Preface xv Acknowledgments xix Introduction xxi About the Companion Website xxxi Part I Linear Viscoelasticity and Experimental Methods 1 1 Phenomenological Description of Linear Viscoelasticity 3 1.1 Basic Modes of Deformation 3 1.1.1 Startup shear 4 1.1.2 Step Strain and Shear Cessation from Steady State 5 1.1.3 Dynamic or Oscillatory Shear 5 1.2 Linear Responses 5 1.2.1 Elastic Hookean Solids 6 1.2.2 Viscous Newtonian Liquids 6 1.2.3 Viscoelastic Responses 7 1.2.3.1 Boltzmann Superposition Principle for ...
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Preface xv Acknowledgments xix Introduction xxi About the Companion Website xxxi Part I Linear Viscoelasticity and Experimental Methods 1 1 Phenomenological Description of Linear Viscoelasticity 3 1.1 Basic Modes of Deformation 3 1.1.1 Startup shear 4 1.1.2 Step Strain and Shear Cessation from Steady State 5 1.1.3 Dynamic or Oscillatory Shear 5 1.2 Linear Responses 5 1.2.1 Elastic Hookean Solids 6 1.2.2 Viscous Newtonian Liquids 6 1.2.3 Viscoelastic Responses 7 1.2.3.1 Boltzmann Superposition Principle for Linear Response 7 1.2.3.2 General Material Functions in Oscillatory Shear 8 1.2.3.3 Stress Relaxation from Step Strain or Steady-State Shear 8 1.2.4 Maxwell Model for Viscoelastic Liquids 8 1.2.4.1 Stress Relaxation from Step Strain 9 1.2.4.2 Startup Deformation 10 1.2.4.3 Oscillatory (Dynamic) Shear 11 1.2.5 General Features of Viscoelastic Liquids 12 1.2.5.1 Generalized Maxwell Model 12 1.2.5.2 Lack of Linear Response in Small Step Strain: A Dilemma 13 1.2.6 Kelvin-Voigt Model for Viscoelastic Solids 14 1.2.6.1 Creep Experiment 15 1.2.6.2 Strain Recovery in Stress-Free State 15 1.2.7 Weissenberg Number and Yielding during Linear Response 16 1.3 Classical Rubber Elasticity Theory 17 1.3.1 Chain Conformational Entropy and Elastic Force 17 1.3.2 Network Elasticity and Stress-Strain Relation 18 1.3.3 Alternative Expression in terms of Retraction Force and Areal Strand Density 20 References 21 2 Molecular Characterization in Linear Viscoelastic Regime 23 2.1 Dilute Limit 23 2.1.1 Viscosity of Einstein Suspensions 23 2.1.2 Kirkwood-Riseman Model 24 2.1.3 Zimm Model 24 2.1.4 Rouse Bead-Spring Model 25 2.1.4.1 Stokes Law of Frictional Force of a Solid Sphere (Bead) 26 2.1.4.2 Brownian Motion and Stokes-Einstein Formula for Solid Particles 26 2.1.4.3 Equations of Motion and Rouse Relaxation Time R27 2.1.4.4 Rouse Dynamics for Unentangled Melts 28 2.1.5 Relationship between Diffusion and Relaxation Time 29 2.2 Entangled State 30 2.2.1 Phenomenological Evidence of chain Entanglement 30 2.2.1.1 Elastic Recovery Phenomenon 30 2.2.1.2 Rubbery Plateau in Creep Compliance 31 2.2.1.3 Stress Relaxation 32 2.2.1.4 Elastic Plateau in Storage Modulus G' 32 2.2.2 Transient Network Models 34 2.2.3 Models Depicting Onset of Chain Entanglement 35 2.2.3.1 Packing Model 35 2.2.3.2 Percolation Model 38 2.3 Molecular-Level Descriptions of Entanglement Dynamics 39 2.3.1 Reptation Idea of de Gennes 39 2.3.2 Tube Model of Doi and Edwards 41 2.3.3 Polymer-Mode-Coupling Theory of Schweizer 43 2.3.4 Self-diffusion Constant versus Zero-shear Viscosity 44 2.3.5 Entangled Solutions 46 2.4 Temperature Dependence 47 2.4.1 Time-Temperature Equivalence 47 2.4.2 Thermo-rheological Complexity 48 2.4.3 Segmental Friction and Terminal Relaxation Dynamics 49 References 50 3 Experimental Methods 55 3.1 Shear Rheometry 55 3.1.1 Shear by Linear Displacement 55 3.1.2 Shear in Rotational Device 56 3.1.2.1 Cone-Plate Assembly 56 3.1.2.2 Parallel Disks 57 3.1.2.3 Circular Couette Apparatus 58 3.1.3 Pressure-Driven Apparatus 59 3.1.3.1 Capillary Die 60 3.1.3.2 Channel Slit 61 3.2 Extensional Rheometry 63 3.2.1 Basic Definitions of Strain and Stress 63 3.2.2 Three Types of Devices 64 3.2.2.1 Instron Stretcher 64 3.2.2.2 Meissner-Like Sentmanat Extensional Rheometer 65 3.2.2.3 Filament Stretching Rheometer 65 3.3 In Situ Rheostructural Methods 66 3.3.1 Flow Birefringence 66 3.3.1.1 Stress Optical Rule 67 3.3.1.2 Breakdown of Stress-Optical Rule 68 3.3.2 Scattering (X-Ray, Light, Neutron) 69 3.3.3 Spectroscopy (NMR, Fluorescence, IR, Raman, Dielectric) 69 3.3.4 Microrheology and Microscopic Force Probes 69 3.4 Advanced Rheometric Methods 69 3.4.1 Superposition of Small-Amplitude Oscillatory Shear and Small Step Strain during Steady Continuous Shear 69 3.4.2 Rate or Stress Switching Multistep Platform 70 3.5 Conclusion 70 References 71 4 Characterization of Deformation Field Using Differen
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