List of Contributors xiii Preface xv 1 Crystallography 1Susan M. Reutzel-Edens and Peter Müller 1.1 Introduction 1 1.2 History 6 1.3 Symmetry 7 1.3.1 Symmetry in Two Dimensions 7 1.3.2 Symmetry and Translation 11 1.3.3 Symmetry in Three Dimensions 12 1.3.4 Metric Symmetry of the Crystal Lattice 13 1.3.5 Conventions and Symbols 14 1.3.6 Fractional Coordinates 15 1.3.7 Symmetry in Reciprocal Space 15 1.4 Principles of X-ray Diffraction 17 1.4.1 Bragg’s Law 17 1.4.2 Diffraction Geometry 19 1.4.3 Ewald Construction 19 1.4.4 Structure Factors 21 1.4.5 Statistical Intensity Distribution 22 1.4.6 Data Collection 23 1.5 Structure Determination 24 1.5.1 Space Group Determination 24 1.5.2 Phase Problem and Structure Solution 25 1.5.3 Structure Refinement 28 1.5.3.1 Resonant Scattering and Absolute Structure 32 1.6 Powder Methods 33 1.6.1 Powder Diffraction 34 1.6.2 NMR Crystallography 35 1.7 Crystal Structure Prediction 39 1.8 Crystallographic Databases 41 1.9 Conclusions 42 References 43 2 Nucleation 47Junbo Gong and Weiwei Tang 2.1 Introduction 47 2.2 Classical Nucleation Theory 48 2.2.1 Thermodynamics 48 2.2.2 Kinetics of Nucleation 51 2.2.3 Metastable Zone 53 2.2.4 Induction Time 58 2.2.5 Heterogeneous Nucleation 60 2.3 Nonclassical Nucleation 63 2.3.1 Two-Step Mechanism 63 2.3.2 Prenucleation Cluster Pathway 66 2.4 Application of Primary Nucleation 66 2.4.1 Understanding and Control of Polymorphism 66 2.4.2 Liquid–Liquid Phase Separation 71 2.5 Secondary Nucleation 73 2.5.1 Origin from Solution 74 2.5.2 Origin from Crystals 75 2.5.3 Kinetics 76 2.5.4 Application to Continuous Crystallization 76 2.5.5 Crystal Size Distribution 79 2.5.6 Seeding 80 2.6 Summary 81 References 82 3 Solid-state Characterization Techniques 89Ann Newman and Robert Wenslow 3.1 Introduction 89 3.2 Techniques 90 3.2.1 X-ray Powder Diffraction (XRPD) 90 3.2.2 Thermal Methods 94 3.2.2.1 Differential Scanning Calorimetry 94 3.2.2.2 Thermogravimetric Analysis (TGA) 95 3.2.3 Spectroscopy 97 3.2.3.1 Infrared (IR) 97 3.2.3.2 Raman Spectroscopy 99 3.2.3.3 Solid-state Nuclear Magnetic Resonance (SSNMR) 101 3.2.4 Water Sorption 105 3.2.5 Microscopy 106 3.3 Case Study LY334370 Hydrochloride (HCl) 109 3.4 Summary 114 References 114 4 Intermolecular Interactions and Computational Modeling 123Alessandra Mattei and Tonglei Li 4.1 Introduction 123 4.2 Foundation of Intermolecular Interactions 124 4.2.1 Electrostatic Interactions 125 4.2.2 van der Waals Interactions 126 4.2.3 Hydrogen-bonding Interactions 127 4.2.4 π–π Interactions 129 4.3 Intermolecular Interactions in Organic Crystals 130 4.3.1 Approaches to Crystal Packing Description 130 4.3.2 Impact of Intermolecular Interactions on Crystal Packing 136 4.3.3 Impact of Intermolecular Interactions on Crystal Properties 138 4.4 Techniques for Intermolecular Interactions Evaluation 140 4.4.1 Crystallography 140 4.4.2 Spectroscopy 141 4.4.3 Computational Methods 142 4.4.3.1 Lattice Energy 144 4.4.3.2 Interaction Energy of Molecular Pairs from Crystal Structures 147 4.5 Advances in Understanding Intermolecular Interactions 149 4.5.1 Crystal Structure Prediction 150 4.5.2 Electronic Structural Analysis 152 References 160 5 Polymorphism and Phase Transitions 169Haichen Nie and Stephen R. Byrn 5.1 Concepts and Overview 169 5.2 Thermodynamic Principles of Polymorphic Systems 175 5.2.1 Monotropy and Enantiotropy 176 5.2.2 Phase Rule 179 5.2.3 Phase Diagrams 179 5.2.4 Phase Stability Rule 182 5.2.4.1 Heat of Transition Rule 182 5.2.4.2 Heat of Fusion Rule 182 5.2.4.3 Entropy of Fusion Rule 183 5.2.4.4 Heat Capacity Rule 183 5.2.4.5 Density Rule 183 5.2.4.6 Infrared Rule 183 5.2.5 Crystallization of Polymorphs 184 5.2.5.1 Ostwald’s Rule of Stages 184 5.2.5.2 Nucleation 184 5.3 Stabilities and Phase Transition 189 5.3.1 Thermodynamic Stability 189 5.3.2 Chemical Stability 189 5.3.3 Polymorphic Interconversions of Pharmaceuticals 192 5.3.3.1 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 223Gislaine Kuminek, Katie L. Cavanagh, and Naír Rodríguez-Hornedo 6.1 Introduction 223 6.2 Structural and Thermodynamic Properties 224 6.2.1 Structural Properties 224 6.2.2 Thermodynamic Properties 226 6.2.2.1 Cocrystal Ksp and Solubility 226 6.2.2.2 Transition Points 229 6.2.2.3 Supersaturation Index Diagrams 231 6.2.3 A Word of Caution About Cmax Obtained from Kinetic Studies 232 6.3 Determination of Cocrystal Thermodynamic Stability and Supersaturation Index 234 6.3.1 Keu Measurement and Relationships Between Ksp, SCC, and SA 234 6.3.2 Cocrystal Solubility and Ksp 241 6.3.3 Cocrystal Supersaturation Index and Drug Solubilization 243 6.4 What Phase Solubility Diagrams Reveal 246 6.5 Cocrystal Discovery and Formation 249 6.5.1 Molecular Interactions That Play an Important Role in Cocrystal Discovery 249 6.5.2 Thermodynamics of Cocrystal Formation Provide Valuable Insight into the Conditions Where Cocrystals May Form 251 6.6 Cocrystal Solubility Dependence on Ionization and Solubilization of Cocrystal Components 253 6.6.1 Mathematical Forms of Cocrystal Solubility and Stability 253 6.6.2 General Solubility Expressions in Terms of the Sum of Equilibrium Concentrations 257 6.6.3 Applications 258 6.7 Conclusions and Outlook 265 References 265 7 Mechanical Properties 273Changquan Calvin Sun 7.1 Introduction 273 7.1.1 Importance of Mechanical Properties in Pharmaceutical Manufacturing 273 7.1.2 Basic Concepts Related to Mechanical Properties 274 7.1.2.1 Stress, Strain, and Poisson’s Ratio 274 7.1.2.2 Elasticity, Plasticity, and Brittleness 276 7.1.2.3 Classification of Mechanical Response 277 7.2 Characterization of Mechanical Properties 278 7.2.1 Experimental Techniques 278 7.2.1.1 Single Crystals 278 7.2.1.2 Bulk Powders 281 7.2.1.3 Tablet Mechanical Properties 282 7.3 Structure–Property Relationship 284 7.3.1 Anisotropy of Organic Crystals 284 7.3.2 Crystal Plasticity, Elasticity, and Fracture 286 7.3.3 Role of Dislocation on Mechanical Properties 287 7.3.4 Effects of Crystal Size and Shape on Mechanical Behavior 289 7.4 Conclusion and Future Outlook 290 References 291 8 Primary Processing of Organic Crystals 297Peter L.D. Wildfong, Rahul V. Haware, Ting Xu, and Kenneth R. Morris 8.1 Introduction 297 8.1.1 Solid Form 297 8.1.2 Morphology 298 8.2 Primary Manufacturing: Processing Materials to Yield Drug Substance 300 8.2.1 Crystallization (Solidification Processing) 301 8.2.1.1 Solvent Power 303 8.2.1.2 Solvent Classification 305 8.2.1.3 Batch Crystallization 307 8.2.1.4 Continuous Crystallization 308 8.2.2 Filtration and Washing 309 8.2.3 Drying (Removal of Crystallization Solvent) 313 8.2.4 Preliminary Particle Sizing 315 8.3 Challenges During Solidification Processing 319 8.3.1 Polymorphism 320 8.3.1.1 Cooling Crystallization 322 8.3.1.2 Solvent Selection 325 8.3.1.3 Antisolvent Crystallization 328 8.3.1.4 Selective Crystallization Using Additives 328 8.3.2 Hydrate and Organic Solvate Formation 329 8.3.2.1 Hydrate Formation 329 8.3.2.2 Organic Solvate Formation 335 8.3.3 Solvent-mediated Transformations (SMTs) 337 8.3.4 Morphology/Habit Control 342 8.3.4.1 Predicting Solvent Effects on Crystal Habit 343 8.3.4.2 Influence of Morphology on Surface Wetting 346 8.3.5 Crystallization Process Control 349 8.4 Summary and Concluding Remarks 350 References 351 9 Secondary Processing of Organic Crystals 361Peter L.D. Wildfong, Rahul V. Haware, Ting Xu, and Kenneth R. Morris 9.1 Introduction 361 9.1.1 Structure and Symmetry 361 9.1.2 Process-induced Transformations (PITs) in 2 Manufacturing 362 9.2 Secondary Manufacturing–Processing Materials to Yield Drug Products 365 9.2.1 Milling of Organic Crystals 366 9.2.1.1 Materials Properties Influencing Milling 366 9.2.1.2 Physical Transformations Associated with Milling 371 9.2.1.3 Chemical Transformations Associated with Milling 375 9.2.2 Pharmaceutical Blending 378 9.2.3 Granulation of Pharmaceutical Materials 382 9.2.3.1 Wet Granulation 384 9.2.3.2 Potential Transformations During Wet Granulation 385 9.2.3.3 Hydration and Dehydration 385 9.2.3.4 Solvent-mediated Transformations (SMT) 388 9.2.3.5 Polymorphic Transitions During Granulation 390 9.2.3.6 Salt Breaking 392 9.2.3.7 Formulation Considerations in Wet Granulation 392 9.2.3.8 Risk Assessment and Summary 394 9.2.4 Consolidation of Organic Crystals 395 9.2.4.1 Materials Properties Contributing to Effective Consolidation 397 9.2.4.2 Structural and Molecular Properties Contributing to Effective Consolidation 402 9.2.4.3 Macroscopic Properties Affecting Effective Consolidation 403 9.2.4.4 Compaction-induced Material Transformations 404 9.2.4.5 Compression Temperature and Material Transformation 407 9.2.5 Data Management Approaches 408 9.3 Summary and Concluding Remarks 411 9.3.1 Development History 411 9.3.2 Risk Assessment 412 References 412 10 Chemical Stability and Reaction 427Alessandra Mattei and Tonglei Li 10.1 Introduction 427 10.2 Overview of Organic Solid-state Reactions 429 10.2.1 Photochemical Reactions 431 10.2.2 Thermal Reactions 432 10.2.3 Mechanochemical Reactions 433 10.2.4 Hydrolysis Reactions 434 10.2.5 Oxidative Reactions 434 10.3 Mechanisms of Organic Solid-state Reactions 436 10.3.1 General Theoretical Concepts 436 10.3.2 Crystal Packing Effects on the Course of Organic Solid-state Reactions 438 10.3.2.1 Perfect Crystals and Topochemical Control of Organic Solid-state Reactions 438 10.3.2.2 Crystal Defects and Nontopochemical Control of Organic Solid-state Reactions 440 10.4 Kinetics of Chemical Reactions: From Homogeneous to Heterogeneous Systems 445 10.4.1 Fundamental Principles of Chemical Kinetics 445 10.4.2 Solid-state Reaction Kinetics 446 10.5 Factors Affecting Chemical Stability 448 10.5.1 Moisture 448 10.5.2 Temperature 448 10.5.3 Pharmaceutical Processing 450 10.6 Strategies to Prevent Chemical Reactions 452 10.6.1 Formulation-related Approaches 453 10.6.2 Prodrugs 454 References 455 11 Crystalline Nanoparticles 463Yi Lu, Wei Wu, and Tonglei Li 11.1 Introduction 463 11.2 Top-down Technology 467 11.2.1 Media Milling (MM) 467 11.2.2 High-pressure Homogenization (HPH) 468 11.3 Bottom-up Technology 471 11.3.1 Precipitation by Solvent–Antisolvent Mixing 471 11.3.1.1 Sonoprecipitation 473 11.3.1.2 CIJP 473 11.3.1.3 HGCP 476 11.3.2 Supercritical Fluid Techniques 476 11.3.2.1 RESS 478 11.3.2.2 SAS 479 11.3.3 Precipitation by Removal of Solvent 479 11.3.3.1 SFL 479 11.3.3.2 CCDF 479 11.4 Nanoparticle Stabilization 480 11.5 Applications 482 11.5.1 Oral Drug Delivery 482 11.5.2 Parenteral Drug Delivery 484 11.5.3 Pulmonary Drug Delivery 485 11.5.4 Ocular Drug Delivery 486 11.5.5 Dermal Drug Delivery 486 11.6 Characterization of Crystalline Nanoparticles 487 11.6.1 Particle Size and Size Distribution 487 11.6.2 Surface Charge 487 11.6.3 Morphology 491 11.6.4 Crystallinity 491 11.6.5 Dissolution 491 References 492 Index 503

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