Polymer Viscoelasticity Basics Molecular Theories Experiments and Simulations 2nd Edition by Yn Hwang Lin ISBN 9814313033 9789814313032

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ISBN 10: 9814313033 
ISBN 13: 9789814313032
Author: Yn Hwang Lin

Polymer Viscoelasticity Basics Molecular Theories Experiments and Simulations 2nd Table of contents:

1. Conformation of Polymer Chains

1.1 Introduction
1.2 Probability Distribution Functions, Moments and Characteristic Functions
1.3 A Central Limit Theorem
1.4 The Freely Jointed Chain Model
1.5 Distribution of the End-to-End Vector
1.6 The Gaussian Chain
Appendix 1.A — The Dirac Delta Function
References

2. Rubber Elasticity

2.1 Introduction
2.2 Entropy and Rubber Elasticity
2.3 Molecular Theory for Rubber Elasticity
References

3. Polymer Chain Dynamics

3.1 Introduction
3.2 The Smoluchowski Equation
3.3 The Langevin Equation
3.4 The Rouse Model
3.5 Diffusion Motion of the Rouse Chain
3.6 The Rouse Normal Modes of Motion
Appendix 3.A — Eigenvalues and Eigenvectors of the Rouse Matrix
Appendix 3.B — The Langevin Equation of a Particle in a Harmonic Potential
Appendix 3.C — The Continuous Rouse Model
Appendix 3.D — Binomial Random Walk
References

4. Linear Viscoelasticity

4.1 Introduction
4.2 Maxwell Equation
4.3 Boltzmann’s Superposition Principle
4.4 Relaxation Modulus
4.5 Steady-State Shear Flow
4.6 Dynamic-Mechanical Spectroscopy
4.7 Steady-State Compliance
4.8 Creep Compliance
Appendix 4.A — The Hopkins–Hamming Method for Converting G(t) into J(t)
References

5. Stress and Strain

5.1 Stress
5.2 Finite Strain
5.3 A neo-Hookean Material
5.4 A Newtonian Fluid
Appendix 5.A — Tensor Operations
References

6. Molecular Theory of Polymer Viscoelasticity — Elastic Dumbbell Model

6.1 Introduction
6.2 The Smoluchowski Equation for an Elastic Dumbbell
6.3 Rheological Constitutive Equation of the Elastic Dumbbell Model
6.4 Applications of the Constitutive Equation
Appendix 6.A — Codeformational (Convected) Time Derivative
References

7. Molecular Theory of Polymer Viscoelasticity — The Rouse Model

7.1 The Smoluchowski Equation of the Rouse Model
7.2 Rheological Constitutive Equation of the Rouse Model
Appendix 7.A — Eigenvalues and the Inverse of the Rouse Matrix
References

8. Molecular Theory of Polymer Viscoelasticity — Entanglement and the Doi–Edwards (Reptation) Model

8.1 Introduction
8.2 The Primitive Chain
8.3 Diffusion Motion
8.4 Relaxation Modulus
8.5 Relaxation of Stress by Reptation
Appendix 8.A — Tension in a Gaussian Chain Between Two Fixed Points
Appendix 8.B — Equivalent Expressions for Rubber Elasticity
References

9. Molecular Theory of Polymer Viscoelasticity — Extended Reptation Model

9.1 Intramolecular Processes
9.2 Contour Length Fluctuations of the Primitive Chain
9.3 Relaxation Processes Before t ≈ Teq
9.4 Universality of the G(t) Line Shape
9.5 Zero-Shear Viscosity and Steady-State Compliance
9.6 Clarification of the Term “Transition Region”
Appendix 9.A — Contour Length Fluctuations
Appendix 9.B — Rouse–Mooney Normal Modes
Appendix 9.C — Rouse–Mooney Matrix Eigenvalues
Appendix 9.D — Time Hierarchies and Universality
References

10. Comparison of ERT with Experiments

10.1 Molecular-Weight Distribution Effects
10.2 G(t) Line Shape Analysis
10.3 Zero-Shear Viscosity and Steady-State Compliance
10.4 Viscoelasticity and Diffusion
10.5 Summary
Appendix 10.A — Why G(ω) Should Be Excluded from Line-Shape Analysis
References

11. ERT vs. Rouse Theory, Concentration Dependence, and Tube Dilation

11.1 Introduction
11.2 Entanglement Region
11.3 Onset of Entanglement
11.4 Tube Dilation
Appendix 11.A — Blending Law in Binary Blends
References

12. Nonlinear Relaxation Modulus of Entangled Polymers

12.1 Chain-Tension Relaxation
12.2 Comparison of Theory and Experiment
References

13. Number of Entanglement Strands per Cubed Entanglement Distance (nt)

13.1 Introduction
13.2 nt as a Universal Constant
13.3 Concentration Dependence
13.4 Polymer Chain Packing
13.5 Comments
Appendix 13.A — Rouse Segment vs. Kuhn Segment
References

14. Glass Transition-Related Thermorheological Complexity in Polystyrene Melts

14.1 Introduction
14.2 G(t) Functional Forms
14.3 J(t) Line-Shape Analyses
14.4 Entanglement-Free System Analyses
14.5 G.(ω) Spectra of Entanglement-Free Systems
14.6 Dynamic Anisotropy
14.7 Comparison of Af G and β Values
14.8 Tg and Structural Relaxation Time
14.9 Dependences on ΔT = T – Tg
14.10 Structure from G(t)
14.11 Frictional Slowdown and Structural Growth
14.12 K Values Near Tg
14.13 Internal and Zero-Shear Viscosity
Appendix 14.A — Calculating G(ω) from G(t)
References

15. Basic Mechanism of Thermorheological Complexity

15.1 TRC Mechanism
15.2 Breakdown of Stokes–Einstein Relation (BSE)
15.3 Comparing TRC and BSE
15.4 TRC and the Glass Transition
15.5 Literature Comparisons
Appendix 15.A — Comparison with Two-State Model of BSE
References

16. Monte Carlo Simulations — Rouse Chains

16.1 Simulation Scheme
16.2 Step Shear Strain Simulation
16.3 Equilibrium Simulation
16.4 Simulation vs. Theory
Appendix 16.A — Stress Tensor Expressions
Appendix 16.B — Relaxation Modulus Functional Form
References

17. Monte Carlo Simulations — Fraenkel Chains (Linear Viscoelasticity)

17.1 Fraenkel Chain Model
17.2 Equilibrium Relaxation Modulus
17.3 Step Strain Simulation
17.4 Simulation vs. Experiment
17.5 Resolving the Rouse–Kuhn Paradox
Appendix 17.A — Virial Theorem for Fraenkel Dumbbell
Appendix 17.B — Dynamic Couplings Contribution
References

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