Model and simulate chemical reactions that create plastics and polymers
Understanding Modeling and Simulation of Polymerization Reactions fills a critical gap in existing literature by teaching the science behind polymer design using advanced mathematical and computational methods and providing tools to predict and control how polymers are formed. The book covers both traditional and cutting-edge polymerization methods and uses four powerful modeling techniques: z-transform, method of moments, Markov chains, and Monte Carlo simulations.
The book emphasizes hands-on, equation-driven approaches that help readers understand the underlying chemistry and physics and relate reaction conditions to specific polymer properties. Real-world examples and practice problems are included to reinforce learning, with an online solutions manual available for adopting professors.
Written by an experienced teaching professor, Understanding Modeling and Simulation of Polymerization Reactions discusses:
- Mechanisms of chain formation from monomers including addition, step-growth, and their combinations
- Theoretical models for predicting composition of propagating species for several types of polymerization reactions including conventional radical, reversible deactivation radical, anionic, and cationic polymerization
- Stochastic models of chain distribution, based on the Markovian process, for addition and step-growth polymerization
- Theoretical models to relate viscosity of the reaction medium to monomer conversion, chain diffusivity, and polymer molecular weight
- Copolymer sequences, monomer sequence distributions, and copolymer randomness
Understanding Modeling and Simulation of Polymerization Reactions is an ideal high-level academic textbook for advanced undergraduate and graduate courses on polymer engineering, polymer science, and polymer materials. With its broad scope, the book is also valuable for practicing professionals in the polymer and materials industries.
Table of Contents:
Preface xvii
Acknowledgment xxi
About the Companion Website xxii
1 Mechanisms and Methods of Polymerization 1
1.1 Introduction 1
1.2 Mechanisms of Polymerization 2
1.3 Living Polymerization 17
1.4 Copolymerization 21
1.5 Architecture of Polymer Chains 22
1.6 Summary 23
1.7 List of Symbols and Abbreviations 24
1.8 Practice Problems 27
2 Elementary Reactions in Polymerization 43
2.1 Introduction 43
2.2 Initiation Reaction 44
2.3 Propagation Reaction 52
2.4 Termination Reactions 52
2.5 Chain Transfer Reactions to Small Molecules 54
2.6 Chain Backbiting Reaction 57
2.7 Chain Combination Reactions 58
2.8 Chain Dissociation Reactions 63
2.9 Summary 64
2.10 List of Symbols and Abbreviations 65
2.11 Practice Problems 69
3 Functions with Distributed Variables 85
3.1 Introduction 85
3.2 Moments of a Distribution 86
3.3 Relating Molar-based Distribution of Polymer Chains to Weight-based Distribution 88
3.4 Relating Molar-based Moments of Polymer Chains to Weight-based Moments 89
3.5 Relating Number-average, Weight-average, and z-average Degree of Polymerization of Polymer Chains to Molar-based Moments of Chain Distribution 92
3.6 Relating Viscosity-average Degree of Polymerization of Polymer Chains to Molar-based Moments of Chain Distribution 94
3.7 Variance and Polydispersity of a Polymer Chain Distribution 97
3.8 Skewness and Kurtosis of a Polymer Chain Distribution 98
3.9 Standard Distribution Functions Used in Polymerization Reactions 101
3.10 Summary 111
3.11 List of Symbols and Abbreviations 111
3.12 Practice Problems 113
4 Z-transform in Polymerization Reactions 121
4.1 Introduction 121
4.2 Definition of Z-transform 122
4.3 Moments of a Distributed Function in Z Domain 122
4.4 Properties of a Function in the Z Domain 124
4.5 Inverse Z-transform 126
4.6 Application of Z-transform in Addition Polymerization 128
4.7 Application of Z-transform in Step-growth Polymerization 130
4.8 Summary 141
4.9 List of Symbols and Abbreviations 142
4.10 Practice Problems 145
5 Conservation of Moments of Distribution of Chains in Polymerization 153
5.1 Introduction 153
5.2 Elementary Reactions in Polymerization in a Differential Time Interval 153
5.3 Mixing Theory of Polymer Chains 154
5.4 Conservation of kth Order Moment of Polymer Chains in a Reaction 158
5.5 Derivation of the General Conservation Equation for kth Order Moment of Polymer Chains in a Reaction 162
5.6 Formation of Reactive Species in Conventional Radical Polymerization and the Quasi-steady State Assumption 174
5.7 Initiation and Formation of Reactive Species in Polymerization 176
5.8 Summary 184
5.9 List of Symbols and Abbreviations 185
5.10 Practice Problems 187
6 Moments of Elementary Reactions in Addition Polymerization 205
6.1 Introduction 205
6.2 Instantaneous kth Order Moments of Propagating Chains After Propagation in Terms of Propagating Chains Prior to Propagation 205
6.3 Instantaneous kth Order Moments of Chains Produced by Termination in Terms of kth Order Moments of Propagating Chains 207
6.4 Instantaneous kth Order Moments of Chains Produced by Transfer Reactions in Terms of kth Order Moments of Propagating Chains 208
6.5 Instantaneous kth Order Moments of Chains Produced by Chain Scission 213
6.6 Summary 218
6.7 List of Symbols and Abbreviations 218
6.8 Practice Problems 221
7 Conservation of Moments Applied to Polymerization Reactions 229
7.1 Introduction 229
7.2 General Conservation Equations for kth Order Moment of Propagating, Dormant, and Terminated Chains 229
7.3 Modeling Radical Polymerization with Termination by Disproportionation in the Absence of Chain Transfer 230
7.4 Modeling Radical Polymerization with Chain Transfer Agent 251
7.5 Modeling Radical Polymerization with Chain Transfer to the Terminated Polymer Chains 256
7.6 Modeling Radical Polymerization with ;;2 Chain Scission 259
7.7 Modeling Radical Polymerization with Photoinitiation 263
7.8 Modeling Reversible-deactivation Radical Polymerization by Atom transfer Radical Polymerization 271
7.9 Modeling Ionic Polymerization 281
7.10 Summary 287
7.11 List of Symbols and Abbreviations 288
7.12 Practice Problems 294
8 Diffusion Controlled Polymerization Reactions 307
8.1 Introduction 307
8.2 Relating Diffusion Coefficient and Viscosity to Molecular Weight 308
8.3 Role of Diffusion in Bulk Polymerization of Methyl Methacrylate 313
8.4 Termination Rate Constant in Diffusion-limited Polymerization Reactions 321
8.5 Quasi Steady State in Diffusion-limited Polymerization Reactions 328
8.6 Modeling Diffusion-limited Radical Polymerization with Termination by Disproportionation and Combination
and Chain Transfer to Monomer 330
8.7 Modeling Diffusion-limited Bulk Radical Polymerization of Methyl Methacrylate 338
8.8 Summary 347
8.9 List of Symbols and Abbreviations 348
8.10 Practice Problems 356
9 Markov Chain Modeling of Polymerization Reactions 367
9.1 Introduction 367
9.2 Definition of a Markov Chain 367
9.3 State Space of a Markov Chain 368
9.4 Initial Probability Vector 368
9.5 One-step Uniform Transition Probability Matrix 368
9.6 n-step Uniform Transition Probability Matrix 369
9.7 n-step Absolute Probability Vector 370
9.8 Types of States in State Space of a Markov Chain 370
9.9 n-step Probability of Reaching an Absorbing State 371
9.10 Matrix Operations 372
9.11 Application of Markov Chains to Radical Polymerization 375
9.12 Application of Markov Chain to Condensation Polymerization 383
9.13 Summary 389
9.14 List of Symbols and Abbreviations 390
9.15 Practice Problems 393
10 Markov Chain Modeling of Copolymerization Reactions 399
10.1 Introduction 399
10.2 Number Representation of Copolymer Sequences 399
10.3 Order of Copolymerization 400
10.4 State Space of Copolymerization Reaction 402
10.5 Conditional Probability Matrix for Copolymerization Reaction 403
10.6 Composition of Copolymer 403
10.7 Copolymer Sequence Distribution 404
10.8 Modeling Terminal Copolymerization of Two Monomers 409
10.9 Modeling Terminal Terpolymerization of Three Monomers 418
10.10 Summary 427
10.11 List of Symbols and Abbreviations 428
10.12 Practice Problems 430
11 Monte Carlo Simulation of Polymerization Reactions 439
11.1 Introduction 439
11.2 Theory of Monte Carlo Simulation 439
11.3 Estimation of an Integral Function with Monte Carlo Method 440
11.4 Probability Distributions of Random Numbers in Monte Carlo Simulation 441
11.5 Error Estimation in Monte Carlo Simulation 443
11.6 Testing Uniformity of Random Numbers 445
11.7 Monte Carlo Simulation of Initiator Dissociation 451
11.8 Monte Carlo Simulation of Methyl Methacrylate Polymerization 452
11.9 Monte Carlo Simulation of Branching in Butadiene Emulsion Polymerization 457
11.10 Summary 467
11.11 List of Symbols and Abbreviations 468
11.12 Practice Problems 472
References 474
Index 481
About the Author :
Esmaiel Jabbari, PhD is Professor of Chemical and Biomedical Engineering at the University of South Carolina. His research focuses on the application of resorbable polymeric biomaterials in medicine for drug delivery and regenerative medicine. He was elected a Fellow of the American Institute of Medical and Biological Engineering in 2013.
