Constitutive Equations for Polymer Melts and Solutions

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 5.2 Gordon-Schowalter Convected Derivative The Stress Tensor The Convected Derivative 5.3 Johnson-Segalman Model Elastic Strain Measure Predictions of the Johnson-Segalman Model Forcing Corotation of Principal Stress and Strain Axes Time-Strain Separability 5.4 Partially-Extending Convected Derivative Shear Damping Function Predictions in Steady Flows Integral Equation 5.5 Irreversibility of Nonaffine Motion Reversing Deformations The Tube Picture Differential Formulation of Irreversibility 5.6 White-Metzner Equation Steady-State Flows Sudden Deformations 5.7 SummaryChapter 6. Nonseparable Constitutwe Models 6.1 Introduction 6.2 Giesekus and Leonov Models Giesekus Model Leonov Model Predictions of the Leonov and Giesekus Models 6.3 Network Models Yamamoto's Model Phan-Thien/Tanner Model Criticisms of the Phan-Thien/Tanner Model Model of Acierno, La Mantis, Marrucci, and Titomanlio Other Structural Models General Network Model: Differential and Integral Form The Equations of Bird and Carreau 6.4 Configuration Distribution Functions Green-Tobolsky Network Model Rouse-Zimm Dumbbell Model Other Models 6.5 SummaryChapter 7. Comparison of Constitutive Equations for Melts 7.1 Introduction Considerations Affecting the Choice of Constitutive Equation Approach Taken in this Chapter 7.2 The Relationship Between Integral and Differential Constitutive Equations Network Integral Equations Differential Analogs for Separable Kaye-BKZ Equations Differential Analogs for Nonseparable Kaye-BKZ Equations Comparison of Kaye-BKZ Equations with their Differential Analogs Comparison of Separable and Nonseparable Differential Constitutive Equations Alignment Strength versus Flow Strength 7.3 Comparing Constitutive Equations to Melt Data Differential Constitutive Equations Alignment Strength and the Damping Function Constitutive Equations with a Dependence on Alignment Strength 7.4 Summary AppendixChapter 8. Viscoelasticity of Dilute Polymer Solutions 8.1 Introduction 8.2 Linear Viscoelasticity Rouse model Hydrodynamic Interaction High frequency Behavior 8.3 Non-Newtonian Viscosity 8.4 Expressions for the Stress Tensor Kirkwood-Riseman Expression Giesekus Expression 8.5 Dumbbells with Shear Thinning Dumbbells with Hydrodynamic Interaction Dumbbells with Excluded Volume Dumbbells with Finite Extensibility Dumbbells with Internal Viscosity Summary of Dumbbell Models 8.6 Extensional Flow The Effect of Finite Extensibility Dumbbells with Variable Drag 8.7 Suspensions of Rigid Particles Rigid Dumbbells Rigid Ellipsoids 8.8 SummaryChapter 9. Constitutive Equations for Special Flows 9.1 Introduction 9.2 Flows of Constant Stretch History Viscometric Flows Steady extensional Flows General Flows of Constant Stretch History Planar Flows of Constant Stretch History 9.3 Retarded Motion Expansion Conditions for the Validity of the Retarded Motion Expansion Numerical Calculations with the Retarded Motion Expansion 9.4 Foundations of Constitutive Theory Oldroyd's General 'Elastico-Viscous Liquid' Coleman and No11's Viscoelastic 'Simple Fluid' Perturbation Expansions for Small Strain Amplitudes 9.5 SummaryChapter 10. Theories for Nondilute Solutions of Rodlike Molecules 10.1 Introduction 10.2 Semidilute Regime Diffusion Coefficient Doi-Edwards Constitutive Equation for Semidilute Solutions of Rods 10.3 The Isotropic to Nematic Transition Onsager theory Flory Lattice Theory Maier-Saupe Theory 10.4 Doi Constitutive Equation for Nematic Polymers Dynamic Equation for the Order Parameter The Stress Tensor Shear Viscosity Predictions 10.5 Statics of Liquid Crystals Theory of Spatially Varying Orientation in Nematics Magnetic Fields Textures of Nematics 10.6 Viscous Flow of Nematics Ericksen's Transversely Isotropic Fluid Leslie-Ericksen Theory Boundary Effects 10.7 Rheology of Liquid Crystal Polymers Temperature-Dependent Rheology Birefringence Relationship Between Linear and Nonlinear Rheology First Normal Stress Difference Complex Time-Dependent Stresses Domain Theories 10.8 SummaryAuthor IndexSubject Index