Constitutive Equations for Polymer Melts and Solutions

Constitutive Equations for Polymer Melts and Solutions presents a description of important constitutive equations for stress and birefringence in polymer melts, as well as in dilute and concentrated solutions of flexible and rigid polymers, and in liquid crystalline materials. The book serves as an introduction and guide to constitutive equations, and to molecular and phenomenological theories of polymer motion and flow. The chapters in the text discuss topics on the flow phenomena commonly associated with viscoelasticity; fundamental elementary models for understanding the rheology of melts, solutions of flexible polymers, and advanced constitutive equations; melts and concentrated solutions of flexible polymer; and the rheological properties of real liquid crystal polymers. Chemical engineers and physicists will find the text very useful.

PrefaceChapter 1. Introduction to Constitutive Equations for Viscoelastic Fluids 1.1 Introduction 1.2 Viscoelastic Flow Phenomena Rod-Climbing Extrudate Swell Tubeless Siphon Vortex Formation in Contraction Flows Other Examples 1.3 Viscoelastic Measurements Shear Thinning Normal Stresses in Shear Time-Dependent Viscosity Stress Relaxation Recoil Sensitivity to Deformation Type 1.4 Deformation Gradient, Velocity Gradient, and Stress The Deformation Gradient The Velocity Gradient The State-of-Stress Tensor 1.5 Relating Deformation and Stress Viscoelastic Simple Fluids The Newtonian Limit The Elastic Limit Frame Invariance Examples of the Finger Tensor Relationship Between the Finger tensor and the Velocity Gradient 1.6 A Simple Viscoelastic Constitutive Equation Integral Version Differential Version Predictions 1.7 SummaryChapter 2. Classical Molecular Models 2.1 Introduction 2.2 The Equilibrium State Configuration Distribution Function Polymer Chains as Hookean Springs 2.3 The Stress Tensor Derivation from Spring Force Derivation from Virtual Work 2.4 Rubber Elasticity Theory 2.5 The Temporary Network Model Derivation of Constitutive Equation Assumptions of the Green-Tobolsky Model Successes and Limitations of the Green-Tobolsky Model 2.6 The Elastic Dumbbell Model The Langevin Equation The Smoluchowski Equation The Constitutive Equation 2.7 The Rouse Model The Langevin Equation Normal Mode Transformation The Stress Tensor and Constitutive Equation Approximation for Slow Modes Assumptions of the Rouse Model 2.8 Linear Viscoelasticity Distribution of Relaxation Times Time-Temperature Superposition Nonlinear Superposition 2.9 SummaryChapter 3. Continuum Theories 3.1 Introduction 3.2 The Constitutive Equation of Linear Viscoelasticity Shear Other Deformations 3.3 Frame Invariance 3.4 Oldroyd's Constitutive Equations Convected Time Derivatives Upper- and Lower-Convected Maxwell Equations Oldroyd's Simple Equations Corotational Maxwell Equation 3.5 The Kaye-BKZ Class of Equations The Strain Energy Function The History Integral Shear Time-Strain Separability Lodge-Meissner Relationship Other types of Deformation 3.6 Other Strain History Integrals Wagner's First Equation Superposition Integral Equation Tanner-Simmons Equation 3.7 SummaryChapter 4. Reptation Theories for Melts and Concentrated Solutions 4.1 Introduction 4.2 Simplifying Features of Melts Chains in melts are ideal No Hydrodynamic Interaction in Melts Stress-Optic Law for Melts 4.3 Crossover to Entanglement Effects Appearance of a Plateau Modulus Meaning of the Plateau 4.4 The Doi-Edwards Constitutive Equation Reptation Nonlinear Modulus The Probability Distribution Function The Free Energy and the Stress Tensor The Constitutive Equation Premises of the Doi-Edwards Model 4.5 Approximations to the Doi-Edwards Equation Currie's Potential Larson's Potential Approximation Based on the Seth Elastic Strain Measure Differential Approximation 4.6 Predictions of Reptation Theories Molecular-Weight Dependence Relaxation Spectrum Nonlinear Viscoelasticity 4.7 Curtiss-Bird Theory 4.8 SummaryChapter 5. Constitutive Models with Nonaffine Motion 5.1 Introduction 5.