Polymer Viscoelasticity: Basics, Molecular Theories, Experiments, and SimulationsThis book covers in great detail the Rouse-segment-based molecular theories in polymer viscoelasticity ? the Rouse theory and the extended reptation theory (based on the framework of the Doi?Edwards theory) ? that have been shown to explain experimental results in a consistently quantitative way. The explanation for the 3.4 power law of viscosity, quantitative line-shape analyses of viscoelastic responses and agreements between different sorts of viscoelastic responses, the consistency between the viscoelasticity and diffusion results, the clarification of the onset of entangelement, the discovery of the number of entanglement strands per cubed entanglement distance being a universal constant and the basic mechanism of the glass transition-related thermorheological complexity are discussed or shown in great detail. The mystery behind the success of the Rouse-segment-based molecular theories over the entropic region of a viscoelastic response is revealed by the Monte Carlo simulations on the Fraenkel chains. Specifically, the simulation studies give a natural explanation for the coexistence of the energy-driven and entropy-driven modes in a viscoelastic response and provide a theoretical basis resolving the paradox that the experimentally determined sizes of Rouse and Kuhn segments are nearly the same. This book starts from a very fundamental level; each chapter is built upon the contents of the previous chapters. Thus, the readers may use the book as a textbook and eventually reach an advanced research level. This book is also a useful source of reference for physicists, chemists and material scientists. |
Contents
1 Conformation of Polymer Chains | 1 |
2 Rubber Elasticity | 16 |
3 Polymer Chain Dynamics | 26 |
4 Linear Viscoelasticity | 51 |
5 Stress and Strain | 78 |
6 Molecular Theory of Polymer Viscoelasticity Elastic Dumbbell Model | 98 |
7 Molecular Theory of Polymer ViscoelasticityThe Rouse Model | 119 |
8 Molecular Theory of Polymer Viscoelasticity Entanglement and the DoiEdwards Reptation Model | 133 |
11 ERT vs Rouse Theory Concentration Dependence and Onset of Entanglement and Tube Dilation | 215 |
12 Molecular Theory of Polymer Viscoelasticity Nonlinear Relaxation Modulus of Entangled Polymers | 242 |
13 Number of Entanglement Strands per Cubed Entanglement Distance nt | 257 |
14 Glass TransitionRelated Thermorheological Complexity in Polystyrene Melts | 269 |
15 The Basic Mechanism for the Thermorheological Complexity in Polystyrene Melts | 328 |
16 Monte Carlo Simulations of Stress Relaxation of Rouse Chains | 341 |
17 Monte Carlo Simulations of Stress Relaxation of Fraenkel Chains Linear Viscoelasticity of EntanglementFree Polymers | 358 |
18 Monte Carlo Simulations of Stress Relaxation of Fraenkel Chains Nonlinear Viscoelasticity of EntanglementFree Polymers | 381 |
Common terms and phrases
analyses Appendix applied beads blend solution Brownian motion chain model Chapter Chem comparison component constitutive equation contour length corresponding curves defined denoted described Doi-Edwards theory dumbbell dynamic dynes/cm² elastic dumbbell entanglement molecular weight entanglement strand entropic region equilibrium equivalent experimental expressed Finger tensor fluctuation Fraenkel chain frictional factor Gaussian chain given by Eq glassy-relaxation process Gs(t Jp(t Kuhn segment Langevin equation length scale line shape line-shape Macromolecules measured melt molecular weight molecular-weight dependence molecular-weight distribution nearly monodisperse polystyrene nonlinear normal modes obtained Osaki Phys polymer polymer chain Polymer Viscoelasticity polystyrene primitive chain relaxation modulus G(t Rouse chain Rouse model Rouse segment Rouse theory shown in Fig simple shear simulation slip-links slow mode solid line strain stress relaxation studied Substituting Eq superposition principle tensile force theoretical tube virial theorem viscoelastic viscoelastic behavior viscosity µx(t ΣΣ