Mathematical Modelling for Polymer Processing: Polymerization, Crystallization, Manufacturing (Hardcover, 2003)

Polymerization.- 1 Mathematical Models for Polymerization Processes of Ziegler-Natta Type.- 1.1 Introduction.- 1.2 Description of the Process.- 1.3 Governing Equations for the Macroscopic Processes (Heat and Mass Transfer).- 1.4 Governing Equation for the Microproblem (Polymerization).- 1.5 Computation of the Coupling Terms. Expansion of the Agglomerate.- 1.6 Rescaling and Simplifications.- 1.7 Summary of the Simplified Model and Sketch of the Proof.- 1.8 Fragmentation.- 1.9 Conclusions and Open Questions.- 1.10 Acknowledgements.- References.- Nucleation.- 2 Classical Kinetic Theory of Nucleation and Coarsening.- 2.1 Introduction.- 2.2 Kinetics of Clusters.- 2.3 Phase Equilibria of a Binary Material.- 2.4 Macroscopic Kinetics.- 2.5 Quasistatic Nuclei.- 2.6 Material and Energy Parameters of Kinetic Theory Determined from Xiao-Haasen Data.- 2.7 Discussion.- 2.8 Acknowledgements.- 2.9 Appendix: BD Kinetics for n nc.- References.- 3 Multidimensional Theory of Crystal Nucleation.- 3.1 Introduction.- 3.2 One-dimensional Theory of Nucleation.- 3.3 Modifications of the Classical Theory.- 3.4 Multidimensional Theory of Nucleation.- 3.5 Some AppHcations.- 3.6 Closing Remarks.- References.- 4 Kinetic Theory of Nucleation in Polymers.- 4.1 Introduction.- 4.2 Nucleation Theory.- 4.3 Kinetic Equations from Non-Equilibrium Thermodynamics.- 4.4 Isothermal Homogeneous Nucleation.- 4.5 Nucleation in Spatially Inhomogeneous Non-Isothermal Conditions.- 4.6 Homogeneous Nucleation in Spatially Inhomogeneous Systems. Diffusion Regime.- 4.7 Nucleation in a Shear Flow.- 4.8 Kinetic Equations for the Crystallinity.- 4.9 Further Extensions.- 4.10 Discussion and Conclusions.- 4.11 Acknowledgments.- References.- Crystallization.- 5 Mathematical Models for Polymer Crystallization Processes.- 5.1 Stochastic Models of the Crystallization Process.- 5.2 The Causal Cone.- 5.3 The Hazard Function.- 5.4 The Random Tessellation of Space.- 5.5 Estimating the Local Density of Interfaces.- 5.6 Interaction with Latent Heat.- 5.7 Simulation of the Stochastic Model.- 5.8 Stochasticity of the Causal Cone.- 5.9 A Hybrid Model.- 5.10 Scaling Limits.- 5.11 Related Mathematical Problems.- References.- 6 Polymer Crystallization Processes via Many Particle Systems.- 6.1 Introduction.- 6.2 The Nucleation Process.- 6.3 Growth of Crystals.- 6.4 The Mass Distribution of Crystals.- 6.5 The Rates.- 6.6 The Time Evolution of the Processes ? N and Y N.- 6.7 Heuristic Derivation of a Continuum Dynamics.- References.- Manufacturing.- 7 Modelling of Industrial Processes for Polymer Melts: Extrusion and Injection Moulding.- 7.1 Introduction.- 7.2 Flow Instabihties in the Extrusion of Polymer Melts.- 7.3 Injection Moulding.- 7.4 Closing Remarks.- References.- Appendix. Color Plates.