Precision crystallization : theory and practice of controlling crystal size

Despite the fact that crystals make up an estimated 80% of chemical and pharmaceutical products, few resources exist that provide practical guidance on achieving precision control of their size and size distribution. Based on a model developed by the author and his colleagues, Precision Crystallization: Theory and Practice of Controlling Crystal Size presents scientists and product engineers with the tools to control crystal nucleation, enabling them to ultimately control crystal size and size distribution for batch and continuous crystallizations.

At the cutting edge of crystallization science and technology, this volume presents information never before available. Introducing the Balanced Nucleation and Growth (BNG) model, the book demonstrates how the results of the nucleation process are quantitatively related to practical experimental control values such as:

reaction addition rate crystal solubility temperature residence time (continuous crystallizations) the effect of ripening agents (crystal supersizing) during nucleation the effect of crystal growth restrainers (crystal nanosizing) during nucleation control of renucleation

The author shows how the BNG theory predicts previously unknown phenomena and also how it corrects erroneous perceptions of the importance of reaction volume on the outcome of crystal nucleation. Going above and beyond classical nucleation theories which rely to a large extent on guesswork, the BNG model gives precise guidance to scientists working in a range of critical areas, leading to promising implications for research, quality control, product development, production processes, pilot plant operations, and manufacturing.

Author Notes

Ingo H. Leubner received a PhD in physical chemistry from the Technical University in Munich, Germany, where he continued his studies with a postdoctoral fellowship. At Texas Christian University, Fort Worth, he held the postdoctoral position of R. Welch Fellow, studying and teaching photochemistry. From there, he accepted the position of senior research scientist at Eastman Kodak Company. His position required working in photographic and precipitation science and product development. His work on the use of silver halides for the development of photographic films and papers led to new insights, contributions to photographic science, and models for the control of crystal nucleation. For his published work he received the Fellowship and Service Awards, and the Lieven-Gevaert medal, the highest award in photographic science, from the Society for Imaging Science and Technology. As a team leader he guided the development of commercially successful products. As a result of his research, he became an experienced author, lecturer, scientist, and technical project manager. After separation from Eastman Kodak Company, he became founder and senior scientist for Crystallization Consulting, a company specializing in consulting, modeling, and teaching of advanced models for high-precision precipitations. His name is listed in American Men and Women in Science and in Who's Who in Science and Engineering. He is a fellow of Sigma Xi, a member of the American Chemical Society, the Society for Imaging Science and Technology, the American Association for the Advancement of Science, the American Geographical Union, the Rochester Academy of Science, and the Rochester Professional Consultants Network.

Preface	p. xiii
Acknowledgments	p. xv
The Author	p. xvii
Chapter 1 Prior Models for Nucleation and Growth	p. 1
The Primitive Model	p. 1
The Total Crystal Number	p. 2
The Classical Nucleation Model (Becker-Doering)	p. 2
Derivation of the Classical Nucleation Model	p. 3
The Klein-Moisar Model	p. 5
Kharitanova Derivation	p. 6
Comments	p. 6
Growth Rate and Maximum Growth Rate	p. 7
Growth Rate below the Maximum Growth Rate	p. 7
Maximum Growth Rate	p. 7
References	p. 8
Chapter 2 The Balanced Nucleation and Growth Model	p. 11
The BNG Model and the Nucleation Phase	p. 11
Assumptions for Modeling	p. 11
Assumptions for Calculations	p. 11
Preliminary Considerations: Nucleation Rate	p. 12
The Balanced Nucleation and Growth Model	p. 13
Modeling Variables	p. 13
Initial Time Interval	p. 13
Second and Following Time Intervals	p. 14
Subsequent Time Intervals	p. 16
End of Nucleation, Final Time Interval for Nucleation, t e	p. 16
Crystal Size and Size Distribution	p. 17
BNG Modeling of the Nucleation Phase and Size Distribution	p. 17
Reaction Parameters for the Calculations	p. 18
Results and Discussion	p. 18
Time Dependence of Nucleation Rate, Growth Rate, and Supersaturation	p. 18
Size Distribution	p. 19
Modeling the Reaction Parameters	p. 20
Addition Rate, R a	p. 20
Maximum Growth Rate, G m	p. 21
Critical Nucleus Size, L n	p. 22
Nucleation Efficiency, F n	p. 23
Practical Considerations	p. 24
Conclusion	p. 26
References	p. 27
Chapter 3 The Analytical BNG Model	p. 29
Crystal Formation (Nucleation) under Kinetically and Diffusion-Controlled Growth Conditions	p. 29
Derivation of the General BNG Nucleation Equation	p. 29
Nucleation under Diffusion-Controlled Growth Conditions	p. 30
Nucleation under Kinetically Controlled Growth Conditions	p. 31
References	p. 32
Chapter 4 Kinetically Controlled Nucleation	p. 33
Experiment: Kinetically Controlled Crystal Nucleation	p. 33
Theory	p. 33
Determination of the Kinetic Integration Constant, K i	p. 34
Mechanism	p. 35
Conclusion	p. 35
Appendix I Experimental Conditions for AgI Precipitation	p. 36
References	p. 36
Chapter 5 Diffusion-Control led Nucleation	p. 37
Reaction Variables, Constants, Predictions	p. 37
Theory	p. 37
Critical Crystal Size, r*, and Supersaturation	p. 37
Reaction Variables T, R, C s	p. 38
Reactant Addition Rate, R	p. 38
Solubility	p. 38
Physicochemical Constants	p. 39
Reaction Volume	p. 40
Constancy of Crystal Number	p. 41
Modeling: Separation of Variables R, C s , and T	p. 43
Theory	p. 43
Diffusion Coefficient, D	p. 43
Surface Energy, ¿	p. 44
Addition Rate, R	p. 44
Solubility, C s	p. 45
Temperature, T	p. 45
Addition Rate	p. 46
Silver Chloride	p. 48
Experimental: AgCI	p. 48
Stirring/Mixing	p. 48
Peptizer	p. 48
Calculation of r*/r	p. 49
Results	p. 49
Silver Bromide	p. 51
Experimental: AgBr	p. 51
Results	p. 51
Practical Applications	p. 52
Solubility	p. 53
Silver Chloride	p. 53
Experimental	p. 53
Results: AgCl	p. 54
Silver Bromide	p. 57
Experimental	p. 57
Results: AgBr	p. 58
AgBr Morphology as a Function of Solubility	p. 61
Temperature	p. 62
Silver Chloride	p. 63
Silver Bromide	p. 65
References	p. 67
Chapter 6 Supersizing with Ripeners	p. 69
Crystal Formation (Nucleation) in the Presence of Ostwald Ripening Agents: Theory	p. 69
Summary	p. 69
Introduction	p. 69
Theory	p. 70
Crystal Formation (Nucleation) of Silver Bromide in the Presence of a Di-Thia Crown Ether as an Ostwald Ripening Agent	p. 73
Introduction	p. 73
Experimental	p. 75
Results and Discussion	p. 75
Crystal Number	p. 75
Crystal Size	p. 76
Conclusions	p. 76
Crystal Formation (Nucleation) of AgClBr (15: 85) in the Presence of Ammonia as an Ostwald Ripening Agent	p. 77
Introduction	p. 77
Experimental	p. 78
Results	p. 78
Crystal Number and Size	p. 78
Ammonia Effects in the Reactor on pH	p. 81
Ammonia Effects in the Reactor on pAg	p. 82
Conclusion	p. 82
Crystal Formation (Nucleation) of AgBrI (97.4: 2.6) in the Presence of l, 8-dihydroxy-3, 6-dithiaoctane as an Ostwald Ripening Agent	p. 83
Introduction	p. 83
Experimental	p. 83
Results	p. 85
6°C Results: Crystal Size/Number with Ripener Correlation	p. 85
All Data: Size/Number with Ripener Correlation	p. 85
Retained Ripener	p. 87
Summary	p. 89
References	p. 89
Chapter 7 Nanosizing with Restrainers	p. 91
Crystal Formation (Nucleation) in the Presence of Growth Restrainers	p. 91
Introduction	p. 91
Model	p. 93
Surface Integration Model of Nucleation and Effect of Crystal Growth Restrainers	p. 93
Surface Adsorption Model	p. 95
Experimental	p. 96
Results	p. 97
Conclusions	p. 99
References	p. 100
Chapter 8 Crystal Growth and Renucleation	p. 101
Crystal Growth, Renucleation, and Maximum Growth Rate: Theory and Experiments	p. 101
Introduction	p. 101
General Experimental Procedures	p. 103
Control of Reactant Addition Rate: Fixed Seed Concentration	p. 103
Control of Crystal Seed Concentration: Fixed Addition Rate	p. 103
The Renucleation Model	p. 103
Crystal Nucleation	p. 104
Crystal Growth	p. 104
Growth Rate and Crystal Number	p. 104
Growth Rate and Surface Area	p. 105
Growth Rate and Crystal Size	p. 105
Substitutions	p. 106
Growth and Renucleation	p. 106
Aspects of the Renucleation Model	p. 107
Determination of a, b, and c	p. 107
Variable Seed Concentration	p. 107
Variable Addition Rate	p. 108
No Seed Crystals	p. 108
Maximum Growth Rate Conditions	p. 109
Renucleation Conditions	p. 109
Experimental	p. 110
Seed Emulsion	p. 110
Precipitation Procedure for Growth/Renucleation Experiments	p. 110
Determination of the Number of Renucleation Crystals, Z n	p. 110
Results and Discussion	p. 111
Summary and Conclusions	p. 114
References	p. 114
Chapter 9 Continuous Crystallization	p. 117
Continuous Crystallization in the Mixed-Suspension, Mixed-Product-Removal (MSMPR), or Continuous Stirred Tank Reactor (CSTR) Crystallizer	p. 117
Introduction	p. 117
Experimental	p. 117
Prior Models: The Randolph-Larson Model	p. 118
Growth	p. 119
Example of Size Distribution in CSTR Precipitation	p. 120
Transient Behavior of Silver Bromide Precipitation in a Continuous Suspension Crystallizer	p. 122
Summary	p. 122
Introduction	p. 122
Model for the Initial Transient Phase	p. 123
Experimental	p. 127
Results and Discussion	p. 128
The Transition Stage	p. 128
Initial Nucleation versus Batch Nucleation	p. 129
Maximum Growth Rate and Critical Supersaturation	p. 131
After the Renucleation Point	p. 132
Summary	p. 133
A New Crystal Nucleation Theory for Size Control in Continuous Precipitations	p. 133
Summary	p. 133
Introduction	p. 134
Theory	p. 134
Preconditions	p. 134
Model Derivation	p. 135
Crystal Nucleation	p. 136
Crystal Growth	p. 138
Crystal Growth and Nucleation in the Continuous Crystallizer	p. 138
Practical Analyses	p. 139
Special Limiting Conditions for Continuous Crystallization	p. 140
Large Average Crystal Size, L	p. 140
Short Residence Time, Plug-Flow Reactor, ¿ -> zero	p. 140
Calculation of Reaction Processes	p. 141
Nucleation versus Growth, R n /R i	p. 141
Nascent Nuclei Size	p. 141
Conclusions	p. 142
Size Dependence on Residence Time in Continuous Precipitations	p. 143
Summary	p. 143
Introduction	p. 143
Experimental	p. 144
Results and Discussion	p. 147
Crystal Size, Addition Rate, and Suspension Density	p. 147
Crystal Size and Residence Time	p. 149
Maximum Growth Rate, G m	p. 149
Minimum Crystal Size (¿ -> 0)	p. 150
Determination of ¿ and L/L e , Supersaturation Ratio, S*; and Supersaturation, C ss	p. 150
Nucleation versus Growth, R n /R i	p. 152
Nascent Nuclei Size	p. 152
Conclusions	p. 153
Size Dependence on Solubility in Continuous Precipitations	p. 153
Summary	p. 153
Introduction	p. 154
The BNG Model for the CSTR System	p. 154
Size Control by Crystal Solubility	p. 155
The Solubility Model	p. 155
Solubility	p. 157
Experimental	p. 157
Results	p. 159
Suspension Density	p. 159
Size-Solubility Correlation	p. 159
Experimental, Critical, and Nascent Crystal Sizes, L, L c , and L n	p. 161
Supersaturation Ratio, S*	p. 162
Reactant Split Ratios, R n /R i , R n /R 0 , and R i /R 0	p. 162
Conclusions	p. 162
References	p. 164
Chapter 10 Crystal Growth in the Continuous Crystallizer	p. 167
Seeded Precipitations in the Continuous Stirred Tank Reactor Crystallizer	p. 167
Summary	p. 167
Introduction	p. 167
Seeded Crystallization in the CSTR System	p. 170
Modeling the Seeded CSTR Crystallizer	p. 171
Mathematical Processing Steps	p. 174
Results and Discussion	p. 174
Addition Rate, R, as a Function of Residence Time, ¿, for Constant Growth Rate, G	p. 175
Steady-State Addition Rate as a Function of Growth Rate, G	p. 176
Steady-State Addition Rate, R, as Function of Residence Time, ¿	p. 177
Steady-State Addition Rate, R, as Function of Seed Size, L 0	p. 178
Steady-State-Addition Rate, R, as a Function of Seed Number Addition Rate, dN 0 /dt	p. 179
Conclusion	p. 180
References	p. 180
Epilogue	p. 183
Final Thoughts	p. 183
Glossary of Terms	p. 185
Bibliography	p. 187
Index	p. 189

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