHA
KsHA
H2Aaq
H+aq + HA−aq
2A
KH
a
HA−aq
H+aq + A2−aq
KHA
a
H2Aaq
H2Am
2A
KH
s
BH+aq
+
H
BH+aq
HABaq
+
BH+m
KBH
s
+
H+aq + AB−aq
KaHAB
HABaq
−ABH+aq
HABH
aq
+ Baq
HABaq + H+aq
2 AB
KH
a
aq
−ABH+aq
H+aq + AB−aq
− ABH
+
KsHAB
HABm
+
−
KBH
a
H2AB+aq
Zwitterionic (−ABH+)
+
+
aq +
Ka−ABH +
+
H
aq
− ABH+m
Subscripts m and aq refer to micellar and aqueous pseudophases, respectively.
KHABH
a
+
Ks−ABH +
256
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
Rmicelle
HAmicelle
KS, R
RHAsolid
Ksp
KS, HA
R
+
HA
KC
RHA
KA
H+ + A–
Figure 6.18 Cocrystal solubility is determined by the fate of its molecular constituents in
solution. This diagram shows cocrystal solution-phase interactions for a cocrystal RHA
composed of nonionizable drug (R) and ionizable coformer (HA) as well as the associated
equilibria common to pharmaceutical dosage forms, including dissociation, complexation,
ionization, and solubilization. Ksp represents the cocrystal solubility product, Ka is the
ionization constant, Kc is the complexation constant, and KsHA and KsR are the solubilization
constants for HA and R, respectively. Source: Reproduced from Roy et al. [45] by permission of
The Royal Society of Chemistry.
Mass balance on R and A gives the total solubility of cocrystal RHA under
stoichiometric conditions as
SRHA, T = R T = A T
6 24
where [R]T and [A]T represent the concentrations of all species in solution. The
cocrystal solubility is
SRHA, T = R aq + RHA aq + R m = HA aq + A −
aq
+ RHA aq + HA m
6 25
where subscript aq represents the aqueous phase and subscript m represents the
micellar phase.
The concentrations of all species in Equation (6.25) can be expressed in terms
of the concentrations of cocrystal components (free and nonionized) R and HA
using the equilibrium constants. This analysis gives the cocrystal solubility in
terms of equilibrium constants (ionization and solubilization of cocrystal components, KaHA , KsHA , and KsR ) and micellar concentration of surfactant [M]:
SRHA, T =
Ksp 1 + KSR M
1+
KaHA
+ KsHA M
H+
6 26
where Ksp is the solubility product given by [R][HA]. The terms in parenthesis
represent ionization and solubilization according to the equilibrium reactions in
Figure 6.18.
6.6 Cocrystal Solubility Dependence on Ionization and Solubilization of Cocrystal Components
The generalized form for a cocrystal RHA under the solubility conditions in
Figure 6.18 gives
SRHA, T =
Ksp δR, S δA, I + δA, S
6 27
and shows how the expressions for the ionization and solubilization terms presented in Table 6.6 can be utilized to obtain the cocrystal solubility equation.
Note that solubilization of ionized species is not considered in the expressions
in Table 6.6.
6.6.2 General Solubility Expressions in Terms of the Sum
of Equilibrium Concentrations
The solution chemistry parameters that we are concerned with here correspond
to ionization and solubilization of cocrystal components. The summation of
ionized and solubilized equilibrium concentrations is defined in terms of equilibrium constants, [H+] and [M], as described below.
Ionization of cocrystal components is defined as the sum of acidic and basic
functional groups of cocrystal components according to
m
δD, I = 1 +
l=1
l
acidic
n = 1 Kan
+ l
H
r
H+
+
q
q
basic
t = 1 Kat
q=1
6 28
for drug, and
g
δCF, I = 1 +
f =1
f
acidic
h = 1 Ka h
+ f
H
j
H+
+
i
i
basic
k = 1 Ka k
i=1
6 29
for coformer, where m and g are the total number of respective acidic groups
and r and j are the total number of respective basic groups [46]. It should be
noted from these equations that when ionization is not considered, both δD,I
and δCF,I reduce to one (as predicted by Equation (6.5)).
In solutions with additives that solubilize cocrystal components, the heterogeneous equilibria between cocrystal and its components are taken into consideration as illustrated in Figure 6.19 [45, 47, 48, 89, 90]. This diagram only represents
solubilization of the drug component of the cocrystal and assumes negligible
solution complexation as well as nonionizing solution conditions [35, 37].
Solubilization of cocrystal components is defined as the sum of all cocrystal
dissolved species (ionized and nonionized) according to
m
δD, S = Ks1 M +
l=1
l
acidic
n = 1 Kan
+ l
H
r
Ksl + 1
+
q=1
H+ q
Ksq + 1
q
basic
t = 1 Kat
M
6 30
257
258
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
Cocrystal
Ksp
KR
s
Aqueous pseudophase
Micellar pseudophase
Figure 6.19 Schematic illustration of the equilibria between the cocrystal solid phase and its
components in the aqueous and micellar solution pseudophases. This scheme represents
preferential micellar solubilization of the drug component, which leads to excess coformer in
the aqueous phase. Source: Reprinted with permission from Huang and Rodríguez-Hornedo
[48]. Copyright 2010, American Chemical Society.
for drug, and
δCF, S =
g
Ks1 M +
f =1
f
acidic
h = 1 Kah
f
+
H
j
Ksf + 1
+
i=1
H+
i
i
basic
k = 1 Kak
Ksi + 1
M
6 31
for coformer, where m and g are the total number of respective acidic groups
and r and j are the total number of respective basic groups. Ks1 represents
the solubilization equilibrium constant for the nonionized species, while
Ksl + 1 , Ksq + 1 , Ksf + 1 , and Ksi + 1 represent the solubilization constants for the respective acidic and basic groups of the drug and conformer as ionization proceeds. It
should be noted from these equations that when solubilization is not considered
(Ks = 0), both δD,S and δCF,S reduce to zero.
6.6.3 Applications
Cocrystal solubility as a function of pH and solubilization can be predicted from
knowledge of Ksp, Ka, and Ks values according to the equations presented above.
6.6 Cocrystal Solubility Dependence on Ionization and Solubilization of Cocrystal Components
Solubility-pH profiles in Figure 6.20 generated from the appropriate
equations illustrate how cocrystal stoichiometry and ionization properties of
drug and coformer can influence cocrystal and drug solubilities [34]. The predictive power of these equations has been confirmed for CBZ [34, 35, 40],
(a)
1.0 × 10–1
IND-SAC
Solubility (m)
1.0 × 10–2
1.0 × 10–3
IND
1.0 × 10–4
1.0 × 10–5
1.0 × 10–6
1
2
3
4
pH
5
7
6
Figure 6.20 Solubility-pH profiles for (a) 1 : 1 HAHX cocrystal calculated using
SHAHX,T =
Ksp 1 +
KaHA
1
H+
1+
KaHX
1
, (b) 1 : 1 RHA cocrystal calculated using Equation
H+
(6.26), (c) 2 : 1 R2HAB cocrystal calculated using SR2 HAB,T =
3
K HAB
Ksp
H+
1 + a1+ + H AB + , and
4
H
Ka22
(d) 1 : 1 BH2A and 2 : 1 B2HA cocrystals calculated using
SBH2 A,T =
SB2 HA,T =
3
Ksp 1 +
H+
KaB1
Ksp
4
H+
KaB1
1+
1+
KaH12 A KaH12 A KaHA
2
+
2
H+
H+
2
1+
KaHA
1
H+
−
and
, respectively. Ksp values were either experimentally
determined or estimated from published work for the selected cocrystal(s) in each graph (a)
indomethacin–saccharin (IND-SAC) [33], (b) carbamazepine–saccharin (CBZ-SAC) [33], (c)
carbamazepine-4-aminobenzoic acid hydrate (CBZ-4ABA-H), and (d) nevirapine-maleic acid
(NVP-MLE), nevirapine–saccharin (NVP-SAC), and nevirapine-salicylic acid (NVP-SLC) [23, 28].
Symbols represent experimentally measured data. Source: Adapted with permission from
Alhalaweh et al. [33], copyright 2012, American Chemical Society, and from Kuminek et al.
[38] with permission of The Royal Society of Chemistry.
259
Solubility (m)
(b)
1.0 × 10–1
CBZ-SAC
1.0 × 10–2
1.0 × 10–3
CBZH
1.0 × 10–4
1
2
3
4
pH
(c)
10
Solubility (mM)
CBZ-4ABA-H
1
CBZH
0.1
(d)
0
2
1
3
100
4
pH
5
6
7
8
NVP-MLE
Solubility (mM)
NVP-SAC
10
NVP-SLC
1
NVPH
0.1
0
1
2
3
pH
Figure 6.20 (Continued)
4
5
6
6.6 Cocrystal Solubility Dependence on Ionization and Solubilization of Cocrystal Components
gabapentin [91], indomethacin (IND) [33], isoniazid [92], ketoconazole [37],
LTG [32, 42], meloxicam [93], and NVP [38] cocrystals.
Cocrystals of nonionizable drugs can exhibit very different solubility-pH
behavior depending on coformer ionization properties (Figures 6.20a–c). While
an acidic coformer results in increases in solubility with increasing pH
(Figures 6.20a and b), an amphoteric coformer leads to a U-shaped cocrystal
solubility curve (Figure 6.20c). The solubility minimum of the curve will reside
within the pH range between the drug and coformer pKa values. A basic drug
and an acidic coformer, as shown in Figure 6.20d, predict a similar U-shaped
behavior where the ionizable groups reside in different molecules. The pH range
of the minimum solubility for this type of cocrystal is dependent upon the difference between the drug and coformer pKa values [34, 94].
In regard to solubilization, Equation (6.26) predicts that cocrystal solubility
SRHA,T will increase with corresponding increases in cocrystal Ksp, KsR , or
[M]. Because Ksp = (SRHA,aq)2, this equation can also be written in terms of
SRHA,aq as
SRHA, T = SRHA, aq
1 + KsR M
6 32
Likewise, the total solubility of the nonionizable drug component R is given by
SR, T = R aq + R m = SR, aq 1 + KsR M
6 33
where SR,aq represents the drug solubility in aqueous pseudophase [45].
While Equation (6.32) shows that cocrystal RHA solubility is a function of
M , Equation (6.33) demonstrates that drug R solubility is a function of
[M] [45]. Therefore, by comparing these two equations, it becomes apparent
that the solubilities of cocrystal RHA and drug R behave differently with changing surfactant concentration [35, 45, 47, 48, 89, 90, 95, 96].
It is also possible to use Equation (6.22) with the appropriate δ expressions
and K values as a guide for solubilizing agent selection that will yield a desired
cocrystal solubility. When values such as Ka and Ks are known, only cocrystal
Ksp needs to be determined to obtain cocrystal solubility [35].
Behavior predicted by solubility equations of the form of Equation (6.22) is in
excellent agreement with experimental values (Figure 6.21). Solubility curves of
cocrystal and drug intersect at transition points defined by S∗ and critical stabilization concentration (CSC). CSC is the solubilizing agent concentration at
the transition point.
The transition point for a given cocrystal and its drug will vary with the extent
of drug solubilization, as illustrated for different solubilizing agents in
Figure 6.22 [96]. A lower CSC is obtained with a stronger drug solubilizing agent
(Ks = 1.5 mM−1) than with a weaker one (Ks = 0.5 mM−1). This means that a
lower concentration of solubilizing agent is required to reach the transition
261
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
Solubility (mM CBZ)
(a)
20
CBZH
15
S*
CBZ-SAC
pH 2.2
10
5
0
CSC
0
10
20
30
40
50
60
70
[SLS] (mM)
(b)
40
CBZH
35
Solubility (mM CBZ)
262
30
25
S*
CBZ-4ABA-H
pH 4.0
20
15
10
5
0
CSC
0
20
40
60
80 100
[SLS] (mM)
120
140
160
Figure 6.21 Solubilities and transition points of carbamazepine (CBZ) cocrystals and
carbamazepine dihydrate (CBZH) induced by sodium lauryl sulfate (SLS) preferential
solubilization of CBZ for (a) 1 : 1 carbamazepine–saccharin (CBZ-SAC) and (b) 2 : 1
carbamazepine-4-aminobenzoic acid hydrate (CBZ-4ABA-H). Transition points are
characterized by a solubility (S∗) and a solubilizing agent concentration (CSC) (dashed lines).
Both S∗ and CSC vary with cocrystal aqueous solubility and stoichiometry. Symbols represent
experimentally measured cocrystal (○) and drug (Δ) solubility values. Predicted drug and
cocrystal solubilities (solid lines) were calculated according to Equation (6.26), and
SR2 HAB,T =
3
Ksp
4
1 + KsR M
2
1+
H+
H AB +
Ka 2
+
KaHAB
H+
+ KsHAB M , with the thermodynamic values
listed in Ref. [35]. Source: Reprinted from Lipert and Rodríguez-Hornedo [96]. Reproduced
with permission of American Chemical Society.
6.6 Cocrystal Solubility Dependence on Ionization and Solubilization of Cocrystal Components
20
Drug
Cocrystal
Drug
Solubility (mM)
15
S*
Cocrystal
10
5
CSCa
0
10
20
CSCb
30
40
50
60
Solubilizing agent (mM)
Figure 6.22 S∗ and CSC values for a cocrystal and its constituent drug in two different
solubilizing agents, a and b. S∗ is constant, and CSC varies with the extent of drug
solubilization by the solubilizing agent. Drug is solubilized to a greater extent by a than by b,
and thus CSCa < CSCb. The curves were generated from Equations (6.32) and (6.33) with
parameter values SD,aq = 0.5 mM, SCC,aq = 2.4 mM (Ksp = 5.76 mM2), and KsD = 1.5 and
0.5 mM−1 for solubilizing agents a and b, respectively. Source: Reprinted from Lipert and
Rodríguez-Hornedo [96]. Reproduced with permission of American Chemical Society.
point when a stronger solubilizing agent is used. Despite a variable CSC, the
transition points of a particular cocrystal and drug will exhibit a constant S∗.
This property of S∗ is found by examining the mathematical models that
describe cocrystal and drug solubilization [96].
Since the cocrystal and drug solubilities are equal at the transition point
SCC, T = SD, T = S ∗ ,
6 34
mathematical expressions that relate S∗ to cocrystal and drug solubilities can be
derived. For a 1 : 1 cocrystal
SCC, aq
S =
SD, aq
2
∗
6 35
The general equation for a cocrystal AyBz is
S∗ =
SCC, aq
SD, aq
y+z
y
6 36
This equation shows that the solubility value at the transition point is governed by aqueous solubilities and not by solubilizing agents. Saq refers to both
263
264
6 Measurement and Mathematical Relationships of Cocrystal Thermodynamic Properties
the ionized and nonionized aqueous solubilities of cocrystal and drug, and
therefore Equations (6.35) and (6.36) apply to a range of ionizing conditions [96].
From the equations presented in this section, it is possible to quantitatively
predict the cocrystal and drug solubilization behaviors and the transition point
as defined by S∗ and CSC. Figure 6.21 shows how these theoretical relationships
compare with the experimental data for two different CBZ cocrystals in the
presence of surfactant.
Under some conditions the assumption that coformer solubilization is negligible (KsCF = 0) is not justified, and an additional term must be included in the S∗
equations to account for situations where KsCF > 0 The factor ε is used to quantitatively represent and correct for this deviation [96]. The solubility at the transition point is
S∗ = ε
SCC, aq
SD, aq
2
6 37
where
ε=
1 + 10 pH −pKa, CF + KsCF M
1 + 10 pH− pKa, CF
6 38
where [M] represents the micellar concentration at the CSC. This equation
shows the importance of both Ks and [M] in determining the value of ε. Small
Ks and large [M] will have a significant influence on deviations of S∗. When
KsCF = 0, then ε =1, and S∗ values calculated from the simpler equation
(Equation 6.35) will approach experimental values [96].
Table 6.8 S∗ deviations due to coformer solubilization.
a
[SLS] at
CSC (mM)a
ε
S pred
with εd
Cocrystal
pH
KsCF
(mM−1)a
CBZ-SLC
(1 : 1)
3.0
0.06
23
1.40
3.3
4.6
4.6
CBZ-SAC
(1 : 1)
2.2
0.013
44
1.14
10.5
12.0
12.0
b
S pred
c
Values reported in Ref. [35].
Calculated from Equation (6.38) [96].
c
Calculated from Equation (6.35) [96].
d
Calculated from Equation (6.37) [96].
e
Determined from the intersection of SCC,T and SD,T curves in Figure 6.21 [96].
b
S obse
References
S∗ and corresponding ε values for CBZ cocrystals in SLS are shown in
Table 6.8. Calculations with ε = 1 provide a first good approximation of S∗ as
ε is less than 1.4.
6.7
Conclusions and Outlook
Cocrystals constitute an important class of pharmaceutical materials with
remarkable solubility properties. As described in this chapter, solution-phase
interactions play an important role in cocrystal solubility and thermodynamic
stability. The influence is greater than for single-component crystals or nonstoichiometric multicomponent phases (crystalline or amorphous) since cocrystals
respond to each molecular state of their components in solution. This property
presents an exceptional opportunity to fine-tune cocrystal solubility and stability by rational approaches based on the mathematical relationships described in
this chapter.
Cocrystal thermodynamic properties, while scarce in the literature, provide an
unexploited spectrum of cocrystal behaviors that up till now may only show up
inadvertently – sometimes to the point of cocrystals appearing risky compared
with other solid-state forms. Cocrystal behavior in solution has been generally
characterized by simply dissolving cocrystals and measuring drug concentrations as a function of time. Such studies by themselves are very limited in scope,
fail to capture important cocrystal properties, and may lead to inaccurate assessment of cocrystal performance.
Cocrystals are being widely considered for pharmaceutical products, and a
bridge between their development and our knowledge of mechanisms governing their properties will lead to robust formulations and processes.
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273
7
Mechanical Properties
Changquan Calvin Sun
Department of Pharmaceutics, College of Pharmacy, University of Minnesota, Minneapolis, MN, USA
7.1
Introduction
7.1.1 Importance of Mechanical Properties in Pharmaceutical
Manufacturing
Mechanical properties of pharmaceutical solids play a central role in the manufacturing and performance of pharmaceutical products. Among those, particle
size reduction by milling and powder tableting are of the most well-recognized
practical importance.
Active pharmaceutical ingredient (API) crystals often need to be milled to
reduce particle size, which is important for improving content uniformity in
tablets [1, 2], delivering drug to the lung [3], and intravenous delivery of poorly
soluble drugs [4]. API size reduction improves dissolution rates mainly because
of the increased surface area [5]. Solubility enhancement is also possible when
nano-sized API crystals are produced because of the Ostwald–Freundlich effect
[6]. Both effects are beneficial for delivering poorly soluble drugs, which account
for approximately 40% of the marketed drugs and 80% of the new chemical entities in the development pipeline [7, 8]. Size reduction can be achieved using
high-energy processes, such as high-pressure homogenization [9], jet milling
[10, 11], and media milling [4, 9]. For a fixed milling process, size distributions
of the resulting powders depend on mechanical properties of the crystals, such
as plasticity, elasticity, and fracture toughness [12–14].
During tablet manufacturing, the mechanical strength of a finished tablet
depends on the interplay between total interparticulate bonding area (BA) and
Pharmaceutical Crystals: Science and Engineering, First Edition.
Edited by Tonglei Li and Alessandra Mattei.
© 2019 John Wiley & Sons, Inc. Published 2019 by John Wiley & Sons, Inc.
274
7 Mechanical Properties
bonding strength (BS) [15]. BA is determined by several factors, such as compaction pressure, tableting speed, particle size, and material mechanical properties.
When other factors are equal, softer crystals undergo more plastic deformation
[16]. Consequently, when particle sizes are the same, a powder consisting of more
plastic crystals consolidates more easily and a larger BA is developed. This favors
tableting performance, provided BS is not too low [17–20]. Thus, for hard or elastic crystals, increasing crystal plasticity by structure engineering is effective in
improving tabletability, as different crystal forms of a drug exhibit different
mechanical properties [17–28]. A more plastic polymorph may exhibit better
tableting performance, but it is often also not thermodynamically stable. In comparison, cocrystallization and salt formation are practically more useful for engineering mechanical properties of drugs, because they can lead to new crystal
forms that exhibit both improved mechanical properties and thermodynamic
stability. Hard crystals are usually more prone to fracture, which is another kind
of permanent deformation that favors larger BA during tableting. However, this
mechanism is generally less effective than plastic deformation especially for
micronized APIs.
Mechanical properties also impact tableting process by affecting stress transmission and ejection force during die compaction. More plastic crystals transmit stresses to die wall more effectively during compression and residual die
wall stress is usually lower at the end of the compression cycle. Consequently,
ejection is usually easier when tableting more plastic crystals. Effective boundary lubricants, e.g. magnesium stearate, themselves are soft crystals [29], that are
characterized by layered structures with weak interlayer interactions [30]. Such
a structural feature is critical for an effective lubricant. When sheared during
blending, molecular layers are easily peeled off and coat surfaces of other particles to reduce friction when they slid over die wall. Although tabletability may
be favored by enhanced plasticity of APIs, more plastic API crystals also exhibit
a higher tendency to punch sticking during tableting [31].
7.1.2 Basic Concepts Related to Mechanical Properties
7.1.2.1 Stress, Strain, and Poisson’s Ratio
Mechanical properties are physical properties of a material that describe its
response to the application of an external force. Mechanical properties important to pharmaceutical materials include elasticity, hardness, tensile strength,
and fracture toughness. These properties are usually obtained from the
stress–strain curves [32, 33]. Stress is the average force acting over unit area
(with an SI unit of Pascal, 1 Pa = 1 N m−2). It can be tensile, compressive, shear,
or hydrostatic. Strain quantifies the degree of deformation in response to a
stress. In a classical tensile test of material strength, a solid bar with a specified
length, l, is pulled with a force, F (Figure 7.1). The corresponding tensile stress
7.1 Introduction
(a)
(b)
(c)
F
A
P
B
D
F
P
B′
θ
l
l + Δl
τ
A′
P
P
τ
P
C
P
P
P
Figure 7.1 Elastic deformation under (a) tension, (b) shear, and (c) hydrostatic pressure.
(σ) is F divided by the cross-sectional area of the bar, A. Under this condition,
the bar will increase in its length by Δl. The linear tensile strain, ϵ, is the fractional increase in length (Δl/l). If the deformation is elastic, ϵ is proportional to σ
according to Hooke’s law, where the proportionality constant is Young’s modulus or modulus of elasticity, E, as shown in Equation (7.1):
σ
ϵ
E=
71
While extending along the direction of the tensile stress and no change in
density, the bar also contracts in the transverse direction (Figure 7.1a). The
transverse strain (ϵt) and axial strain (ϵa) are related by Poisson’s ratio (ν)
according to Equation (7.2):
ν= −
ϵt
ϵa
72
The value of ν ranges between −1 and 0.5. For a material with a ν of 0.5, such as
rubber, the total volume does not change when pulled or compressed. However,
many organic materials have ν values approximately 0.3. For those materials, the
total volume decreases and density is increased under tension.
When a specimen is sheared by a shear stress (τ) (Figure 7.1b), shear strain (γ)
is defined as the tangent of the distorted angle of the specimen, θ
(Equation (7.3)):
γ=
AA
= tan θ
AD
73
Again, proportionality between γ and τ exists, and the shear modulus (G) is
defined in Equation (7.4):
G=
τ
γ
74
275
7 Mechanical Properties
Under a hydrostatic pressure, P, the solid volume decreases (Figure 7.1c). The
relationship between P and volume strain (ΔV/V) is given in Equation (7.5),
where K is the bulk modulus. Bulk modulus is relevant to die compression at
high compaction pressures:
K=
P
−ΔV V
75
Relationships among the four elasticity constants are given in Equations (7.6)
and (7.7). Thus, all four elastic constants can be obtained if two of them are
experimentally determined:
E
2 1+ν
E
K=
3 1 − 2ν
76
G=
77
The rigidity of a crystal, quantified by various elastic moduli, depends on the
strength of the intermolecular interactions. Thus, studying elasticity is a useful
approach for probing the nature of these interactions. Knowledge in the relationship between molecular structure and elasticity is essential for altering crystal mechanical properties through crystal structure modification.
7.1.2.2 Elasticity, Plasticity, and Brittleness
Figure 7.2 shows a typical stress–strain curve from a uniaxial tensile test. Here,
stress initially increases linearly with strain up to point A. If the stress is
decreased in this region, line AO is followed, i.e. the bar has restored its original
shape and size and no irreversible deformation has occurred. The reversible
elastic deformation behavior is described by the Hooke’s law, where the slope
of line OA is E. When the stress is increased above point A, some of the deformation is no longer reversible. For example, if the stress is decreased to zero
Figure 7.2 A classical stress–strain curve.
C
σy
B
A
Stress
276
O
O′
0.002
Strain
7.1 Introduction
(b)
(a)
A
B
Stress
Stress
A
B
C
C
D
O
Strain
O
Strain
Figure 7.3 Stress–strain curves. (a) A specimen undergoes brittle fracture if it breaks at point
C before plastic yield takes place. (b) Comparison of materials exhibiting different degree of
brittleness (A > D > C > B). Mechanical rigidity follows the order of A > B > C > D.
from point B, the path BO is followed. The strain OO is the irreversible portion
of the deformation, corresponding to the permanent plastic deformation. However, the position of point A may not be determined precisely from Figure 7.2.
Thus, a straight line parallel to OA, usually with 0.002 strain offset, is drawn.
The stress corresponding to the point of crossing is used to quantify the yield
strength of the material, σ y. When strain is further increased, stress gradually
increases instead of staying constant until the material undergoes fracture
(point C in Figure 7.2). This phenomenon is known as work hardening or strain
hardening. The fracture is ductile in this situation. An analogous analysis can be
carried out for uniaxial compression test, which usually yields very similar yield
strength as that from the tensile test.
For some materials, permanent deformation takes place in the form of a brittle fracture, i.e. the material fractures when deformed before an appreciable
amount of plastic deformation takes place (Figure 7.3a). The smaller the strain
corresponding to the point of fracture, the more brittle the material is. For materials that undergo ductile fracture, the lower the stress corresponding to the
onset of the yielding, i.e. yield strength, the more plastic the material is. Experience suggests that a material that yields or fractures at a higher stress usually
also fractures at a lower strain, i.e. they are more brittle. However, higher rigidity
of a material does not necessarily correspond to higher brittleness. For example,
a material exhibiting line OD stress–strain behavior has the lowest rigidity in
comparison with materials that follow the other curves in Figure 7.3b. However,
it is still more brittle than materials represented by lines OB and OC.
7.1.2.3
Classification of Mechanical Response
Mechanical responses of crystals to an external stress may be classified as shown in
Figure 7.4. When a crystal is subject to an external stress, it initially undergoes
277
278
7 Mechanical Properties
Reversible
Mechanical
response of
crystals
Elastic deformation
Fracture
Brittle
Irreversible
Cleave
Slip
Yield
Twinning
Ductile
Kinking
Figure 7.4 Classification of crystal mechanical responses to an external stress.
reversible elastic deformation (linear portion of stress–strain curves in Figure 7.3). If
the stress exceeds the elastic limit of the crystals, irreversible deformation takes
place, in the form of a brittle fracture, cleavage, or plastic yield. Yield of a crystal
can occur mainly through slip, twinning, or kinking [34]. Among these three yield
mechanisms, slip is perhaps more universally applicable. Regardless of the yield
mechanism, the crystal is ductile as long as cleavage and brittle fracture are avoided.
7.2 Characterization of Mechanical Properties
7.2.1 Experimental Techniques
Since mechanical properties can be described by stress–strain curves, quantifying mechanical properties only requires access to accurate measurements
required for calculating stress and strain. Any techniques capable of accurately
measuring force, contact area, and specimen length or volume can be used to
experimentally determine mechanical properties.
7.2.1.1 Single Crystals
7.2.1.1.1 Microindentation and Nanoindentation
Hardness (H) is a good measure of crystal plasticity and is approximately three
times the value of σ y. A crystal with a lower H is more plastic. For sufficiently
large single crystals, microindentation can be performed to measure the crystal.
In this method, a known force is applied, and the area of the indent (typically
tens of micrometers or larger in size) is determined by optical microscopy.
When sufficiently large crystals are not available, a much smaller indenter tip
must be used to quantify crystal mechanical properties. This can be done by
nanoindentation, where the indent size is in the range of tens of nanometer
to several micrometers. It is useful to mention that indentation H depends
7.2 Characterization of Mechanical Properties
on indent size when the size is very small, such as that by nanoindentation
[35–37]. Since accurate area determination is not possible by optical microscopy, which can resolve about 0.2 μm, for small indents, a depth-sensing technique is used to extract the information of the indent area from the knowledge
of tip size and geometry as well as force–displacement data [38]. The key step
for successfully extracting data to calculate E and H by nanoindentation is correcting for elastic yielding of the tested surface and topographical changes, such
as pileup, around the indentation [35, 39]. For each indenter tip, the tip area
function is derived by performing a series of indentations on a standard with
known modulus. If the E of indenter (Ei) and Poisson’s ratios of the specimen
(ν) and the indenter (νi) are known, E of the specimen can be calculated from Er,
using Equation (7.8):
1
1 −υ2
1 −υi 2
+
=
Er
E
Ei
78
Although the initial applications were on inorganic materials, nanoindentation has been adopted to characterize the mechanical properties of organic crystals in recent years [40–44]. Nanoindentation experiments can be performed
under either force- or displacement-controlled mode [45]. The indenter tip
can also be held at either maximum penetration depth (to measure force decay
with time) or at maximum force (to monitor creep behavior) to study relaxation
of the substrate. In addition to providing H, σ y of the material (point B in
Figure 7.2), which corresponds to the limit of elastic deformation beyond which
permanent plastic deformation takes place, can also be determined by performing partial loading and unloading experiments [27, 46]. Before yielding, the crystal undergoes reversible elastic deformation, and the indentation curves can be
modeled using the classical theory of elastic contact mechanics [47].
For obtaining high-quality data by nanoindentation, crystal surfaces must be
flat. Surface asperities can lead to errors in penetration depth data, which lead to
large errors in calculated Er and H. Flat surfaces can be obtained either by growing high-quality single crystals through carefully controlled crystal growth or by
cleaving large single crystals [47].
7.2.1.1.2
X-ray Diffraction, Ultrasound, and Brillouin Scattering
For high-quality single crystals, strain can be quantified from the fractional
changes in d-spacing of molecular planes when the crystal is under stress. This
can be achieved experimentally by monitoring 2θ diffraction angles of the
planes of interest during X-ray diffractometry when the single crystal is subject
to a series of known stresses. An increase in the diffraction 2θ angle corresponds
to smaller d-spacing according to Bragg’s law [48]. The fractional change in
d-spacing is strain along the direction perpendicular to the corresponding
planes. If the resolved stress along the same direction as the strain can be
279
280
7 Mechanical Properties
calculated, E along that direction can be calculated. Although only performed
using a compression stage [48], this experiment can be performed under tensile
conditions in theory.
Ultrasonic method can be used to measure elastic constants, if sufficiently
large single crystals are available. This is possible because the speeds of longitude and transverse components of ultrasonic sound when traveling through
the solid depend on E and G (as well as material density), respectively. From
the time of flight and thickness of the specimen, velocities of these two sound
waves can be calculated, which are then used to calculate E and G [49, 50]. Then,
ν and K can be calculated from E and G according to Equations (7.6) and (7.7).
To fully describe elastic properties of a solid, a set of elastic constants must be
determined. The number of independent elastic constants varies with the crystal symmetry. For a cubic crystal, three independent elastic constants are
required to fully describe the crystal elastic properties. For lower symmetry
crystals, a larger number of elastic constants are required. This is extremely difficult to achieve using indentation and X-ray diffraction methods. However,
Brillouin scattering could be used to experimentally determine the full set of
elastic constants of single crystals [51, 52]. In this method, frequency shift of
the scattered light is measured using an interferometer under carefully selected
scattering geometry. That, along with the scatter angle, allows the calculation of
velocity of sound wave, which is then used to calculate elastic constant.
7.2.1.1.3 Computer Modeling
When applying a uniaxial stress, the ratio of stress to strain defines the value of E
along that axis. From a known crystal structure, E can be calculated by computationally applying a small and homogeneous deformation strain to the crystal
structure. The stress corresponding to the strain is calculated by applying an
appropriate force field [53–56] or by ab initio quantum mechanical calculations
[57, 58].
7.2.1.1.4 Qualitative Characterization
In addition to characterizing crystal mechanical properties by determining E
and H, single crystals can also be studied qualitatively to gain knowledge of
mechanical properties. When poked with a needle, which is essentially a qualitative version of the microindentation test, plastic single crystals undergo facile
deformation, while hard crystals do not. The different mechanical responses
were the basis for sorting two polymorphs of 6-chloro-2,4-dinitroaniline, which
were optically indistinguishable [59]. In another method analogous to threepoint bending, a crystal is held against two supports and pressed with a needle
in the middle from the opposite side. This test is performed under a microscope
for qualitatively assessing mechanical properties. Crystals can then be
classified into bending, shearing, brittle, or elastic types according to their
behavior [24, 25, 60–62].
7.2 Characterization of Mechanical Properties
Bending and shearing organic crystals can generally be expected when the
molecules are connected by weak and strong interactions in mutually orthogonal
directions [61, 63–65]. This understanding led to improved ability to design
organic bendable crystals [66]. Structural insight has enabled the design of crystals with diverse mechanical properties through crystal engineering [60, 64]. It is
also possible to design multicomponent crystals to maintain bending property in
a single component crystal by preserving structural anisotropy [67].
7.2.1.2 Bulk Powders
7.2.1.2.1 In-die Compression Data Analysis
Using an instrumented die, it is possible to obtain the elastic properties of a
material from the in-die powder compression data. In this method,
Equations (7.9) and (7.10) are used for extracting elastic parameters, assuming
the linear stress–strain relationship is followed during unloading [68]:
σ rad = ν σ rad + σ ax + E εrad
σ ax − 2 υ σ rad = E − E
h
h0
79
7 10
where εrad is radial strain, σ ax and σ rad are axial and radial stresses, and h and h0
are the in-die thickness under pressure and the minimum thickness at the maximum compaction pressure, respectively.
Thus, the ν value may be obtained from the slope of σ rad vs. (σ rad + σ ax) plot
based on Equation (7.9), and the E value may be calculated from the intercept
of the plot of (σ ax − 2υσ rad) vs. h based on Equation (7.10). Subsequently, the values
of G and K can be calculated from E and ν using Equations (7.6) and (7.7) [69]. This
method yields reasonably accurate elastic constants. For example, the values
obtained using this method with microcrystalline cellulous and dibasic calcium
phosphate anhydrate were in excellent agreement with those obtained using a
three-point bending method [68]. This method also provides critical insight into
powder compaction behavior, such as tendency to undergo capping [70].
7.2.1.2.2
Out-of-die Compressibility Data Analysis
The powder compressibility data, i.e. tablet porosity (ε) – pressure (P), can be
analyzed using appropriate equations to derive information useful for characterizing deformability of the material. Presently, the Heckel equation
(Equation (7.11)) is most commonly used for this purpose [71, 72]:
− ln ε = K P + A
7 11
where A and K are constants. The Heckel equation was derived on the assumption that the rate of pore elimination is proportional to the porosity of the powder bed [71]. It was suggested that the value of 1/K is approximately three times
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7 Mechanical Properties
the yield strength [72]. Thus, 1/K can be used as a useful parameter for characterizing plasticity of the material. However, data at low pressures frequently
deviate from the linearity assumed by the Heckel equation, and it is not always
easy to identify a linear portion for determining K. In addition, the Heckel analysis results are affected by factors, such as die diameter and lubrication and
compression speed [73].
Compared with the Heckel equation, another equation (Equation (7.12))
derived by Kuentz and Luenberger can more accurately describe powder compressibility data over the entire pressure range [74]:
P=
1
ε
ε − εc −εc ln
C
εc
7 12
where εc and 1/C are constants. Similar to 1/K in the Heckel analysis, 1/C is a
parameter that can be used to quantify material plasticity. The improved ability
of the Kuentz–Leuenberger equation in describing the entire set of compressibility data is because the rate of pore elimination by pressure was correctly
recognized as a function of porosity of a powder bed, which was inaccurately
assumed to be constant when deriving the Heckel equation. At high pressures,
when tablet porosity no longer undergoes significant reduction by an increase in
pressure, the assumption of constant rate of pore elimination is approximately
valid. In that situation, the Kuentz–Leuenberger equation is reduced to the
Heckel equation [75].
7.2.1.3 Tablet Mechanical Properties
Since pharmaceutical tablets consist of solid and air, mechanical properties of
tablets (S) depend on tablet porosity (ε). Several equations have been proposed
to describe the effects of porosity on mechanical properties, e.g. tensile strength,
E, H, and a brittleness index. However, an exponential decay function
(Equation (7.13)) appears to satisfactorily account for the effects of porosity
on several important mechanical properties of pharmaceutical materials [76–79]:
S = S0 e −bε
7 13
where S0 is the mechanical properties at zero porosity, which can be obtained by
extrapolation if the mechanical properties of tablet at different porosities can be
experimentally determined. S0 may be used to quantify corresponding intrinsic
mechanical properties of the constituent solid.
7.2.1.3.1 Tablet Hardness Determination by Macroindentation
Similar to the determination of H of single crystals, H of a tablet can be determined by indentation using a suitable indenter to apply forces at controlled
speeds with or without holding at the maximum force. However, the indented
7.2 Characterization of Mechanical Properties
area needs to be sufficiently large to cover at least several particles in order for
the measurement to be a representative of the tablet. Otherwise, great variability
in measured H can be expected. This is usually achieved by using a spherical
indenter with a diameter of 3–4 mm, such as in macroindentation tests [80].
The area of indent after the indenter has been withdrawn can be accurately
measured under a microscope. For spherical indents, area determination is relatively simple. The circumference of the indent is fitted with a circle and the
projected area, A, is calculated. The use of contrasting agent, such as graphite,
can greatly facilitate the accurate determination of the indent area. An average
H is calculated using Equation (7.14) [81]:
H=
F
A
7 14
where F is applied force. For spherical indenter, H can be calculated using a
more sophisticated Equation (7.15) [82]:
H =
2F
πD D − D2 −d 2
7 15
where D is the diameter of the indenter and d is the diameter of the impression
(d < D). However, for different D and a wide range of d, H is not significantly
different than H . Since Equation (7.14) can be used regardless of indenter geometries, while Equation (7.15) is applicable to spherical indenters only,
Equation (7.14) is usually preferred for practical reasons.
7.2.1.3.2
Tablet Brittleness Determination
Tablet brittleness was originally quantified using a brittle fracture index
(BFI), which is obtained from the ratio between the tensile strength of a
defect-free tablet and a tablet with a central hole [83]. For purely brittle fracture, i.e. when the tablet does not yield before fracture (Figure 7.3a), the
ratio is three. However, the ratio is close to unity, if the material undergoes
extensive plastic deformation. In addition to some theoretical shortcomings
[84], this approach is relatively material and labor intensive. Thus, it has not
been broadly adopted by the pharmaceutical industry despite the initial
enthusiasm after its introduction. Later, a brittle–ductile index (BDI) was
proposed in an effort to improve BFI. BDI exhibits several improved features
than BFI, but it still fails to account for the dependence of brittleness on
porosity [83]. More recently, a tablet brittleness index (TBI) was introduced,
which is defined as the reciprocal of elastic strain, leading to either fracture
or plastic yield of tablet [83]. It was validated against tablet friability, a tablet
property known to correlate with brittleness. As such, TBI can be easily calculated from the original tablet dimension and the force–displacement
curve during tablet breaking tests [83].
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7 Mechanical Properties
7.2.1.3.3 Tablet Elasticity Modulus Determination
For rectangular tablets, or ribbons, the three- or four-point bending method can
be used to determine E [85, 86]. In a three-point bending test, E is calculated
using Equation (7.16):
E=
FL3
1
=
4W YT 3 4W
F
Y
L
T
3
7 16
where F is the maximum force at the breaking point of the ribbon, Y is the deflection of the ribbon at fracture point, L is the gap distance between the two lower
supports, W is the width of the tablet, and T is the thickness of the ribbon.
Another useful method for measuring elastic modulus of tablet is monitoring the
propagation of ultrasonic waves through the tablet [87]. This method is essentially
the same as that described earlier for determining E and G of single crystals, except
tablets with sufficiently large sizes are more readily available than single crystals.
7.2.1.3.4 Tablet Tensile Strength Determination
Tensile strength of rectangular tablets can be determined by three-point bending method using Equation (7.17). Here, the parameters are the same as those in
Equation (7.16):
3FL
7 17
2WT 2
For cylindrical tablets, tensile strength can be determined from a diametrical
breaking test, using Equation (7.18) [88]:
TS =
2F
7 18
π d H
where F, d, and H are the breaking force, tablet diameter, and thickness,
respectively.
TS =
7.3 Structure–Property Relationship
Successful engineering of crystals to attain desired mechanical properties
through structure modifications depends on adequate understanding of the
relationship between crystal structure and mechanical properties [89]. This
section summarizes several aspects of crystal structure important to understanding crystal mechanical properties.
7.3.1 Anisotropy of Organic Crystals
Because of the low symmetry, intermolecular interactions in a molecular crystal
are usually direction dependent, i.e. organic crystals are anisotropic. Therefore,
Miller’s index of the crystal face, which is being studied for mechanical
7.3 Structure–Property Relationship
properties, should be identified when possible [46, 90, 91]. For an anisotropic
crystal, it is possible to identify parallel layers within its structure, within which
the intermolecular interactions are strong (e.g. fortified through hydrogen
bonds). In contrast, interactions among molecules in adjacent layers are much
weaker. For a crystal with such structural anisotropy, relative movement among
these layers dictates their mechanical response to an external stress. Even in
structures devoid of hydrogen-bond fortified layers, molecular packing density
and strength of intermolecular interactions still vary with the orientation of the
molecular planes. Thus, for a given crystal, there are always orientation(s) of
planes with higher molecular density and higher interaction strength between
molecules within that plane. Interaction strength between these plane(s), quantified by the attachment energy, is necessarily weaker, because the total lattice
energy of the crystal is constant. In other words, a primary slip system always
exists in any crystal. Whether or not that slip system can be activated depends
on the direction and magnitude of the applied external stress. It should be noted
that attachment energy is only one of the factors that influence plasticity of crystals. The ease of slip between layers is also affected by the layer surface topology.
Flat layers with smooth surfaces favor slip, while rough or interlocked surfaces
hinder it. Therefore, a crystal with lower attachment energy between adjacent
slip layers may not necessarily be more plastic, if the layers are more rough, corrugated, or interlocked.
One consequence of the structure anisotropy is the presence of face-specific
mechanical properties. Measured E and H of the same crystal are likely different,
when tested on different crystal faces. The magnitude of difference may be used
to characterize crystal anisotropy. For example, crystals with dense hydrogenbonded structure, such as sucrose, are more isotropic, and mechanical properties measured on different crystal faces may not differ much [12, 47]. However,
much larger difference may be observed for more anisotropic organic crystals,
e.g. acetaminophen and aspirin [46, 90–93]. The structure anisotropy also
explains some peculiar observations in the load–displacement curves collected
during nanoindentation of single crystals with 2D hydrogen-bonded rigid
layered structure. When the load is applied at a direction perpendicular to
the layers, layers are initially elastically deformed. When the elastic strain
exceeds the elastic limit of the crystal, the elastic energy is released by the breakage of the layers. This is reflected as an excursion in the loading curve, where the
indenter penetrated some significant distance without requiring any increase in
load. This phenomenon is known as “pop in,” and it corresponds to pile up of
materials around the indenter [34]. When the load is applied along the direction
parallel to the stacking layers, layers accommodate the stress through slip. The
load–displacement curve is smooth, i.e. no “pop in” event, because no stored
elastic energy needs to be released at once. The structure anisotropy also
explains why some crystals exhibit different mechanical responses during bending experiments [25, 66].
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7 Mechanical Properties
7.3.2 Crystal Plasticity, Elasticity, and Fracture
The different mechanical responses of a crystal to an external stress can be
understood by considering the structural anisotropy of molecular crystals. As
discussed above, any crystal may be approximated as stacking 2D layers
(Figure 7.5). Considering the situation where the crystal is subject to an external
tensile stress, the separation between layers increases with increasing tensile
stress if the external stress is perfectly perpendicular to these 2D layers. If
the tensile stress is removed, the planes will return to their rest state, i.e. the
deformation is elastic (Figure 7.5a). If the tensile stress exceeds the elastic limit,
the crystal undergoes brittle fracture, and each piece of the broken crystal
returns to their structure at rest (Figure 7.5d). This phenomenon is known as
crystal cleavage, which usually leads to microscopically smooth surfaces. If
the applied stress is at an angle other than 90 to these layers, it can be resolved
into two components. One is tensile stress perpendicular to the planes; the other
is shear stress parallel to the planes. If the elastic limits in both directions are not
exceeded, the applied stress only causes reversible elastic deformation. If the
tensile stress exceeds the elastic limit, the crystal cleaves (Figure 7.5d). If the
shear stress exceeds the elastic limit, slip occurs, and the crystal undergoes nonreversible plastic deformation (Figure 7.5b). As a result of the slip, the layers are
more aligned with the direction of the applied stress. The crystal becomes not
only longer along the direction of the applied stress but also thinner
(Figure 7.5c). Since the resolved shear stress along these layers increases due
to the favorable change the orientation of the slip planes, the crystal will
Figure 7.5 Models for different mechanical
response of a crystal to stress. (a) Elastic
deformation, (b) plastic deformation, (c) more
extensive plastic deformation with time under
a constant tensile force, and (d) brittle
fracture.
(a)
(b)
(d)
(c)
7.3 Structure–Property Relationship
continue to plastically deform, if the strain-hardening effect is insignificant or if
the applied stress is sufficiently high. For crystals containing dislocations, the
slip occurs at the energetically most favored location first and continues until
molecular layers are eventually sheared off completely. This leads to ductile
fracture (Figure 7.2). More isotropic crystals tend to be more brittle because
the probability of meeting the conditions for plastic slip of layers is lower compared with that for brittle fracture.
When the applied stress is compressive, similar stress analysis can be made to
explain the elastic and plastic deformation of crystals. A tensile stress causes
crystal to cleave (Figure 7.5d) when plastic deformation is avoided. Compressive
stresses can cause crystals to either cleave or fracture, even for anisotropic crystals containing cleavage planes with significant energetic preference. If the
direction of the compressive stress is close to being perpendicular to the cleavage planes, those planes can break off, a phenomenon known as crystal fracture.
Compared with cleavage, fracture usually leads to rough and uneven surfaces
[94]. The low attachment energy associated with cleavage planes means that
cleavage planes can often times serve as slip planes. However, as mentioned
before, even planes with large interplanar separation and weak interactions
may not slip easily, when the layer surfaces are rough or when the layers interlock. Obvious cleavage or slip planes can be identified by visualizing their structures based on high molecular density or large interlayer separations. Such
planes in less anisotropic crystal structures cannot be easily identified by structure visualization but can be revealed based on attachment energy calculations,
i.e. they are planes exhibiting the lowest attachment energy in the crystal structure. However, accuracy in the identification of cleavage or slip planes based on
attachment energy calculation depends on the accuracy of the method used.
7.3.3
Role of Dislocation on Mechanical Properties
For crystals with layered structures, movement of molecules along the layer
(molecular slipping) is energetically easier than moving them from one layer
to the adjacent layer (molecular jumping). However, moving the entire
layer, even weakly interacting ones, can still be energetically prohibitive. In reality, defects in crystals influence plasticity of a given crystal. For a chemically pure
single-phase crystal, there are four possible kinds of defects: (i) zerodimensional (0D) disorders, e.g. point vacancy and interstitial impurity;
(ii) 1D disorders, e.g. line dislocation; (iii) 2D disorders, e.g. screw dislocations
and twinning; and (iv) 3D disorders, e.g. grain boundaries and domain. A line
dislocation may be thought as the insertion of an extra half row of molecules
into an otherwise perfect crystal. The presence of a low concentration of dislocations facilitates plastic deformation [95]. This is because that when slip
occurs, molecules in the slip layers do not move simultaneously. Instead, the
intermolecular bonds surrounding the dislocations will be broken first due to
287
288
7 Mechanical Properties
pre-existing strain, and the molecules move one by one or line by line instead of
the whole layer. Thus, the slip of molecules can occur much more easily than
moving the whole molecular layer. However, dislocations can be pinned, when
they intersect each other. In such a situation, the crystal appears to be hardened.
Thus, the presence of a low concentration of dislocations facilitates plastic
deformation, but a very high concentration of dislocations hardens the crystal.
Consequently, an optimum level of dislocation that favors plastic deformation
of crystals exists. Since dislocations multiply during plastic flow, that critical dislocation concentration will eventually be exceeded during the course of plastic
deformation, which leads to higher hardness of the crystal. This explains the
phenomenon of work hardening [96]. Moreover, the movement of dislocation
cannot pass from one crystal to the next during powder compaction. Thus, the
extent of plastic deformation is affected by particle size. This, in part, explains
the observed effect of particle size on tableting performance of drugs that
undergo predominantly plastic deformation under stress.
Experimentally, stress is observed to continually rise, instead of remaining
unchanged, with increasing strain beyond the elastic limit (Figure 7.2). Molecular packing on crystal surface is inherently different from the bulk crystal.
Thus, surface may be viewed as a source of dislocations. Thus, plastic deformation can be initiated at the surface at the points of contact when an external
stress is applied. Hence, while movement of dislocations is necessary for plastic
deformation to proceed, the presence of dislocations in bulk crystal is not. That
is, plastic deformation by dislocation movement is a universal mechanism
regardless of the perfection of crystal structure. It should be mentioned that dislocations affect crystal plasticity much more than affecting elasticity. This is
because elastic deformation only concerns mechanical response of a crystal
before plastic deformation occurs. When a dislocation is introduced into an
otherwise perfect crystal, plastic deformation will occur at a much lower shear
stress, but the stress–strain relationship during elastic deformation, i.e. E,
remains essentially unchanged. Even if the crystal surface is perfect, and not
a source of dislocations the slip of layers still follows the same mechanism of
propagation of dislocation because of the same energetic argument. In this situation, the surface molecules at the contact point are displaced from their original positions into the bulk. This creates a condition that is analogous to the
introduction of dislocations. Subsequently, the slip occurs through dislocation
propagation instead of simultaneous movement of the entire plane. The only
difference is that dislocation propagation now starts at the contact points rather
than in the crystal. Therefore, reliable predictions of plasticity of crystals must
start from a realistic model of dislocations in organic crystals. This can be done
by applying a stress to a perfect crystal, since dislocations can be induced from
the surface. Consequently, modeling plastic deformation only requires energy
calculations within a small volume, e.g. with less than 10 molecular diameter,
near a dislocation, which requires substantially less computation power [97].
7.3 Structure–Property Relationship
7.3.4
Effects of Crystal Size and Shape on Mechanical Behavior
It is clear that for a given drug, the crystal structure determines the intrinsic
mechanical properties. However, it should be pointed out that deformation
behavior of organic crystals depends on not only mechanical properties but also
crystal geometrical factors, such as shape and size. For a given material, there is a
critical size that marks the transition between brittle fracture and plastic deformation behavior. The material can fracture only when the size is larger than the
critical value. If a crystal is smaller than the critical size, it only yields when sufficiently stressed [14]. This size-dependent fracture behavior is applicable to
pharmaceutical crystals as well [98]. Thus the qualitative classification of crystal
deformation behavior needs to be specified with crystal dimensions. For
example, a crystal that exhibits plastic bending behavior may break when the
size is sufficiently large. In contrary, a brittle crystal may undergo plastic deformation when size is very small. Because of the nature of such qualitative crystal
bending experiments, the longest dimension of a crystal is usually several millimeters in order for manipulation of crystals to be feasible. Thus, the qualitative
classification of crystal deformation behavior implies millimeter size scale. At
that scale, one also needs to consider the effect of crystal shape on the deformation behavior.
The crystal structure in Figure 7.6a consists of corrugated layers, which are
rigid and well separated. Thus, such crystals can be easily cleaved along these
layers. However, slip along these layers is difficult because of the high friction
between corrugated layers. Such crystals appear brittle and elastic. They
undergo more extensive elastic recovery during compaction, which leads to
poor tabletability. Crystals with more isotropic structure (Figure 7.6b) tend
to be brittle. If molecular interactions are fortified by a 3D hydrogen-bond network, the brittle crystal is also hard. If molecules interact through only van der
Waals forces, such crystals are not hard and can readily undergo brittle fracture.
In either case, tableting performance is not ideal.
Crystals consisting of rigid flat layers are plastic (Figure 7.6c and d). They usually exhibit superior compressibility and tabletability. The maximum attainable
tablet tensile strength depends on the magnitude of the interlayer interactions.
Thicker layers with shorter interlayer separation correspond to higher crystal
strength, and therefore maximum tablet tensile strength at zero porosity. If
these layers are perpendicular to the long dimension of the crystal
(Figure 7.6c), the crystal is expected to shear easily. However, if these layers
are parallel to the long crystal dimension (Figure 7.6d), the crystal more likely
exhibits plastic bending behavior.
Crystals consisted of interlocked rigid layers are not plastic (Figure 7.6e and
f ). If these layers run parallel to the long dimension of the crystal, the crystal
undergoes elastic bending (Figure 7.6e). However, similar to that in
Figure 7.6a, the crystal can exhibit brittle behavior, if these layers are
289
290
7 Mechanical Properties
(a)
(e)
(b)
(f)
(c)
(d)
(g)
Figure 7.6 The interplay between crystal structure and crystal geometry determines
mechanical behavior of single crystals. Needle-shaped crystals tend to break more easily
along the long axis. (a) Brittle/elastic, (b) brittle/elastic/hard, (c) shearing, (d) bending, (e)
elastic, (f ) brittle/elastic, and (g) bending/plastic.
perpendicular to the long dimension of the crystal (Figure 7.6f ). Finally, crystals
consisting of flat layers formed by stacking rigid molecular columns are plastic
(Figure 7.6g). They are expected to bend easily regardless of the orientation of
the layer to the long dimension of the crystal because of the existence of
multiple slip systems that can accommodate stresses through facile plastic
deformation [23, 26].
7.4 Conclusion and Future Outlook
The mechanical properties are important for successful development of drug
products. Future research should be focused on better understanding the
structure–mechanical property relationship, which is greatly facilitated by
advances in nanomechanical testing and X-ray crystallography. Such knowledge
is critical for designing new crystals with desired mechanical properties while
simultaneously improving or maintaining other desired pharmaceutical properties, such as high solubility, good stability, and low punch sticking tendency.
There is a need for more accurate calculations of mechanical properties from
References
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The ultimate goal is to attain the ability to design high quality, manufacturable
drug products in silico, once the molecular structure of an API is identified.
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297
8
Primary Processing of Organic Crystals
Peter L.D. Wildfong,1 Rahul V. Haware,2,3 Ting Xu,3 and Kenneth R. Morris3
1
Graduate School of Pharmaceutical Sciences, School of Pharmacy, Duquesne University, Pittsburgh, PA, USA
College of Pharmacy & Health Sciences, Campbell University, Buies Creek, NC, USA
3
Department of Pharmaceutical Sciences, Arnold and Marie Schwartz College of Pharmacy, Long Island University,
Brooklyn, NY, USA
2
8.1
Introduction
In this chapter, the solidification of small molecule organic crystals (SMOCs) as
bulk materials is examined. Essentially, this is driven by a central question,
namely, what is the interplay between intrinsic physicochemical properties of
the SMOC and the processing environment in which they are generated that
determines the quality, purity, and downstream handling of bulk materials? Synthesis of molecular precursors for bulk crystallization is left to other resources.
Instead, this chapter focuses on the so-called “finishing steps” in API synthesis
and begins by exploring how small molecules interact with crystallization
solvents and processing equipment and how this influences the resulting bulk
materials. While earlier chapters discuss nucleation and growth mechanisms,
crystal structure, and physical forms of solid materials in detail, to the extent
that is necessary, these will be revisited throughout the present chapter.
8.1.1
Solid Form
The organization of molecules in three dimensions determines the suitability of
any solid material to subsequent processing. Molecules may solidify without
long-range order (amorphous solids), but, for the purposes of this discussion,
solidification will be considered to result in a periodic arrangement of molecules
Pharmaceutical Crystals: Science and Engineering, First Edition.
Edited by Tonglei Li and Alessandra Mattei.
© 2019 John Wiley & Sons, Inc. Published 2019 by John Wiley & Sons, Inc.
298
8 Primary Processing of Organic Crystals
whose positions relative to one another are dictated by the symmetry afforded
by the space group into which the molecules crystallize. The practical question
considered in this chapter is what conditions direct the incorporation of
molecules into the desired crystalline form? “Desirable” solid forms are often
dictated by a balance between maximizing apparent solubility and minimizing
the potential for spontaneous phase changes during storage of the material
under various conditions. This is meant to provide a SMOC drug substance
with predictable and reproducible bioavailability when the material is eventually
contextualized in a formulation. To that end, “desirable” also represents how
easily the material moves through secondary manufacturing steps (see
Chapter 9), where solid form dictates a host of important physicochemical
properties including dissolution rate, thermal expansion, melting, response to
mechanical stress, and proclivity to transform to other solid forms when
exposed to stimuli such as temperature and pressure. The wide range of
properties exhibited by different solid forms of the same molecule are extensive;
for a more complete list, refer to Brittain [1].
Consider the case of indomethacin, in which the γ-polymorph is the stable
form, most commonly obtained from crystallization. The anhydrous metastable
α-form can be crystallized by precipitation from ethanol using distilled water,
while the benzene solvate (β-form) can be crystallized from benzene solution
[2]. Directed crystallization of indomethacin can also result in the methanolate
and t-butanolate forms, while the metastable δ-form can be prepared by
desolvation of the methanolate under vacuum [3]. Additional indomethacin
solvates with acetone, dichloromethane, tetrahydrofuran, propanol, chloroform, and diethyl ether have all been isolated and characterized [4]. In addition,
a multitude of studies on the persistent amorphous form of this molecule have
been conducted, demonstrating its solidification by various means. Needless to
say, indomethacin represents just one of many SMOCs for which the primary
processing conditions have tremendous influence on the solid form of the material, necessitating a study of the ways in which bulk substance manufacturing
can be performed.
8.1.2 Morphology
During crystallization, molecular anisotropy will influence the shape of the
resulting crystals, depending upon which solvents and conditions are used,
including the presence or level of impurities. In general, the crystal will grow
fastest in the direction of the shortest lattice d-spacing, so the face perpendicular to this direction will not be dominant in resulting habit. In contrast,
slow-growing faces, parallel to the direction of shortest d-spacing, will be highly
expressed and dominate the morphology. Figure 8.1 illustrates this trend for
acetaminophen [6] and orotic acid [7] crystals, whose predicted morphologies
show the largest planes parallel to closest-packed directions.
8.1 Introduction
(a)
(b)
Figure 8.1 Predicted BFDH morphology of (a) acetaminophen (CCDC refcode HXZCAN01)
crystals and (b) orotic acid (CCDC refcode OROTAC) crystals. Source: Adapted from Groom
et al. [5].
Crystal engineering is in large part concerned with controlling crystal shape
and size, with the remaining attention focused on which solid form results from
crystallization [8–10]. The importance of crystal morphology/habit rests in the
potential for particle shapes to affect filtration, powder flow, and most
secondary processing steps, such as blending and compaction. Since different
crystalline morphologies tend to exaggerate the occurrence of one face over
another, each face contains a specific organization of functional groups packed
into those crystallographic planes by means of the molecular orientation and
crystal symmetry. This, in turn, can influence wettability and, therefore, potentially facilitate (or inhibit) dissolution of the solid during water-intensive processing steps, such as wet granulation. Similarly, different polymorphs of a SMOC
drug substance may exhibit different functional groups on the faces of their
respective crystals [11], potentially impacting powder behavior, such as particle
cohesion, leading to poor flow properties or responses to mechanical stress.
Ultimately, rigorous analysis of primary processing schemes enables
prediction of and control over the resulting bulk material. As shown in
Figure 8.2, manufacturing that involves SMOCs is best represented as two
separate, yet related stages: Primary (1 ) processing, or raw materials generation, involves a series of steps that result in a material having a defined structure.
That structure begets properties, which enable the use of the material in secondary (2 ) processing. This second stage, to be covered in the next chapter of this
volume (see Chapter 9), is more generally termed “pharmaceutical manufacturing” and involves the combination and manipulation of raw materials to form a
composite product.
299
300
8 Primary Processing of Organic Crystals
1° Processing
Properties
Structure
2° Processing
Properties
Structure
Raw materials
manipulation
Performance
Raw materials
generation
Figure 8.2 Schematic emphasizing the branch of SMOC manufacturing that involves primary
(1 ) processing or bulk raw materials production. Exclamation points are meant to emphasize
that the structure following processing will dictate the eventual properties of the processed
material.
Central to this chapter will be a discussion of how specific elements of 1
processing define and alter the structure of bulk materials, resulting in properties that affect their suitability for downstream, 2 processing. In particular we
attempt to provide a theory, illustrated by examples, which demonstrates the
benefits of understanding these processes and controlling them for the production of materials useful for pharmaceutical manufacturing.
8.2 Primary Manufacturing: Processing Materials
to Yield Drug Substance
The successful generation of bulk drug substance and excipients, i.e. raw materials (1 processing), is beholden to controls over the crystallization and purification of small organic molecules. As a separate process, distinct from 2
manufacturing, the 1 manufacturing step has its own inherent goals, which,
although they may not align perfectly with those of 2 manufacturing, should
be optimized to do so.
During the 1 manufacturing sequence, the key objectives are centered
around:
1)
2)
3)
4)
Purification of raw materials (bulk drug substance or excipients).
Efficient yield of the desired solid form of the material.
Removal of solvents/reactants that facilitated crystallization.
Preliminary sizing of the solidified product prior to shipping.
In contrast, 2 manufacturing processes tend to focus on manipulation of a
drug substance and excipient raw materials for the purposes of forming a useful
8.2 Primary Manufacturing: Processing Materials to Yield Drug Substance
composite (i.e. a drug product). In either case, the efficiency and success of
processing SMOC materials will often rely on scale, where moving from benchtop to industrial-scale processes relies on identification of critical process parameters whose control directly affects attributes of the material related to
performance.
8.2.1
Crystallization (Solidification Processing)
Theoretical models for crystallization are discussed in detail in previous
chapters of this book and elsewhere [12, 13]. Solidification processing is enabled
by directed nucleation and growth, which should result in a solid, crystalline
material having a minimum of impurities (e.g. residual solvents, degradants,
components from preceding synthetic or extraction steps, etc.), a desired solid
form (polymorph, solvate/hydrate, salt form, etc.), and a morphology and size
distribution suitable for downstream processing and material performance.
Industrially, crystallization is solvent based, necessitating care in the selection
of an appropriate solvent.
The main driving force for crystallization from solution is the degree of
supersaturation S (Equation 8.1):
S=
C
Cs
81
where C is the concentration of molecules in solution and Cs is the equilibrium
solubility in the solvent (at a given temperature). For nucleation to occur within
a practical time frame, S must be greater than 1, often by a critical, multiplicative
factor. In his text [12], Mullin suggests an estimate for a critical supersaturation
(Scrit), assuming an “acceptable” nucleation rate of 1 nucleus/s per unit volume
of solution (Equation 8.2):
lnScrit =
16πγ 3 Vm2
3 kB3 T 3 ln A
1
2
82
Above, γ is the interfacial tension between the nucleating solid and the
solution from which it forms, Vm is the molecular volume, kB is Boltzmann’s
constant, T is the temperature of the solution, and A expresses the nucleation
rate in terms of the Arrhenius reaction velocity.
Considerable attention has been given to predicting induction times and rates
of nucleation for various systems, although this is often limited to inorganic
solids, such as BaSO4 [14]. Batch crystallization in industry aims to optimize
the supersaturation ratio by maintaining the crystallization solution within
the “metastable zone” (Figure 8.3), in order to yield quality product without
sacrificing process efficiency [15].
301
8 Primary Processing of Organic Crystals
Cmet ; S > 1
Concentration
302
Labile zone
Copt
C
—=1
Cs
Metastable zone
Stable zone
T (K)
Figure 8.3 Schematic for a single-component cooling crystallization scheme highlighting
the relationships between the solution stable zone, metastable zone, and labile zone.
In the simple case of crystallization by slow cooling of a hot, concentrated
solution, the stable zone represents combinations of concentration and temperature at which the solution is undersaturated and crystallization is not possible.
At some critical value of S > 1 (Equation 8.1), and represented by the dashed
boundary and metastable supersaturation concentration, Cmet, in Figure 8.3,
the solution has a large driving force for crystallization. Termed the labile zone
or metastable limit, crystallization is expected to be spontaneous and rapid
under these conditions, but likely uncontrollable. As such, the metastable zone,
represented by the conditions between the solid and dashed boundaries in
Figure 8.3, represents conditions under which the driving forces for primary
nucleation are favorable, but spontaneous crystallization remains unlikely. If,
however, seeds are introduced to a crystallizer containing a metastable solution,
secondary nucleation will occur, allowing the opportunity for controlled
growth [12].
In the interest of process efficiency, the kinetics of crystallization help establish an optimum supersaturation, Copt < Cmet, which in industrial settings is kept
somewhere between 0.1 < Copt/Cmet < 0.5 [15]. Practically speaking, the width of
metastable zones can be difficult to predict and cumbersome to determine
empirically [16].
Predictions of metastable zone widths are helpful for determining primary
processing parameters and essential for targeting growth of a specific median
particle size. Equation (8.3) suggests that the overall nucleation rate (B) under
a specific set of conditions can be considered a combination of mechanisms:
B = Bhom + Bhet + Bsurf + Batt
83
8.2 Primary Manufacturing: Processing Materials to Yield Drug Substance
where Bhom represents homogeneous nucleation, Bhet represents the rate of
nucleation on foreign particles, Bsurf is the rate of nucleation on crystals present
in the system, and Batt is the attrition-induced secondary nucleation caused by
both mechanical agitation and collisions of growing particles. Of these, surface
nucleation is expected to be the most significant in industrial seeded-batch
crystallizers, owing to the ubiquitous presence of crystals [15].
Mersmann and Bartosch proposed a simplified model for predicting metastable zone widths in seeded-batch crystallizers, which was tested using 28 systems
for which metastable zones had been measured and reported in the literature.
Their model suggested that the zone widths depended not only on a number of
molecule and solvent-specific factors but also upon the cooling rate of the
system and the ability to detect the dimensions of crystallites at which a shower
of nuclei occurred [15].
Kubota [17] also modeled the metastable zone width in relation to various
primary processing conditions and proposed Equation (8.4):
ΔTm =
Nm
kn V
1
n+1
n+1
1
Rn + 1
84
where ΔTm is the metastable zone width (in units of temperature), Nm/V is the
number density of nuclei (a value shown to be dependent on the method used to
detect critical nucleation), kn is the number-basis nucleation constant, n is the
nucleation order, and R is the cooling rate. It was determined that the metastable zone width tended to increase with increasing R, owing to a reduction in
nucleation frequency per unit change in undercooling.
Kubota did note that estimates of ΔTm depended on the method used to
detect the “avalanche” point, at which the solution has accumulated a critical
number of nuclei. Measurements of the Nm/knV term by three different methods yielded three different values, varying over an order of magnitude according
to their relative insensitivity to detecting critical nuclei formation. It was also
determined that if the measurement method for Nm/V was kept constant,
the metastable zone width was expected to be independent of the volume of
the crystallizer, facilitating reasonable scale-up. Additionally, it was found that
ΔTm decreased with increasing agitation, potentially explained by increasing
secondary nucleation with increased stirrer speed, allowing Nm/V to be detected
at an earlier time point [17].
8.2.1.1
Solvent Power
Since S serves as such a significant driving force for crystallization (see Equation 8.1), selection of an appropriate solvent is critical to a well-controlled primary process. In general, the solvent should have adequate “power,” which is
defined by Mullin as the solute mass capable of dissolving per mass of solvent,
at a specified processing temperature, which effectively determines the volume
303
304
8 Primary Processing of Organic Crystals
Drug discovery/drug development interface
Preformulation/formulation
(early product development)
Formulation and
product Mfg Dev’t
10’s
mg to g
1 000’s
g to kg
Drug substance synthesis
and initial scale-up
Drug substance/solidification
processing scale-up
Clinical studies
10 000s
kg
Clinical supply Mfg and
product Mfg scale-up
1 000 000s
tons
Regulatory inspection and
batch validation
Regulatory inspection and
batch validation
Approved drug product launch to market
Sustainable market supply of reproducible drug product and drug substance
Figure 8.4 Schematic outlining drug development activities. Drug product (left) and drug
substance (right) development are performed in parallel. Feedback between the two
separate process streams is required in support of ever-increasing requirements of both
viable products and materials needed to produce them. Following approval, both process
streams need to function efficiently to supply a sustainable market supply of reproducible
drug product and drug substance to the market for many years.
of the crystallizer required to produce a desired mass of material [12]. Given the
expression for Scrit in Equation (8.2), the solvent power must also support a volume capable of producing this critical mass of drug substance in order to get
meaningful yields.
Early in drug substance development, crystallization may only generate gram
quantities of bulk material; however, as scale-up proceeds many kilograms are
needed for clinical supply lots and 2 manufacturing process development. By
the time a drug is approved, the 1 processing of bulk drug substance needs to
be able to meet a regular demand on the order of several tons per year in support
of a drug product manufacturing campaign (Figure 8.4). The solidification medium
is, therefore, selected based on adequate solubility of the drug in the solvent.
The equation for equilibrium solubility is shown in Equation (8.5), which
highlights some of the important parameters considered during solvent
selection [18]:
− ln χ =
ΔHf Tm −T
TTm
R
+
Vm φ 2
δ 1 − δ2
RT
2
85
8.2 Primary Manufacturing: Processing Materials to Yield Drug Substance
Above, χ represents the mole fraction solubility, ΔHf the heat of fusion of the
solid solute, and Tm its melting temperature. T is the temperature of the solvent,
and R the ideal gas constant. The first term (to the left of the addition sign) is
familiar as the van’t Hoff expression for ideal solubility. To the right of the
addition sign, the nonideality of solutes is captured in Vm (molar volume of
the solute molecule) and φ (volume fraction of solvent in solution), and δ1
and δ2 are, respectively, the solubility parameters (commonly represented as
the cohesive energy density, δtot) of the solvent and solute [18], or, as shown
in Equation (8.6), the three-dimensional or Hansen partial solubility
parameters, which account for contributions to the cohesive energy density
from the dispersive or London forces (δd), permanent dipole–permanent dipole
polar interactions (δp), and hydrogen bonds (δh) [19, 20]:
δ2tot = δ2d + δ2p + δ2h
86
Although helpful in suggesting parameters that may be important in selecting
a solvent, based on attributes of the molecule to be crystallized, empirical data
show that predictions of solubility based on Equation (8.6) are particularly problematic for solute species having multiple heteroatomic groups or the ability to
form strong, specific interactions with the solvent (e.g. hydrogen bonds) [21].
Quantitative structure–property relationships (QSPRs) have been used to
empirically correlate structural elements of drug molecules with solvent properties but may be most useful for establishing solubility for a series of structurally
related compounds [21].
In addition to appropriate solvent power, the solvent pH, polarity, potential
impurities, and other work hazards also need to be determined. Highly viscous solvents are generally avoided, as crystal growth rates may be unfeasibly
slow (or inhibited altogether), and complications with respect to filtration,
washing, and drying reduce process yield [12]. Solvents that cause chemical
degradation of the drug substance during solidification are obviously not
acceptable.
8.2.1.2
Solvent Classification
Since practical crystallization methods will leave some residue, one of the
most important factors that impacts solvent selection is ensuring that residual chemicals do not exceed regulatory limits for toxicity. Known and suspected carcinogens and environmental hazards (Class I solvents) should be
avoided entirely, while solvents known to cause irreversible toxicity (Class
II solvents) should be restricted to use in circumstances where their need
outweighs the toxic risk to patients [22, 23]. Solvents designated as Class
III (having low toxicity) are allowable, as these do not pose human health
hazards at expected levels. A partial list of Class III solvents is provided in
Table 8.1.
305
306
8 Primary Processing of Organic Crystals
Table 8.1 Class III solvents recommended for solidification processing of pharmaceutical
drug substances.
Water
Ethanol
Methyl acetate
Acetic acid
Ethyl acetate
3-Methyl-1-butanol
Acetone
Ethyl ether
Methyl ethyl ketone
Anisole
Ethyl formate
2-Methyl-1-propanol
1-Butanol, 2-butanol
Formic acid
n-Pentane
Butyl acetate
n-Heptane
1-Pentanol
t-Butyl methyl ether
Isobutyl acetate
1-Propanol, 2-propanol
Dimethyl sulfoxide
Isopropyl acetate
Propyl acetate
Source: Examples from Ref. [22].
Note that the suitability for Class III solvent use is determined by quantification of residue content following solidification that needs to be below
the determined permitted daily exposure (PDE), which for Class III solvents
is typically >50 mg day−1 [22]. In a survey of the Cambridge Structural Database, Hosokawa et al. found that of the reported structures solidified from a
single solvent (whose file indicated the solidification procedure), approximately 30% were from Class III solvents, with ethanol reported as the most
common solvent used in recrystallization [24]. Although several of the solvents listed in Hosokawa et al. are Class I or II, it is worth noting that the
Cambridge Structural Database is not exclusive to pharmaceutically relevant
materials.
As a potentially complicating matter, solvent selection may be further limited
by the propensity of the solid to incorporate solvent molecules into its structure
during crystallization, resulting in an undesirable solid form (see Section 8.2.2).
The crystallization temperature can impact the likelihood of solvation, where
lower temperature processing conditions have the potential to result in higher
solvate stoichiometries [25]. From Jack Z. Gougoutas’ personal communication,
it has been observed for several compounds that the voids in desolvated crystals
of different solvates retained the geometry of the original solvent (e.g. methanol,
isopropyl alcohol, water), to the degree that the original solvent was identifiable
from the void structure.
A properly selected solvent requires precise control of conditions during
solidification, to prevent excursions in medium conditions that might
result in uncontrolled growth, solidification of undesirable solid forms
(including mixtures of forms). This includes cooling rates, rates of
antisolvent addition, agitation rates and vessel and impeller geometry,
and seeding conditions.
8.2 Primary Manufacturing: Processing Materials to Yield Drug Substance
8.2.1.3
Batch Crystallization
The majority of crystallization in support of drug substance development is
done via batch processing, using one of several different pieces of equipment.
For a more thorough review of the different types of crystallizers common to
primary processing, see Mullin [12] and Myerson [13].
Although the designs of different types of batch crystallizers vary, the basic
steps of the process are fairly consistent. A schematic overview of batch crystallization is shown in Figure 8.5. Here, rigorous control over both the S and T (see
Equations 8.1 and 8.2) of a continuously mixed solvent is used to direct nucleation of the desired solid phase. Seeds are typically introduced to the crystallizer
to facilitate 2 nucleation and serve as templates for growth of the desired phase.
The use of seeding is common and may be particularly important if the desired
product is a metastable solid form [26]. In contrast to 1 nucleation, seeding the
batch provides a reduction in the interfacial energy (γ) cost of establishing a
solid growth front that is incoherent with the solvent medium. With a lower
thermodynamic energy barrier, 2 nucleation may be practical at lower degrees
of S, reducing the potential for uncontrolled, rapid recrystallization that may
result from very high S media [12].
Crystallization
S,T of solvent controlled
to facilitate crystallization
Seeds are potentially
added for 2° nucleation
Filtration
Slurry discharge separated via filter
Washing/refiltration
Drying
Milling/sizing
Residual solvent removed
to complete purification
Figure 8.5 A schematic representation of a batch crystallization sequence used to generate
solid organic crystalline materials.
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8 Primary Processing of Organic Crystals
Although intentional seeding can be a good means of directing growth of a
desired solid form, unintentional seeding can have the opposite result, as is
suspected in the now classic case of ritonavir polymorphs, where it has been
suggested that spontaneous crystallization of a previously unidentified, thermodynamically stable polymorph was the result of the inadvertent transfer of seeds
of the undesired Form II from the clothing of scientists from one manufacturing
facility to another [10, 27].
In addition to having the internal structure of the desired crystalline phase, seed
crystals should also have a very narrow particle size distribution (PSD) in order
for their addition to the crystallizer to direct controlled growth of the desired
solid. For eventual use in 2 manufacturing, the crystallized product should, itself,
be relatively small, having a narrow PSD, often requiring that 1 processing
involves even smaller seed crystals, having dimensions on the order of microns
[13]. Seeds are generally prepared by either wet or dry milling and usually consist
of fines, considered too small for effective downstream processing [26].
8.2.1.4 Continuous Crystallization
Although the majority of industrial-scale crystallization in the pharmaceutical
industry is done as batch processes, issues related to batch-to-batch variability
present challenges with respect to supplying drug substances having reproducible critical materials properties in sufficient quantities to meet the needs of
drug product manufacturing. Continuous crystallization processes potentially
afford several advantages over batch crystallization, including a smaller physical
footprint needed for the continuous manufacturing equipment and the
potential for reduced operating expenses. More importantly, with respect to
the need for reproducible solid materials, once continuous crystallizers reach
steady state, crystallization occurs under controlled, uniform conditions, allowing more control over solid form and generating more uniformly sized and
shaped particles having less potential need for milling [13, 28].
In contrast to the batch crystallization scheme shown in Figure 8.5, continuous processing is typically accomplished by combining API solution and an
antisolvent in a series of reactors. When the desired slurry is formed, it is
filtered, washed, and dried similar to what is described above for batch processing, with the same goals in mind. Continuous crystallization of SMOCs
generally uses one of two types of equipment: a mixed suspension–mixed
product removal (MSMPR) crystallizer or a multistage plug flow reactor
(PFR) system. Schematics of each are illustrated in Figure 8.6.
The MSMPR crystallizer works by mixing a continuous stream of solution
and antisolvent into a stirred reaction vessel (Figure 8.6a). As precipitation
occurs, the solid phase is constantly removed in order to maintain steady-state
conditions [13]. In contrast, the PFR system works by pumping a solution
through a jacketed reaction vessel, containing a static mixing element
(Figure 8.6b). Antisolvent is injected at sequential ports to drive precipitation
and the mixture flows out to filtration steps [29].
8.2 Primary Manufacturing: Processing Materials to Yield Drug Substance
(a)
Co-addition of solution
and antisolvent begins
precipitation
Solution at
controlled S
Antisolvent
Slurry is continuously discharged as more
solvent/antisolvent is added to maintain steady state
(b)
Antisolvent
Multiple injection ports for antisolvent
Filtration
Solution at
controlled S
Jacketed crystallizer allows T control
Figure 8.6 Schematics of (a) mixed suspension-mixed product removal (MSMPR) continuous
crystallizer. Source: Adapted from Chen et al. [28]. Reproduced with permission of American
Chemical Society. (b) Multistage plug flow reactor (PFR) system. Source: Adapted from Alvarez
and Myerson [29]. Reproduced with permission of American Chemical Society.
The type of system selected for continuous crystallization largely depends on
the process kinetics. As reviewed by Chen et al., solids in MSMPR systems
usually have much longer residence times compared with PFR systems [28],
suggesting that a PFR may be more suitable to isolating metastable solids.
Alvarez and Myerson demonstrated the use of a PFR setup for crystallization
of ketoconazole (in methanol/water), flufenamic acid (in ethanol/water), and
L-glutamic acid (in water/acetone). The authors showed that PFR continuous
crystallization resulted in small crystals having a narrow PSD, where the injection of antisolvent at multiple points enabled a certain degree of control over the
median particle size [29].
8.2.2
Filtration and Washing
In either batch or continuous crystallization methods, the slurry containing
solidified phase requires filtration and washing. Of all the steps involved in
1 manufacturing, there is none where the impact of crystallite shape is more
important than filtration.
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8 Primary Processing of Organic Crystals
Cake filtration is the most common method used in the pharmaceutical
industry to isolate API, where it has been shown that the particle size of the solidified phase can affect cake filterability. Small crystallites change the bed height
and permeability of the cake relative to larger crystallites despite the same mass
accumulation on the filter. The rate of crystallite accumulation is determined by
the rate at which slurry is added to the filtration vessel, and the pressure drop
across the cake will vary accordingly.
Although reported less formally, crystallite shapes can also impact the parameters and efficiency of filtration. During filtration, acicular needles may align
in the cake along the long axis. Such preferential orientation of the solid can
restrict or prevent fluid flow and may even result in filter “breakthrough,”
requiring batch rework at best or complete batch loss at worst. This is further
exacerbated by the combination of anisotropic morphology and small particle
size, which is why most of crystal engineering are focused on controlling these
crystallite attributes.
The basic relationship describing constant rate cake filtration is described by
Darcy’s law (Equation 8.7):
v=
kΔP
μl
87
where v is the velocity of the liquid, ΔP is the pressure drop across the bed of
thickness (where ΔP/l is the pressure gradient), μ is the viscosity of the liquid,
and k is the permeability of the bed, which is effectively a proportionality
constant having dimensions of l2. Equation (8.7) shows that the pressure drop
across the bed is proportional to not only the bed thickness but also the permeability. Preferentially oriented needles will often result in a dramatically lower
bed permeability having the same thickness, but comprised isotropic morphology crystals. This can lead to failed drug substance harvesting, and even filter
failure, resulting in lost batches and/or unprovable processes.
As mentioned above, crystal engineering combines the knowledge of the
crystal structure with the thermodynamics of the system to select the appropriate conditions (i.e. solvents, cooling curves, and seeding) to control the
morphologies of the crystallites in the bulk. For example, needles are often
the result of rapid precipitation from highly supersaturated solutions, while
conditions that favor slower growth may produce more regular shapes. Crystal
engineering must balance all of these variables to ensure sufficient yield, purity,
and properties for a commercially viable process [30].
Häkkinen et al. [31, 32] also studied the influence of solvent composition,
cooling rate, cooling profile, and mixing conditions on the size and shape of
crystals and the resulting filtration characteristics of suspensions of sulfathiazole particles. Binary solvent mixtures of water and n-propanol yielded crystals
having a broader size distribution with more elongated habits than was obtained
from either pure water or n-propanol (Figure 8.7). Two parameters, cake
8.2 Primary Manufacturing: Processing Materials to Yield Drug Substance
Water
3:1 – w:p
1:3 – w:p
1:1 – w:p
n-Propanol
Figure 8.7 Examples of the sulfathiazole crystals obtained from different water : n-propanol
mixtures. Source: Reprinted from Häkkinen et al. [31]. Reproduced with permission of John
Wiley & Sons.
porosity and specific cake resistance, were used to evaluate the filtration properties of sulfathiazole slurries following crystallization. It was shown experimentally that the suspensions composed of the largest sulfathiazole crystals had the
highest cake porosity and lowest specific cake resistance, while there was no
significant difference in filtration characteristics observed between the slurries
having similarly shaped crystals (grown at the same cooling rates) but harvested
from different solvents. The authors also found that an almost negligible
difference in crystallite size distributions led to a significant difference in cake
porosities, suggesting that the difference was mostly due to differences in the
crystal morphology.
Cornehl et al. [33] studied the influence of crystal size and shape on the
scalability of filtration for lysozyme crystals in pressure filters. Deviations of
the filtration behavior for different filter areas were also studied by monitoring
wall friction during filtration. Different sizes and shapes of lysozyme crystallites
were formed under different stirring conditions (Figure 8.8). The authors
studied mass-specific filter cake resistances (αM) for slurries produced under
different conditions, which resulted in solids having different particle sizes
and morphologies (corresponding, respectively, with panels a–e in
Figure 8.8). In general, a value of αM = 108 is typical of a solid that is easily
filtered, while values approaching 1013 suggest poor filtration performance.
Poor filtration of lysozyme crystallites was confirmed for those that grew as fine
needles (see Figure 8.8e), which had a mean particle size of 47 μm, and αM =
1.21 × 1012 m kg−1, the smallest for any of the filtrates. The authors noted that
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8 Primary Processing of Organic Crystals
(a)
(b)
(c)
(d)
(e)
Figure 8.8 Photomicrographs of lysozyme crystal slurries prepared under different
crystallization conditions. (a) isometric crystals, (b–d) different crystal aggregates, and
(e) needlelike crystals. Slurries were obtained by different stirring conditions during the
crystallization process. Source: Reprinted from Cornehl et al. [33]. Reproduced with
permission of John Wiley & Sons.
dimensionally similar, small aggregates (see Figure 8.8d) having a mean particles
size of 35 μm resulted in poor filtration, where αM = 2.13 × 1011 m kg−1 [33].
These results suggest that particular care needs to be taken when filtering slurries consisting of anisotropic-shaped crystallites. Although it is considered
“common knowledge” that needle-shaped crystals are problematic during filtration operations, the relative paucity of published data to this effect illustrates
that the phenomenon is likely under-reported in the open literature.
8.2 Primary Manufacturing: Processing Materials to Yield Drug Substance
8.2.3
Drying (Removal of Crystallization Solvent)
The solidification sequence is completed with a drying stage, which is used
to remove residual solvent left over from the precipitation or washing steps,
yielding material that is suitable for dry and impact- or attrition-based sizing.
Similar to drying processes used in 2 manufacturing (see Chapter 9), drying
precipitates requires considerable control to assure that the drug substance
retains the internal structure grown and selected during earlier steps. Process
efficiency is important; however, care should be taken, especially in regard to
the temperature of the air used to remove the solvent.
Prolonged exposures to temperatures in excess of enantiotropic transition
temperatures (Ttr) can facilitate partial or complete conversion to an unwanted
polymorphic form, which itself is metastable at room temperature. Such a
scheme is illustrated in Figure 8.9, which plots the free energy–temperature
(G–T) diagram for a pair of hypothetical enantiotropes having a Ttr = 50 C.
Assuming that Form I in the scheme is the desired precipitate, but efficient
drying requires exposure to airflow at 80 C (assumed to be less than the melting
temperatures of both forms, Tm,I and Tm,II), and takes several hours to
accomplish, the free energy of the drying solid follows the trajectory between
GL
Free Energy (J mol−1)
Liquid
GII
GI
Form-II
4.
Form-I
1.
2.
3.
Temperature (K)
Ttr
Tm,I Tm,II
Figure 8.9 Free energy–temperature diagram for hypothetical enantiotropic solids I and II,
exhibiting a solid transition temperature Ttr = 50 C. Following the trajectory between points
1 and 2 represents heating Form-I through Ttr without melting. Spontaneous conversion from
Form-I to II follows the free energy trajectory between points 2 and 3. Re-cooling Form-II
through Ttr (between points 3 and 4) results in eventual re-conversion to Form-I along the
free energy path from point 4 to 1.
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8 Primary Processing of Organic Crystals
points 1 and 2 on Figure 8.9. At this drying temperature, and in the presence of
excess solvent, Form II is thermodynamically stable, and a likely result if the
conversion kinetics are favorable (profile follows free energy gradient trajectory
between points 2 and 3). At the completion of drying, when the solid cools back
to ambient temperature, the free energy profile traces the trajectory between
points 3 and 4, and the process has resulted in generation of a metastable phase,
different from the intended form by virtue of processing. Conversion kinetics at
ambient temperature dictate the rate of reconversion between Form II and
Form I (profile follows the free energy gradient trajectory between points 4
and 1); although reconversion may not be complete during this process, a
mixture of forms is problematic, as the material is subject to ongoing conversion
throughout its lifetime. This scenario, while specific, is certainly feasible for
SMOC materials, where enantiotropic transition temperatures are expected
to be similar to regular drying temperatures.
The crystal structure of the drying material may also be altered, depending on
the rate at which the solvent of crystallization is removed. As was reported in the
case of glycine, the metastable α-phase was kinetically trapped as water was
rapidly evaporated. Although the thermodynamically stable γ-glycine was the
target of crystallization, dissolution of glycine at crystal surfaces occurred until
the surrounding water reached Cs. As this represented supersaturation with
respect to the α-phase [34], the metastable solid preferentially recrystallized
as the water was rapidly removed [35].
In addition to contributing to the possibility of phase change due to solventmediated transformations, drying rate has also been shown to potentially result
in desolvation of the crystallized solid, resulting in a structure change that alters
the physicochemical properties in such a way that downstream processing or
product performance is negatively affected. A review of conditions resulting
in the loss of the solvent of crystallization is provided in Byrn et al. [36].
A particularly dramatic example in which drying results in significant changes
in the crystal structure of the dried solid was reported for the acetonitrile solvate
of quinipril∙HCl. Guo et al. demonstrated that upon desolvation, quinipril∙HCl
converted to an amorphous solid, as evidenced by a nearly complete loss in
crystallinity. In this case, the transformation was not just dramatic, representing
a complete lattice collapse as the acetonitrile lattice constituents left, but the
increased mobility of molecular functional groups that resulted from conversion to the amorphous solid made the quinipril∙HCl considerably more labile
to chemical degradation by cyclization [37].
Additional materials for which desolvation may result in the formation of an
amorphous phase can be anticipated in circumstances when the crystal
structure contains numerous coordinated solvent molecules, as observed with
raffinose pentahydrate. As reported by Bates et al., dehydration of the pentahydrate at 60 C resulted defect generation, eventually resulting in a lattice
collapse and conversion to the amorphous state [38]. Although this particular
study was not conducted to specifically highlight the potential effects of
8.2 Primary Manufacturing: Processing Materials to Yield Drug Substance
desolvation at the end of a crystallization routine, it certainly presents a cautionary tale with respect to drying certain solvated precipitates, especially if the
resulting amorphous solid does not possess the physical attributes or chemical
stability needed for inclusion in a viable drug product.
Issues of crystal structure conversion notwithstanding, drying of harvested
bulk solids is essential to later processing from a materials handling perspective.
The presence of residual moisture makes powders more cohesive, giving rise to
clump and cake formation. Although particle size enlargement can facilitate
better flow properties, unintentional agglomeration of solids can lead to homogeneity issues when combined together with other materials during 2 processing. In general, the presence of residual moisture in bulk materials is
deleterious to handling properties, as formation of capillary bridges between
particles makes individual particle movement difficult. This was the case for
hydroxypropyl methylcellulose (HPMC), a common solid polymeric excipient
used in pharmaceutical formulation. Sorption of water at modest relative
humidities caused substantial reduction in the flow index measured by means
of shear testing, indicating that the material was most cohesive when moist [39].
8.2.4
Preliminary Particle Sizing
The endpoint of solidification processing usually involves a sizing step, which is
needed to comminute particles otherwise too large for subsequent 2 processing. Greater detail pertaining to the fundamental underpinnings of particle size
reduction as it relates to working with SMOC materials is detailed in the next
chapter (see Chapter 9). Used in the context of 1 manufacturing, particle size
reduction is used as an early size homogenization step that enables supply of raw
materials having a relatively narrow PSD, with a workable median particle size
(d50). Figure 8.10 suggests a descriptive continuum of particle size nomenclature, as well as some associated uses in 2 processing.
To be suitable for downstream 2 manufacturing processes, most raw materials will be sized so that the d50 falls somewhere on the fine to coarse particle
size scale (between approximately 50 and 1000 μm). These dimensions are targeted for raw drug substance particles to better enable blending with excipients
during 2 processing. To facilitate comminution at this stage, the materials need
to be dry and sufficiently brittle to allow for particle fracture and attrition. To
this end, most sizing processes at this stage use impact-driven mills and coarse
screens.
The sizing step at the end of 1 processing, though seemingly simple, is not
without its challenges. Most bulk material supply manufacturing is done at facilities separate from where 2 manufacturing will take place, requiring shipment
and storage until the materials are used. Sized materials are packaged at the 1
processing site into lined drums or sacks (for commodity materials), which are
transported by various means to product manufacturing facilities. During longdistance transport, these materials are likely to experience substantial agitation
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8 Primary Processing of Organic Crystals
Coarse emulsions,
flocculated particles
(10 – 50 µm)
Pharmaceutical granules
(200 – 1200 + µm)
Suspensions, fine emulsions
(0.5 – 10 µm)
Granular
Colloid
10 nm
Powder
1µm
100 µm
Fine powders (50 – 100 µm)
Ultrafine powders (1 – 50 µm)
1 mm
Coarse powders
(150 – 1000 µm)
Figure 8.10 Descriptive nomenclature for particle sizing used in pharmaceutical 1 and 2
manufacturing.
along the way. Once shipped, static samples of loose powder beds, such as those
stored in drums, will tend to settle under gravity, potentially forming dense
cakes (via concretion), which require rebreaking before further processing
can be done.
Fine particles subject to lengthy vibration (as might be experienced in a crosscountry rail or truck shipment) will tend to consolidate, particularly toward the
bottom of shipping containers, a phenomenon that is exacerbated if the particles are cohesive. The extent to which a powder consolidates due to agitation in
a vessel of fixed volume is easily observed using a method such as that described
in USP <1174> Powder Flow [40], in which the Compressibility Index is determined (Equation 8.8):
Compressibility Index = 100 ×
ρtapped − ρbulk
ρtapped
88
In this procedure, a loose sample of powder is placed into volumetric cylinder
and weighed (allowing calculation of ρbulk). The cylinder is placed on a platform,
which is agitated up and down at a fixed oscillating frequency and amplitude to
simulate tapping. Movement of the powder particles with successive taps results
in expulsion of entrapped air, causing the sample to settle. When the tapped
volume reaches a plateau, it is measured and used to calculate ρtapped, which
in turn is used to calculate the Compressibility Index. As shown in Table 8.2,
powders that undergo very small changes in relative density (<10%) are
classified as free flowing, while those that become extensively consolidated
(>38% relative density change) have exceedingly poor flow properties [40].
8.2 Primary Manufacturing: Processing Materials to Yield Drug Substance
Table 8.2 Descriptions of powder flowability with reference to expulsion of air
voids upon agitation.
Measured % change in bulk
density by tapping (Compressibility Index)
Description of powder flowability
<10
Excellent
11–15
Good
16–20
Fair
21–25
Passable
26–31
Poor
32–37
Very poor
>38
Very, very poor
Source: Data from USP <1174> [40].
While the Compressibility Index is a simple, qualitative means of assessing
how particle size might influence consolidation and cohesion during shipping,
more quantitative methods can provide important data, particularly if direction
is needed with respect to how specifically solids need to be sized at the end of 1
processing.
Numerous techniques for static and dynamic assessments of powder flow can
be used to discern important quantitative trends [41–44]. Perhaps the most
applicable in this circumstance is the Jenike shear cell, for which a cross
section is depicted in Figure 8.11a. Powder is loaded into a cylindrical cell,
having a fixed base and an upper movable ring. A lid is affixed and used to apply
a normal load (FN), which translates into a normal stress, σ, and is used to
preconsolidate the powder bed. Parallel to the powder surface, a shear force
(FS) is applied, resulting in a shearing stress, τ, which opposes the normal load.
The measurement determines the resistance to flow in shear, against an applied
normal stress, representing the cohesion of the powder (Figure 8.11b).
The theoretical underpinnings of consolidation due to vibration of loose
powders are complicated, although research has indicated that the rate at which
a powder bed is compacted and its final density, are both very sensitive to the
history of vibration intensities that it experiences [45].
Roberts used a modified version of the shear cell depicted in Figure 8.11a,
which allowed vibration of cell at fixed frequencies in order to determine the
impact on consolidation [46]. This work demonstrated that the dynamic shear
strength of a powder (τf) that has been exposed to vibrations depends on a
number of different factors:
τf = f σ 1 , σ, ϕ, x, ρ, H, d50 , T
89
317
8 Primary Processing of Organic Crystals
(a)
FN
Fs
Lid
Ring
Powder sample
Fixed base
(b)
35
Shear stress (Pa)
318
Figure 8.11 (a) Schematic of a
shear cell for determining
powder flow properties. (b)
Simplified yield data typical of
a shear cell measurement.
Note: Yield loci are often
interpreted in terms of Mohr
circle plots. For details of this
interpretation, see Hiestand
[41] and Schwedes [42].
Source: Panel (b) reprinted
from Geldart et al. [44].
Reproduced with permission
of Elsevier.
30
25
End
point
20
15
10
Cohesion
5
0
Normal stress (Pa)
Equation (8.9) reports the dynamic shear strength measured using a device
such as a modified Jenike dynamic shear cell, is a function of several parameters. The major consolidating stress, σ 1, can be applied to a loose powder
bed during the measurement of τf or, in a practical sense, is the pressure
owing to the mass of powder in a storage bin, which likely varies at different
strata in the drum (suggesting that the most significant densification occurs
at the bottom). The normal stress required to initiate shear failure σ is an
experimental parameter specific to the measurement of τf in a shear cell.
The remaining variables, which include vibrational frequency (ϕ), vibrational
amplitude (x), bulk density of the powder bed (ρ), sample moisture content
(H), particle median particle size (d50), and product temperature (T), all suggest
the various means by which the experience of the milled particles in drums
during shipping will determine the extent to which vibration is problematic.
Of particular relevance to the present discussion, Roberts showed that there
was a significant impact of particle size on vibrational consolidation,
concluding that vibrated powder beds consisting of fine particles had a markedly higher τf relative to vibrated powder beds consisting of coarse particles [46].
Additionally, Roberts showed that powder beds having a moisture content of
just 5% resulted in a far more cohesive mass following vibration, relative to rigorously dried powders [46]. This seems particularly relevant when shipping
8.3 Challenges During Solidification Processing
from one site to another exposes the sized bulk materials to a range of
relative humidities.
In their work exploring the effects of vibration on the flow properties of
monodisperse fine glass beads, Soria-Hoyo et al. [47] estimated the cohesion
(C) and angle of internal friction (φ) for differently sized glass beads subject
to controlled vibration. The authors found that their experimental observations
correlated well with the Mohr–Coulomb criteria for flow (Equation 8.10), which
suggests that in order for flow to occur along some plane, the shear stress (τ)
acting on that plane must exceed a critical value, which depends on a stress acting normal to that plane (σ):
τ = σ tan φ + C
8 10
In their experiments, loosely packed beds, having a relative density of ~0.5,
were consolidated by vibration, ultimately reaching a limiting density of
~0.64, which approximates the random close-packing limit of hard spheres.
The general observation of this work was that C increased significantly, while
φ increased somewhat as consolidation due to vibration of the samples was
increased [47]. Applying these data to the dependence of consolidation on particle size observed by Roberts [46] suggests that too finely sized particles emerging from 1 processing are more likely to be subject to densification during
shipping, making them far more difficult to remove from containers when they
are dispensed prior to 2 manufacturing.
Further complicating scenarios in which sized particles may undergo deleterious consolidation during shipping, Nowak et al. demonstrated that vibrated
materials first undergo irreversible densification with the removal of low density
regions such as air bubbles and particle bridges, which is followed by establishment of a steady-state, reversible densification [45]. Although their work
focused on monodisperse glass beads, the authors also found that the results
were reasonably reproduced for irregular, polydisperse alumina particles. These
findings suggest that over the course of shipping, as sized particles are exposed
to a range of vibrations and agitations, they may consolidate differently, resulting in batch-to-batch variability in handling properties as the bulk material is
received. As discussed in the next chapter (see Chapter 9), the most likely first
step in 2 manufacturing is often milling, in order to reverse some of these issues
arising during transfer from one facility to another.
8.3
Challenges During Solidification Processing
Aside from the goal of supplying solid raw materials suitable for formulation
and secondary manufacturing, solidification is done with the intent of serving
as a final purification step. While solidification can be used to effectively exclude
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chemical impurities from a growing lattice, it is also important to consider
challenges associated with crystallizing a phase-pure solid having desirable
shape and dimensions.
Directed solidification is done by rigorously controlling the conditions inside
the crystallizer, in order to result in growth of a unique phase. Essentially, this is
a process control concession to Ostwald’s Rule of Stages, which suggests that
the most likely phase to be formed is the one having the smallest free energy
difference with respect to the crystallization conditions [12, 48, 49], so that
the desired phase is grown rather than that representing the closest convenient
stop along the thermodynamic trajectory. According to Tung, construction of
an empirical solubility map, analogous to Figure 8.3 or Figure 8.12, can be
beneficial for working toward a particular outcome. For example, the author
suggests that if the goal of solidification is to generate fine, crystalline particles,
but the resulting product is too coarse to be useful, the experiments can be
reconditioned to a higher solution concentration, where a greater extent of
nucleation is more likely [26].
The general scheme of the crystallization process is outlined in Section 8.2.1.
To enable more precise control over the emerging product, variations on this
scheme are employed. Comprehensive texts and reviews on crystallization are
recommended for details regarding equipment and strategies [12, 13, 26, 50];
herein, common crystallization techniques are addressed with respect to some
of the issues that may arise with respect to the generation of bulk materials.
8.3.1 Polymorphism
As described in a previous chapter in this text, organic molecules can solidify in
different three-dimensional arrangements, resulting in growth of completely
different crystals. Termed polymorphs, the chemical identity of the molecule
is preserved (of primary concern from a therapeutic standpoint); however,
the different crystalline forms have the potential for very different physicochemical properties, presenting various challenges in dealing with these materials
during downstream manufacturing. Polymorph control during primary
processing is, therefore, a matter of key importance [48–51]. Polymorphs
having very similar free energies will have overlapping crystallization zones,
requiring precise control over 1 processing conditions to yield the desired
phase-pure form. In many ways, a necessary condition for a drug product successfully reaching the market depends on the ability to reproducibly generate
sufficient quantities of the correct polymorph during solidification processing
to supply the quantities needed to support a 2 manufacturing campaign.
Traditionally, solid form selection is informed by a polymorph screen, the
information that can be fed back to help scale up bulk materials manufacturing
[25, 49, 52]. Recent advancements in high-throughput solid form screening
allow rapid identification of the various phases that can emerge from different
8.3 Challenges During Solidification Processing
(a)
Form II
Concentration
Form I
3.
Copt,II
(b)
1.
Copt,I
2.
Ttr
Temperature (K)
Concentration
Form II
Form I
3.
Copt,II
2.
Copt,I
1.
Temperature (K)
Figure 8.12 Solubility–temperature diagrams for (a) hypothetical enantiotropic solids I and II.
The dashed lines each corresponds to the metastable supersaturation curves (per Figure 8.3)
for the respective forms; (b) hypothetical monotropic solids I and II. As in (a), the dashed lines
each corresponds to the metastable supersaturation curves for the respective forms.
crystallization conditions [53–56]. It is unlikely that any screening method will
definitively identify all possible solid forms for a molecule; however, finding the
most probable growth outcomes of solidification processing under different
conditions is still useful for minimizing the likelihood of surprises related to
unanticipated polymorphism. In a pertinent paraphrasing of what several
resources refer to as the “McCrone Rule” [36, 48, 49, 57], the number of polymorphs that will ultimately be discovered for a SMOC material will more likely
321
322
8 Primary Processing of Organic Crystals
depend on how much time and effort is spent trying to find them. It is reasonable to suspect then that most, if not all, pharmaceutically relevant organic
molecules are capable of solidifying in more than one polymorphic form.
Table 8.3 provides a very brief list of some well-characterized SMOC materials
subject to polymorphism because of crystallization conditions. Most of the
materials in Table 8.3 list numerous solved structures; for reference, sample
index codes from the Cambridge Structural Database [5] are provided. In many
cases, details on the crystallization procedure were found in other resources,
which are cited in the Crystallization Conditions column.
As different solid forms are isolated during a polymorph screen, characterization allows their free energy–temperature and solubility–temperature
relationships to be established. Under most circumstances, 1 processing will
be designed to selectively produce the most thermodynamically stable phase
known and to reduce the likelihood of manufacturing-induced or storagerelated physical stability issues. Controlled crystallization of polymorphs essentially requires management of the nucleation, growth, and transformation
mechanisms of the desired solid. Kitamura details the key factors involved in
1 processing including supersaturation, temperature, crystallizer agitation,
addition rate of an antisolvent, and presence or absence of seed crystals. Secondary to these factors but still important are solvent type, use of additives, interfacial selectivity, and solution pH [70]. Basic strategies for crystallization of
polymorphs are described below. These involve cooling crystallization, solvent
selection, use of antisolvents, and selective crystallization using additives.
8.3.1.1 Cooling Crystallization
The solid form is controlled by directing nucleation, the most important step in
the process [50]. If the thermodynamic relationships between polymorphs are
known, in combination with their respective metastable zone widths, precise
cooling of a supersaturated solution can promote growth of the desired phase.
If available, the addition of form-specific seeds circumvents the need for nucleation, as seed crystals will template growth of a particular polymorph [49].
To reinforce the utility of this strategy, consider the solubility–temperature
relationships drawn in Figure 8.12, for pairs of hypothetical enantiotropes
and monotropes, Form I and Form II. In the enantiotropic system
(Figure 8.12a), cooling along the trajectory indicated by arrow 1, at T > Ttr,
enables an optimal supersaturation specific to Form I (Copt, I) to be reached
in the metastable zone specific to Form I. Growth of Form II under these
conditions should be impossible, because the solution remains undersaturated,
and therefore stable, with respect to Form II. Similarly, cooling at T < Ttr, along
the trajectory indicated by arrow 2, reaches Copt, II in the metastable zone for
Form II while remaining undersaturated with respect to Form I. Process design
to avoid a cooling trajectory such as that shown along arrow 3 is recommended.
Cooling at T close to Ttr runs the risk of overlapping metastable zones, enabling
nucleation and growth of a mixture of forms.
8.3 Challenges During Solidification Processing
323
Table 8.3 A brief list of some SMOC materials subject to polymorphism as a result of crystallization
conditions.
Material
Polymorph
[CSD refcode]
Acetaminophen Form I
[HXACAN04]
Cimetidine
Famotidine
Glycine
Indomethacin
Ribavirin
Sulfamerazine
Crystallization conditions
Recrystallization from ethanol [58]
Form II
[HXACAN08]
Seeded recrystallization from benzyl alcohol or industrially
methylated spirits (IMS) [59]
Form III
[HXACAN29]
Recrystallization from molten Form I; confined thermal
cycling [60]
Form A
[CIMETD03]
Recrystallization from warm 80% v/v methanol–water [61]
Form B (struct.
Not solved)
Recrystallization by slow cooling of hot 15% w/w aqueous
solution [61]
Form C (struct.
Not solved)
Recrystallization by rapid cooling of 5% w/w aqueous solution
to 5 C [61]
Form D
[CIMETD04]
Recrystallization by rapidly cooling distilled water without
agitation [62]
Form A
[FOGVIG04]
Multiple conditions/solvents [63]
Form B
[FOGVIG03]
Multiple conditions/solvents [63]
α-form
[GLYCIN03]
Recrystallization by slow cooling of aqueous solution [64]
β-form
[GLYCIN25]
Recrystallization by slow cooling 5 : 1 v/v water–acetic acidsaturated solution [65]
γ-form
[GLYCIN15]
Recrystallization from aqueous solution acidified with acetic
acid [66]
α-form
[INDMET02]
Addition of water to solution of hot ethanol; recrystallization
by cooling 60 : 40 v/v water:acetic acid [67]
γ-form
[INDMET01]
Recrystallization by slow evaporation of 60% aqueous ethanol
[67]
Form I
[VIRAZL]
Slow evaporation of water [68]
Form II
[VIRAZL01]
Rapid cooling of 50% aqueous ethanol [68]
Form I
[SLFMNA01]
Recrystallization from water [69]
Form II
[SLFMNA02]
Very slow-seeded solvent-mediated transformation of Form
I suspended in acetonitrile [69]
Source: CSD refcodes are provided for access to details [5].
324
8 Primary Processing of Organic Crystals
Phase purity may also be dictated by the crystallization kinetics in an
enantiotropic system. If, for example, in Figure 8.12a crystallization requires
cooling at temperatures close to Ttr, nucleation of a mixture of forms is
expected, particularly if the two polymorphs solidify at similar rates. In contrast, two forms having overlapping metastable zones that have very different nucleation kinetics will most likely result in the form that crystallizes
most rapidly.
The monotropic system (Figure 8.12b) provides some contrast with cooling crystallization of enantiotropes, because there is no Ttr of which to take
advantage. Exclusive solidification of the thermodynamically stable form
occurs by maintaining precise control over T and S, so that the system does
not become supersaturated with respect to the metastable form [49]. This
window may be very narrow, or nonexistent, depending on the energetic
difference between monotropes. Cooling along the trajectory of arrow 1
reaches Copt, I but does so at a concentration that is also supersaturated
with respect to Form II. Although Copt, I may not be sufficiently supersaturated with respect to Form II to drive much nucleation, if Form II grows
rapidly, crystallization can still result in a mixture of forms. Arrow 2 potentially exacerbates growth of a mixture of forms; although Copt, II is within
the metastable zone for Form II, it is in the labile zone for Form I. Again,
the extent to which crystallization results in a mixture of polymorphs
depends on their relative nucleation kinetics. Finally, the trajectory of
arrow 3 reinforces the utility of solubility–temperature plots for directed
crystallization. Overcooling the solution to this temperature shifts the solution to the labile zones for both Forms I and II, likely resulting in very
rapid, uncontrolled nucleation and growth of both phases. In cases where
overlapping metastable zones is unavoidable, seeding can yield a phasepure solid, as long as the zones are not so unstable as to permit crossnucleation [49].
As an example of kinetics influencing the isolation of a particular polymorphic form, consider the polymorphs of sulfamerazine studied by Zhang et al.
[69]. The enantiotropes were determined to have a transition temperature
between 51 and 54 C [69]. The unit cells of sulfamerazine Forms II and
I are shown in Figure 8.13 and indicate that both polymorphs are orthorhombic
with comparable densities. While Form II is thermodynamically stable at room
temperature, the metastable Form I is most practically solidified, owing to the
very slow growth of Form II under conventional conditions. Zhang et al. [69]
were able to obtain purified Form II at lab scale but suggested that the very slow
kinetics for the formation of this polymorph would make its occurrence during
solidification processing highly unlikely. These authors also noted that the
solid-state conversion from Form I to Form II was very slow, affording sufficient
physical stability for Form I to be useful in subsequent manufacturing and
storage.
8.3 Challenges During Solidification Processing
(a)
(b)
Sulfamerazine Form II
Sulfamerazine Form I
Polymorph
Form-II (Pn21a)
Form-I (Pbca)
a, b, c (Å)
14.474, 21.953, 8.203
9.145, 11.704, 22.884
V (Å3)
2606.48
2449.35
ρt (g
cm−3)
1.546
1.534
Z, Zʹ
8.0
8.0
Tm
212 – 214 °C
237 °C
Figure 8.13 Unit cells for (a) sulfamerazine Form II (CCDC refcode SLFNMA02) and (b)
sulfamerazine Form I (CCDC refcode SLFNMA01). Source: Structures obtained from
Cambridge Crystallographic Database. Adapted from Groom et al. [5].
8.3.1.2
Solvent Selection
Appropriate selection of crystallization solvent is also informed by early screening efforts, which often focus on what polymorphs can be generated under different solution conditions [50]. A coarse list of potential solvents and conditions
can emerge, such as those reported for cimetidine Forms A–D [61] or sulfathiazole Forms I–V [71]. Additionally, solvents that risk forming unwanted solvates
(see Section 8.3.2) may be excluded, helping narrow the possibilities.
Consideration should also be given to solvents that can help facilitate or
restrict the organization of molecules in specific crystal motifs [48]. For example, strong adhesion between methanol and ranitidine HCl tended to disrupt
cohesive hydrogen bonds between ranitidine molecules, making nucleation
and growth of the Form II polymorph more likely. In contrast, recrystallization
of ranitidine HCl from a less polar solvent, less capable of adhesive solute–
solvent hydrogen-bond formation, promoted formation of cohesive hydrogen
325
8 Primary Processing of Organic Crystals
100
80
Concentration (mg ml−1)
326
II
I
60
D
40
C
B A
III
20
0
0
20
40
60
Temperature (°C)
80
100
Figure 8.14 Recrystallization behavior of aqueous solutions of famotidine relative to
concentration and nucleation temperature. Conditions in zone I result in solidification of
Form B, zone II result in a mixture of Forms A and B, while zone III result in Form A. According
to the legend of the original publication, (–) represents the solubility curve of Form A, ( )
represents the solubility curve of Form B, and (– –) represents the supersaturation curve of
Form B (high temperature) and Form A (low temperature). Source: Reprinted from Lu et al.
[63]. Reproduced with permission of American Chemical Society.
bonds between ranitidine molecules, making nucleation and growth of the
Form I polymorph more likely [72].
The role of solvent in polymorphism was also demonstrated for the two
monotropically related polymorphs of famotidine, Form A and Form B, where
Form A is the thermodynamically stable phase. Lu et al. investigated solidification of famotidine from water, methanol, and acetonitrile at various starting
concentrations and temperatures, with and without seeding. The authors experimentally determined a “polymorphic window” for crystallization from aqueous
solutions, which is shown in Figure 8.14. The authors explained that by following the line segment AD (representing reductions in nucleation temperatures)
that solidification conditions first favor purification of Form B (zone I), followed
by cosolidification of both phases (zone II), and followed finally by purification
of Form A when the solvent was held at the lowest temperatures [63].
In addition to nucleation temperature and solution concentration, Lu et al.
also showed that depending on the crystallization solvent, the cooling rate
8.3 Challenges During Solidification Processing
(a)
(b)
Famoditine-A (FOGVIG04)
Famoditine-B (FOGVIG03)
Figure 8.15 Asymmetric unit and unit cells from crystal structures of (a) famotidine Form
A (CCDC refcode FOGVIG04) and (b) famotidine Form B (CCDC refcode FOGVIG03). Dashed
lines in asymmetric units show intramolecular H-bonds that contribute to conformational
differences. Source: Structures obtained from Cambridge Crystallographic Database Adapted
from Groom et al. [5].
was also observed to result in different solid forms, or a mixture of forms,
depending on the respective nucleation rates in a given solvent. Additionally,
solute–solvent interactions also played a major role in selectively determining
the nucleation and growth phase.
In the case of famotidine, Form B is characterized by intramolecular hydrogen
bonding, resulting in a bent conformation, relative to Form A (see Figure 8.15).
When crystallized from water, the solvent can act as a strong hydrogen-bond
donor and acceptor with the famotidine molecules, providing a bridge that helps
stabilize the Form B conformer. In contrast, crystallization experiments from
either methanol (a weaker hydrogen-bond donor/acceptor) or acetonitrile
(dipolar aprotic hydrogen-bond acceptor) resulted in preferential growth of
Form A. Neither of these solvents was able to stabilize the Form
B conformer in the same way as water, suggesting that solvent selection may
play as critical a role in form purification as other crystallization conditions [63].
Scenarios such as those described above suggest the importance of
communication between characterization groups (usually associated with
327
328
8 Primary Processing of Organic Crystals
preformulation activities tied to 2 manufacturing) and drug substance manufacturers attempting to scale production of a candidate molecule showing
promise in early development. Primary manufacturing is ultimately more efficient if it results in both chemically pure and phase-pure API raw materials.
8.3.1.3 Antisolvent Crystallization
Related to solvent selection, crystallization of a solid from a concentrated solution by addition of a miscible antisolvent can also be used to select a desired
polymorph, with reasonably high yield. Antisolvent can be added to a concentrated solution (forward addition), or the concentrated solution can be added to
the antisolvent (reverse addition). Crystallization of metastable α-indomethacin
was selectively performed using water as an antisolvent. Takiyama et al. determined that forward addition of water into an ethanolic solution of indomethacin
resulted in crystallization when the ratio of ethanol : water reached 1 : 3. The
results were mixed, with this method sometimes selective for α-indomethacin,
and other times resulting in an α/γ mixture. In contrast, reverse addition of an
indomethacin–acetone solution into water, until a 3 : 7 acetone : water ratio was
reached, resulted in solidification of the pure α-form [73].
In addition to precise solubility curves for the solvent–antisolvent mixture,
careful study of how the rate of antisolvent addition affects the growing form
is important. Rapid addition usually results in quick, uncontrolled precipitation
of the solid, while slow addition can result in a longer approach to supersaturation, potentially favoring a different form. The feed rate of heptane antisolvent
to an indomethacin–acetone solution was found to influence the polymorph
that resulted, as the stability relationship changed with changing solvent composition [73]. When performed isothermally, the desired γ-form of indomethacin was selectively grown using a solvent addition rate determined using a
phase diagram. Care was taken, owing to discovery of an acetone solvate
(termed α ), which had very similar solubility to γ, meaning that the solution
trajectory was controlled so that it exceeded the solubility of γ, while not that
of α . Rather than isothermal antisolvent addition, when the solution was
heated, it was determined that the heptane could be added more rapidly, while
maintaining control over selection of γ, at higher yields than the isothermal
methods. Ultimately, the authors recommended establishing a precise ternary
phase diagram for the system, accompanied by temperature studies to optimize
the primary processing conditions [74].
8.3.1.4 Selective Crystallization Using Additives
A final strategy for selective crystallization of polymorphs uses soluble additives
to the solution, which promote or inhibit various synthons or growth motifs.
Blagden and Davey used trimesic acid to direct growth of the metastable α-form
of L-glutamic acid. The additive was found to be conformationally similar to the
8.3 Challenges During Solidification Processing
glutamic acid in the stable β-form, depositing on the fastest-growing surfaces of
β, leading to disruption of formation along the principal growth axis. In contrast,
since the conformations of trimesic acid and L-glutamic acid in the α-phase did
not match well, uninhibited growth of the metastable polymorph occurred [51].
Heterogeneous additives, such as polymers, can also be used to direct growth.
Unlike soluble additives, however, polymer only interacts at the interface
between the solution and the growing solid, allowing control over the specific
face at which adsorption occurs. López-Mejías et al. showed that the thermodynamically stable monoclinic phase of acetaminophen could be grown on
poly-(n-butyl methacrylate), while the metastable orthorhombic form was
observed to grow on the more structurally similar poly-(methyl methacrylate).
The authors suggested that selectivity was based on the difference in accessibility of the functional groups on the surfaces of polymer heteronucleants, which
directed growth of a specific plane of molecules in which the acetaminophen
molecules packed [75]. Polymeric heteronuclei were also suggested for use in
high-throughput solid form screening, providing the opportunity to direct
growth of a particular phase using a single solvent, which was demonstrated
for acetaminophen, sulfamethoxazole, carbamazepine, and the multiform drug
substance intermediate ROY [76].
8.3.2
Hydrate and Organic Solvate Formation
In addition to polymorphism, solidification of SMOC materials may also have
the associated risk of forming crystalline solvates (sometimes called pseudopolymorphs [36] or solvatomorphs [1]), where the growing solid incorporates
molecules from the crystallization medium into its lattice, resulting in a material
having very different physical properties relative to the anhydrous or unsolvated
phase. Some estimates have suggested that up to one-third of small molecules
can form hydrates during solidification [11], and a partial (and by no means
comprehensive) list of SMOC hydrates and solvates is listed in Table 8.4.
8.3.2.1
Hydrate Formation
Spontaneous hydration (incorporation of water molecules in growing lattices) is
the most common type of solvate formation among SMOC [97], owing to the
small molecular size of water, which facilitates its ability to fill intermolecular
voids. Additionally, the capacity of water to form hydrogen bonds in multiple
directions increases its ability to associate with a wide range of molecules as they
crystallize [11].
During 1 processing that involves recrystallization from either aqueous solvent or cosolvent containing water, certain conditions may be established that
allow for equilibrium between an anhydrous and hydrated lattice, analogous to
enantiotropic polymorphism. Grant and Higuchi considered this from a
329
330
8 Primary Processing of Organic Crystals
Table 8.4 Examples of small-molecule organic crystalline hydrates and solvates.
Molecule
Solvent of
crystallization
Coordination [D:S]
Caffeine [77]
Water
Caffeine H2O
CAFINE01
Theophylline [78]
Water
Theophylline H2O
THEOPH01
Fenethazine HCl [79]
Water
Fenethazine HCl H2O
DIKSOF
Fluconazole [80]
Water
Fluconazole H2O
IVUQIZ
CSD refcode
Meloxicam [81]
Water
Meloxicam H2O
WODBIA
Carbamazepine [82]
Water
Carbamazepine 2H2O
FEFNOT
Cefradine [83]
Water
Cefradine 2 H2O
MIHZUA
Ampicillin [84]
Water
Ampicillin 3H2O
AMPCIH01
Raffinose [85]
Water
Raffinose 5H2O
RAFINO01
Bosutinib [86]
Water
Bosutinib∙7H2O
ABEBUH
β-Cyclodextrin [87]
Water
β-Cyclodextrin∙12H2O
BCDEXD10
Indomethacin (J.G.
Stowell, et al., 1-(4Chlorobenzoyl)-5methoxy-2-methyl-1Hindole-3-acetic acid
methanol solvate, Private
Communication, 2002)
Methanol
Indomethacin∙CH4O
BANMUZ
Sulfanilamide [88]
Methanol
Sulfanilamide∙CH4O
COVXIU
Quinestrol [89]
Ethanol
Quinestrol(2 : 1)C2H6O
TOYJUM01
Cholesterol [90]
Ethanol
Cholesterol(2 : 1)C2H6O
CHOLEU10
Clindamycin∙HCl [91]
Water and ethanol
Clindamycin∙HCl H2O C2H6O
KUQLUE
Rifampin [92]
Ethylene glycol and
water
Rifampin∙2(C2H6O2) 2H2O
OWELOS
Warfarin∙Na [93]
2-Propanol
Warfarin∙Na(2 : 1)C3H8O
EFIWIZ01
Carvedilol∙H2PO4 [94]
2-Propanol
Carvedilol∙H2PO4 C3H8O
PUJTOE
Tramadol∙HCl [95]
Acetonitrile
Tramadol∙HCl C2H3N
VISQAR
Fluconazole [80]
Ethyl acetate
Fluconazole(4 : 1)C4H8O2
IVUQEV
Hydrocortisone [96]
Dimethylformamide
Hydrocortisone∙C3H7NO
COWNEI
Source: For reference, the reference codes from the Cambridge Structural Database are provided [5].
8.3 Challenges During Solidification Processing
thermodynamic perspective [98], beginning their development by considering
the saturation solubility of an anhydrous crystal, A(s):
As
A aq
The activity-based (a) equilibrium constant for the solubility expression is K:
K=
a A aq
aA s
8 11
Similarly, the saturation equilibrium of a hydrated crystal, A mH2O (s), is
A mH2 O s
AmH2 O aq
and the activity-based (a) equilibrium constant for hydrate solubility is K :
K =
a A aq a H2 O m
a A∙mH2 O s
8 12
Combination of the solubility equilibria for each form gives the equilibrium
for spontaneous hydration:
A s + mH2 O
A mH2 O s
for which the equilibrium constant for hydration (Kh) can be written using
Equation (8.13):
a A∙mH2 O s
a A s a H2 O m
K
∴Kh =
K
Kh =
8 13
8 14
The free energy change that occurs during hydration can then be written as
ΔGh = − RT lnKh = − RT ln
K
K
8 15
Suggest that hydrate formation will be spontaneous if K > K . As stated in Tian
et al. [97], if it is assumed that the activity of both solid phases is equal to unity,
Kh can also be simplified to
Kh = a H2 O
−m
8 16
meaning that hydration will depend on the solvent composition and its effect on
the activity of water. Ultimately, since Equations (8.15) and (8.16) show that Kh
depends on temperature and solvent composition, spontaneous transition
between an anhydrate and its hydrated counterpart will depend on how both
are controlled in the crystallizer.
During 1 processing, crystallization can be driven by a reduction in temperature (see Figure 8.3), particularly for substances whose solubility is highly
dependent on the temperature of the crystallizer. In these circumstances, process
yield can potentially be increased by the addition of a suitable water-miscible
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8 Primary Processing of Organic Crystals
organic cosolvent, such as ethanol or acetone [97, 98]. Tian et al. reviewed the
case of anhydrous carbamazepine whose yield on cooling was improved relative
to recrystallization from absolute ethanol by changing the solvent to a mixture of
water and ethanol, without the risk of forming the dihydrate [97].
Selection of a single growth product can be more complicated if the crystalline
hydrate has its own polymorphic system, as is the case for nitrofurantoin (NF)
monohydrate, which has two polymorphs, Form I and Form II. The metastable
Form I has a less extensive hydrogen-bonding pattern with NF, relative to the
more stable Form II [99]. By estimating the metastable zone boundary for
cooling crystallization from water–acetone solvents, it was found that selective
growth of Form II was possible. This was suggested to occur owing to the much
slower growth kinetics of Form I, potentially meaning that the relatively rapid
growth observed for Form II could suppress growth of the metastable form [97].
In contrast, when NF was crystallized from a water–acetone mixture by evaporation of the cosolvent, a mixture of Forms I and II resulted, the proportions of
which depended on the rate of change of the activity of water during the solidification process [97, 99]. Tian et al. observed that the fraction of Form I in the
final product tended to increase in cosolvent mixtures having decreased water
activity. Since water and acetone have different volatilities, acetone removal was
more rapid during evaporation, resulting in a continually increasing water activity over the course of the process, but at different rates, depending on the starting composition of the cosolvent. The varying water–acetone mixtures
0.006
NF mole fraction in solution
332
S6
0.005
S5
0.004
S4
0.003
0.002
NF solubility
S3
0.001
0.000
S2
S1
0.0
0.2
0.4
0.6
0.8
Water mole fraction in solvent
1.0
1.2
Figure 8.16 Evaporative crystallization of nitrofurantoin (NF) from different water–acetone
mixtures (S1–S6). As shown, S1 was supersaturated with NF to begin with, S2 began with a
saturated solution, and S3–S6 each began as undersaturated solutions. Evaporation of the
cosolvent mixture resulted in increasing water activities as acetone was removed more
quickly. The increasing supersaturation with solvent evaporation occurred at different rates
for each solution, and the unique profiles each resulted in different mixtures of Form I and
Form II monohydrates in the final product. Source: Reprinted from Tian et al. [99]. Reproduced
with permission of Elsevier.
8.3 Challenges During Solidification Processing
(denoted S1–S6 in Figure 8.16) all resulted in unique supersaturation-water
activity profiles, which resulted in different mixtures of Form I and Form II
in the crystallized product [99]. These results reinforce the necessity of rigorous
process control during crystallization to ensure growth of the desired solid.
An alternative approach to temperature-controlled crystallization can use an
antisolvent to induce supersaturation. Form selection using this technique can
be more complicated to control, potentially resulting in the formation of
hydrates, if the stability relationship between anhydrate and hydrate is not precisely determined over the whole solvent composition range used throughout
the process [97]. Byrn et al. also warn against crystallization using waterimmiscible solvent mixtures as potentially causing difficulties with unanticipated hydrate formation. Because these organic liquids have very low aqueous
solubility, water activity can vary widely with small changes in water concentration, meaning that molecules capable of forming hydrates may be prone to do
so, a result that may be greatly exacerbated at production scales [36].
Whatever the source of their generation (intentional or not), crystalline
hydrates generally fit into one of three classifications, based on how water molecules are incorporated in their structures [1, 11, 36, 97], examples of which are
shown in Figure 8.17.
Class I (isolated site) hydrate: Water molecules are isolated from direct contact with one another by the small-molecule drug substance comprising the lattice. In the case of cephradine dihydrate (Figure 8.17a), the water molecules at
isolated sites make direct formation from the anhydrous solid very difficult.
Instead, crystallization of the dihydrate is accomplished by forming a slurry
of the anhydrous solid in water at 20 C, which is dissolved upon addition of
sodium carbonate. The solution is filtered, and the filtrate is cooled, whereupon
concentrated HCl is added slowly, along with seed crystals of the dihydrate.
Acid addition lowers the pH to 5.5–6.0, and continuous agitation allows growth
of the hydrated form. The slurry is filtered and washed with cold water followed
by an aqueous acetone mixture. Drying in a fluidized bed at room temperature
results in the characteristic prisms of this form [100]. Inasmuch as direct
formation from the anhydrous crystals can be difficult, as with cephradine,
the isolated water molecules can make dehydration of Class I hydrates difficult.
Dehydration rates are expected to be slow, and potentially various, as water
molecules hydrogen-bonded to different structural moieties in the lattice,
resulting in separate dehydration processes [1]. In some cases, dehydration
may result in crystal fracture as the water molecules seek a route to escape,
potentially resulting in lattice collapse. Additional Class I hydrates include
olanzapine∙2H2O [101], siramesine∙HCl H2O [102], and morphine∙H2O [103].
Class II (channel) hydrate: Water molecules have direct contact with one
another via adjacent unit cells, organizing in lattice channels along a crystallographic axis. These channel hydrates can be rapidly dehydrated, especially if
damage to crystallites intersects the channel axis of the lattice. Caffeine monohydrate (Figure 8.17b) is a classic channel hydrate example, which is solidified
333
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8 Primary Processing of Organic Crystals
(a)
Class I hydrate:
Cephradine∙2H2O
Isolated H2O
molecules
(b)
Class II hydrate:
Caffeine·H2O
H2O aligned in
channels
(c)
Class III hydrate:
Fenethazine∙HCl∙H2O
H2O coord.
with Na
Figure 8.17 Examples of different classes of SMOC hydrates: (a) Class I (isolated site) hydrate,
cephradine∙2H2O (CSD refcode: MIHZUA), (b) Class II (channel) hydrate, caffeine∙H2O (CSD
refcode: CAFINE01), and (c) Class III (ion-associated) hydrate, fenethazine∙HCl H2O (CSD
refcode: DIKSOF). Source: Adapted from Groom et al. [5].
by slow recrystallization from water, followed by equilibration at 75% RH [77].
The resulting monoclinic crystals contain what the authors termed “escape
tunnels” parallel to the c-axis, allowing rapid dehydration of these crystals at
relatively low temperatures (40 C) [77]. Work done by Byrn and Lin [104]
showed that rapid anisotropic dehydration of caffeine monohydrate occurred
after cutting both ends of single crystals, perpendicular to the channel axis, with
the reaction front proceeding parallel with the channel direction. Additional
Class II hydrates include cefazolin∙Na 5H2O [105], theophylline∙H2O [78],
and carbamazepine 2H2O [82]. Spontaneous formation of the Class II dihydrate
pseudopolymorph of carbamazepine is discussed as a potential consequence of
water-intensive secondary manufacturing processes (see Chapter 9).
Class III (ion-associated) hydrate: Water molecules are associated with metal
counterions in crystallized salts. Byrn et al. note that sodium salts are
8.3 Challenges During Solidification Processing
particularly prone to forming Class III hydrates, mainly because of the high
affinity that the charged sodium ion has for coordination with water. It is also
noted that hydrochloride salts represent the complement to sodium in terms of
affinity for hydrate formation, although these hydrates are less prevalent than
their sodium counterparts [36]. Figure 8.17c shows fenethazine∙HCl H2O
monohydrate, which illustrates the coordination between the individual water
molecules and the chloride counterions. Additional Class III hydrates include
fenoprofen sodium∙2H2O [105], risedronate sodium∙2H2O [106], and monensin
sodium∙H2O [107].
Beyond these three classifications, crystal lattices may also incorporate
water molecules nonstoichiometrically during or after solidification.
A good example is addressed in the case of cromolyn sodium, the structure
of which is discussed by Stephenson and Diseroad [105]. The paper refers to
the structure as a “pentahydrate,” with quotations reflecting a sense of uncertainty regarding the number of water molecules accommodated by the lattice.
The authors describe “large tunnels that run along the a-axis,” conforming to
a shape that is “approximately ellipsoidal.” Two sodium ions were identified
in the structure, one of which is highly ordered, and coordinated with two
correspondingly ordered water molecules. The other sodium, however,
appears to be disordered over two positions. Stephenson and Diseroad also
note finding seven water molecules in total, four of which are held in close
proximity to the sodium ions, while the other three are contained in the interstitial space of the solvent channels [105]. The authors also noted that an
older study suggested that the lattice was identified with as many as nine
unique water molecules, which the authors state could easily be accommodated, given the dimensions of the identified channels [105]. Vippagunta
et al. also mention the hydrated structure of cromolyn sodium as one whose
erratic sorption and liberation of water molecules potentially give rise to a
wide range of nonstoichiometric hydrate structures [11], reinforcing the
potential challenges associated with materials of this type emerging from
primary processing.
8.3.2.2
Organic Solvate Formation
The formation of organic solvates is analogous to hydrate formation but may be
more common during solidification of pharmaceutically relevant SMOC
materials (relative to other organic solids), owing to the use of mixed-solvent
systems, and can be particularly problematic for certain classes of drugs, such
as steroids and sulfonamides [36]. Like hydrates, the presence of organic
molecules of solvation adds noncovalent interactions to the growing crystal
lattice, which can help stabilize the solid. A similar classification scheme for
solvates is also possible, considering the positioning of solvate molecules either
at discrete positions in the lattice or within channels or tunnels. For examples
and structural implications, see Brittain et al. [108].
335
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8 Primary Processing of Organic Crystals
When antisolvents are added to concentrated solutions of API molecules,
solidification is driven by a lower solubility of the solute in the addition phase.
If the solubility of the drug decreases continuously with the addition of antisolvent, then nucleation and growth will likely result in an unsolvated crystal. In
contrast, discontinuous solubilities with the addition of antisolvent may indicate
conditions under which solvated crystal growth is likely [36].
In the laboratory, crystalline solvates can be grown from numerous organic
solvents, many of which are those listed in Table 8.1. Inasmuch as spontaneous
hydration is made possible by the small size of water molecules that fit well in
vacancies in many crystal structures, solvent molecules, depending on their size
and shape, may be less amenable to coordinated growth with an API molecule.
As such, solvent molecules whose shape enables efficient packing that promotes
stabilizing interactions (e.g. hydrogen-bond formation with API molecules) may
be more likely to form in a solvated crystal structure [36]. Additionally, Byrn
et al. list lower temperatures during crystallization as a factor that potentially
increases the likelihood of spontaneous solvate formation, owing to the
increased strength of hydrogen bonds at lower temperatures [36].
The antifungal drug substance fluconazole has several solid forms, including a
monohydrate and an ethyl acetate solvate. The monohydrate is formed at cool
temperatures (5 C) after dissolution in purified water at 40 C, while the ethyl
acetate solvate is formed 48 hours after dissolution of fluconazole in ethyl
acetate and subsequent cooling to 20 C [80].
Evaluation of the monohydrate crystals revealed a relatively straightforward
Class I structure solidifying in the triclinic P1 space group with each water
molecule hydrogen-bonded to three fluconazole molecules at isolated sites
[80]. Dehydration kinetics of fluconazole monohydrate were consistent with
other Class I hydrates and showed that drug–water hydrogen-bond dissociation
had a higher activation energy relative to diffusion of water molecules out of the
lattice [109].
In contrast, the more complicated ethyl acetate solvate crystallizes as much
larger, monoclinic P21/c crystals commensurate with accommodation of the
molecules of solvation. The structure is more complicated, consisting of two independent fluconazole molecules that are oriented as near mirror images and
aligned in columns along the a-axis. Each ethyl acetate molecule coordinates with
four fluconazole molecules, in narrow channels, lined by the both difluorophenyl
and triazolyl rings, which are angled with respect to the solvent channel direction.
This coordination provides extra steric hindrance to the solvent movement,
which corresponds with a higher observed thermal stability of the ethyl acetate
solvate [80]. Indeed, desolvation of the ethyl acetate solvate had a higher activation energy barrier [109], and was not observed using TGA until 120–130 C, a
temperature that was 30–40 C higher than that needed for dehydration of the
monohydrate [80].
From a 1 processing perspective, fluconazole, as an example, illustrates a few
important points. First, crystallization from organic solvents does not always
8.3 Challenges During Solidification Processing
result in a solvated form. Caira et al. noted that recrystallization of fluconazole
from propan-2-ol resulted in formation of the anhydrous polymorph, Form III,
suggesting that under the conditions used, these solvent molecules could not be
accommodated by the growing fluconazole lattice [80]. Second, postcrystallization removal of coordinated solvent molecules can result in formation
of the same polymorph. Complete dehydration of the monohydrate and complete desolvation of the ethyl acetate solvate resulted in formation of anhydrous
fluconazole Form I [80]. Finally, solvents coordinated in lattice channels do not
always result in easier solvent removal. Although the monohydrate forms with
water at isolated sites, the activation energy for dehydration (90 kJ mol−1) was
considerably lower than the activation energy for desolvation (153 kJ mol−1)
for the ethyl acetate solvate [109]. In fact, the higher temperature required
for desolvation was needed to overcome the steric barrier presented by the orientation of ring groups from the fluconazole molecules along channels, causing
their constriction [80].
Even with efforts to control solid form during primary processing, some SMOC
materials remain highly susceptible to post-crystallization solvation, posing
potentially toxic consequences. Although solidification is preferably done using
Class III solvents that demonstrate low toxicity [23], a solid form screening
can help identify possible pseudopolymorphs from other classes of solvent and
help mitigate the risk of unanticipated changes to bulk materials. Consider the
case of rifampin, which can be extemporaneously compounded using glycerol
and propylene glycol. An observation was made that certain compounded rifampin formulations formed suspensions that contained large, needle-shaped crystals, which did not pass easily through a syringe. Evaluation of the crystals
determined that they belonged to two previously unknown solvated forms.
The first, a 1 : 2 : 2 rifampin : ethylene glycol : dihydrate structure, was extensively
hydrogen-bonded, utilizing nearly every donor and acceptor group from the drug,
ethylene glycol, and water molecules [92]. The second, a 1 : 2.9 : 2.8 rifampin : ethylene glycol : hydrate structure, also had extensive hydrogen bonding between the
molecules in the structure but formed with more distinct separate layers of
rifampin and solvate molecules [92]. In either case, the solubility of the solvated
forms was less than rifampin, suggesting an increased potential for precipitation
following lattice incorporation of the ethylene glycol molecules. Of importance
in this case was the observation that rifampin, USP, spontaneously incorporated
ethylene glycol (an acutely toxic Class II solvent unlikely to be used for
crystallization of an internally consumed API), speculated to be present as trace
impurities in the glycerol and propylene glycol [92].
8.3.3
Solvent-mediated Transformations (SMTs)
As indicated throughout this text, SMOCs can exist in several different solid
forms, each of which has its own free energy dictated by the unique periodic
arrangement of molecules and interactions between them. A solid in
337
8 Primary Processing of Organic Crystals
Predominantly B nuclei
S
Solubility
338
Growth of B
phase
Form B
1
Dissolution of B;
nucleation of A
Cs,B 2
Form A
Growth of A
phase
3
Cs,A
4
Temperature
Figure 8.18 Solvent-mediated transformation schematic for two polymorphs, A and B.
Ostwald’s rule of stages suggests that at a given crystallization temperature, Form B may
nucleate and grow first (points 1–2). Below Cs,B, metastable solid redissolves, driving
nucleation and growth of the stable Form A. Source: Adapted from Cardew and Davey [34].
continuous contact with solvent follows the thermodynamic gradient to
spontaneously convert to the most thermodynamically stable phase.
Figure 8.18 illustrates the means by which an SMT occurs. Following the
trajectory from point 1 to point 2, the concentration of the solution is reduced
from S as Form B nucleates and grows. At Cs,B, the system equilibrates by
dissolution of excess metastable phase while remaining supersaturated with
respect to Form A. At point 3, the solution is no longer saturated with respect
to Form B, and further dissolution of this phase enables nucleation and growth
of Form A. Eventually, the system reaches point 4 (Cs,A), at which the solution is
saturated with respect to Form A, and growth stops [34].
In a well-agitated system, dissolution of the metastable phase and subsequent
growth of the stable phase are complete. In some circumstances, nucleation of
the stable phase occurs rapidly on the surface of the metastable particles.
Eventually, growth of the solid phase can occlude metastable particle surfaces
and prevent further contact with the solvent. In these cases, SMTs may be partial, resulting in a mixture of phases. Such a circumstance is conceivable with
carbamazepine, as shown in Figure 8.19.
In complementary experiments done by Murphy et al., it was shown that the
stable dihydrate nucleated on the surfaces of anhydrous carbamazepine
8.3 Challenges During Solidification Processing
Figure 8.19 SEM illustrating nucleation and growth at 25 C of carbamazepine 2H2O on the
surfaces of anhydrous carbamazepine in slightly supersaturated aqueous solutions (S = 1.15)
containing 0.5% sodium lauryl sulfate. Source: Reprinted from Rodríguez-Hornedo and
Murphy [110]. Reproduced with permission of Elsevier.
particles, subsequently growing as needlelike crystallites in aqueous solutions at
25 C. Intrinsic (disk) dissolution studies were used to confirm the transformation, where it was observed that the dissolution rate decreased over time, commensurate with growth of the less soluble dihydrate on disk surfaces [111].
As introduced, the direction of the SMT is always toward the most thermodynamically stable phase. This can include transformations between anhydrous
polymorphs, conversion from an anhydrous form to a hydrated form, or
conversion of an amorphous solid to a more stable crystalline phase. In the
study by Murphy et al., nucleation and growth of carbamazepine dihydrate
on exposure to water was determined to be faster when anhydrous carbamazepine was milled prior to testing. The authors concluded that the SMT was
better facilitated from the amorphous regions on the carbamazepine crystals
that resulted from milling, which was confirmed by rapid growth of the dihydrate on the surfaces of purely amorphous samples of carbamazepine [111].
339
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8 Primary Processing of Organic Crystals
In addition to their thermodynamic explanation of SMTs, Cardew and Davey
[34] also modeled different factors that affected the kinetics of SMTs. Assuming
a supersaturation ratio with respect to both the metastable (phase 1) and stable
(phase 2) solids of σ 12 = (x1 − x2)/x1, these authors considered two extreme
kinetic conditions under which SMTs could occur. In the first, dissolution
rate-limited transformations were approximated by a dissolution time, τD,
which was used to describe the time required for initially L-sized metastable
crystallites (L1i) to completely dissolve at their maximum rate, described by rate
constant kD:
L1i
8 17
τD =
kD σ 12
In the second kinetic extreme, growth rate-limited transformations were said
to occur with a growth time, τG, assuming that the stable phase grew at a
sufficiently slow rate that dissolution maintained supersaturation ≈σ 12 until
all of the metastable phase dissolved:
τG =
L2f
kG σ 12
8 18
In Equation (8.18), the final-sized stable form crystallites (L2f) grow at a rate
described by constant kG. The transformation time, τ, of an SMT was defined as
the time required for complete conversion from metastable to stable phase, τ,
and was assumed to be the sum of τD and τG (Equation 8.19):
τ = τG + τD
8 19
Cardew and Davey used these equations to model several different
experimental conditions to show the time frames associated with dissolution
rate-limited and growth rate-limited conversions. In their data for nonseeded
crystallization, it was found that conditions favoring dissolution rate-limited
SMT required less time relative to growth rate-limited SMT. For models of
SMT under seeding, Cardew and Davey confirmed the expected trend that with
increased seeding, the SMT was accelerated, reducing τ for the entire process
[34]. In all, these data suggest that solvent-mediated conversions can be
reasonably well modeled, potentially allowing the opportunity for 1 processing
control to enable selection of a particular form of a solid.
Returning to the example of sulfamerazine shown earlier (see Figure 8.13 for
crystal structures of each enantiotrope), Gu et al. [112] explored the influence of
the solvent on the SMT kinetics involved in transforming Form I into the more
thermodynamically stable Form II. The authors found that the transformation
rate was determined by both the solubility of sulfamerazine in the solvents used
and the strength of the solvent–solute interactions, particularly the potential to
form hydrogen bonds. Table 8.5 excerpts data from the study, specifically highlighting how the rates of solvent-mediated conversion from Form I to Form II
for sulfamerazine in the various solvents are used.
8.3 Challenges During Solidification Processing
341
Table 8.5 Polymorphic transformation rates of sulfamerazine Form II in various solvents.
Solvent
Induction
time (h)
Transformation time (10–75%) for
solutions containing
sulfamerazine Form II (h)
Sulfamerazine form II
solubility in corresponding
solvents (mM)
Acetonitrile
2
1
16.0
Nitromethane
72
54
15.1
Acetone
192
8
40.9
Tetrahydrofuran
144
24
70.2
Methanol
120
1
14.9
Ethanol
>360
—
7.91
2-Propanol
>360
—
1.28
Water
>360
72
Acetic acid
>360
>72
1.05
Dichloromethane
>360
—
4.12
Chloroform
>360
—
1.59
4 : 1 Water/
acetonitrile
1
0.25
1 : 4 Water/
acetonitrile
>360
54
9 : 1 Water/
methanol
24
1.5
13.4
1 : 4 Water/
methanol
24
1.5
12.3
1 : 1 Water/
methanol
>360
7.5
1 : 1 Methanol/
dicholoromethane
24
—
27.8
1 : 2 water/
acetone
72
—
16.6
35.0
38.2
3.69
4.43
Source: Adapted from Gu et al. [112]. Reproduced with permission of Elsevier.
Gu et al. suggested that solute–solvent interactions might affect the nucleation rate in two ways. First, in order to be incorporated into a growing lattice, the
solvated solute molecules must desolvate (break interactions between the solute
and solvent) prior to addition. Strong solute–solvent interactions resist desolvation, lending themselves to potentially longer induction times. Second, the
surfaces of growing crystallites will adsorb solvent molecules, which must be
desorbed in order for surface birth and growth (2D surface nucleation) [12].
In these cases, strong solute–solvent interactions resist surface displacement
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8 Primary Processing of Organic Crystals
of adsorbed solvent molecules, lending themselves to slower conversion of the
converting phase. Gu et al. suggested based on their results with sulfamerazine
that solidification of a metastable polymorph requires selection of a solvent in
which the substance is poorly soluble, as this will significantly slow the SMT to
the stable phase. In contrast, if solidification persistently yields metastable solid,
and solvent-mediated conversion is required to harvest the stable phase, the
authors suggest suspending in a solvent in which the substance is readily soluble
but capable of modest solute–solvent interactions [112].
8.3.4 Morphology/Habit Control
Controlling crystal morphology during 1 processing is a complicated matter,
but one that is known to affect important properties of bulk materials. The
morphology of solidified crystals is important, not only from the perspective
of providing materials that are usable in secondary manufacturing but also
within the various steps of 1 processing, including separation, handling,
packaging, and storage [113]. Uncontrolled growth of highly anisotropic
morphologies, such as fine needles, can result in difficulties with filtration.
As discussed above, slurries composed of fine or ultrafine acicular particles
are prone to clogging filters, or potentially resulting in filter breakthrough owing
to large pressure build-up [33]. In these cases, inefficient filtration or poor scalability is potentially the “best” outcome, with the possibility of entire batch loss
(or reworking) necessitated in extreme cases.
Chen et al. [28] proposed an optimized solidification procedure, which takes
into account both solid form and morphology to result in the best possible
material moving forward. According to their sequence, scale-up of a desired
polymorph should involve:
1) API synthesis yielding solid having the highest possible purity.
2) Identification of all possible/likely solid forms using high-throughput
screening methods.
3) Design of a crystallization procedure that controls for a specific solid form
(selected based on its having desired properties for downstream handling).
4) Solid-state characterization (using thermal methods, spectroscopic methods, X-ray diffractometry, microscopy, etc.) to verify phase purity.
5) Optimization of crystallization conditions for particle size and morphology
control.
6) Scale-up of the desired method/conditions.
7) Solidification and preliminary sizing of the desired material.
8) Packaging, storage, and shipment for 2 manufacturing under conditions
that maintain the desired form and associated properties.
Each element of this sequence is echoed throughout the preceding sections
and important because of its acknowledgment that 1 manufacturing should
8.3 Challenges During Solidification Processing
be designed around selection of a specific solid form of a material having
optimized dimensions and shape in order to facilitate downstream processing.
It should be noted that the recommended optimizations are not trivial and
require exquisite process control. Although beyond the scope of this chapter,
readers are referred to various works that describe technologies used to monitor
and control solidification processes [114–116].
8.3.4.1
Predicting Solvent Effects on Crystal Habit
Specific morphology control can be difficult to achieve. Attempts to predict
morphology that results from growth in a particular solvent remain elusive,
although general rules are possible. Docherty et al. review some options for
morphological prediction, which focus on crystal shape as a result of internal
structure [113].
One common approach is to consider the attachment energy (EA) of various
families of planes, relative to the total cohesive energy of a lattice, EL, which
collectively considers all the strong and weak intermolecular and interionic
interactions in the crystal [113, 117]. The attachment energy of a particular
hkl plane is the difference between ELand the slice energy ES (Equation 8.20):
EA = EL − ES
8 20
where ES is the sum of the intraplanar interactions in a particular crystallographic plane. Crystal faces having the lowest EA will tend have the slowest
growth and, therefore, be most pronounced in the resulting crystal shape [113].
Although useful, in silico simulations of EA assume crystal growth in a
vacuum, which excludes the impact of the solvent from calculations. A more
practical treatment of crystal morphology needs to consider the three regions
established during crystal growth: (i) the bulk crystal, (ii) the bulk solvent,
and (iii) the interfacial boundary layer between the solvent and the growing
crystal [118]. This can be accommodated in the EA model by assuming that
the energy cost associated with removing the solvent molecules from the surface
before its growth can occur and reduce the value of EA, which can be
represented in Equation (8.21):
EAsol = EA − Esol = EA − ΔEIsol ∙Ahkl ∙
NA
N
8 21
Here, EAsol is the corrected attachment energy, accounting for the effect of the
solvent, and Esol is the solvent layer attachment energy. The solvent layer attachment energy can be estimated by determining the potential energy change per
unit area in the solvent layer (ΔEIsol ), the surface area of a given hkl plane, Ahkl,
the number of molecules, N, in the hkl plane, and Avogadro’s number (NA).
Under these circumstances a particular morphological face is more important
in the growth model if EAsol for a specific hkl slice is decreased more by the
solvent interactions, relative to the other slices [118].
343
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8 Primary Processing of Organic Crystals
(a)
(b)
002
111
210
200
210
020
111
Figure 8.20 (a) Predicted morphology of RDX using the attachment energy procedure,
assuming growth in a vacuum. (b) Observed growth of RDX crystals grown from
γ-butyrolactone. Source: Reprinted from ter Horst et al. [118]. Reproduced with permission of
Elsevier.
This solvent compensation technique was demonstrated for RDX, an organic
molecule that crystallizes in the orthorhombic Pbca space group. Figure 8.20a
shows the predicted morphology using the attachment energy method, assuming growth in a vacuum, with the most important faces corresponding to {111},
{200}, {020}, and {002} [118].
Simulated morphology of RDX using Equation (8.21) showed that the
induced potential energy change in the solvent layer on {210} surfaces was much
higher for γ-butyrolactone relative to the {200} surfaces, predicting that {210}
should be morphologically more important than {200}. When RDX was grown
using γ-butyrolactone as a solvent, the most prominent faces were {210} and
{111}, with {002} less important, and {200} and {020} completely absent
(Figure 8.20b) [118], confirming that this approach could be used to incorporate
solvent effects in more traditional EA approaches. Although RDX is not a
pharmaceutically relevant crystal, as an organic solid, these data also suggest
that similar approaches could be taken to predict the morphology for drug
substances crystallized from a particular solvent.
Parmar et al. studied the influence of solvent on the growth of different polymorphs of sulfathiazole, which commonly manifests as one of five different
polymorphs (conventionally labeled Forms I–V). The authors suggested two
types of dimers, α and β, which formed clusters in the presence of different solvents. For example, 1-propanol and 1-butanol led to α-type dimer clusters,
which tended to result in growth of metastable sulfathiazole polymorphs. In
contrast, the stable form was more probable when β-type dimer clusters formed,
8.3 Challenges During Solidification Processing
which tended to occur in the presence of short-chain alcohols, such as methanol
or ethanol. When low concentrations of methanol were added to a 1-propanol
crystallization solution, the authors found that the methanol molecules promoted local formation of β-clusters, which acted as directed growth synthons
that adsorbed to growing surfaces. It was found that addition of 10% methanol
to 1-propanol sulfathiazole solution resulted in specific growth of the stable
Form I, but with a habit modification, owing to specific inhibition of the fastest
growing (010) face. This was proposed to be due to blocking of the α-type
dimers, which normally connect along this face, by β-dimers in the methanol-doped solution. This resulted in slower growth of (010) and its observation
in the Form I crystals that grew [71].
In more general terms, the solvent is expected to affect the morphology by
preferentially allowing growth of faces that are more energetically stable in
the crystallization medium. Faces having the greatest density of functional
groups that promote favorable interactions with the solvent molecules will form
a more stable, coherent interface in the solvent, and will thus grow more slowly.
In contrast, faces dense with molecules oriented so that the functional groups
having the fewest favorable interactions with the solvent will form less stable
interfaces and grow rapidly so that the solid can be stabilized by growing these
faces out of the expressed morphology.
Mullin reviews solvent effects on morphology for succinic acid, which was
observed to grow in very different habits from water versus isopropanol [12],
while Byrn et al. show photomicrographs of aspirin crystals having strikingly
different habits as a result of growth from hexane, benzene, acetone, ethanol,
and chloroform [36]. Figure 8.21 captures how the crystal habit of aspirin is
affected by the 1 processing conditions, showing SEM images of rodlike crystallites solidified from acetone (Figure 8.21a) and platelike crystallites solidified
from ethanol (Figure 8.21b) (T. Li, Private Communication. 2017).
Sun and Grant also observed that L-lysine monohydrochloride dihydrate grew
as short prisms from 1 : 1 v/v water : ethanol mixtures and plates when grown
from 2 : 1 v/v water : acetone mixtures. These different habits held different slip
plane densities, which dramatically affected their mechanical properties (see
also Chapter 9) [119]. Acetaminophen crystals, which are notorious for their
poor compressibility, were recrystallized from ethanol in the presence of different molecular weights of a polymer additive. The results showed that high
molecular weight poly(vinyl pyrrolidone), PVP, resulted in nearly spherical crystallites consisting of agglomerated, rod-shaped microcrystals [120], which
proved to be far more compressible than conventionally grown acetaminophen
particles [121].
Even if ab initio prediction of morphology as a result of specific 1 processing
conditions remains elusive, Morris et al. addressed the problem in reverse, using
different modeling software to predict crystal habit and then powder X-ray diffraction (PXRD) to suggest which predicted morphology best reflected the
345
346
8 Primary Processing of Organic Crystals
(a)
200 μm
250 μm
200 μm
250 μm
(b)
Figure 8.21 Scanning electron micrographs of aspirin crystals solidified from (a) acetone and
(b) ethanol. Source: SEM images provided by Tonglei Li (T. Li, Private Communication. 2017).
“average shape” of acetaminophen and ibuprofen particles. Essentially, the
method evolved from the common observation that powders consisting of particles having a highly exaggerated dimension or particularly dominant faces will
preferentially orient when packed into a confined volume (such as a PXRD sample holder). Diffraction patterns for these crystallites will often have correspondingly intense peaks associated with the preferred planes. By comparing
with a diffraction pattern calculated from the crystal structure, and quantitatively determining how the expressed areas of an average particle affect the
observed diffraction pattern, a morphology representing the average particle
in the sample can be assigned, in an effort to help describe how habit can affect
bulk powder properties [122].
8.3.4.2 Influence of Morphology on Surface Wetting
Crystal morphology can also be important in terms of the surface wetting
behavior that results. When a liquid contacts a solid at its surface, the balance
between adhesive interactions (those between molecules of the liquid and the
solid) and cohesive interactions (those between molecules of the liquid and
itself ) will determine the extent to which that liquid will spread on the solid
8.3 Challenges During Solidification Processing
surface. As a visual image, consider the beading of water droplets on the surface
of a freshly waxed car, where the work of cohesion (Wc) will exceed the work of
adhesion (Wa). The difference between these two terms is called the spreading
coefficient, S, which is shown in Equation (8.22):
S = Wa − Wc = γ S − γ L + γ SL
8 22
where γ S is the surface tension of the substrate, γ L is the surface tension of the
liquid, and γ SL is the interfacial tension between the two. If S is positive, the liquid is said to spread on the substrate [123].
One of the most common representations of this is captured in Young’s equation (Equation 8.23), which considers a droplet of a liquid when it first contacts a
solid substrate:
γ S −γ SL = γ L cos θ
8 23
Each of the interfacial terms is the same as defined for Equation (8.22), while θ
represents the contact angle, drawn through the droplet to a tangent on the
droplet surface originating at the point of contact (Figure 8.22a). As shown
in Figure 8.22b, the magnitude of the contact angle can be used to reflect
how well the droplet wets the substrate surface, with smaller values of θ representing better interaction between the liquid and solid and better wetting. In
practice, contact angle experiments are straightforward, although factors such
as the solubility of the solid in the liquid, viscosity of the droplet, and porosity of
the substrate can all affect the measurement of θ [124].
γLcos(θ)
(a)
γL
γSL
θ
γS
(b)
θ = 0°
θ < 90°
θ = 180°
Figure 8.22 (a) Representation of Young’s experiment, showing the relationship between
the liquid surface tension, γ L, solid surface tension, γ S, and interfacial tension between the
two γ SL. The magnitude of the contact angle (θ) represents the ease with which a droplet
spreads on a solid surface. (b) Values of θ = 0 reflect perfect wetting, while θ = 180 reflect no
wetting. Values in between, such as θ < 90 , represent some coherency of interactions
between the solid and liquid across the interface, but not so much as to fully exceed the value
surface tension of the liquid droplet.
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8 Primary Processing of Organic Crystals
Earlier in this section, the influence of solvent on crystal habit was considered,
where it was generally stated that the morphologically dominant faces will represent those expressing functional groups having the greatest coherence with
structure of the surrounding solvent molecules. Thus, very different habits
may be expressed by changing the solvent, without impacting the internal lattice
structure [12, 36, 119]. The impact that this will have on wetting (downstream
interaction of bulk solids generated in 1 processing with water-dependent processes, e.g. 2 manufacturing steps, dissolution of drug substances, etc.) will be
determined by the density of polar functional groups expressed on the major
faces of crystalline particles.
Consider the different habits expressed by aspirin when recrystallized from
different solvents (Figure 8.21). Different crystal faces are more pronounced,
depending on the orientation of aspirin functional groups in response to the solvent that surrounded it as the crystals grow. Consequently, the different faces
will have different contact angles with water, reflective of their relative polarity
(or not). Figure 8.23 shows the crystal structure of aspirin [125] alongside sessile
drop measurements of the (100) and (002) faces of aspirin, resulting in values of
θ(100) = 68 and θ(002) = 56 , respectively. The larger contact angle with water on
(100) relative to that on (002) suggests that the orientation of aspirin on (100)
exposes less polar functional groups than on (002). Indeed, the crystal structure
of aspirin shows that the molecules are oriented so that the carboxyl group
dominates (100), while (002) takes a more polar slice of the unit cell, exposing
more atoms capable of hydrogen bonding with the water droplet across the
solid–liquid interface.
θ(100)~68°
(002)
θ(002)~56°
(100)
Figure 8.23 Contact angle measurements of water on different surfaces of aspirin (CSD
refcode ACSALA01) crystals [5]. Note that the larger value of q corresponds with the (100)
face, which is dominated by the carboxyl portion of the aspirin molecules, while the smaller
value of θ corresponds with the (002) face, cross-sections the unit cell to expose more atoms
capable of hydrogen bonding. Source: Photomicrographs from Ken Morris.
8.3 Challenges During Solidification Processing
8.3.5
Crystallization Process Control
Systems that can provide feedback and control of a crystallization process
potentially allow 1 manufacturing to be selective for desirable process and
product attributes. Advancements in online spectroscopic monitoring
have enabled crystallization modeling using real-time measurements and
predictions of key properties/outcomes of the process, even in slurries or
solvent–antisolvent mixtures.
Yu et al. from FDA reviewed various platforms for use in controlling
crystallization as part of the process analytical technologies (PAT) initiative.
It was proposed that application of PAT to crystallization processes would be
maximally beneficial if supersaturation could be monitored throughout the
process, coupled with quality endpoint measurements of crystal size, morphology, and solid form [126]. Table 8.6 summarizes suggestions for monitoring and
control of these parameters.
Togkalidou et al. demonstrated that chemometric treatment of ATR-FTIR
spectroscopic data was capable of measuring and predicting supersaturation,
which was used to generate solubility curves for polymorphic small-molecule
systems in both single and multisolvent mixtures [127], consistent with the suggestion in Table 8.6. These results were especially promising when coupled with
advanced chemometric techniques as reviewed in Braatz [115]. Likewise, Abu
Bakar et al. demonstrated the use of focused beam reflectance measurement
(FBRM) for providing direct nucleation control in their crystallization
processes, enabling production of larger-sized crystals having a narrow
PSD [114].
Table 8.6 Summary of suggestions for PAT strategies associated with crystallization process
monitoring and control of product quality attributes.
Process parameter or
product attribute
Potential sensor for use in PAT strategy
Supersaturation
Attenuated total reflection-Fourier transform infrared spectroscopy
(ATR-FTIR)
Particle size
Diffusing wave spectroscopy (DWS)
Frequency-domain photon migration (FDPM)
Laser backscattering focused beam reflectance measurement (FBRM)
Particle morphology
Online image analysis
Polymorphic form
Offline PXRD, DSC, NMR (traditional solid form characterization)
Online Raman or NIR spectroscopy, X-ray analysis
Source: Yu et al. [126]. Reproduced with permission of Elsevier.
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8 Primary Processing of Organic Crystals
Additional details on monitoring and control strategies are provided in Fujiwara et al., where control strategies for crystallization based on either a first
principles approach or a direct design approach were compared [116]. The first
principles approach involved providing direct feedback control using a laser
backscattering FBRM to measure changes in particle size as crystallization
occurs. Fujiwara et al. suggested that first principles modeling requires accurate
predictions of process kinetics, which may be confounded by agglomeration,
dendritic growth, or poor control over solid form selection [116]. In contrast,
the direct design approach attempts to experimentally determine an operating
profile somewhere near the center of the metastable zone that avoids uncontrolled nucleation typical of exceeding the metastable limit while also preventing undesirably slow crystallization observed by maintaining conditions too
close to the solubility curve. The authors propose that a supersaturation setpoint curve can be established using an ATR-FTIR probe, enabling creation
of an automated crystallizer [116].
8.4 Summary and Concluding Remarks
In this chapter we have attempted to link the internal structure of crystalline
solids to the conditions used to generate bulk raw materials during 1 processing. The impact of crystal structure on materials properties will be most important later in downstream, 2 manufacturing processes, ultimately affecting
dosage form performance. Control over 1 processing is intended to result in
reproducible generation of the desired solid form by a robust process. Real-time
monitoring with process feedback is desirable and in line with regulatory guidance. Although variations in clinical response are seldom traced back to 1 processing, the preceding discussion, accompanied by the next chapter (see
Chapter 9), makes clear that decisions well removed from the patient interface
can still affect how the material will perform as part of a composite dosage form
and ultimately in vivo.
Dosage form-related patient-based failure modes: Even though it may not
be apparent to the scientists and engineers doing post-discovery drug development on a daily basis, or academic research, the motivation for everything done
in dosage form and processing design is, or should be, based on the patient
response to a particular patient-related risk mode that is either known or might
be expected to occur. Foundational to understanding possible dosage formrelated patient failure modes is understanding the potential impact of changes
in API characteristics.
As discussed, many of the solid-state characteristics of the API may impact
dissolution, physical stability, and/or chemical stability, any or all of which
may have clinical impact and must, therefore, be anticipated and controlled
as the target product profile is created to facilitate dosage form and 2 process
design. This is particularly important during scale-up of API synthesis because,
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443–448.
Byrn, S.R. and Lin, C.-T. (1976). The effect of crystal packing and defects on
desolvation of hydrate crystals of caffeine and L-(−)-1, 4-cyclohexadiene-1alanine. Journal of the American Chemical Society 98 (13): 4004–4005.
Stephenson, G. and Diseroad, B. (2000). Structural relationship and desolvation
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Gossman, W.L., Wilson, S.R., and Oldfield, E. (2003). Three hydrates of the
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Barrans, Y., Alleaume, M., and Jeminet, G. (1982). Complexe de sodium de
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108 Brittain, H.G., Morris, K.R., and Boerrigter, S.X. (2009). Structural aspects of
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109 Alkhamis, K.A., Salem, M.S., and Obaidat, R.M. (2006). Comparison between
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dehydration and desolvation kinetics of fluconazole monohydrate and
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the effect of lattice disorder. International Journal of Pharmaceutics 246 (1):
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Abu Bakar, M.R., Nagy, Z.K., Saleemi, A.N., and Rielly, C.D. (2009). The impact
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9
Secondary Processing of Organic Crystals
Peter L.D. Wildfong,1 Rahul V. Haware,2,3 Ting Xu,3 and Kenneth R. Morris3
1
Graduate School of Pharmaceutical Sciences, School of Pharmacy, Duquesne University, Pittsburgh, PA, USA
College of Pharmacy & Health Sciences, Campbell University, Buies Creek, NC, USA
3
Department of Pharmaceutical Sciences, Arnold and Marie Schwartz College of Pharmacy, Long Island University,
Brooklyn, NY, USA
2
9.1
Introduction
In the previous chapter, primary (1 ) processing was used to generate bulk
small-molecule organic crystals (SMOC). As a continuation in this chapter,
manufacturing and manipulation, or secondary (2 ) processing of materials
comprised of SMOC, is examined. Essentially, this is driven by a central question, namely, what are the important physicochemical properties of SMOC that
determine how they respond to the stresses experienced during the variety of
secondary processing steps to which they may be potentially exposed? This is
the real question for both understanding pertinent phenomena and anticipating
changes for crystalline drug substances. As with the 1 processing chapter, a
brief reintroduction of crystal structure, physical forms of solid materials,
and mechanical properties will be provided, as needed, in the context of specific
2 processing steps.
9.1.1
Structure and Symmetry
The three-dimensional (3D) periodicity and symmetry of crystalline materials is
the starting point of materials understanding, and, particularly in the context of
stresses involved in 2 processing, the two manifestations of particular importance are the lattice energy and its anisotropy, i.e. how that energy varies
Pharmaceutical Crystals: Science and Engineering, First Edition.
Edited by Tonglei Li and Alessandra Mattei.
© 2019 John Wiley & Sons, Inc. Published 2019 by John Wiley & Sons, Inc.
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9 Secondary Processing of Organic Crystals
directionally within the structure. The beauty of crystalline structure is that it dictates not only that a molecule/atom can always be found in exactly the same position relative to its symmetry-related partner(s) but also that the energy of
interaction between these molecules will always be the same (with a margin of
error for both position and energy). The more practical question addressed in this
chapter is, therefore, what stress is required to permanently disrupt the material
structure? The actual disruption may be due to dissolution, thermal expansion,
melting, mechanical displacement/failure, amorphization, and other stresses typically experienced during processing routines. The possible impacts of these disruptions are the symptoms usually misidentified as the “problems” observed
during 2 processing, which can include physical form changes (polymorphism,
hydration/solvation, salt breaking/disproportionation, amorphization), particle
size (PS)/shape changes and the related dissolution failures, flowability, compaction issues, chemical instability, etc. The list of possible issues is extensive; for a
more comprehensive list, see Brittain [1]. These issues are further complicated
because each of the possible symptoms may have more than one cause, which
makes understanding the real problem at the materials level essential.
In general, the higher the symmetry of a crystal structure, the lower is its anisotropy. However, the vast majority of pharmaceutically relevant crystal structures are built from triclinic, monoclinic, or orthorhombic crystal systems [2],
placing them into space groups having relatively low symmetry compared with
inorganic compounds. Therefore, SMOC structures often exhibit significant
anisotropy and the related directional dependence of properties, such as
responses to mechanical stress, interactions with light, and thermal properties.
As shown in Figures 9.1 and 9.2, many SMOC solidify as layered structures, in
which the layers are often separated by larger distances (d-spacing) than the inplane molecules. In some cases, this may not only promote deformation and bonding of crystals during tableting but may also facilitate phase transformation and
disordering during the same process. Although the attachment energies (EA) of
these planes in the crystal may be calculated and correlated with the ease of displacement under mechanical stress [3], their correlation to predictable behavior
is not always straightforward [4]. Whether a crystal under a given mechanical stress
undergoes a transformation (e.g. martensitic polymorphic, disorder polymorphic,
desolvation–crystallization) or amorphization is directly dependent upon the
packing motif of the crystal, its symmetry, and the anisotropic energies of interaction (i.e. both the interplanar and intraplanar intermolecular interactions).
9.1.2 Process-induced Transformations (PITs) in 2 Manufacturing
Of course, in addition to understanding the role of the crystal structure on the
material response to processing stress, an analysis of the thermodynamic driving forces must be included when considering which of the possible changes are
likely to occur. Process-induced transformation (PIT) [6] is a general term for
Figure 9.1 (a) Extreme layering in orotic acid (CCDC refcode OROTAC01) and (b) intraplanar
packing of orotic acid [5]. Source: Groom. http://journals.iucr.org/b/issues/2016/02/00/
bm5086/. Licensed under CC BY 2.0 https://creativecommons.org/licenses/by/2.0/.
Figure 9.2 Herringbone packing pattern for acetaminophen (CCDC refcode: HXACAN01) [5].
Source: Groom. http://journals.iucr.org/b/issues/2016/02/00/bm5086/. Licensed under CC BY
2.0 https://creativecommons.org/licenses/by/2.0/.
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9 Secondary Processing of Organic Crystals
the changes that may be observed during process development and 2 manufacturing. In essence, a well-controlled process stream is one in which the possible transitions in response to a process environment have been anticipated
and controlled.
The possible states that a SMOC solid can assume are dictated by thermodynamics; however, which state is attained also depends upon the kinetics associated with formation. In that sense, a process stress can kinetically “trap” a
substance in a metastable state (e.g. rapid drying, resulting in a metastable polymorphic form) or may provide sufficient time to allow the molecules in a
higher entropic state to “relax” to a more stable form (e.g. the steps preceding
crystallization from an amorphous solid). Ultimately, controlling the process
means balancing the duration of the stress with the kinetics of a transition,
which, in turn, requires a thorough understanding of the materials properties
and characterization of the phase domain.
The types of transitions that may occur and the stresses resulting from common unit operations are categorized in Figure 9.3 below. The left-hand side lists
the common types of transitions experienced by SMOCs, while the right-hand
side lists stresses typically occurring as they are processed. All of the possible
stresses may induce most of the transformations shown. Figure 9.3 highlights
the advantage of understanding the relationships between materials properties
and processing stresses as a means of reducing the number of necessary experiments and unexpected changes that might occur in a normal manufacturing
sequence, in order to develop a reproducible product.
Process induced
transformations
Kinetic trapping or
relaxation
Induced
transformations
Process
stresses
Induced
polymorphism
Mechanical
stress
Solvent
exposure
Thermal
stress
Solvation –
desolvation
Milling and
comminution
Wet
granulation
Drying
steps
Induced
disorder
Dry granulation or
roll compaction
Crystallization or
solidification
Process
friction
Morphology
Tableting or
consolidation
Lyophilization or
spray drying
Particle size
Chemical
reactivity
Figure 9.3 Stresses and transformations involved in processing of SMOCs.
Sterilization
steps
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
1° processing
Structure
Properties
Structure
2° processing
Properties
Raw materials
generation
Raw materials
manipulation
Performance
Figure 9.4 Schematic emphasizing the branch of SMOC processing that involves secondary
(2 ) processing, or raw materials manipulation. Exclamation points are meant to emphasize
that the structure following processing will dictate the eventual properties of the processed
material.
Ultimately the practical reason for all of the analyses is to determine the
impact of processing on the materials performance as part of dosage form development. Figure 9.4 highlights the general materials and process flow and points
of concern. In this chapter, the 2 processing branch is emphasized yet still
beholden to issues encountered in the previous chapter (see Chapter 8), in particular, ensuring that the material has a defined structure and associated characteristics following 1 processing. The second stage shown in Figure 9.4 is
generally what people think of when the term “pharmaceutical manufacturing”
is used and involves the combination and manipulation of raw materials to form
a composite product. Similar to 1 processing, these manufacturing steps all
play a role in defining and altering the structure of the composite materials
(or some part thereof ), resulting in properties that dictate the performance
of the resulting product. In this chapter, we try, by way of principle and example,
to present the possible PITs and their relative likelihood and hopefully insight
needed to avoid them.
9.2 Secondary Manufacturing–Processing Materials
to Yield Drug Products
As outlined in Figure 9.4, processing organic materials in the pharmaceutical
industry is roughly broken into 1 and 2 manufacturing steps. Ideally, the result
of successful 1 manufacturing is organic solid material having a desirable internal structure that begets predictable (and desirable) properties suitable for
downstream processing. As such, feedback between 1 and 2 manufacturing
365
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9 Secondary Processing of Organic Crystals
is essential to make the latter steps successful in the generation of a final product
having predictable performance characteristics. Perhaps complicating 2 manufacturing is considering the additional complexity required in combining multiple solid materials together to result in a composite structure having defined
attributes. This further requires understanding of how processing steps interact
with materials structure. In the sections that follow, key unit operations in solid
dosage form manufacturing are reviewed from the perspective of how solids
respond to attempts to combine multiple materials together and manipulate
them in a predictable way.
9.2.1 Milling of Organic Crystals
As indicated in the previous chapter, crystallization conditions control particle
morphology and size (and distribution) as well as the solid form of SMOC materials. Despite process control, it is often difficult to achieve an ideal PS and narrow
particle size distribution (PSD) through controlled crystallization [7]; therefore,
milling very often serves as a key first step in 2 manufacturing to achieve a desirable PSD of the materials that better facilitates downstream processing [8].
Although preliminary sizing likely occurs as the last step following API solidification (see Chapter 8), resizing raw materials may be necessary should they
undergo consolidation during shipping or storage. Additionally, milling is frequently employed as an intermediate step following either wet or dry granulation
in the manufacturing sequence needed for preparation of solid dosage forms [9].
Ordinarily, milling will precede mixing/blending steps, owing to the known
effects that PS/PSD has on subsequent unit operations and final dosage form
performance. Blend homogeneity or content uniformity for solid dosage forms
and nano-formulations may depend on the initial PS of the raw materials [10,
11], while the initial PSD can also dictate the powder compressibility [12].
A reduced PS and the associated increase in particle specific surface area have
been shown to increase final product bioavailability [13], in some cases, doubling it [14]. Therefore, a PS reduction and homogenization is an important step
in solid dosage form design. Successful milling in turn, will be a function of
materials properties, mill properties, and the operating conditions employed
in the process.
9.2.1.1 Materials Properties Influencing Milling
Any discussion of milling crystalline materials usually begins with Griffith’s
model of linear elastic fracture mechanics (LEFM), which reconciled the observation that the theoretical strength of a material (σ th) substantially overestimates the observed strength (Equation 9.1):
σ th =
Eγ
a0
91
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
where E is Young’s modulus, γ is the interfacial energy of the solid particle, and
a0 is the equilibrium spacing of lattice constituents in the crystal structure. First
principle derivation of σ th begins by considering the resistance to separation of
two planes of atoms (or molecules) comprising a crystal. The overestimation by
this model stems from the assumption that infinite plane separation (representing fracture) requires simultaneous breakage of all interplanar interactions.
Griffith postulated that flaws within the material actually serve as stress concentrators, which drive crack propagation throughout the solid, reducing the need
to break all the interactions at once [15]. According to Griffith’s equation, the
critical stress (σ c) required to fracture a body under tension, containing an elliptical flaw of half-length, c is
σc =
E2γ
πc
92
where E and γ are the same as in Equation (9.1). As shown, the stress required to
initiate and propagate a crack is inversely related to the square root of the flaw
size, suggesting that with each successive fracture cycle, particles become
increasingly resistant to breakage.
Fracture by crack propagation has also been described in terms of the stress
intensity factor (K), which describes how stress is concentrated at a crack tip.
When K reaches a critical value, often denoted Kc, the crack emerging from
an elliptical flaw is said to propagate:
Kc = σ πc f
c
w
93
In Equation (9.3), stress and crack length are as defined above, and f(c/w)
represents a scaling function that shows how Kc varies with increasing sample
thickness. This value is highly material dependent and is termed the fracture
toughness. In metallic and ceramic samples, additional subscripts are used to
denote specific mechanical loadings used to initiate crack propagation. Roberts
et al. [16] measured critical stress intensity factors using three-point single edge
notched beam testing (Kc = K1C) for various SMOC materials, where selected
results are tabulated in Table 9.1. For comparison, K1C for characteristic metallic and inorganic materials is also provided.
Table 9.1 shows a distinct difference in fracture toughness between SMOC
and inorganic/metallic solids, where the latter are orders of magnitude larger
than the former. A simple comparison of the types of bonds from which these
crystalline solids are comprised provides an obvious reason (i.e. covalent, ionic,
and metallic interatomic interactions are much stronger than noncovalent
interactions, leading to stronger solid materials). In a follow-up to these measurements, Roberts, Rowe, and York attempted to relate K1C with the molecular
structure of the SMOC they studied and found a simple relationship with cohesive energy density (see Chapter 8, Equation 9.6), which they suggested could
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9 Secondary Processing of Organic Crystals
Table 9.1 Fracture toughness (K1C) values for select materials.
Material
K1C (MPa∙m0.5)
Anhydrous β-lactose
0.7597a
17.9b
α-Lactose monohydrate
0.3540a
3.2b
a
E (GPa)
Acetaminophen
0.1153
8.4c
Sucrose
0.2239a
32.3c
Aspirin
a
0.1561
7.1c
Ibuprofen
0.1044a
5.0d
e
Aluminum
24–40
69–72e
Steel
55–105e
205–215e
Alumina (Al2O3)
3–5
e
380–390e
Silicon carbide (SiC)
2–5e
440–460e
a
Values reported from Roberts et al. [16].
Values reported from Bassam et al. [18].
c
Values reported from Duncan-Hewitt and Weatherly [19].
d
Values reported from Rowe and Roberts [20].
e
Values reported from Bowman [17].
b
provide a useful tool for predicting comminution behavior [21]. Similar conclusions can be drawn from the reported values of Young’s modulus, also in
Table 9.1, where the internal lattice structure clearly dictates the relative resistances to deformation and, according to Griffith’s equation (Equation 9.2),
makes them more resistant to fracture.
The materials properties most responsible for the breakage of solid particles
are initial PS, elastic shear modulus, material hardness, and critical stress intensity factor [22–24]. These determine the resistance of a material to elastic deformation, plastic deformation, and crack propagation during comminution [25];
therefore, these factors prescribe the amount of energy required for the milling
operations.
Ghadiri et al. developed a model (Equation 9.4) based on materials properties
and impact velocity, giving a dimensionless attrition propensity parameter (η)
[24]. The model describes the semibrittle failure of materials after impact attrition and was used to explain chipping, during which material loss form particle
corners and edges occurs, owing to localized loading experienced upon impact.
The resulting plastic deformation at the impact site is substantial and leads to
formation of radial and sub-surface lateral cracks:
η=
ρν2 lH
Kc2
94
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
In Equation (9.4), η is a dimensionless attrition propensity parameter, ρ is the
particle density, ν is the impact velocity, l is a characteristic PS, H is the material
hardness, and Kc is the fracture toughness. This model predicts linear dependence of η with l; however, there exists a lower limit for the validity of this relationship at a given velocity. Since the attrition propensity is based on the assumption
that each impact velocity is sufficient to initiate a lateral crack, the reduction in
the PS is assumed to eventually lead to the development of a critical dimension at
which the incident energy is insufficient to initiate further cracks. Also consistent
with fracture theory was the observation that decreasing the PS of a material
increased its hardness. Consequently, it can be expected that milling fine particles will consume more energy than what is required to mill coarser particles [26].
Shariare et al. showed that the initial median PS (d50) of three grades of predominantly brittle lactose monohydrate (d50: 102.79 μm; 52.06 μm; 13.93 μm)
markedly affected the extent to which the PS could be reduced [22]. The magnitude of the effect of various milling parameters was studied, and grinding pressure, injector pressure, and feed rate were all evaluated by calculating the
differences between d50 for each batch at low and high levels for each parameter.
This study showed that the extent to which these process parameters affected the
resulting material depended on the initial PS. Smaller PS lactose monohydrate
samples (13.93 and 52.06 μm) were less sensitive to size reduction than the larger
samples (102.79 μm), especially with respect to the application of grinding pressure. Fragmenting lactose monohydrate showed a brittle–ductile transition
below 23.7 μm [27], and comminution of lactose monohydrate particles having
PS < 23.7 μm occurred predominantly via attrition forces at particle edges and
corners, rather than via brittle fracture of the particles themselves [28]. Therefore, PS reduction of coarse lactose monohydrate is expected to happen via brittle
fracture, while finer particles of lactose monohydrate are primarily reduced
through shearing and abrasion. This explains the limited impact that varied
grinding pressures had on the PS of finer grades of lactose monohydrate [22].
As mentioned above, the attrition propensity factor is inapplicable after a critical size limit is reached, at which the formation of lateral cracks may potentially
be described by another relationship (Equation 9.5) [29, 30]. The critical PS (dcl)
is an ultimate limit for reduction, below which it is not possible to propagate a
crack using any impact velocity or load, as it approaches the limit of crack propagation predicted by Griffith’s law [15]:
dcl
Ht
Ktc
−2
1
Et2
1
4
Ht
1
1
ρ − 4ν − 2
95
In Equation (9.5), Ktc reflects the fracture toughness, Ht is the hardness, and Et
is Young’s modulus of the target materials. Clearly, the critical particle dimensions have a strong dependence on the ratio of hardness to fracture toughness [Ht/Ktc], which is commonly referred to as the “brittle index” [24].
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9 Secondary Processing of Organic Crystals
Materials having dominant brittle failure modes are more prone to chipping
than ductile materials, owing to the formation of lateral cracks; therefore, brittle
materials may have a lower critical PS limit. In contrast, ductile particles predominantly deform plastically with minimal elastic deformation. This accounts
for the higher stress requirement for initiating crack propagation in plastic
materials relative to brittle materials. Clearly, ductile materials are less susceptible to chipping than brittle materials. The critical PS is inversely related with
impact velocity, and, as a result, dcl decreases with increasing impact velocity. It
should be noted that it is not possible to propagate any crack below dcl regardless of impact velocity, as the failure mode of the material switches from plastic–
elastic to the fully plastic [31].
Recall that the attrition propensity (Equation 9.4) is proportionally related to
the material hardness. This indicates that harder materials are more likely to
undergo attrition if the other materials properties are constant. Additionally,
since η is inversely proportional with the square of the material toughness, this
suggests its strong role in resisting particulate attrition. Hutchings et al. demonstrated the less significant role played by material toughness relative to hardness
for ductile materials [32]; however, as pharmaceutical materials are typically
neither completely plastic, elastic, nor entirely subject to fragmentation, a combination of ρH Kc2 that incorporates all of the material mechanical properties
might be best for analyzing of hardness and toughness on the propensity for PS
reduction.
Additional analysis of the interplay between materials properties and the
milling process was studied in terms of frictional loss from particle surfaces following impact. It was assumed that, during milling, each mother particle loses
some amount of material in the form of debris following every impact. This
instantaneous loss depended on both materials properties and impact velocity.
Zhang et al. [33] expressed this relationship as Equation (9.6):
ξ = αη
96
where ξ is the frictional loss from a particle due to impact, α is a proportionality
factor, and η is the dimensionless attrition propensity parameter discussed
above (Equation 9.4), which includes all required materials properties such as
density, dimension, hardness, fracture toughness, and impact velocity. It was
observed that a linear relationship occurs between the frictional loss, the impact
velocity, and the hardness. This suggests that materials demonstrate increasing
hardness following each impact, a phenomenon commonly referred to as
work-hardening [33], where, as a consequence, material chipping occurs more
readily from the mother particles. Furthermore, the kinetic energy of particles
increases with larger PS; therefore, larger particles harden at a faster rate relative
to smaller particles [33]. This behavior is significant with plastically deforming
materials compared with brittle or elastic materials, for which the rate of hardening is more dependent on materials properties.
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
Work-or strain-hardening is a phenomenon often observed in metals, which
become increasingly resistant to plastic deformation after being “worked” multiple times [34, 35]. The phenomenon can be modeled by the Holloman relationship (Equation 9.7), which relates the true flow stress (σ f) with the true
plastic strain (εp) by means of a strength coefficient, K and a strain-hardening
exponent, n:
σ f = K εpn
97
Both K and n are determined empirically for metals, by measuring stress–
strain relationships beyond the elastic limit but may show complex behavior
in certain materials [36]. The basic strain-hardening phenomenon is interpreted
as a manifestation of dislocation propagation and entanglement following
repeated cycles of plastic flow [37].
Various examples of work-hardening in SMOC are reported, especially as a
result of roll compaction. Bultmann et al. reported a reduction in the bonding
strength of Avicel PH® 101 (microcrystalline cellulose) granules following multiple roll compaction cycles, where subsequent tablet preparation resulted in
compacts having a reduced mechanical strength [38]. He et al. reported that roll
compacted Avicel PH® 102 showed increased dynamic hardness, decreased plastic deformation, and the formation of weaker tablets, which was referred to as
“loss of reworkability” of the materials [34]. Malkowska et al. studied the effect
of recompression on the tableting properties of directly compressible starch,
dicalcium phosphate dihydrate, and microcrystalline cellulose and showed both
significant reductions in the crushing strength of the tablets prepared from
reworked materials and that the phenomenon was more prominent when the initial compaction was carried out at high pressures [39]. In typical dry granulation
lines, this effect can be exacerbated as work-hardened ribbons are milled prior to
compaction, requiring three consecutive opportunities for decreasing workability
in this particular secondary manufacturing line.
9.2.1.2
Physical Transformations Associated with Milling
Milling operations expose SMOC materials to high-shear mechanical energy,
which may be sufficient to induce solid-state transformations. The susceptibility
of milling-induced transformations also depends on intrinsic materials properties, as has been reported throughout the literature. As mentioned above, continuous application of stress initiates crack propagation from small flaws in the
material, which leads to fracture. Continuous milling causes particle fragmentation, which eventually reduces particles to their minimum obtainable size
given the energy input relative to the mechanical properties. Once the fracture
limit is reached, the stress required for subsequent size reduction becomes prohibitive [15], and the mechanical stress is further dissipated by generation and
translation of lattice dislocations. Some lattice dislocations are the natural
consequence of crystal growth, and occur when molecules are not spaced at
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9 Secondary Processing of Organic Crystals
their equilibrium positions dictated by lattice symmetry. Plastic deformation
translates these dislocations through neighboring unit cells causing further misalignments, which propagate, in a chain-reaction-like sequence. Eventually, the
number of dislocations reaches a critical density, which causes these defects to
inhibit further movement [40, 41]. At this point, the accumulated dislocations
promote overall lattice perturbations, leading to loss of the collective interactions defining the periodicity required by the crystalline state, potentially allowing transformation of the materials into disordered solids [42].
Tromans and Meech proposed a thermodynamic model for crystalline-toamorphous transformations occurring as a result of milling, in an attempt to
explain observations of increased dissolution of minerals following milling of
ores [43]. In their work, the amorphous state was assumed to have a similar free
energy to the liquid state, and the free energy required to completely transform a
crystal to its amorphous phase (ΔGam) was assumed to be
ΔGam =
ΔHf
Tm
Tm − Texpt
98
where ΔHf is the enthalpy of fusion, Tm is the melting temperature of the crystal,
and Texpt is the experimental temperature, or the temperature experienced during milling. It was assumed that the application of continuous milling energy
primarily caused the formation and propagation of dislocations, whose density
(ρd) was related to the free energy required for their incorporation in a lattice
(ΔGd) using Equation (9.9):
ΔGd = ρd MV
2 ρd− 0 5
b2 μ s
ln
4π
b
99
Here, MV is the molar volume of the molecules comprising the crystalline
solid, b is the magnitude of Burger’s vector, and μs is the elastic shear modulus.
Assuming that complete disordering occurs by this mechanism (i.e. ΔGd = Δ
Gam), the critical dislocation density (ρcrit) required for lattice collapse is given
by Equation (9.10):
ΔHf
Tm
Tm − Texpt = ρcrit MV
−0 5
b2 μ s
2 ρcrit
ln
4π
b
9 10
According to this model, complete disordering is allowed if ρcrit < 1017m−2,
a prohibitive dislocation density, based on the dimensions of the inelastic core
of a typical dislocation [42]. Beyond this prohibitive dislocation density (ρ∗),
either the accumulation of dislocations required for lattice collapse
exceeds a meaningful value or the materials properties of the SMOC result
in ΔGd ΔGam.
Wildfong et al. adapted the model in Equation (9.10) for use with SMOC, 7 of
which were continuously milled using a cryogenic impact mill (Texpt = 77 K).
Based on the dislocation model, the disordering potential for 6/7 SMOC
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
materials was correctly predicted, suggesting that the properties contained
within the model were reasonably predictable of the phenomenology [42]. Further exploration of dislocation-based disordering was done by Lin et al. [10],
where the original 7 material library from Wildfong et al. was expanded to
include 23 SMOCs. In addition to the parameters contained within
Equation (9.10), Lin et al. also explored additional thermal and mechanical
properties, all of which were correlated with observed disordering via logistic
regression. The results of this modeling indicated that, while any one parameter
in Equation (9.10) was insufficient to completely describe the disordering
potential (or resistance) of the 23-member SMOCs library, a bivariate model
combining MV, and the material glass transition temperature (Tg), was capable
of correctly predicting material behavior during milling [10]. The 23-member
SMOCs library has, over the years, been subsequently expanded to contain
additional materials, as shown in Figure 9.5.
Note that the inclusion of additional materials to the SMOCs library did not
result in any phenomenological misclassifications, suggesting that the combination of MV and Tg are capable of describing complete disordering potential
during continuous milling. Relative to the original bivariate model (dashed
line in Figure 9.5), the adjusted model changes slope slightly, as more properties are leveraged against the observed data. It is expected that, if the model
holds, additions to the library may cause further adjustments to the slope but
without misclassified behavior (e.g. the presence of a material observed to be
resistant to disordering, represented by circles in Figure 9.5, falling to the
right of the decision boundary). Note also the assumptions of Lin et al. that
this model, and subsequent iterations, is for predictions of complete disordering resulting from continuous and lengthy milling, likely not experienced during typical secondary manufacturing [10]. It is expected, however, that
materials predicted to completely disorder by this model (combinations of
MV and Tg to the right of the decision boundary) are likely to correspond with
materials susceptible to partial disordering under more practical milling
conditions.
In cases where disordering may not be feasible, defect accumulation in SMOC
may follow particular symmetries rather than random arrangements, causing
the material to transform to a metastable polymorph during milling [44]. Such
a transformation may result in different or undesirable physico-mechanical and
biopharmaceutical properties of the milled materials relative to the parent API
(Figure 9.6).
Additional work that characterizes PITs as a result of milling are described by
Otusuka et al., who demonstrated that the hygroscopicity of cephalexin
increased after four hours grinding, attributable to decreased crystallinity
[45]. Kaneniwa et al. also showed that the therapeutically active, metastable
forms of chloramphenicol palmitate (Forms B and C) transformed into a therapeutically inactive, stable Form A after two hours of milling [46].
373
9 Secondary Processing of Organic Crystals
550
Original
450
Mv (cm3 mol−1)
374
Expanded
350
250
150
50
220
270
320
Tg (K)
370
Figure 9.5 Molar volume (MV) and glass transition temperature (Tg) for 27 SMOC materials
subjected to continuous cryogenic impact milling. Materials to the left of the decision
boundary (○) are resistant to complete disordering as a result of continuous milling, while
materials to the right of the decision boundary (Δ) completely disorder as a result of
continuous milling. The dashed decision boundary separating the two groups of materials
represents the original bivariate model from Lin et al. [10], while the solid boundary
represents the revised model including the materials in the expanded library. Source:
Reproduced with permission of Elsevier.
Reduced crystallinity or
partial amorphization
SMOC
materials
Material intrinsic properties
Complete
amorphization
Solid-state
phase
transformation
High shear
milling
Amorphization with
polymorphic transition
Different/undesirable
physicochemical
and biopharmaceutic
properties
Direct polymorphic
transition
Shear energy input
Desolvation or
dehydration
Figure 9.6 Possible solid-state phase transformations occurring as a result of milling.
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
375
Table 9.2 Examples of solid-state transformations of various pharmaceutical materials induced
during milling.
Pharmaceutical
material
Mill type
Solid-state transformation
β-Succinic
acid [7]
Ball mill,
Jet mill
Crystalline to partially amorphous solid Partial
conversion to α-succinic acid
Cephalexin
[45, 47]
Agate shaker mill
Agate centrifugal
ball mill
Crystalline to completely amorphous solid
Chloramphenicol
palmitate [46–48]
Agate centrifugal
ball mill
Form B (metastable) to Form A (stable) Form
C (metastable) to Form A (stable)
Cephalothin
sodium [49]
Agate centrifugal
ball mill
Crystalline to partially amorphous solid ( 30%
crystallinity after 2 h milling)
FR 76505 [50]
(Uricosuric agent)
Ball mill
Form B (metastable) to completely amorphous solid
( 3 h milling) Form A (stable) to Form B ( 5 min) to
completely amorphous solid ( 3 h milling)
Indomethacin [51]
Agate centrifugal
ball mill
α-Form (4 C, 30 C) and γ-Form (4 C) to completely
amorphous solid ( 10 h milling) γ-Form to α-Form
(metastable) (30 C after 10 h milling)
Ranitidine HCl [52] Oscillatory ball
mill
Form I to completely amorphous solid ( 12 C,
milling) to Form II ( 12 C, 3 h milling)
Salbutamol
sulfate [26]
Air jet mill, Ball
mill
Crystalline to partially amorphous solid
TAT-59 [53]
(Anticancer drug)
Agate planetary
ball mill
Crystalline to partially amorphous solid ( 9%
crystallinity after 2 h milling)
Numerous other researchers have carried out studies to better understand
transformations induced during milling, some of which are summarized
in a review on the topic [6]. Table 9.2 summarizes a few additional examples,
and although not exhaustive, it provides a fair survey of the types of observations made following milling of pharmaceutical materials. As these
examples illustrate, a thorough understanding of the basis for transformations
that may occur during milling is imperative during early and late stage
drug development.
9.2.1.3
Chemical Transformations Associated with Milling
During milling operations, pharmaceutical materials are trapped between the
colliding grinding media and the mill wall, which transfer mechanical energy
to material surfaces as normal and shear stresses act on them. The externally
imposed stress state induces a strain field in the bulk of the solid, which may
2.5 h
376
9 Secondary Processing of Organic Crystals
shift atoms from their stable equilibrium positions in the lattice. Alternatively,
the strain field may also cause changes in the bond lengths, and angles, or excitation of electron subsystems. Therefore, mechanical energy can alter the structure and physicochemical properties of pharmaceutical materials [54].
The “triboplasma approach” used to explain mechanochemical transformations assumes that repetitive, intense impact events lead to a quasi-adiabatic
local energy accumulation, which can eventually increase local temperatures
up to 104 K at submicroscopic impact zones [44]. This stimulates the formation
of metastable structures, releasing part of the accumulated energy in order to
achieve a more thermodynamically stable form. One of the possible ways to
relax the strain is to rupture chemical bonds, in addition to loss of heat and plastic deformation [55]. Adrjanowicz et al. reported significant chemical degradation of pure furosemide following milling [56], where it was found that
cryogenic grinding activated and accelerated both structural changes (solidstate amorphization) and chemical decomposition into 4-chloro-5sulfamoylanthanilic acid. Sheth et al. studied mechanochromism of piroxicam
under mechanical stress [57], showing that the colorless, crystalline, neutral piroxicam molecules were transformed into yellow, amorphous, zwitterionic
molecules during cryogrinding. The yellow coloration of the amorphous solid
was attributed to charged molecules, which had a strong propensity to recrystallize to a colorless crystalline phase. This intermolecular proton transfer,
accompanied by both solid-state disorder and a change in color, was induced
by the mechanical stress.
In a study by Otsuka et al. [45], changes in the chemical structure of cephalexin Phase IV were reported during grinding in an agate shaker mill. Cephalexin Phase IV has a characteristic β-lactam ring associated carboxyl group
(νC=O), as evidenced by specific bands at 1760 and 1580 cm−1 in infrared spectra
[58]. The peak intensities of the β-lactam (νC=O) at 1760 cm−1 and carboxyl
group at 1580 cm−1 of cephalexin Phase IV were observed to change with
increasing grinding time, while the absorbance ratios of the 1580 and 1760
cm−1 peaks showed a proportional relationship with the degree in crystallinity,
which was used to track changes as a result of milling. This absorbance ratio
decreased with increasing grinding time, demonstrating that cephalexin Phase
IV was rendered amorphous by milling [45]. In a related study, the authors
attributed a decrease in the chemical stability of cephalothin sodium to this
decrease in crystallinity during grinding [49], where it was proposed that grinding opened the β-lactam ring as crystallinity was reduced, also increasing its
reactivity.
Matsunaga et al. studied the physicochemical stability of an anticancer drug,
TAT-59 under different grinding conditions [53]. TAT-59 degraded to its
hydrolytic product, DP-TAT-59 and phosphoric acid. Grinding of TAT-59 in
an agate planetary ball mill led to complete amorphization after two hours.
Although it was shown that intact crystalline TAT-59 was stable for 28 days,
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
disordered, ground TAT-59 showed the presence of DP-TAT-59, the amount of
which increased with grinding time. In contrast, this research showed an exponential decrease in DP-TAT-59 formation with increasing crystallinity of TAT59 samples [53].
Characterization of the effects of processing on SMOC materials is an important element of drug development research, an illustration of which is given in
Zong et al., who modeled the solid-state degradation kinetics of gabapentin
Form II as a result of milling [59]. Gabapentin molecules are subject to chemical
degradation by intramolecular cyclization, resulting in the formation of gabapentin-lactam (gaba-L), a toxic degradant that the FDA specifies should be present in quantities <0.4% in manufactured gabapentin tablets [59]. In their work, it
was shown that the material underwent structural disordering during the application of high-shear mechanical stress, which consequently increased the rate of
lactam formation increased milling duration [60]. These data illustrate the
importance of evaluating the effects of processing stresses on the materials used
in 2 manufacturing. Figure 9.7 shows that only the unmilled gabapentin was
likely to meet the specification of <0.4% gaba-L on storage, suggesting that even
modest milling can potentially compromise this material.
In a complementary study, it was proposed that the accelerated degradation
to gaba-L as a result of milling could not be completely explained by changes
in specific surface area alone. Rather, the role that localized surface damage
played in accelerating the reaction also needed to be considered. It was also
4
60 min milled
gaba-L (mol %)
3
2
45 min milled
15 min milled
1
0
unmilled
0
200
400
600
800
1000
1200
1400
h
Figure 9.7 Rate of gaba-L formation increased with increasing exposure to high-shear
mechanical stress in a planetary mill (50 C, 11% RH). Source: Reprinted from Zong et al. [59].
Reproduced with permission of Elsevier.
377
9 Secondary Processing of Organic Crystals
Gaba-L concentration (mol %)
378
4
3
2
1
0
0
20
40
Hours
60
80
100
Figure 9.8 Formation of gaba-L in milled samples stored for 24 hours at 25 C under different
relative humidity conditions (○) 81% RH and (□) 0% RH. Source: From Zong et al. [60].
Reproduced with permission of Springer).
noted in this study that the role of moisture in the chemical reaction was
unexpected. In contrast to many reactions, which are accelerated in the presence of environmental water, gabapentin was more stable at high relative
humidity, where the lactam conversion rate was negligible at 74% RH. In
comparison, samples held at 5% RH underwent lactamization at an initial rate
of 0.7 mol% day−1. Illustrative of the role that damage induced through milling
plays in the destabilization of the gabapentin, it was hypothesized that adsorption of environmental water led to annealing of surface disorder, reducing lactam formation. The results are shown in Figure 9.8, which compares milled
gabapentin stored for 24 hours at either 0% RH or 81% RH prior to thermal
stressing. The data appear to confirm the authors’ hypothesis, indicating that
the milled samples stored under desiccated conditions underwent lactamization, whereas the milled samples stored at 81% RH appear to have negligible
lactam formation [60].
9.2.2 Pharmaceutical Blending
Mixing of pharmaceutical powders is another important 2 processing step,
used to ensure the content uniformity during the preparation of both solid
and semisolid dosage forms [61], and involves the basic steps of convection,
shear, and diffusion.
Categorized by desired outcome, mixing can be classified as either ordered or
random. Ordered mixing involves the adsorption of the fine particles of a component on the surface of a coarse “host” particle, owing to strong adhesive forces
between guest and host [62]. These adhesion forces may be electrostatic or
interfacial [62–64], and should ideally result in an even coating of fine particles
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
on the coarse host, with a resulting PSD having zero standard deviation with
respect to the guest particles. In a practical sense, the ideal state is unlikely
to be achieved, while analytical and sampling errors are also likely to cause variance [65]. Ultimately, the initial host or carrier PS can influence blending outcome, limiting homogeneity and segregation in the mixture.
In contrast with ordered mixtures, random powder mixing is facilitated by
noncohesive and noninteractive particulate systems [66], which involve repetitive cycles of powder bed splitting and recombination to provide an equal
chance for every individual particle to be a part of the mixture at any one time
[65]. Although both ordered and random mixing involve gravitational and surface electrical forces, the impact of the former is expected to be much less relative to the latter in the formation of ordered mixtures, while the exact opposite
is true for random mixtures [65].
Various equations are applied for statistical analysis of randomized mixing
process outcomes. A few important and pioneering relationships are summarized here. Lacey et al. [66] developed a relationship to calculate the standard
deviation of a random binary mixture (Equation 9.11):
σ2 =
αβ
n
9 11
where σ 2 is the variance, α and β are the mean proportions of each component,
and n is the number of particles present in the mixture. While Equation (9.11) is
suitable for describing mixing monodisperse spherical particles, its applicability
to real systems is likely limited. A simplified equation from Stange et al. can be
used to understand the mixing of the multicomponent systems (Equation 9.12)
[67, 68]:
x2 =
O −E
E
9 12
where O and E are the observed and expected drug particle characteristics (e.g.
particle number)s and x2 is the variance, which is independent of the proportions of the components.
Poisson distributions provide another approach for modeling random mixtures, assuming that the coarse component comprises approximately 20%
w/w of the mixture (Equation 9.13) [69]:
CA =
100 mA
MA
9 13
where CA is the variation coefficient of component A, MA is the mean content
mass of A, and mA is the representative mean particle mass of A. One of the
limitations of this model is its inadequate ability to handle the sampling variability. Thus, sources of sampling error, such as drug content variability, agglomeration, and mixer choice might cause deviation from the perfect mix.
379
380
9 Secondary Processing of Organic Crystals
Segregation or demixing involves the separation of fine and coarse particles
during powder flow or powder bed vibration [70], which includes three main
mechanisms. The first, segregation by percolation, occurs when smaller particles separate from larger particles owing to buoyancy and draining. Since smaller particles better fit into the interstitial voids between larger particles in
powder mixtures, the differently sized particles move in opposite directions
[71]. The second mechanism, segregation owing to differences in particle density, occurs during powder flow when heavier particles remain where they have
fallen, while lighter particles fall to the sides, as is commonly observed during
angle of repose measurements or weighing. Alternatively, during bed vibrations,
larger, dense particles can move upward toward the top strata of the mixture,
while compact, smaller particles move downward toward the lower strata [70].
Finally, in the third mechanism involving trajectory segregation, the distance
traveled by particles having equal density at the same velocity in free flight is
proportional to the square of the particle diameter. Thus, larger particles will
travel longer distances toward the mixer wall, while smaller particles, traveling
shorter distances, will remain localized toward the center [72]. Segregation is
statistically quantified by its scale and intensity; two parameters that provide
quantitative information needed to understand the “goodness” of mixture.
Powder physicochemical properties and their interactions with processing
equipment have been shown to influence the degree of mixing, homogeneity,
and mixing stability (resistance to segregation); however, many different factors
can play important roles, which increase process complexity. As such, there is
no simple set of rules that can guarantee that a perfect or acceptable powder
mixture will result. A complete review of how process conditions (e.g. mixer
types, mixing time, mixing speed, etc.) is beyond the scope of this chapter
and can be found elsewhere [73]. Instead, the present discussion is focused
on the influence of powder properties such as PS, size distribution, particle morphology, particle density, surface texture, particle charge, flow properties, and
proportions of the ingredients to be mixed governs the achievable degree of
mixing [74–79].
Particle dimensions have a substantial effect on powder mixing, owing to the
significant increase in specific surface area with reductions in the PS. Interparticulate attractions, therefore, increase with decreasing PS, and overwhelm
gravitational forces during mixing of smaller particles. This can be advantageous with respect to forming ordered mixtures, where the stability increases
with a decrease in the PS below 100 μm, with the likely formation of a “completely” ordered mixture for particles sized less than 40 μm. It is noted, however,
that smaller particles may still percolate through the voids between larger particles, causing segregation in some cases [61, 65]. Powders having a wide PSD
can produce both random and ordered mixtures (sometimes termed a “total
mixture”) in which randomized and ordered regions are in equilibrium with
one another [65].
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
Particle shapes and textures affect both mixing time and the mixture stability
of pharmaceutical powders. Nearly spherical particles have minimal interparticulate contact areas relative to irregularly shaped particles. As such, more regular particles (especially those whose shape approximates a sphere) show better
flowability, as reflected in any metric representing the term, relative to irregular
particles. It is, therefore, conventional knowledge that random mixtures are
easier to obtain from powders consisting of nearly spherical particles, characterized by shorter mixing times to produce a homogeneous blend. In contrast,
irregular particles have high internal and surface frictional angles and, therefore,
stronger interparticulate cohesion.
Random mixtures may be difficult to form if strong, adhesive interactions
drive particle segregation [71]. Conversely, in the case of ordered mixture formation, Wong and Pilpel [78, 80] showed that irregularly shaped and roughly
textured calcium carbonate (guest particles having a larger shape coefficient)
more strongly adhered (Figure 9.9a) with a lactose carrier (host particles) relative to regularly shaped and smooth-textured calcium carbonate having a smaller shape coefficient. In turn, ordered mixtures comprised of irregular calcium
carbonate adhered to lactose were observed to be less likely to segregate [80]. In
additional work, Wong and Pilpel also showed that irregular, rough lactose carrier particles having a large shape coefficient demonstrated stronger adhesion
with the calcium carbonate guest particles (Figure 9.9b). These two studies illustrated that mixing time had to be increased as the irregularity or shape coefficient of calcium carbonate and lactose was increased; however, the resulting
ordered mixtures were more stable [78].
Differences in particle density can also pose problems during mixing of
SMOC powder components. Denser particles are pulled downward owing to
a greater gravitational force, while lighter particles remain on top of denser
ones. This can lead to segregation, especially when the mixtures are vibrated
[61, 81], such as during shipping or transfer. Rippie et al. showed that the relative energy required for mixing and segregation was not greatly affected by the
Figure 9.9 Relative particle adsorption of (a) irregular, rough-textured small guest particles
on regularly shaped, large host particles [80]; (b) regular, smooth-textured, small guest
particles adsorbed on regularly shaped, smooth-textured large host particles; (c) regular,
smooth, small guest particles on irregular, rough-textured, large host particles [78]. Source:
Adapted from Refs. [78, 80]. Reproduced with permission of John Wiley & Sons.
381
382
9 Secondary Processing of Organic Crystals
particle density alone, rather it was also a function of particle shape and size
[82]. Lloyd et al. reported that differently shaped particles having large
disparities in density could segregate; however, PS differences were
determined to most influence this [83]. These results notwithstanding, it is
recommended to avoid mixing particles having densities that differ by a factor
of approximately 3, as they are more likely to segregate, particularly with
other factors in play.
Particle surface properties can be modified by altering surface charges.
When two particles having similar surfaces, or dissimilar materials having different surface roughness, are moved past one another, asymmetric heating can
increase localized temperatures at the points of contact, which in turn
increases the concentration of mobile charged carriers. This leads to charge
transfer from the smaller area to the larger area, which eventually contaminates the whole particle, leading to electrostatic attraction between these particles [84]. This phenomenon, called triboelectrification, is used in ordered
mixing to provide opposite charges to the host and guest particles and increase
interparticulate adhesion. In general, the drug or guest particles are negatively
charged, while the excipient or host particles are positively charged. This ultimately increases the stability of the ordered mixtures [61, 85]. Various other
properties at the contact surfaces, such as layers of surface water, oxides,
hydrocarbons, and yield strengths of the materials can also influence triboelectrification [86].
Triboplasma-induced triboelectrification is another way to modify surface
charges, which may occur during sliding contact of the particles.
A triboplasma is defined as a gas discharge generated by tribological activation.
Tribological activation at material surfaces may generate various physical processes like photon emission, electron and lattice component, triboelectrification, triboplasma generation, lattice vibration excitation, lattice and electron
defects formation and migration, amorphization, impurities insertion, and plastic deformation [87].
9.2.3 Granulation of Pharmaceutical Materials
Successful 2 processing of SMOC depends heavily on the workability of materials as they proceed through the various stages of dosage form manufacture.
Various types of granulation processes are employed throughout the pharmaceutical industry, all of which have an end goal of PS enlargement, normally to
improve downstream flow properties for gravity-fed processing steps or to
improve compactability necessary for forming viable tablets. Table 9.3 provides
an overview of size-enlargement methods [88].
Granulation methods are classified by a number of different means, including
binder type (e.g. use of dry binders vs. liquid binders), temperature conditions,
or general process descriptors (e.g. wet granulation, dry granulation, or hot-melt
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
383
Table 9.3 Overview of size-enlargement methods used in 2 manufacturing of SMOC.
Method
Granule Relative granule
diameter density
Industrial capacity Capabilities/restrictions
Mixer/granulators
High-shear
batch
granulator
0.1–
2.0 mm
Low-shear
batch
granulator
Up to 500 kg
batch−1
(depending on
equipment size)
Choppers, impellers, agitator bars
enable handling of cohesive
powders
Low
(agglomerates)
Moderate
(layered
granules)
100–900 kg
batch−1
50 ton h−1
(continuous
operations)
May not be appropriate for
cohesive or poorly flowing
powders; capable of applying
layered coatings; scalability
generally not an issue
Low
Up to 1500 kg h−1 Solid may be susceptible to
throughput
amorphization depending on
processing conditions; granular
morphology generally spherical
High
Moderate
(variable)
Granule properties can be highly
variable depending on equipment
and process parameters
Fluidized bed granulators
Fluidized bed
Spouted bed
Wurster
coaters
0.1–
2.0 mm
Spray granulators
Spray dryer
0.05–
0.5 mm
Dry granulators
Melt
extrusion
Roll
compactor
Pellet mill
>0.5 mm High to very
>1.0 mm high
Up to 5 ton h−1
Up to 50 ton h−1
Very narrow PSD, very sensitive to
powder flow and mechanical
properties; subject to work
hardening; completed by
milling step
Source: Adapted from Ennis [89].
granulation). Among these, dry granulation is considered a combination of
compaction and milling, which will be discussed in a later section. However
the materials are processed, consistent bioavailability and predictable stability
remain the basic quality and regulatory requirements for the development
and manufacture of pharmaceutical products from safety and efficacy standpoints. As such, the API must maintain its specific structural motif and specified
solid forms during and after each secondary manufacturing step. As described
in previous chapters, and sections of the present chapter, crystalline solids having various polymorphic and/or solvate/hydrate forms should be monitored
throughout granulation, as many of these forms may be accessible owing to processing stresses introduced in this stage of manufacturing.
384
9 Secondary Processing of Organic Crystals
9.2.3.1 Wet Granulation
What clearly distinguishes wet granulation from all other post-crystallization
unit operations is the thorough wetting of the formulation during processing.
During the process a granulation fluid (normally a polymeric binder dispersed
in aqueous solvent) is applied to facilitate agglomeration by the formation of a
wet mass by particle adhesion. The amount and rate of granulating fluid addition is critical for predicting the endpoint. Relative to solution or suspension
formation, the liquid content used in wet granulation is much lower, as the fluid
acts as a bridge between particles, rather than a continuous phase in which particles are dispersed.
High-shear wet granulation is depicted in Figure 9.10, which captures the traditionally described sequence of events, leading to the formation of granules,
and illustrates the role played by the granulating fluid in the process. Briefly,
dry particles are mixed in a product bowl by means of a rapidly moving chopper
(a)
Continuous mixing
with chopper/impeller
ensures wetting of
dynamic bed
Dry mixing via
chopper/impeller
(f)
Initial wetting with
granulating fluid
(b)
(c)
Heated air supply
Pendular stage
Wet
massing
Drying granules removes solvent from
agglomerates
Capillary stage
Funicular stage
(e)
(d)
Granulation
endpoint
Droplet stage
Overwetting with
excess fluid
Capillary stage
Figure 9.10 Progression of granule formation typical of high-shear wet granulation. The
materials are initially (a) dry mixed to form a homogeneous blend; (b) wetting initiates liquid
bridge formation; (c) agglomerates proceed through the pendular and funicular stages as
more liquid bridges build, eventually reaching (d) the capillary endpoint, where
interparticulate liquid bridges are maximized. Overwetting can lead to (e) droplet stage,
where the particles become dissolved or suspended in the granulating fluid, leading to batch
failure. The process is finished when (f ) solvent is removed by drying agglomerates.
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
and impeller, so that when wetting is initiated, agglomeration will take place
between particles of a homogeneous blend. As the granulating solution accumulates, it forms liquid bridges between particles, which consolidate as more
fluid is added. Eventually, a point of maximum agglomeration is reached, at
which particles are held together by capillary forces. Care should be taken
not to exceed this endpoint, as excess granulating fluid can result in suspension
of the particles, usually resulting in batch loss. Following the endpoint of wet
massing, solvent is removed by drying, allowing solidification of the viscous polymeric binder, and retaining the agglomerate shape.
Wet granulation can also be accomplished in a fluidized bed, which replaces
the mixing implements (impeller and chopper) by entraining particles in a column of moving air. Because the consequence of overgranulation is usually batch
loss, considerable research has been conducted to monitor and predict that endpoints have been reached. For greater details, please refer to the Handbook of
Pharmaceutical Granulation Technology [88].
9.2.3.2
Potential Transformations During Wet Granulation
Although the amount of granulating fluid is relatively low, continuous, intimate
contact with the API for a relatively long period of time may be sufficient to facilitate a phase transition. Owing to this, anhydrous solids capable of spontaneous
hydration, or undergoing solvent-mediated transformation (SMT) to a hydrated
phase, may be particularly prone to changes during wet massing, as has been
reported for a number of drugs, including caffeine [90, 91], nitrofurantoin
[92], chlorpromazine hydrochloride [93], nimodipine, and indomethacin [94].
Following wet massing, granules are dried, during which the excess solvent is
removed by heating in either a tray (e.g. Figure 9.10) or fluidized bed dryer.
Exposure to thermal stress can result in physical or chemical transformations
of the materials and should be considered during formulation and manufacturing development. Below is a list of some examples of material responses to the
process environments involved in wet granulation.
9.2.3.3
Hydration and Dehydration
When considering the rank order of free energies of a SMOC material at a given
temperature and humidity range, a crystalline hydrate is the most thermodynamically stable crystal form, owing to the increased number of noncovalent intermolecular interactions contributed by the coordinated water molecules. As a process
stream is considered, anhydrous solids having a known hydrated form should
avoid granulation involving water, particularly if the hydration kinetics are rapid.
Development scientists might circumvent this danger by selecting the hydrate as
the starting material for wet granulation, as its risk of process-induced conversion
could be minimized. Depending on the apparent solubility of the hydrate, this
may not be a viable option for drug delivery, and the anhydrous solid should,
therefore, be granulated using a solvent-free route (i.e. roll compaction).
385
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9 Secondary Processing of Organic Crystals
Wet massing
Drying
Further processing/storage
Crys
talliz
Anhydrous
crystal
(stable)
Hydration
Anhydrous
Anhydrous
crystal
Crystal
Crystalline
Crystalline
hydrate
Hydrate
Anhydrous
crystal
Crystal
(stable)
(stable)
ion
at
lliz te
ta
ys dra
Cr hy
as
Dehydration
ation
Anh. crystal
(metastable)
(metastable)
Hy
dr
at
io
n
Crystalline
hydrate
Isomorphic
on
rati
dehydrate Rehyd
n
io
at
t
ys
Cr
Amorphous
solid
liz
al
as
e
at
dr
hy
Anh. crystal
(metastable)
llization
Crysta
Figure 9.11 Possible transformations that can occur during wet granulation when formation
of a hydrate is involved. Source: Reprinted from Morris et al. [95]. Reproduced with permission
of Elsevier.
A potential risk of moving forward with a hydrated form is that the stability of
this phase depends on the relative humidity and/or temperature of the environment. In other words, depending on processing and storage conditions following wet massing, the hydrated form may readily dehydrate if exposed to dry
atmosphere or elevated temperatures. As illustrated in Figure 9.11, hydration
and dehydration during wet granulation may result in transformation to one
of several phases, including an amorphous solid, an isomorphic dehydrate, a
metastable anhydrate, or the thermodynamically stable anhydrous form at room
temperature, some of which have their own potential for further conversion
[95]. This makes it important to consider the potential for API conversion
not only during the solvent-laden steps of processing but also during the subsequent granule drying phase. The likelihood of observing a given transformation pathway is determined by the kinetics of the conversion under the specific
processing conditions, as well as the duration of a particular step. For example,
in Figure 9.11, if the dehydration and lattice collapse to an amorphous solid is
faster than the overall granular drying, then the likelihood of forming an amorphous solid is high.
The transformation from anhydrous theophylline to its monohydrate has
been extensively explored [90, 96, 97]. Rodriguez-Hornedo et al. reported that
theophylline monohydrate is most thermodynamically stable below 60 C,
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
leaving the anhydrous form metastable under ambient conditions [98]. Aqueous
dissolution of the anhydrous form will be more rapid at temperatures below
60 C, allowing nucleation and crystal growth of the monohydrate via SMT.
This particular conversion requires that wet massing involves sufficient water
at particle surfaces to allow dissolution of the metastable phase to take place,
which will then be followed by heterogeneous nucleation of the monohydrate
crystals on the surfaces of the anhydrous crystalline particles [98].
The existence of two distinct anhydrous theophylline polymorphs was reported
by Suzuki et al. [99], where Form I is the high temperature stable phase and Form
II is the low temperature stable phase. Enantiotropism between Forms I and II was
confirmed by Legendre and Randzio [100] based on the heat of fusion rule,
although the transition between the two forms was not observed, and therefore,
the region of thermodynamic stability of the two polymorphic modifications
could not be determined. A third polymorph (named Form II∗) was also reported
as the consequence of dehydration of theophylline monohydrate, and this phase is
metastable and monotropically related to Form II, according to Phadnis et al.
[101] and later confirmed to appear upon wet granulation and fluid-bed drying
of a theophylline formulation as reported by Morris et al. [95].
During the drying phase of wet granulation, theophylline monohydrate was
observed to convert via the metastable anhydrous Form II∗ to the more stable
anhydrous Form II [101, 102]. Form II∗ was the predominant form of theophylline after batches were dried at 40–50 C, and a small amount of Form II∗
remained even when samples were dried at temperatures greater than 50 C
and produced mostly Form II [95]. A fluidized bed dryer was used to compare
the effects of practical drying methods on the transitions theophylline, while
variable-temperature powder X-ray diffraction (VT-PXRD) was used to dry
samples in situ. By using either means, the same temperature-dependent pathway was followed [103].
Similar transformations have been reported for carbamazepine [104, 105].
Carbamazepine (CBZ) is a poorly water-soluble drug commonly manifest as
one of four well-characterized anhydrous crystal forms [p-monoclinic (III), triclinic (I), trigonal (II), and c-monoclinic (IV)] [106]. Thermochemical data indicate an enantiotropic relationship between Form III (p-monoclinic) and Form
I (triclinic) [104]. Powder X-ray diffraction (PXRD) and differential scanning
calorimetry (DSC) characterization of samples obtained from granulating carbamazepine Form I (labeled metastable β-CBZ in this study) with 50% ethanol
solution indicated a transformation to the dihydrate [107].
Han and Suryanarayanan studied the effect of environmental conditions on
the kinetics and mechanisms of the dehydration of CBZ 2H2O and showed
VT-PXRD data for granules dried under different conditions (using different
water vapor pressures). Depending on the drying conditions, transformations
from the hydrate to either an amorphous solid or Form III (labeled γ-CBZ in
this study) were observed [104].
387
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9 Secondary Processing of Organic Crystals
It should be noted that different hydrates of drug substances might follow different transformation pathways when dehydrated during drying. Given sufficient time, a drug substance subjected to processing stress, such as drying,
should yield the thermodynamically stable form. If the conversion kinetics
and processing conditions are different, however, a mixture of solid forms
may result. Two possible transformation pathways could be responsible for
the existence of metastable forms and amorphous solids observed in the final
product. In first scenario, the hydrate can transform and become kinetically
trapped as a metastable anhydrate. In second scenario, the evacuation of water
molecules from the hydrate lattice can result in a structurally weak crystal that
transforms to an amorphous solid by “lattice collapse.” This second scenario
may be more likely for the sudden loss of all the water of crystallization in highly
coordinated hydrates (e.g. levothyroxine sodium pentahydrate [108–110]);
however, monohydrates have also been reported to follow this sequence, including theophylline monohydrate and nitrofurantoin monohydrate [102].
Complicated hydration/dehydration pathways can make for difficult decisions involving exposure of certain substances to a particular 2 processing
sequence. For example, starting wet granulation with an anhydrous metastable
polymorph may lead to formation of a stable anhydrate, which results from
hydration during wet massing and subsequent dehydration during drying.
For example, Chlorpromazine HCl (CPZ (II)) undergoes a phase change to a
hemihydrate (CPZ (I)-H) during wet granulation; however, after drying, the
material additionally transforms, resulting in final granules comprised of either
a partially dehydrated hemihydrate (CPZ (I)-H ) or a new anhydrous solid CPZ
(I), depending on the temperatures used to dry the product. The dehydrated
hemihydrate, CPZ(I)-H , can either take up or lose water molecules to, respectively, form either CPZ (I)-H or CPZ (I) without a marked change in the lattice
structure. The starting material, CPZ (II), is the anhydrous metastable form at
room temperature, while anhydrous CPZ (I), observed in some granules, is the
room temperature stable form, suggesting that the apparent solubility of CPZ
may be different prior to and after the granulation process, potentially affecting
drug delivery. It should be noted that technically, CPZ (I) is a pseudopolymorph,
since the conversion from CPZ (II) to CPZ (I) with the application of temperature occurs only through intermediate formation of a hydrate, and not through
a direct solid–solid equilibrium phase change. The complicated transformation
scheme is shown in Figure 9.12 [93].
9.2.3.4 Solvent-mediated Transformations (SMT)
During wet granulation, the risk of an SMT occurring is particularly high. The
theory behind SMTs is described in greater detail in the previous chapter (see
Chapter 8). Driven by the difference in apparent solubility between metastable
and stable phases, these conversions become problematic in this processing
context, depending on the transition kinetics, which can result in the
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
CPZ (I) – Hʹ
RH > 53%
(25 °C)
CPZ (II)
Wet granulation with
ethanol : water
80 5.22 9 (by volume)
CPZ (I) – H
Ambient
conditions
(20 – 26 °C,
30 – 40% RH)
70 °C (Vacuum, silica gel)
RH > 53% (25 °C)
70 °C
(Vacuum,
silica gel)
CPZ (I)
132 – 134 °C
Figure 9.12 Interconversions of chlorpromazine HCl (CPZ) involving hydration/dehydration
experienced during wet granulation and drying. Source: Reprinted from Wong and Mitchell
[93]. Reproduced with permission of Elsevier.
production of several different forms [111]. Anhydrous drug substances prone
to rapid, spontaneous hydrate formation are particularly susceptible to SMT
during wet granulation, when the API is placed in direct, intimate contact with
a solvent (usually water) for prolonged periods of time. Formulation can potentially be used to mitigate this risk, and research has shown that suitable polymeric excipients (e.g. hydroxypropyl methylcellulose (HPMC) or
hydroxypropyl cellulose (HPC) can be used to inhibit SMT during wet granulation as shown for caffeine [112, 113] and carbamazepine [114]. Wikström et al.
[115] monitored the conversion of anhydrous theophylline to its monohydrate
during high-shear wet granulation with water. It was shown that changes in formulation had little effect on preventing the SMT, with the exception of some
polymeric binders. At pharmaceutically relevant levels of methylcellulose, the
onset of transformation was delayed, and the kinetics of the SMT were slowed,
whereas the conversion was prevented entirely in the presence of HPMC.
The drying phase can also potentially induce transitions by a solventmediated mechanism, manifest as a nucleation and precipitation of different
forms from the solution during solvent evaporation. Depending on the rate
of solvent removal and the difference in solubility between the solid forms, this
can result in solidification of either the stable or metastable phase. Soluble excipients might also affect the transformation of the API by influencing the activity
coefficient of the API. For example, Figure 9.13 shows that mannitol converts
from its metastable σ-form to the stable β-form when small-scale wet granulation (kneading in a mortar with purified water) was immediately followed by
vacuum drying [116]. The authors hypothesized that the conversion was facilitated by water molecules, which disrupted the hydrogen bonds in the lattice of
the σ-form, followed by reconstruction as the more stable β-mannitol crystals. It
was noted that this transformation was problematic for downstream manipulation of mannitol-based granules, as the σ-mannitol had better plastic
389
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9 Secondary Processing of Organic Crystals
(a)
(b)
(c)
5
10
15
20
25
30
35
40
2 θ(°)
Figure 9.13 PXRD patterns of (a) σ-mannitol after wet granulation and vacuum drying and
(b) σ-mannitol prior to wet granulation and drying. For comparison, the PXRD pattern of (c)
β-mannitol is provided, demonstrating a σ to β transition as a consequence of this process.
Source: Data from Yoshinari et al. [116]. Reproduced with permission of Elsevier.
deformation characteristics relative to the stable form, consistent with the general rule-of-thumb that metastable phases are easier to plastically deform.
9.2.3.5 Polymorphic Transitions During Granulation
As discussed in other chapters in this book, the two basic ways in which polymorphs are related to one another is monotropism and enantiotropism. Monotropically related polymorphs are usually termed “irreversible” as the free
energies of the two solids are never equal below the melting temperatures of
either solid (Figure 9.14a). In contrast, enantiotropically related solids are characterized by a solid transition temperature, Ttr, below the melting temperature
for either solid (Figure 9.14b). Predicting transitions for monotropic systems is
fairly straightforward compared with enantiotropic systems, as the relative stability of the forms persists over all temperatures.
Thermodynamics dictate that spontaneous polymorphic transformations
occur with the thermodynamic gradient (i.e. from high free energy to low free
energy). At any temperature, therefore, a polymorph will only transform from
the metastable form to the stable one. In Figure 9.14a, this means that solid-state
transformations can only occur from Form II to Form I. In contrast, the enantiotropes shown in Figure 9.14b will spontaneously convert from Form II to
Form I at T < Ttr, or from Form I to Form II at T > Ttr but below the melting
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
(a)
Monotropism
GL
Free energy (J mol−1)
Liquid
GII
GI
Form II
Form I
Tm,II
Temperature (K)
(b)
Tm,I
Enantiotropism
GL
Free energy (J mol−1)
Liquid
GII
GI
Form II
Form I
Temperature (K)
Ttr
Tm,I Tm,II
Figure 9.14 Gibbs free energy vs. temperature (G–T) phase diagrams for two related
polymorphs, Form I and Form II. By comparison (a) monotropically related polymorphs are
characterized by intersection with the liquidus line at a temperature greater than the
transition temperature (Ttr), while (b) enantiotropes intersect the liquidus line at
temperatures greater than the transition temperature (Ttr).
temperature for either phase. The reversibility associated with enantiotropism
(if kinetically permissible) involves temperature fluctuations around Ttr, as discussed in the previous chapter (see Chapter 8). The effects of high-shear wet
granulation using an ethanolic hydroxypropyl cellulose solution as a liquid
binder were investigated for both nimodipine and indomethacin [94]. The
mechanism, kinetics, and factors affecting the polymorphic transformations
indicated that both drugs converted directly from the metastable to stable following a two-dimensional nucleation and growth mechanism.
391
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9 Secondary Processing of Organic Crystals
Seemingly counterintuitive to the thermodynamics of polymorphic transitions, conversions from stable to metastable forms may also be observed during
rapid drying and cooling steps. Some anhydrous stable forms may dissolve in the
granulating fluid during prolonged wet massing steps but solidify as the metastable phase if drying is done rapidly and nucleation and growth of the metastable solid exceeds that of the stable solid. Termed “kinetic trapping,” such a
transformation was observed for fosinopril sodium [95]. Of its two enantiotropic polymorphs, Forms A and B, the former is more stable at ambient conditions
yet was trapped as metastable Form B under simulated granulation conditions
and rapid drying of the alcoholic granulation fluid.
9.2.3.6 Salt Breaking
Williams et al. [117] used FT-Raman spectroscopy to follow transformations of
an unnamed Compound A from the stable hydrochloride salt to its amorphous
free base as a result of wet granulation using a hydroalcoholic binder solution
(Figure 9.15). The higher water content in the liquid binder combined with a 4-h
delay prior to drying the wet mass was found to increase the dissociation of the
drug. The authors concluded that the delayed drying step allowed the moisture
to facilitate the transformation to the amorphous free base. Furthermore, a significant increase in transformation to the amorphous free base was observed
after exposing tablet of Compound A to extreme storage conditions (high temperature and high %RH) for long periods of time. Based on these results, the
authors recommended that processing and storage of Compound A should
avoid water or at least require immediate and rapid drying after wetting in order
to minimize the crystalline-to-amorphous transformation.
9.2.3.7 Formulation Considerations in Wet Granulation
Excipients used in pharmaceutical formulations are an important factor to consider, especially when they are crystalline and soluble in the granulation solutions
used during processing. Many excipients are themselves SMOC materials and,
therefore, subject to the same processing stresses with similar potentials to
undergo phase transformations as a result. If the formulation components respond
to processing in an unanticipated way, there is a potential to change their interaction with the API during 2 manufacturing, likely affecting downstream processing
properties as well as final product behavior during storage. Consider the example
of mannitol described above, where the conversion of the diluent as a consequence
of processing resulted in a less deformable solid [116]. Formulations containing
β-mannitol will, therefore, consolidate differently under stress than those containing σ-mannitol, leading to tablets having different mechanical properties.
In addition to changes, excipients that dissolve or become suspended in granulating solutions can serve as heterogeneous nucleation sites for the API (or
other excipients), potentially altering the product of recrystallization to varying
extents. Ultimately, informed formulation is done by choosing the “right”
(a)
1.00
Raman units
0.75
0.50
0.25
0.00
1200 1150 1100 1050 1000 950 900 850 800 750 700 650 600 550 500
Wavenumber (cm–1)
(b)
0.6
0.5
Raman units
0.4
0.3
0.2
0.1
0.0
900
875
850
825
800
775
750
725
700
675
650
625
600
Wavenumber (cm–1)
Figure 9.15 FT-Raman spectra of (from top to bottom) Compound A HCl, Compound A free
base amorphous solid, spectral subtraction of placebo from active granules prepared using
absolute ethanol, spectral subtraction of placebo from active granules prepared using 96%
ethanol, and spectral subtraction of placebo from active granules prepared using 90%
ethanol. Panel (a) show granules prepared with no delay between granulation and drying,
while panel (b) shows spectra for granules held for four hour between wet granulation and
drying [117]. Source: Reprinted from Williams et al. [117]. Reproduced with permission of
Elsevier.
394
9 Secondary Processing of Organic Crystals
excipients that can help stabilize the API during processing, making them more
capable of emerging from secondary manufacturing in a predictable way. In wet
granulation, this has mostly involved research regarding which excipients are
used to minimize or slow hydration of the drug substance during the wetting
phase, either by influencing the mechanism and kinetics of hydrate formation
or by changing the initiation and rate of transformations.
The influence of excipients having different water sorption behaviors on API
hydrate formation during wet massing has been reported [115, 118–120]. Prevention or minimization of spontaneous hydration often depends on the
amount of excipient present in the formulation, its relative ability to imbibe
and retain water from the process, and the ways in which the excipients and
active substances interact. In general, the water sorption potential of an organic
material depends on its degree of crystallinity (i.e. amorphous materials sorb
more water than partially crystalline materials). Airaksinen et al. observed that
only amorphous hydroxypropyl cellulose (HPC) was capable of slowing hydrate
formation of nitrofurantoin when exposed to excess water [120]. HPMC worked
even better in formulations with anhydrous theophylline by completely preventing the formation of the monohydrate during wet granulation experiments
[115]. In contrast, hygroscopic, partially amorphous silicified microcrystalline
cellulose (SMCC) was only able to inhibit hydration of anhydrous theophylline
at moisture contents less than the amount needed to form granules, while a
crystalline excipient such as α-lactose monohydrate was unable to control
hydrate formation for either theophylline [119] or nitrofurantoin [120].
Beyond wet massing, the dehydration mechanisms of theophylline monohydrate, nitrofurantoin monohydrate, and sodium naproxen tetrahydrate were all
reported to be changed by excipients during drying, with each solid transforming
into new, unknown, and stable anhydrous forms as a result. In particular, the presence of lactose monohydrate and sodium carbonate in formulations were
reported to be responsible for the respective transformations of sodium naproxen
tetrahydrate and theophylline monohydrate/nitrofurantoin monohydrate [118].
The effect of excipients on other types of polymorphic transformations has
also been studied and reported. The influence of surfactants and a water-soluble
polymer on the transition of clarithromycin (CAM) during wet granulation has
been studied [121]. When wet massing was done using additives bearing polyoxyethylene chains, the thermodynamically stable form of CAM (Form II) was
shown to result, regardless of the original starting form (either metastable Form
I or stable Form II) or the type of granulation solvent (either water or ethanol).
9.2.3.8 Risk Assessment and Summary
As suggested by the preceding examples, wet granulation is a complicated process, during which SMOC materials can respond in a number of different ways.
Table 9.4 summarizes the risks and outcomes involved in both wet granulation
and melt granulation of SMOC materials.
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
395
Table 9.4 Risk assessment of primary stresses and impacts during granulation processing of SMOC
materials.
Wet
granulation
Process
Stresses
Wetting
Liquid
stress
Derivative
behaviors
Dissolution
Primary impacts
If hydrate exists, then hydration
will be the most probable phase
change
If hydrate does not exist,
polymorphic change from
metastable form to stable form
will be preferred
Drying
9.2.4
Mechanical
stress
Shearing/failure
Polymorphic transformation/
amorphization
Thermal
stress
Thermal
expansion,
recrystallization/
amorphization
All possible phase changes depend
on materials properties and drying
conditions
Consolidation of Organic Crystals
Tablets are the most commonly used dosage form in the world, owing to their
convenience to the patient, and the relatively low costs associated with mass
production. Tablets are solid composites formed by consolidation of powders
or granules through the application of stress by means of punches within a confined volume die. The resulting volume reduction allows formation of a compact that remains intact following stress removal, having formed strong
interparticulate interactions when surfaces are brought into intimate contact
under pressure. The compaction process is comprised of both a compression
and consolidation phase, as illustrated in Figure 9.16.
Particles experiencing relatively low compression stress initially respond by
rearrangement as the porosity of the powder bed is reduced by expulsion of
air pockets. Given a maximum packing density of 0.64 for monodisperse
spheres, it is clear that both PSD and particle morphology contribute to denser
rearrangements, as fine particles fill the voids between the coarser particles at
this stage. As rearrangement reaches a maximum packing density, increasing
compression stress results in strain responses that include fragmentation into
smaller particles, reversible elastic deformation, and irreversible plastic deformation (termed the compression phase in Figure 9.16) [123].
The ability of powder particles to undergo volume reduction with the application of pressure is termed “compressibility” [122, 124, 125] and is a key measure of how SMOC materials respond to this stage of 2 manufacturing. The
compression phase brings particle surfaces into very close proximity, facilitating
396
9 Secondary Processing of Organic Crystals
Increasing
pressure
Low pressure
Repacking
Pore
reduction
Initially filled die
Pressure
exceeding yield
strength
Compression
phase
Brittle fracture
(fragmentation)
High pressure
Compact
formation
Plastic flow
(deformation)
Interparticulate bond formation
(solid bridges/intermolecular
forces/mechanical interlocking)
Consolidation phase
Figure 9.16 Overview of the powder compaction process. Source: Adapted from
Haware [122].
the formation of interparticulate bonds under pressure. Bonding between particles is limited to solid bridges consisting of noncovalent intermolecular interactions between exposed surfaces on particles, and/or mechanical interlocking
in the case of dry powders. Given well-known distances and angles necessary for
the formation of these types of noncovalent interactions (e.g. hydrogen-bond
strength is maximized at a distance of 2.4 Å and angle of 180 between donor
and acceptor groups [126]), the necessary role of stress becomes apparent in its
ability to force surfaces this close together. Formation of these collective bonds
between particles is termed “consolidation,” and the ability of a powder to form
a compact having sufficient tensile strength to maintain its shape after the pressure has been relieved is called the “compactability” [122, 124, 125].
When the compaction stress is released, the materials will decompress to
some extent, first by in-die elastic expansion, which continues as compact relaxation following ejection from the die [122, 127]. Compact expansion is composed of both immediate elastic and time-dependent viscoelastic recoveries.
The in-die compact expansion is primarily characterized by rapid elastic recovery before the upper punch leaves the tablet surface. Although some fraction of
viscoelastic recovery can occur, it is expected to be minor at this stage. In contrast, out-of-die compact expansion is dominated by time-dependent viscoelastic recovery, which can continue for days, depending on the materials. The total
elastic recovery of the compact is the sum of its elastic and viscoelastic
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
recoveries [127–129], and the compact mechanical strength is a function of the
consolidation of particles during the compression phase versus the elastic relaxation (bond breakage) during the decompression phase. As would be expected,
particle consolidation and elastic relaxation are material-specific properties that
have the potential to respond differently to different compression process
parameters.
9.2.4.1
Materials Properties Contributing to Effective Consolidation
The majority of small-molecule drug substances, and many excipients, exist in
crystalline forms rather than as amorphous solids. As discussed previously, crystalline solids consist of regularly arranged molecules with long-range, 3D symmetry [130], while amorphous solids are comprised of molecules having shortrange ( 30–50 Å), aperiodic arrangements [131]. The internal arrangement of
molecules in a material determines its physical and mechanical properties, as
well as how they respond to secondary processing, formulation, and ultimately
final product performance [130]. The basic building block of a crystalline material is its unit cell, which contains the structural features and symmetry elements
needed to describe the crystal structure. Crystal growth results in regular repetition of these unit cells in three dimensions [130].
Unlike space groups typical of atomic crystals, SMOC solids are typically built
from anisotropic unit cells, where orientation and coordination of lattice bonds
are different in x-, y-, and z-directions. The internal structure of SMOC materials is typified by a large number of relatively weak intermolecular interactions
like van der Waals forces ( 0.5–2 kJ mol−1), stronger intermolecular interactions like hydrogen-bonding ( 30 kJ mol−1), and yet stronger intramolecular
and interionic interactions ( 150 kJ mol−1) [130]. Because intermolecular interactions are dependent on the separation distance and orientation of specific
molecules, it is not surprising that the formation of what Hartman and Perdok
referred to as “periodic bond chains” (PBC) should form in some directions, but
not others. As reviewed in Mullin [132], crystal growth optimizes the formation
of strong bonds in uninterrupted chains that form PBC in certain directions.
Consequently, mechanical compliance differs directionally within a crystal,
resisting deformation along these strongest bonded directions and yielding in
the least well-bonded directions.
Growth also requires symmetrical organization of typically asymmetric molecules. To maximize the energy of their interaction, high density packing
arrangements are favored, which was captured in the “close-packing theory”
proposed by Kitaigorodskii [2, 133]. According to his model, as a lattice forms
during nucleation, molecules approach one another in conformations and
orientations that maximize low energy attractive and repulsive interactions,
which dictates the packing density of the molecules in the resulting solid.
The closest-packed or most dense crystal forms possess the lowest free energy
and usually exhibits the greatest stability [2]. In metallic crystals, highly
397
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9 Secondary Processing of Organic Crystals
symmetric space groups allow spherical atoms to pack in hexagonal or cubic
packing arrangements. Despite asymmetrical shapes, it has been observed that
organic molecules pack in arrangements that range between 0.65 and 0.77 [134,
135]. Kitaigorodskii observed that, as a unit cell forms, molecules orient themselves to simultaneously maximize packing density and the formation of hydrogen bonds [134], which corresponds with observations of increasing in enthalpy
of fusion for crystals having greater packing densities [2]. As mentioned above,
lattice directions along with molecules that are most closely packed (and interactions are expected to be strongest) are expected to be more resistant to the
application of mechanical stress. It is important to note that in certain cases,
complex hydrogen-bonding patterns can cause less dense packing of a material,
where favorable bond distances necessitate greater intermolecular spacing than
would be predicted from the closest-packed geometrical arrangement (e.g. ice),
resulting in a thermodynamically stable arrangement despite less dense packing
[136, 137].
Collective consideration of how packing influences strong and weak intermolecular and interionic interactions in the crystal allows calculation of the lattice
energy (EL), also termed the crystal binding or cohesive energy. The EL can be
calculated by summing all the coulombic- and nonbonded van der Waals-type
interactions between a central molecule and all of the surrounding molecules
[138]. In solids comprised of charged and highly polar molecules, ion–ion contributions can significantly affect the overall crystal packing energy [139]. As the
value of EL increases, this suggests formation of a stronger and more stable crystal having a higher enthalpy of fusion. The impact of EL on consolidation behavior can be demonstrated by considering how the lattice differs in specific planes.
The attachment energy, EA, of a particular hkl plane represents the difference
between the EL and the slice energy, ES (Equation 9.14) [140]. In other words, ES
is the sum of the intraplanar interactions in a particular crystallographic plane,
while EA considers the interplanar interactions between the same hkl planes:
EA = EL − ES
9 14
Lattice energy calculations can be used to generate a predicted crystal morphology from the internal structure [42], which has been used to interpret
mechanical responses in terms of crystal structure.
Osborn et al. predicted slip planes in several SMOC, using EA calculations to
rank order the expected interplanar interactions associated with the particular
arrangements of the molecules in the crystal structures. For compounds, such as
aspirin, ibuprofen, and tolbutamide, one particular surface was found to have a
much smaller EA relative to others in the respective lattices, which was interpreted as the most likely slip/cleavage plane in the solid [138]. This makes sense
from a mechanical standpoint, given that plastic deformation of crystalline
solids occurs as a dislocation-mediated process, requiring propagation and
movement of linear defects on slip planes. Low EA planes suggest the least
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
resistance to dislocation movement, so solids having an unambiguous slip plane
are likely to exhibit plastic behavior. Likewise, cleavage, which occurs when
interplanar interactions are broken, resulting in crystal fracture, requires propagation of a crack as the result of an applied stress (see Equation 9.2). Planes
across which interplanar bonding is weakest provide the least resistance to crack
propagation and the most likely site of fragmentation.
Sun and Kiang [4] later reexamined the EA calculation approach to slip plane
prediction and found <50% successful slip plane prediction for a set of 14 SMOC
materials. Slip planes were visualized using 3D lattices simulated from the crystal structures. Slip planes were identified as those having the largest d-spacing,
with the greatest intraplanar molecular packing. EA calculations using various
force fields were completed similar to the methods used by Osborn et al. [138],
and the predicted slip planes were compared with those visually identified from
the crystal structures. It was generally observed that lattices having layered
structures, with widely spaced, open gaps between a particular set of planes,
normally resulted in a single, unambiguously low calculated EA that corresponded with that family of planes [4] (i.e. predictions and observations of slip
systems agreed with one another). As an example, the crystal structure of 2amino-5-nitropyrimidine, Form I is shown in Figure 9.17a. Visualization of
the 102 slip plane is obvious, with very weakly interacting, large d-spacing
planes most likely to be amenable to slip-mediated deformation. The authors
found that EA calculations based on the Dreiding force field confirmed this
as the weakest plane in the simulated lattice; however, the cvff and COMPASS
force fields, respectively, predicted that (020) and (011) were the likely slip
planes.
In contrast, slip planes identified by visualization failed to agree with those
predicted by EA calculation, using any force field for sulfamerazine Form II
(Figure 9.17b). Unlike the slip planes in 2-amino-5-nitropyrimidine Form I,
those in sulfamerazine Form II are characterized by a common motif in SMOC
materials: the herringbone plane (see also acetaminophen in Figure 9.2). In this
motif, the molecules adopt a conformation to optimize packing density, which
results in portions of molecules filling negative space across the planes. Packing
motifs such as the herringbone result in greater opportunity for interplanar
interactions and more resistance to slip. Sun and Kiang found that, among their
test set, EA calculations were most likely to predict slip planes other than those
visualized from the crystal structure, because these packing patterns result in
larger attachment energies, which may be less distinctive from other families
of planes in the crystal [4].
Even with the shortcomings of EA predictions of slip planes described above,
the approach has merit in predicting consolidation behavior. Sulfamerazine
Form I contains obvious slip planes, while sulfamerazine Form II does not. Sulfamerazine Form I shows better plasticity, compressibility, and tabletability than
sulfamerazine Form II [141]. Bandyopadhyay et al. used the crystal structure to
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9 Secondary Processing of Organic Crystals
(a)
2-Amino-5-nitropyrimidine Form I
(b)
Sulfamerazine Form II
Figure 9.17 Crystal structures for (a) Form I of 2-amino-5-nitropyrimidine (CCDC refcode
PUPBAD01) and (b) Form II of sulfamerazine (CCDC refcode SLFNMA01) obtained from
Cambridge Crystallographic Database [5]. In Sun and Kiang [4], slip planes identified by
visualization from the crystal structure and calculated using the EA method agreed for
PUPBAD01, while they disagreed for SLFNMA01.
identify the slip planes in L-lysine monohydrochloride 2H2O (LHP) and modeled the deformation behavior under uniaxial compression [142]. The z-plane
in LHP crystals has the lowest EA and acts as a cleavage plane during compaction. In a specific comparison between the x- and z-planes, LHP showed greater
plastic deformation and better compression and tableting properties relative to
the x-plane.
Sun and Grant demonstrated that orientation of the LHP slip plane relative to
the compressive load influenced compact properties. In their work, LHP was
grown in two distinct habits: prisms and plates; the latter of which was prone
to preferential orientation in tableting dies, which resulted in alignment of
the slip planes with the normal stress applied by the punches. In contrast,
the prisms tended to align in tablet dies with the slip planes perpendicular to
the compressive load, resulting in a much lower resolved shear stress on these
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
planes, allowing for less plastic deformation [143]. The observations for LHP
above are consistent with Schmid’s law for deformation by slip in single crystals,
which is shown in Equation (9.15):
τcrit = σ y cos θ cos λ
9 15
Accordingly, slip occurs by translation of dislocations in the slip direction
(SD) when the application of the yield stress, σ y, is resolved to a critical shear
stress, τcrit, on the slip plane. As shown in Figure 9.18a, the magnitude of the
shear stress in the slip plane depends on the orientation of the slip plane to
the normal load, where θ is the angle between the slip plane normal (SPN)
and the direction of the applied stress, while λ is the angle between the SD
(a)
(b)
τcrit
SPN
SD
θ
SPN
λ
SD
τ crit
Axial stress completely resolves on
slip plane; slip maximized
(c)
SPN
SD
τcrit = σY cos θ cos λ
Axial stress does not resolve to
shear on slip plane; slip minimized
Figure 9.18 (a) Orientation of slip plane normal (SPN) and slip direction (SD) to applied
compressive stress. Deformation occurs by slip, when the resolved shear stress on the
highlighted plane resolves to exceed a critical value (τcrit). (b) Example of slip planes
preferentially oriented with SD parallel to compressive axis. The entirety of the compressive
load is resolved on the slip plane, allowing for maximal dislocation motion and plastic
deformation. (c) Example of slip planes preferentially oriented perpendicular to compressive
load. With λ = 90 , no shear components of the load are resolved on the slip planes,
preventing deformation by slip. Source: (b) and (c) adapted from Ref. [143]. Reproduced with
permission of Elsevier.
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9 Secondary Processing of Organic Crystals
and the direction of the applied stress. When SD, SPN, and compressive axis are
all coplanar, Equation (9.15) can be rearranged as
σy =
2τcr
sin 2λ
9 16
Equation (9.16) confirms that when the SD is oriented closer to the compressive axis, more of the stress is resolved as a shear component, and yield is minimized, making dislocation movement in SD and deformation by slip more
likely. In contrast, when the compressive axis is perpendicular to the slip plane,
no stress is resolved in shear, maximizing the yield requirements, meaning that
the slip plane will not be active in this orientation.
Returning to the example of LHP, Sun and Grant obtained PXRD from compacts formed from the plate habit, which showed reduced diffraction attributable to (002), suggesting preferential orientation of these planes perpendicular
to the compact surface, in the same direction as the principal compressive axis
[143]. As illustrated in Figure 9.18b, such an orientation of the slip planes
entirely resolves the applied axial stress on the slip planes, parallel to SD, minimizing σ y and predicting maximal deformation. Sun and Grant also observed
that plates of LHP resulted in compacts having a higher tensile strength at comparable porosity, suggestive of greater interparticulate bond formation on compaction [143]. Essentially, increased plastic deformation due to slip created a
greater number of clean surfaces across which interparticulate bonds formed
when brought into close contact, resulting in stronger tablets. In contrast, compacts of the more isotropic LHP prisms showed substantial diffraction intensity
of the (002) plane, suggestive of preferential orientation of the slip planes perpendicular to the axial compressive load. As shown in Figure 9.18c, and
Equation (9.16) when λ is equal to 90 , the yield stress is maximized with no
resolved shear on (002). With these slip planes in LHP inactive during consolidation, fewer clean surfaces were formed, resulting in fewer interparticulate
bonds, consistent with the observation that LHP prisms form compacts having
lower tensile strengths at equivalent porosity, relative to LHP plates [143].
9.2.4.2 Structural and Molecular Properties Contributing to Effective
Consolidation
As discussed, the arrangement of molecules in a given solid dictates the
mechanical properties, which, in turn, influence the processability of SMOC
materials during 2 manufacturing. In contrast to crystalline materials, amorphous solids, which lack long-range order in molecular packing, are typically
less dense than their crystalline counterparts [2]. Mechanically, amorphous
solid materials have similar properties in x-, y-, and z-directions (i.e. spatial isotropy) and predominantly undergo plastic deformation [144, 145]. The influence
of long-range order in crystalline materials results in a greater diversity of
mechanical responses, including combining plastic deformation (e.g. for
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
microcrystalline cellulose or NaCl), brittle fracture or fragmentation (e.g. for
lactose monohydrate or dicalcium phosphate dihydrate), or elastic deformation
(e.g. for starch) [145–147]. As such, the crystal structure of pharmaceutical
materials offers valuable information to help tailor formulations intended for
consolidation, even at early development stages.
Various studies have been conducted to understand the different mechanical
properties of pharmaceutical materials based on data informed by the crystal
structure. For example, theophylline monohydrate is known to form compacts
having higher mechanical strength than those made from anhydrous theophylline, which is attributed to the greater number of hydrogen bonds available to
participate in interparticulate bond formation during consolidation [148]. Similarly, Sun et al. found that the monohydrate of 4-hydroxybenzoic acid exhibited
better plastic deformation than the anhydrous form, owing to the presence of
specifically coordinated water molecules in the crystal structure [149].
Haware et al. developed an approach to measure anisotropic crystal deformation using a new in situ compression stage housed in a powder X-ray diffractometer [150]. Both experimental measurements using single crystals and
ab initio computations using crystal structures allowed estimation of the anisotropic elastic moduli in the x-, y-, and z-planes of acetaminophen and aspirin.
The study showed a proportional relationship between changes in d-spacing
and fundamental strain. The y-plane of acetaminophen has a larger d-spacing
and lower elastic modulus than either the x- or z-planes. The x- and z-aspirin
planes were relatively easy to compress using the compression stage relative to
the y-plane, which is consistent with their relative calculated attachment energies. The experimentally measured anisotropic moduli showed good agreement
with the computationally calculated anisotropic moduli and demonstrated that
crystal structure information can be used to identify slip planes, attachment
energy, anisotropy moduli, and predominant planes that facilitate deformation.
This may be a useful approach in an early development stage, where limited
amount of material is available for the preformulation studies.
9.2.4.3
Macroscopic Properties Affecting Effective Consolidation
As mentioned previously, macroscopic properties of materials, such as PS, specific surface area, and particle morphology can affect the interparticulate bonding during powder compression. As a rule of thumb, powders consisting of
smaller particles will consolidate to form a tablet having a higher mechanical
strength, relative to compaction of larger particles of the same material. The
bonding, however, completely depends on the predominant deformation
behavior of the materials.
There are three types of general relationships, which can be observed between
the PS and tablet mechanical strength. Materials undergoing limited fragmentation (e.g. lactose) show increasing tablet tensile strength with reductions in PS.
Both α-lactose monohydrate and anhydrous α-lactose formed harder tablets
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with a commensurate decrease in their PS, attributable to corresponding
increases in the powder-specific surface area, and the increased number of
potential bonding sites between particles [151, 152]. In contrast, extensively fragmenting materials, such as dicalcium phosphate dihydrate or saccharose, form
compacts having tensile strengths that are essentially independent of the PS.
Alderborn and Nyström explained this relationship as the “masking” of PS differences before the actual compression event, owing to the extent to which particles fragment during compression [153]. Plastically deforming sodium chloride
showed an increase in tablet mechanical strength with increasing PS, which was
more evident when comparisons began from the lower PS range [154]. These
materials lose their tendency to plastically deform with large PS reductions
and may exhibit mechanical behavior characteristic of ductile materials [31].
Plastic deformation encourages interparticulate bond formation [155]; therefore, the bond strength between larger particles of plastic materials is expected
to be stronger relative to smaller particles [154]. In the case of sodium bicarbonate, another plastically deforming compound, tablet tensile strength was shown
to be relatively independent of the PS [156], indicating a complex relationship
between the initial PS of the materials and the tablet mechanical strength.
Similarly sized particles might differ with respect to their length, breadth,
thickness, and surface texture, potentially influencing the mechanical strength
of tablets from which they are formed. Lazarus and Lachman showed the formation of stronger tablets from large, irregular particles of potassium chloride
[157], while other studies showed that dendritic sodium chloride produced
stronger tablets relative to the cubic form, owing to its greater propensity for
fragmentation [158]. As discussed above, different morphologies of LHP
resulted in different compressibility, compactability, and tabletability of the
materials, which were explained in terms of the relative orientations and expression of slip planes critical to plastic deformation [143].
9.2.4.4 Compaction-induced Material Transformations
The mechanical stress used to consolidate SMOC can induce structural changes
in the materials during processing. These stress-induced phase changes likely
occur at individual contact points between the particles where localized shear
stresses may be extremely large. In general, high pressures are expected to elicit
transitions toward highly ordered and dense structures [159].
Compaction processes consolidate powders by densification, the main effect of
which is to reduce porosity under mechanical stress. Volume reduction of amorphous powders can narrow the density differences between amorphous and crystalline materials, which may also facilitate the intermolecular interactions necessary
for nucleation, increasing the probability of crystallization. The compression process does not transmit uniform stress throughout the powder bed, which can generate density gradients that influence both nucleation rates and subsequent
crystallization behavior. Accordingly, crystallization from an amorphous starting
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
material can result in a nonuniform distribution of phases within the final tablet
[160]. Such was the case for amorphous indomethacin when it was compressed
at different pressures [160]. Thakral et al. reported more extensive crystallization
when amorphous indomethacin when compressed at higher pressures, although
the extent of crystallization was higher along the radial surface of the tablets, owing
to high friction between the tablet surface and the die wall. This was confirmed
when lubrication with magnesium stearate was used to reduce the surface-die wall
friction that resulted in a pronounced decrease in the observed crystallization.
Compaction stresses have also been shown to partially or completely disrupt
the molecular order in a crystal structure, resulting either in a phase change or,
more rarely, induce a chemical transformation. Nogami et al. reported the polymorphic transformation of barbital [161], which exists in three different polymorphic forms. Barbital Form II underwent a gradual transformation into
Form I under pressure, with complete transformations occurring at stresses
greater than 254 MPa compression pressure.
Summers et al. reported a reduction of the transition temperature of both sulphathiazole and barbitone polymorphs due to application of stresses typical of
tablet compaction [162], which was attributed to the introduction of crystal dislocations and distortions at crystal boundaries. These observations are consistent with work by Tromans and Meech, who suggested that when the application
of stress results in accumulation of dislocations, the resulting free energy change
(ΔGd) can elicit a polymorphic change if it is equal to the free energy difference
between the two crystalline forms [43].
Additional transformations have been observed for the metastable Forms II
and III of phenylbutazone, which converted into stable Form IV during compaction [159]. Ghan and Lalla also reported a reduction of α-Indomethacin Tm on
application of the compression stress [163], which slowly approached that of
β-Indomethacin. In contrast, the Tm of β-Indomethacin did not change before
or after compression.
Kaneniwa et al. reported the reduction of cephalexin Form IV crystallinity
during compression [164], commensurate with a decrease in the dehydration
and decomposition temperatures following compression. In addition to physico-mechanical transformation, the crystallinity of the anticancer drug TAT59 was reduced, while the hydrolysis product DP-TAT-59 was increased with
increasing compression pressure [53].
The transformations of chlorpropamide during compaction have been studied extensively. Matsumoto et al. [165] reported that chlorpropamide Form
A and C both underwent transformation with reduction in crystallinity when
studied at varying compression energies and temperatures. Application of
11.1 × 103 J/kg of compression energy at 45 C resulted in conversion of
30.9% of Form A into 14% Form C, and 16.9% noncrystalline solid. When
the experiments were repeated using the same compression energy at 0 C,
however, only 16.4% of the Form A was converted into 6.2% Form C and
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10.2% noncrystalline solid. The authors suggested that the reduction in Form
A conversion at a lower temperature was due to a greater resistance to plastic
deformation by the material at 0 C. When Form C was compacted at 14.8 ×
103 J/kg, approximately 10.1% was converted into Form A, while 3.9% was converted to the noncrystalline solid at both 0 and 45 C. In contrast with Form A,
the authors described the deformability of Form C as temperature independent,
albeit less deformable than Form A.
These results are important because they suggest a mechanical basis for the
transformations of chlorpropamide polymorphs rather than a strictly temperature-driven phenomenon. Forms A and C are enantiotropically related, and
the common protocol for making phase pure Form C is to heat isothermally
at 110 C for approximately one hour. The observed transformation from
Form A to C might be suggested as a result of localized temperatures exceeding
the solid transition temperature, allowing thermodynamics to drive the conversion to the high-temperature stable Form C. The problem with this suggestion is
that the same localized temperature increase cannot explain the reverse conversion from C to A under similar conditions. Consider also the kinetics of the A–C
transformation at 110 C, which are orders of magnitude slower than the transformations observed during the timescale allowed by tableting, and that the
transformation kinetics from A to C are exceedingly slow at 60 C [166], which
is a temperature more typically estimated during consolidation [167].
Building on previous observations [165, 168–171], Wildfong et al. sought to
elucidate the mechanism underlying the interconversion between chlorpropamide Forms A and C. Using quantitative PXRD, it was shown that pure Form
A converted into Form C, when the compaction stress exceeded approximately
10.5 MPa. Likewise, pure Form C, converted into Form A under the same compressive load. The quantitative data showed that the extent of either conversion
increased with increasing pressure but reached a plateau as compacts were densified to their maximum solid fractions. Examination of the two crystal structures showed that Forms A and C have a common slip system, which
preserves the relative molecular positions, even as the transformation between
them occurs. Application of shear stresses during compaction initiated the
deformation responsible for lattice distortion, allowing for the simultaneous,
reversible conformational changes of molecule necessary to move from formto-form [172]. Such a transformation is different than nucleation from an amorphous intermediate. Instead, conformation, and slight changes in the molecular
mass centers (see Figure 9.19), results in facile conversion without the mobility
requirements needed for diffusion-based solid-state nucleation and growth
mechanisms. A collective shift of molecules on a common slip plane is consistent with the deformation-mediated transformation suggested above [165], in
that it occurs as a result of slip plane activation. The extent of transformation
in the work by Matsumoto et al. corresponded with the resistance to deformation, which in Wildfong et al. corresponds with the observation that the
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
Slip vector
Form A
Form C
Figure 9.19 Chlorpropamide enantiotropes, Form A and Form C. Transformation requires
conformational changes, facilitated by slip on a common plane. The figures shown above
each conformer view each crystal structure oriented with its slip plane parallel to the page
(slip vector indicated). Spheres represent mass centers for the molecules and illustrate a
collective displacement in the slip plane as the molecules conform during deformation.
conversion reaches a limiting plateau when the maximum solid fraction is
reached, and shear-based deformation in response to mechanical stress stops.
A shear-based mechanism is also supported in the observation that the Form
A
Form C interconversion does not occur under purely hydrostatic loads,
where the material is not subject to any shear stress [172].
9.2.4.5
Compression Temperature and Material Transformation
The friction between moving particles and machine tooling can raise the overall
powder temperature by more than 30 C above ambient temperature during
high-speed tableting operations [167]. Consequently, the material comprising
pharmaceutical tablets experiences a peak transient temperature at its center,
and at the interface between the powder and die-wall, where friction is at a maximum. This temperature increase is the result of the inability of the compact to
conduct heat into the cooler stainless steel tooling, owing to a combination of
very short compaction durations, and the relatively low thermal conductivity of
SMOC materials [173, 174].
Picker-Freyer and Schmidt studied the sensitivity of various excipients for compression-induced temperature changes occurring within tablets [175]. The
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authors reported that the tablet temperatures increased with increasing compression speed, the extent to which was dependent on the materials. Based on the
SMOC materials studied, tablet temperatures were measured in the following rank
order: microcrystalline cellulose > spray-dried lactose > pregelatinized starch >
dicalcium phosphate dihydrate. Out of these materials, the MCC FT-Raman spectra showed a partial change from cellulose I to cellulose II [176]. The FT-Raman
spectra of spray-dried lactose showed doublets changing to singlet bands at wavenumbers of 440, 1140, 1330, and 2980 cm−1, while one band at 2900 cm−1 disappeared entirely. Pregelatinized starch FT-Raman spectra showed an increase in
band intensity at wavenumbers of 290, 510, 650–680, and 1040–1080 cm−1 with
the loss of one band at 3250 cm−1. On the other hand, dicalcium phosphate dihydrate showed no spectral differences after tableting. The reasons for the observed
spectral changes for spray-dried lactose and pregelatinized starch are not yet
known; however, Roos [177] reported the changes in the food quality.
Maarschalk et al. reported on the impact of the compression temperature on
consolidation of methyl methacrylate copolymerized with lauryl methacrylate at
different ratios [178]. Poly-(methyl methacrylate-co-lauryl methacrylate) copolymers showed different properties 20 K below and above their respective Tg.
Young’s moduli and yield strength values decreased dramatically when the compression temperature was approximately equal to the polymer Tg, whereas
stored energy values increased exponentially when the compaction temperature
was 20 K above Tg, indicating the large stress relaxation propensity of the materials in the rubbery state. The authors also reported tablet capping after compaction of polymers at T > Tg, demonstrating the completely different
mechanical properties of materials in the glassy state (T < Tg) versus the rubbery
state (T > Tg) and the impact these properties have on the resulting compacts
[179]. In another study, Otsuka et al. reported increased plastic deformation
of chlorpropamide Form A at 45 C as the primary reason for stronger tablets
[169]. York et al. studied the compression properties of α-lactose, chloroquine
diphosphate, and calcium carbonate at various temperatures [180], and
although this study did not report a distinct phase change associated with
the materials, the studies suggested that increases in the tablet mechanical
strength may have been due to localized melting of the materials at interparticulate contact points under pressure, which was hypothesized to be responsible
for the formation of solid bonds and stronger tablets.
9.2.5 Data Management Approaches
A fundamental understanding of the critical quality attributes (CQAs) of pharmaceutical materials, the critical steps of 2 manufacturing processes, and their
interplay is important to develop optimal formulations in early development.
This is also necessary to understand and address formulation problems occurring in late stage development or to troubleshoot routine manufacturing
9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products
problems. It is also necessary in accordance with regulatory recommendations
per the International Conference of Harmonization (ICH) Q8 or “Process Analytical Technology” (PAT) Guidance issued by the United States Food and Drug
Administration [181, 182].
Material CQAs or materials properties that influence formulation properties
can originate at the molecular and/or macroscopic levels. Likewise, formulation
properties are influenced by critical process parameters. 2 manufacturing, as
described herein, consists of several unit operations, which combine into a complex process by which a final drug product is prepared. Each operation is sensitive
to both the collective materials properties of blends, and the process parameters,
exemplified by the complexity of the powder compaction process. While the
deformation behavior of single materials is described above, tableting has been
shown to be very sensitive to the consolidation properties of blends of materials,
blend hygroscopicity, or the response of a formulation to the addition of other
materials such as lubricants [147]. These varied material responses also make
the compression process sensitive to operating parameters including tooling,
machine speed, compaction pressure, etc. [122]. Therefore, understanding the
overall picture of how materials and processes combine to make a final product
having desirable quality and performance attributes is imperative, albeit daunting.
Various analytical tools such as scanning electron microscopy, powder laser
diffraction, PXRD, FTIR, sorption analysis, DSC, TGA, solid-state NMR, and
others are useful to evaluate the molecular and macroscopic properties of materials [183–186]. State-of-the-art processing equipment, such as an instrumented tablet press or compaction simulators, can be employed to understand and
monitor the specific unit operations. Individual unit operations can also be
monitored by coupling processing equipment with spectroscopic tools, such
as NIR or Raman spectroscopy. Such PATs can be very useful, although it is also
necessary to carefully select a viable experimental setup in order to decode the
spectral data in ways that can inform the complex relationships between materials and their processing environments. Statistical design of experiments (DoE)
has been shown to be useful tools for this purpose, by allowing the maximum
amount of information to be captured with the minimum number of experiments. Such an approach does, however, impose a tremendous challenge to
the preformulation or formulation scientist owing to the generation of huge
datasets containing subtle information. It is important to assemble, obtain,
and model meaningful information from these data, which can be utilized to
understand and monitor the pharmaceutical processes in order to predict desirable end-product outcomes. To address this need, Haware et al. developed the
DM3 approach (Figure 9.20) [187], which evaluated the interplay between the
molecular and macroscopic materials properties and process parameters by
combining traditional DoE and multivariate analysis tools. The DM3 approach
was utilized to evaluate the impact of properties such as powder flow and tablet
mechanical strength for a model coprocessed excipient (MicroceLac® 100)
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9 Secondary Processing of Organic Crystals
Materials properties
(Macroscopic level)
Particle size (d50)
Particle morphology
Specific surface area
Basic flow energy
(Molecular level)
Sorption–desorption isotherm
relaxation time (ssNMR)
% Order
% Moisture
Dehydration temperature
Dehydration ethalpy(∆dh)
Anhydrate Ttr
Anhydrate transition enthalpy (∆at)
(M1)
Design of
experiments
(D)
Critical product attributes
Basic flow energy
Tablet mechanical strength
Disintegration time
Lubricant sensitivity ratio
Manufacturing factors
Lubricant fraction
Blending time
(M2)
Multivariate analysis
(M3)
DM3 approach
Figure 9.20 The DM3 approach of pharmaceutical process outcome analysis. Source:
Adapted from Haware et al. [188]. Reproduced with permission of Elsevier.
stored at different conditions [187]. Dave et al. used this same approach to
understand how different grades of starches impacted their tabletability [186].
As mentioned above, advanced analytical tools such as PXRD, NIR, FTIR, or
Raman spectroscopy are utilized to characterize and monitor pharmaceutical
processes, intermediates, and products [183–185]. These analytical techniques
generate large data matrices, which are typically complex and difficult to interpret, requiring that end users have an appropriate method for data management
in order to extract and model the information needed for subsequent predictions of process outcomes. These tools also pose another obstacle, in the sense
that a single tool might not be appropriate for all measurements. As an example,
FTIR might not be ideal for use with heterogeneous, multicomponent, and
solid-state pharmaceutical mixtures [189], while PXRD is far more suited to
structural characterization rather than chemical interrogation of the single or
multicomponent systems. To this end, the individual dataset from each technique contains different kinds of information.
9.3 Summary and Concluding Remarks
Different datasets can be combined to improve the predictive efficiency of the
model relative to individual treatments, using a technique known as “data fusion,”
which facilitates the faultless integration of information from various sources to
develop a single model or decision. Haware et al. used a data fusion approach to
characterize and quantify multicomponent, pharmaceutical samples of aspirin,
acetaminophen, caffeine, and ibuprofen using FTIR and PXRD [189]. The calibration dataset for these mixtures was developed using a four-component
simplex-centroid experimental design. The authors used multivariate methods
like principal component analysis (PCA) and partial least square regression
(PLS regression) for FTIR and PXRD data integration. Calibration models were
developed with fused preprocessed data (FDP) and fusion of principal component
scores (FPCS) of the data obtained with FTIR and PXRD. The authors reported
that a PLS model developed with FPCS showed better prediction accuracy than
FDP-based calibration model. The improvement in the prediction accuracy of the
FPCS-based calibration model may be attributed to the use of PCA as a preprocessing tool, enabling both noise removal and data reduction.
9.3
Summary and Concluding Remarks
In this chapter, we have attempted to link the fundamental understanding of the
properties of small-molecule organic crystalline solids to the prediction, or at
least anticipation, of the possible impacts of 2 processing stresses on these
properties. The impact of such materials properties on dosage form performance may be desired or undesired; however, their prediction and/or control
requires understanding of both the principles treated in the previous chapters
as well as the nature and duration of the processing stresses contributed by each
unit operation covered in this chapter. Once elucidated, the control of conditions to generate the desired solid state requires either real-time monitoring
of the process with feedback control or such a robust process design and design
space that traditional testing is statistically sufficient to insure product quality
[181]. This is also in line with the ICH Q6 guidance [190] that assumes that specifications for control of product quality are established prior to going into the
clinic for phase or biological studies. Variations in clinical response can, therefore, be attributed to physiologic variations as opposed to a conflation of clinical
and pharmaceutical variability.
9.3.1
Development History
A proper product development history is required for the majority of FDA filings and should be a part of all development projects. This must include the
demonstration of the understanding and control of the phenomena discussed
in this chapter. As in any scientific investigation, the history will typically be
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developed by a combination of prior knowledge in the form of vetted literature
and institutional document knowledge, as well as data and understanding generated from new investigation. A hierarchical approach to incorporating the
physicochemical properties of SMOC crystalline APIs is shown in Figure 9.4
in the introduction. However, this has to be populated with subsections that
reflect the specific dosage form, materials properties, and processes intended
for use. This is aided by the decision trees in ICH Q6 and elsewhere, which
can serve to help organize the analytical approach to elucidating the properties
of the crystalline APIs.
9.3.2 Risk Assessment
The potential processing-induced transformation for each solid form and the
associated processing stress is illustrated in Figure 9.3 (and exemplified
throughout the chapter). This, combined with the earlier chapters in this volume, completes the underpinnings for risk assessment of what events are most
probable and what is the impact on quality and the likelihood of detection, i.e. a
risk classification and risk priority that is in accordance with current regulation
and guidance (ICH Q9 [191]). Risk assessment helps in designing the development project and provides metrics as the project proceeds to know when quality
goals have been achieved. Figure 9.3 is an example of a general risk assessment
tool appropriate for the use in designing a development project where the processing stressed discussed in this chapter are in effect. As a project progresses,
the level of risk and risk reduction/remediation achieved during development
and is captured in expanded versions of the table, all of which are captured
in the development report.
The combination of a proper development history and risk assessment to generate a rigorous knowledge base goes a long way to ensuring the success of a
product development project and while embodying the principles of QbD.
As shown in this chapter, this process rests in large measure on understanding
the materials properties and response to processing stress of SMOCs.
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10
Chemical Stability and Reaction
Alessandra Mattei1 and Tonglei Li 2
1
2
AbbVie Inc., North Chicago, IL, USA
Department of Industrial and Physical Pharmacy, Purdue University, West Lafayette, IN, USA
10.1
Introduction
Stability of pharmaceuticals refers to the capacity of a given drug substance or a
formulated product to remain within the established specifications of identity,
potency, and purity throughout its shelf life. It is the extent to which a product
retains within specified limits the same properties and characteristics throughout its period of storage and use. During manufacturing, processing, and storage, a drug substance can be exposed to conditions that can have significant
effects on its chemical and physical integrity.
Drug substances can undergo chemical and/or physical degradation, as
depicted in Figure 10.1. Chemical reactivity can be defined as any process involving modifications of the drug molecule by covalent bond cleavage or formation
that generates new chemical entities. Physical reactivity refers to any changes of
the microscopic physical state of pharmaceuticals, including conversion of the
amorphous drug substance to its more thermodynamically stable crystalline
state over time, polymorphic transformations resulting from variations in temperature and humidity or extended storage, and changes in crystal habit during
storage. Presented in Chapter 5 of this book is a systematic and comprehensive
review of polymorphism and consequent phase transitions. This chapter will be
focused on the chemical stability of drug substances in the solid state. It is
appropriate to preface that this chapter contains references to physical transformations, which are sometimes associated with the mechanism of chemical reactions involving solids, because physical changes can exert significant effects on
concurrent or subsequent chemical processes.
Pharmaceutical Crystals: Science and Engineering, First Edition.
Edited by Tonglei Li and Alessandra Mattei.
© 2019 John Wiley & Sons, Inc. Published 2019 by John Wiley & Sons, Inc.
428
10 Chemical Stability and Reaction
Degradation of drug
substance
Chemical reactivity
Physical reactivity
Photolysis
Crystallization of
amorphous
Thermolysis
Crystal growth
Mechanochemistry
Moisture adsorption
Hydrolysis
Transitions in crystalline
state
Oxidation
Polymorphic
transformations
Loss of solvent
Figure 10.1 Categories of drug degradation and examples of degradation mechanisms.
The chemical stability of a drug substance is of crucial importance.
A marketable drug must be stable under a variety of conditions, including
low or high temperature and relative humidity. Chemical instability of pharmaceuticals results in altered therapeutic efficacy and toxicological effects. Knowledge of the conditions that lead to degradation of the parent compound can help
define appropriate controls during manufacturing, processing, and product
storage.
A wide range of solid-state reactions have been studied. Examples of solidstate reactions in molecular organic crystals were reported in the nineteenth
century, including dimerization, polymerization, cis–trans isomerization, and
phase transition (i.e. polymorphic transformations) [1–4]. The way in which
reactions occur in the solid state of organic compounds has long been of interest. On one hand, this interest has arisen from the potential utilization of the
limited motion available to the reacting molecules in the solid state toward
the synthesis of novel materials [5]. On the other hand, attention has been
driven by the aim of probing the reaction mechanisms. Indeed, the range of
topics investigated includes the analysis of the influence of the structure on
10.2 Overview of Organic Solid-state Reactions
the organic solid-state reaction process [1], the identification of small changes in
molecular packing and their effect on the onset of photoinduced reactions [6],
and the control of crystal morphology by the addition of tailor-made impurities
[7]. However, solid-state reaction mechanisms can be challenging to understand, as similar mechanisms to those applied to the reactions in gas or solutions
have sometimes been inadequate. A distinguishing characteristic of solids is
their structure, specifically the local structure associated with the reacting species in the crystalline state. Thus, it is not surprising that most studies on
organic solid-state reactions have been focused on X-ray structural analysis
of reactant and product crystals. The rapid progress of single-crystal X-ray diffraction and spectroscopic techniques made it possible to understand and
explain the dynamic process of a reaction in a crystal.
This chapter examines chemical reactivity as it pertains to drug substances
mainly in the crystalline state. Pathways and mechanisms of solid-state reactions, as well as various examples of solid-state reactions in pharmaceutical
applications, are reviewed. A general account, including theories and models
of chemical kinetics in solution and solid state, is provided. Factors that affect
the rate of chemical reactions are then discussed. Finally, approaches to mitigate
chemical reactions and/or stabilize drug substances are presented.
10.2
Overview of Organic Solid-state Reactions
Organic reactions in the solid state occur more efficiently and selectively than
those in solution, because molecules in organic crystals are arranged tightly and
regularly. Solid-state reactions have several distinct features compared with
reactions in solution. Benefits of conducting chemical organic reactions in
the solid state include the high stereochemical control of reactivity and the formation of unique products that may be otherwise inaccessible in solution [8]. In
solution, molecules exist as a mixture of rapidly interconverting conformational
isomers, resulting in the formation of coexisting different stereoisomers, thus
compromising selectivity. Organic solid-state reactions often afford stereochemical products in quantitative yield [9]. In addition, solid-state reactions
are namely solvent-free reactions and thus are particularly advantageous from
the viewpoint of green and sustainable chemistry [10]. This has resulted in
major changes in the way synthetic chemists develop processes.
The process of controlling reactivity in molecular crystalline solids relies
upon weak intermolecular interactions to organize reactant molecules into
suitable positions for the reaction [11, 12]. In such a case, the course and outcome of a reaction is established by the mutual arrangement of reactant molecules in the crystal. Weak intermolecular interactions have been exploited to
build supramolecular assemblies of unsaturated substrates that participate in
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10 Chemical Stability and Reaction
stereoselective photodimerizations. Particularly good examples of crystal engineering [11] and the related supramolecular chemistry [13] are offered by halogen substitution. Halogen atoms attached to an aromatic ring possess the
ability to steer a molecule such that it adopts a structure wherein neighboring
olefins are photoreactive. As a result of the electro-withdrawing nature of the
halogen atoms and the consequent favorable electronic attraction between electron-poor and electron-rich aromatic rings, halogen bonding and/or π–π interactions are favored, thus enabling a better offset of the aromatic rings [12, 14].
Strategies including π–π stacking, template-oriented hydrogen bonding [15],
and coordination complexes [16] have all been employed to induce a welldefined orientation of organic molecules in crystalline materials. These clever
approaches ultimately provide opportunities to give rise to the distinguished
stereo- and regiochemical selectivity in the solid state.
The combination of principles of organic solid-state chemistry and
supramolecular assembly of bifunctional building blocks has paved the way
for template-assisted solid-state reactions. The method employs templates that
juxtapose suitably functionalized olefins for intermolecular photodimerizations. A template molecule displays two functional groups that serve as hydrogen bonding donors and are strategically positioned in such a way to bring two
substrates into close proximity [12, 15, 1