<p>Preface ix</p> <p><b>1 Introduction 1</b></p> <p>1.1 Special Features of Polymers 1</p> <p>1.2 Structures in Polymers and Their Influence on Processing and Application Properties 3</p> <p>1.2.1 Chain Length, Molecular Mass, Moments, and Mean Values 3</p> <p>1.2.2 Rheological Properties 6</p> <p>1.2.3 Constitutional Isomers 7</p> <p>1.2.4 Architectural Isomers 9</p> <p>1.2.5 Copolymers 11</p> <p>1.3 Some Analytical Methods for Model Validation 13</p> <p>1.4 Description of Polymer Properties 15</p> <p>1.4.1 Chemical Master Equations 17</p> <p>1.4.2 Approaches to Polymer Properties 21</p> <p>1.4.3 Stochastic and Deterministic Simulation 22</p> <p><b>2 Polymer Reactions 25</b></p> <p>2.1 Module Concept 25</p> <p>2.2 Rate Coefficients in Polymerization Reactions 26</p> <p>2.3 Building Macromolecules 28</p> <p>2.4 Only Chain-Forming Reactions Take Place, Step-Growth Polymerization 30</p> <p>2.4.1 Only One Type of End Group: The A − A Case, A Reacting with A 31</p> <p>2.4.2 Two Types of Functional Groups A and B at One Molecule; A Reacts with B 40</p> <p>2.4.3 Introducing Monofunctional Molecules to Control Degree of Polymerization 41</p> <p>2.4.4 Addition of a Second Bifunctional Monomer, Two Functional Groups on Two Different Molecular Species 43</p> <p>2.4.5 Reversible Reactions 49</p> <p>2.5 Chain-Growth Polymerization – Initiation Required 58</p> <p>2.5.1 Living Polymerization – Only Initiation and Propagation (Chain Growth) Take Place 59</p> <p>2.5.1.1 Moment Equations 65</p> <p>2.5.2 Living Polymerization Together with Chain Depropagation 68</p> <p>2.5.3 Initiation and Chain Growth with Transfer Reactions 75</p> <p>2.5.4 Initiation and Chain Growth with Deactivation 76</p> <p>2.5.5 Initiation and Chain Growth with Chain Termination 77</p> <p>2.5.5.1 Termination by Disproportionation 84</p> <p>2.5.5.2 Termination by Combination 84</p> <p>2.5.5.3 Transfer to Monomer or Transfer Agent 86</p> <p>2.5.5.4 Transfer to Polymer 87</p> <p>2.5.5.5 Propagation with Change of Characteristics 89</p> <p>2.5.5.6 𝛽-Scission 90</p> <p>2.6 Copolymerization 91</p> <p>2.6.1 Conventional Description of Copolymer Composition 91</p> <p>2.6.2 Characteristic Values for the Characterization of Copolymers 94</p> <p>2.6.3 Modules for the Description of Copolymerization 97</p> <p>2.6.4 Extended Description of a Copolymer 101</p> <p>2.6.5 Distributed Counters 104</p> <p>2.7 Nonlinear Polymerization 106</p> <p>2.7.1 Branching; Graft Polymers via Copolymerization, (Grafting through) 106</p> <p>2.7.2 Cross-Linking via Copolymerization 107</p> <p>2.7.3 Nonlinear Structures by Polymerization from an Existing Chain, Grafting from 109</p> <p>2.7.4 Cross-Linking of Preformed Linear Macromolecules by Low-Molecular-Mass Compounds 111</p> <p>2.7.5 Nonlinear Step Growth 111</p> <p>2.7.6 Higher Dimensional Models 113</p> <p>2.8 List of Modules 114</p> <p>2.8.1 Elemental Kinetic 115</p> <p>2.8.2 Combination (P, Q, T, A) 116</p> <p>2.8.3 Statistical Degradation (P, Q, T, A, B) 119</p> <p>2.8.4 Change of Characteristics (P, Q, A, B) 120</p> <p>2.8.5 Intermolecular Transfer (P, Q, T, R, A) 121</p> <p>2.8.6 Cross Transfer (P, Q, T, R, A) 123</p> <p>2.8.7 Initiation (P, A, B, C, m) 124</p> <p>2.8.8 Propagation (P, Q, M, A, m) 125</p> <p>2.8.9 Depropagation (P, Q, M, A, B, m) 127</p> <p>2.8.10 Transfer (P, Q, T, M) 128</p> <p>2.8.11 Disproportionation (P, Q, R, T, A) 129</p> <p>2.8.12 Transfer to Polymer (P, Q, T, R, A) 131</p> <p>2.8.13 Scission (P, Q, T, A, B) 132</p> <p>2.8.14 Cross-Linking (P, Q, T, A) 133</p> <p>2.8.15 Flow (A1,A2) 134</p> <p>2.8.16 Phase Transfer (A1,A2) 135</p> <p>2.8.17 Example System 135</p> <p><b>3 Reactors for Polymerization Processes 139</b></p> <p>3.1 Introduction 140</p> <p>3.2 Well-Mixed (Ideal) Batch Reactor (BR) 141</p> <p>3.2.1 Aspects of the Overall Mass Balance 143</p> <p>3.2.2 Heat Balance in a Batch Reactor 144</p> <p>3.2.3 Polymer Properties in Batch Reactors 148</p> <p>3.3 Semi-Batch Reactor (Semi-BR) 149</p> <p>3.4 The Continuous Stirred Tank Reactor (CSTR) 151</p> <p>3.4.1 Homogeneous Continuous Stirred Tank Reactor (HCSTR) 151</p> <p>3.4.2 Cascade of HCSTR 156</p> <p>3.4.3 Segregated Continuous Stirred Tank Reactor (SCSTR) 157</p> <p>3.5 Tubular Reactors 158</p> <p>3.5.1 Plug Flow Reactor (PFR) 158</p> <p>3.5.2 Laminar Tubular Reactor 159</p> <p>3.6 Nonideal Reactor Models with Partial Backmixing 159</p> <p>3.7 Comparison of Reactors 161</p> <p><b>4 Phases and Phase Transitions 163</b></p> <p>4.1 Treatment of Volumes and Concentrations 164</p> <p>4.2 Phase Transfer Modules 165</p> <p>4.2.1 Two-Film Theory 166</p> <p>4.2.2 Examples for Phase Transfer Steps 169</p> <p>4.2.2.1 Evaporation of a Pure Volatile Compound 169</p> <p>4.2.2.2 Vapor–Liquid Equilibrium of Volatile Compounds 170</p> <p>4.2.2.3 Adsorption of Gaseous Compounds 170</p> <p>4.2.2.4 Vapor Pressure Above a Polymer Solution 172</p> <p>4.2.2.5 Demixing in Polymer Solutions 174</p> <p>4.2.3 Example: Phase Transfer During Polymerization; Living Anionic Polymerization of Butadiene 175</p> <p>4.2.4 Summarizing Remarks to the Phase Change Module 178</p> <p>4.3 Multiphase Polymerization Systems 179</p> <p>4.3.1 Suspension Polymerization 179</p> <p>4.3.2 Precipitation/Dispersion Polymerization 180</p> <p>4.3.3 Emulsion Polymerization 181</p> <p><b>5 Numerical Methods 193</b></p> <p>5.1 Introduction 193</p> <p>5.2 Ordinary Differential Equations 195</p> <p>5.2.1 Consistency and Convergence 195</p> <p>5.2.2 Stability 197</p> <p>5.2.3 Error Control 200</p> <p>5.2.4 A Practical Guide to ODE Solvers 205</p> <p>5.2.4.1 List of Explicit Methods and Solvers for Non-Stiff ODEs 206</p> <p>5.2.4.2 List of Implicit Methods and Solvers for Stiff ODEs and Differential Algebraic Equations (DAEs) 206</p> <p>5.3 Countable Systems of Ordinary Differential Equations – CODEs 208</p> <p>5.3.1 Theoretical Aspects 208</p> <p>5.3.2 The Chain-Length Range 209</p> <p>5.3.3 Initialization of Polymer Distributions 211</p> <p>5.3.4 Approximation Schemes 212</p> <p>5.4 Estimating the Numerical Error 217</p> <p>5.5 Monte Carlo Methods 220</p> <p>5.6 The Modeling Cycle: Dealing with Different Errors 223</p> <p><b>6 Parameter Estimation 227</b></p> <p>6.1 Introduction: Forward and Inverse Problems 227</p> <p>6.2 General Theory 230</p> <p>6.2.1 Introduction 230</p> <p>6.2.2 The Minimization Problem 232</p> <p>6.2.3 Sensitivity Analysis 235</p> <p>6.3 Correlated Parameters 236</p> <p>6.3.1 Damping 237</p> <p>6.3.2 Essential Directions 238</p> <p>6.4 Example: Parameter Dependencies and Condition 240</p> <p><b>7 Styrene Butadiene Copolymers 251</b></p> <p>7.1 Model Description 251</p> <p>7.2 Components of the Model 251</p> <p>7.2.1 Low-Molecular-Weight Compounds 251</p> <p>7.2.2 Polymer Distributions 252</p> <p>7.2.3 Sequence Distributions 253</p> <p>7.2.4 Counters 253</p> <p>7.2.5 Computation of Characteristic Values for Copolymers from Counters 254</p> <p>7.3 Reaction Modules 254</p> <p>7.3.1 Chain Initiation 254</p> <p>7.3.2 Chain Propagation 255</p> <p>7.3.3 LiH-Elimination 256</p> <p>7.3.4 Chain Transfer 256</p> <p>7.3.5 Re-Initiation by 1-Phenyl-1-Lithium Ethane 257</p> <p>7.3.6 Balance Steps 257</p> <p>7.4 Exemplary Simulations 258</p> <p>7.5 Exemplification of the Modeling Cycle for the Styrene–Butadiene Example 266</p> <p>References 269</p> <p>Appendix 277</p> <p>Index 283</p>