Understanding Modeling and Simulation of Polymerization Reactions

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.

• Preface xviiAcknowledgment xxiAbout the Companion Website xxii1 Mechanisms and Methods of Polymerization 11.1 Introduction 11.2 Mechanisms of Polymerization 21.3 Living Polymerization 171.4 Copolymerization 211.5 Architecture of Polymer Chains 221.6 Summary 231.7 List of Symbols and Abbreviations 241.8 Practice Problems 272 Elementary Reactions in Polymerization 432.1 Introduction 432.2 Initiation Reaction 442.3 Propagation Reaction 522.4 Termination Reactions 522.5 Chain Transfer Reactions to Small Molecules 542.6 Chain Backbiting Reaction 572.7 Chain Combination Reactions 582.8 Chain Dissociation Reactions 632.9 Summary 642.10 List of Symbols and Abbreviations 652.11 Practice Problems 693 Functions with Distributed Variables 853.1 Introduction 853.2 Moments of a Distribution 863.3 Relating Molar-based Distribution of Polymer Chains to Weight-based Distribution 883.4 Relating Molar-based Moments of Polymer Chains to Weight-based Moments 893.5 Relating Number-average, Weight-average, and z-average Degree of Polymerization of Polymer Chains to Molar-based Moments of Chain Distribution 923.6 Relating Viscosity-average Degree of Polymerization of Polymer Chains to Molar-based Moments of Chain Distribution 943.7 Variance and Polydispersity of a Polymer Chain Distribution 973.8 Skewness and Kurtosis of a Polymer Chain Distribution 983.9 Standard Distribution Functions Used in Polymerization Reactions 1013.10 Summary 1113.11 List of Symbols and Abbreviations 1113.12 Practice Problems 1134 Z-transform in Polymerization Reactions 1214.1 Introduction 1214.2 Definition of Z-transform 1224.3 Moments of a Distributed Function in Z Domain 1224.4 Properties of a Function in the Z Domain 1244.5 Inverse Z-transform 1264.6 Application of Z-transform in Addition Polymerization 1284.7 Application of Z-transform in Step-growth Polymerization 1304.8 Summary 1414.9 List of Symbols and Abbreviations 1424.10 Practice Problems 1455 Conservation of Moments of Distribution of Chains in Polymerization 1535.1 Introduction 1535.2 Elementary Reactions in Polymerization in a Differential Time Interval 1535.3 Mixing Theory of Polymer Chains 1545.4 Conservation of kth Order Moment of Polymer Chains in a Reaction 1585.5 Derivation of the General Conservation Equation for kth Order Moment of Polymer Chains in a Reaction 1625.6 Formation of Reactive Species in Conventional Radical Polymerization and the Quasi-steady State Assumption 1745.7 Initiation and Formation of Reactive Species in Polymerization 1765.8 Summary 1845.9 List of Symbols and Abbreviations 1855.10 Practice Problems 1876 Moments of Elementary Reactions in Addition Polymerization 2056.1 Introduction 2056.2 Instantaneous kth Order Moments of Propagating Chains After Propagation in Terms of Propagating Chains Prior to Propagation 2056.3 Instantaneous kth Order Moments of Chains Produced by Termination in Terms of kth Order Moments of Propagating Chains 2076.4 Instantaneous kth Order Moments of Chains Produced by Transfer Reactions in Terms of kth Order Moments of Propagating Chains 2086.5 Instantaneous kth Order Moments of Chains Produced by Chain Scission 2136.6 Summary 2186.7 List of Symbols and Abbreviations 2186.8 Practice Problems 2217 Conservation of Moments Applied to Polymerization Reactions 2297.1 Introduction 2297.2 General Conservation Equations for kth Order Moment of Propagating, Dormant, and Terminated Chains 2297.3 Modeling Radical Polymerization with Termination by Disproportionation in the Absence of Chain Transfer 2307.4 Modeling Radical Polymerization with Chain Transfer Agent 2517.5 Modeling Radical Polymerization with Chain Transfer to the Terminated Polymer Chains 2567.6 Modeling Radical Polymerization with ;;2 Chain Scission 2597.7 Modeling Radical Polymerization with Photoinitiation 2637.8 Modeling Reversible-deactivation Radical Polymerization by Atom transfer Radical Polymerization 2717.9 Modeling Ionic Polymerization 2817.10 Summary 2877.11 List of Symbols and Abbreviations 2887.12 Practice Problems 2948 Diffusion Controlled Polymerization Reactions 3078.1 Introduction 3078.2 Relating Diffusion Coefficient and Viscosity to Molecular Weight 3088.3 Role of Diffusion in Bulk Polymerization of Methyl Methacrylate 3138.4 Termination Rate Constant in Diffusion-limited Polymerization Reactions 3218.5 Quasi Steady State in Diffusion-limited Polymerization Reactions 3288.6 Modeling Diffusion-limited Radical Polymerization with Termination by Disproportionation and Combinationand Chain Transfer to Monomer 3308.7 Modeling Diffusion-limited Bulk Radical Polymerization of Methyl Methacrylate 3388.8 Summary 3478.9 List of Symbols and Abbreviations 3488.10 Practice Problems 3569 Markov Chain Modeling of Polymerization Reactions 3679.1 Introduction 3679.2 Definition of a Markov Chain 3679.3 State Space of a Markov Chain 3689.4 Initial Probability Vector 3689.5 One-step Uniform Transition Probability Matrix 3689.6 n-step Uniform Transition Probability Matrix 3699.7 n-step Absolute Probability Vector 3709.8 Types of States in State Space of a Markov Chain 3709.9 n-step Probability of Reaching an Absorbing State 3719.10 Matrix Operations 3729.11 Application of Markov Chains to Radical Polymerization 3759.12 Application of Markov Chain to Condensation Polymerization 3839.13 Summary 3899.14 List of Symbols and Abbreviations 3909.15 Practice Problems 39310 Markov Chain Modeling of Copolymerization Reactions 39910.1 Introduction 39910.2 Number Representation of Copolymer Sequences 39910.3 Order of Copolymerization 40010.4 State Space of Copolymerization Reaction 40210.5 Conditional Probability Matrix for Copolymerization Reaction 40310.6 Composition of Copolymer 40310.7 Copolymer Sequence Distribution 40410.8 Modeling Terminal Copolymerization of Two Monomers 40910.9 Modeling Terminal Terpolymerization of Three Monomers 41810.10 Summary 42710.11 List of Symbols and Abbreviations 42810.12 Practice Problems 43011 Monte Carlo Simulation of Polymerization Reactions 43911.1 Introduction 43911.2 Theory of Monte Carlo Simulation 43911.3 Estimation of an Integral Function with Monte Carlo Method 44011.4 Probability Distributions of Random Numbers in Monte Carlo Simulation 44111.5 Error Estimation in Monte Carlo Simulation 44311.6 Testing Uniformity of Random Numbers 44511.7 Monte Carlo Simulation of Initiator Dissociation 45111.8 Monte Carlo Simulation of Methyl Methacrylate Polymerization 45211.9 Monte Carlo Simulation of Branching in Butadiene Emulsion Polymerization 45711.10 Summary 46711.11 List of Symbols and Abbreviations 46811.12 Practice Problems 472References 474Index 481