لایب سان

y 2 Kinematics and Stresses of Deformable Bodies, 15 2.1 Introduction, 15 2.2 Description of Motion, 16 2.3 Some Representative Flow Fields, 18 2.3.1 Steady-State Shear Flow Field, 18 2.3.2 Steady-State Elongational Flow Field, 19 xii CONTENTS 2.4 Deformation Gradient Tensor, Strain Tensor, Velocity Gradient Tensor and Rate-of-Strain Tensor, 20 2.4.1 Deformation Gradient Tensor, 20 2.4.2 Strain Tensor, 22 2.4.3 Velocity Gradient Tensor and Rate-of-Strain Tensor, 25 2.5 Kinematics in Moving (Convected) Coordinates, 29 2.5.1 Convected Strain Tensor, 30 2.5.2 Time Derivative of Convected Coordinates, 32 2.6 The Description of Stress and Material Functions, 35 Appendix 2A: Properties of Second-Order Tensors, 38 Invariants, 38 Principal Values and Principal Directions, 39 The Polar Decomposition Theorem, 40 Appendix 2B: Tensor Calculus, 41 Curvilinear Coordinates and Metric Tensors, 41 Time Derivatives of Second-Order Tensors, 42 Problems, 45 Notes, 48 References, 48 3 Continuum Theories for the Viscoelasticity of Flexible Homogeneous Polymeric Liquids, 50 3.1 Introduction, 50 3.2 Differential-Type Constitutive Equations for Viscoelastic Fluids, 51 3.2.1 Single-Mode Differential-Type Constitutive Equations, 51 3.2.2 Multimode Differential-Type Constitutive Equations, 58 3.3 Integral-Type Constitutive Equations for Viscoelastic Fluids, 60 3.4 Rate-Type Constitutive Equations for Viscoelastic Fluids, 64 3.5 Predicted Material Functions and Experimental Observations, 66 3.5.1 Material Functions for Steady-State Shear Flow, 66 3.5.2 Material Functions for Oscillatory Shear Flow, 72 3.5.3 Material Functions for Steady-State Elongational Flow, 76 3.6 Summary, 80 Appendix 3A: Derivation of Equation (3.5), 81 Appendix 3B: Derivation of Equation (3.16), 82 Appendix 3C: Derivation of Equation (3.29), 83 Appendix 3D: Cayley–Hamilton Theorem, 83 Appendix 3E: Derivation of Equation (3.97), 84 Appendix 3F: Derivation of Equation (3.103), 85 Problems, 86 Notes, 88 References, 90 4 Molecular Theories for the Viscoelasticity of Flexible Homogeneous Polymeric Liquids, 91 4.1 Introduction, 91 CONTENTS xiii 4.2 Static Properties of Macromolecules and Stochastic Processes in the Motion of Macromolecular Chains, 93 4.2.1 Static Properties of Macromolecules, 94 4.2.2 Stochastic Processes in the Motion of Macromolecular Chains, 97 4.3 Molecular Theory for the Viscoelasticity of Dilute Polymer Solutions and Unentangled Polymer Melts, 102 4.3.1 The Rouse Model, 103 4.3.2 The Zimm Model, 106 4.3.3 Prediction of Rheological Properties, 109 4.4 Molecular Theory for the Viscoelasticity of Concentrated Polymer Solutions and Entangled Polymer Melts, 112 4.4.1 Reptation Mechanism and the Tube Model, 115 4.4.2 The Dynamics of a Primitive Chain, 117 4.4.3 Contour Length Fluctuation and Constraint Release Mechanism, 120 4.4.4 Constitutive Equations of State, 125 4.4.5 Comparison of Prediction with Experiment, 131 4.5 Summary, 142 Appendix 4A: Derivation of Equation (4.6), 143 Appendix 4B: Derivation of Equation (4.71), 145 Problems, 146 Notes, 147 References, 151 5 Experimental Methods for Measurement of the Rheological Properties of Polymeric Fluids, 153 5.1 Introduction, 153 5.2 Cone-and-Plate Rheometry, 154 5.2.1 Steady-State Shear Flow Measurement, 154 5.2.2 Oscillatory Shear Flow Measurement, 160 5.3 Capillary and Slit Rheometry, 163 5.3.1 Plunger-Type Capillary Rheometry, 163 5.3.2 Continuous-Flow Capillary Rheometry, 166 5.3.3 Slit Rheometry, 173 5.3.4 Critical Assessment of Capillary and Slit Rheometry, 180 5.3.5 Viscous Shear Heating in a Cylindrical or Slit Die, 188 5.4 Elongational Rheometry, 189 5.5 Summary, 193 Problems, 195 Notes, 198 References, 198 xiv CONTENTS Part II Rheological Behavior of Polymeric Materials 6 Rheology of Flexible Homopolymers, 203 6.1 Introduction, 203 6.2 Rheology of Linear Flexible Homopolymers, 204 6.2.1 Temperature Dependence of Steady-State Shear Viscosity of Linear Flexible Homopolymers, 204 6.2.2 Temperature Dependence of Relaxation Time and First Normal Stress Difference in Steady-State Shear Flow of Linear Flexible Homopolymers, 210 6.2.3 Temperature-Independent Correlations for the Linear Dynamic Viscoelastic Properties of Linear Flexible Homopolymers, 213 6.2.4 Effects of Molecular Weight and Molecular Weight Distribution on the Rheological Behavior of Linear Flexible Homopolymers, 219 6.3 Rheology of Flexible Homopolymers with Long-Chain Branching, 233 6.4 Summary, 241 Problems, 241 Notes, 243 References, 244 7 Rheology of Miscible Polymer Blends, 247 7.1 Introduction, 247 7.2 Phase Behavior of Polymer Blend Systems, 248 7.3 Experimental Observations of the Rheological Behavior of Miscible Polymer Blends, 252 7.3.1 Time–Temperature Superposition in Miscible Polymer Blends, 252 7.3.2 Rheology of Polymer Blends Exhibiting UCST, 261 7.3.3 Rheology of Polymer Blends Exhibiting LCST, 269 7.4 Molecular Theory for the Linear Viscoelasticity of Miscible Polymer Blends and Comparison with Experiment, 273 7.4.1 Linear Viscoelasticity Theory for Miscible Polymer Blends, 274 7.4.2 Comparison of Theory with Experiment, 279 7.5 Plateau Modulus of Miscible Polymer Blends, 286 7.6 Summary, 288 Problems, 290 Notes, 291 References, 292 CONTENTS xv 8 Rheology of Block Copolymers, 296 8.1 Introduction, 296 8.2 Oscillatory Shear Rheometry of Microphase-Separated Block Copolymers Exhibiting Upper Critical Order–Disorder Transition Behavior, 301 8.2.1 Oscillatory Shear Rheometry of Symmetric or Nearly Symmetric Block Copolymers, 302 8.2.2 Oscillatory Shear Rheometry of Highly Asymmetric Block Copolymers, 306 8.2.3 Effect of Thermal History on the Oscillatory Shear Rheometry of Block Copolymers, 319 8.3 Oscillatory Shear Rheometry of Microphase-Separated Block Copolymers Exhibiting Lower Critical Disorder–Order Transition Behavior, 327 8.4 Linear Viscoelasticity of Disordered Block Copolymers, 331 8.4.1 Effect of Molecular Weight on the Zero-Shear Viscosity of Disordered Diblock Copolymers, 332 8.4.2 Effect of Block Length Ratio on the Linear Dynamic Viscoelasticity of Disordered Block Copolymers, 337 8.4.3 Molecular Theory for the Linear Viscoelasticity of Disordered Block Copolymers, 345 8.5 Stress Relaxation Modulus of Microphase-Separated Block Copolymer Upon Application of Step-Shear Strain, 355 8.6 Steady-State Shear Viscosity of Microphase-Separated Block Copolymers, 359 8.7 Summary, 363 Notes, 364 References, 365 9 Rheology of Liquid-Crystalline Polymers, 369 9.1 Introduction, 369 9.2 Theory for the Rheology of LCPs, 379 9.2.1 Theory for Rigid Rodlike Macromolecules with Monodomains, 379 9.2.2 Theory for Rigid Rodlike Macromolecules with Polydomains, 394 9.3 Rheological Behavior of Lyotropic LCPs, 400 9.4 Rheological Behavior of Thermotropic Main-Chain LCPs, 406 9.4.1 Effect of Thermal History on the Rheological Behavior of Thermotropic Main-Chain LCPs, 406 9.4.2 Transient Shear Flow of Thermotropic Main-Chain LCPs, 413 9.4.3 Flow Aligning Behavior of Thermotropic Main-Chain LCPs, 424 9.4.4 Intermittent Shear Flow of Thermotropic Main-Chain LCPs, 426 9.4.5 Evolution of Dynamic Moduli of Thermotropic Main-Chain LCPs Upon Cessation of Shear Flow, 428 xvi CONTENTS 9.4.6 Effect of Preshearing of Thermotropic Main-Chain LCPs on the Rheological Behavior, 430 9.4.7 Reversal Flow of Thermotropic Main-Chain LCPs, 433 9.4.8 Effect of Molecular Weight on the Rheological Behavior of Thermotropic Main-Chain LCPs, 435 9.4.9 Effect of Bulkiness of Pendent Side Groups on the RheoOptical Behavior of Thermotropic Main-Chain LCPs, 441 9.5 Rheological Behavior of Thermotropic Side-Chain LCPs, 444 9.6 Summary, 451 Appendix 9A: Derivation of Equation (9.3), 454 Appendix 9B: Derivation of Equation (9.11), 455 Appendix 9C: Derivation of Equation (9.15), 457 Appendix 9D: Derivation of Equation (9.23), 458 Appendix 9E: Derivation of Equation (9.28), 460 Appendix 9F: Derivation of Equation (9.30), 461 Appendix 9G: Derivation of Equation (9.49), 462 Appendix 9H: Derivation of Equation (9.50), 463 Notes, 464 References, 465 10 Rheology of Thermoplastic Polyurethanes, 470 10.1 Introduction, 470 10.2 Effect of Thermal History on the Rheological Behavior of TPUs, 474 10.2.1 Time Evolution of Dynamic Moduli of TPU during Isothermal Annealing, 474 10.2.2 Thermal Transitions in TPU during Isothermal Annealing, 477 10.2.3 Hydrogen Bonding in TPU during Isothermal Annealing, 479 10.3 Linear Dynamic Viscoelasticity of TPUs, 484 10.3.1 Frequency Dependence of Dynamic Moduli of TPU under Isothermal Conditions, 484 10.3.2 Temperature Dependence of Dynamic Moduli of TPU during Isochronal Dynamic Temperature Sweep Experiment, 486 10.4 Steady-State Shear Viscosity of TPU, 488 10.5 Summary, 490 References, 491 11 Rheology of Immiscible Polymer Blends, 493 11.1 Introduction, 493 11.2 Experimental Observations of Rheology–Morphology Relationships in Immiscible Polymer Blends, 495 11.2.1 Effect of Flow Geometry on the Steady-State Shear Viscosity and Morphology of Immiscible Polymer Blends, 495 11.2.2 Effect of Blend Composition on the Steady-State Shear Flow Properties of Immiscible Polymer Blends, 504 CONTENTS xvii 11.2.3 Linear Dynamic Viscoelastic Properties of Immiscible Polymer Blends, 511 11.2.4 Extrudate Swell of Immiscible Polymer Blends, 512 11.3 Consideration of Large Drop Deformation and Bulk Rheological Properties of Immiscible Polymer Blends in Pressure-Driven Flow, 519 11.3.1 Finite Element Analysis of Large Drop Deformation in the Entrance Region of a Cylindrical Tube, 524 11.3.2 Theoretical Approach to the Prediction of Rheology– Morphology–Processing Relationships in Pressure-Driven Flow of Immiscible Polymer Blends, 536 11.4 Summary, 542 Problems, 543 Notes, 544 References, 544 12 Rheology of Particulate-Filled Polymers, Nanocomposites, and Fiber-Reinforced Thermoplastic Composites, 547 12.1 Introduction, 547 12.2 Rheology of Particulate-Filled Polymers, 548 12.2.1 Rheology of Particulate-Filled Molten Thermoplastics and Elastomers, 549 12.2.2 Rheology of Molten Thermoplastics with Chemically Treated Fillers, 559 12.2.3 Theoretical Consideration of the Rheology of Particulate-Filled Polymers, 565 12.3 Rheology of Nanocomposites, 569 12.3.1 Rheology of Organoclay Nanocomposites Based on Thermoplastic Polymer, 575 12.3.2 Rheology of Organoclay Nanocomposites Based on Block Copolymer, 583 12.3.3 Rheology of Organoclay Nanocomposites Based on End-Functionalized Polymer, 593 12.4 Rheology of Fiber-Reinforced Thermoplastic Composites, 603 12.4.1 Theoretical Consideration of Fiber Orientation in Flow, 603 12.4.2 Experimental Observations, 609 12.5 Summary, 614 Appendix 12A: Derivation of Equation (12.19), 615 Appendix 12B: Derivation of Three Material Functions for Steady-State Shear Flow from Equation (12.30), 616 Problems, 617 Notes, 618 References, 620 xviii CONTENTS 13 Rheology of Molten Polymers with Solubilized Gaseous Component, 623 13.1 Introduction, 623 13.2 Rheological Behavior of Molten Polymers with Solubilized Gaseous Component, 624 13.2.1 Experimental Methods for Rheological Measurements of Molten Polymers with Solubilized Gaseous Component, 624 13.2.2 Experimental Observations of Reduction in Melt Viscosity by Solubilized Gaseous Component, 629 13.3 Theoretical Consideration of Reduction in Melt Viscosity by Solubilized Gaseous Component, 639 13.3.1 Depression of Glass Transition Temperature of Amorphous Polymer by the Addition of Low-Molecular-Weight Soluble Diluent, 639 13.3.2 Depression of Melting Point of Semicrystalline Polymer by the Addition of Low-Molecular-Weight Soluble Diluent, 641 13.3.3 Theoretical Interpretation of Reduction in Melt Viscosity by Solubilized Gaseous Component, 641 13.4 Summary, 647 Problems, 648 Notes, 649 References, 649 14 Chemorheology of Thermosets, 651 14.1 Introduction, 651 14.2 Chemorheology of Unsaturated Polyester, 656 14.2.1 Viscosity Rise during Cure of Neat Unsaturated Polyester, 658 14.2.2 Chemorheological Model for Neat Unsaturated Polyester, 660 14.2.3 Cure Kinetics of Neat Unsaturated Polyester, 664 14.2.4 Effects of Particulates on the Chemorheology of Unsaturated Polyester, 673 14.2.5 Effects of Low-Profile Additive on the Chemorheology of Unsaturated Polyester, 677 14.2.6 Oscillatory Shear Flow during Cure of Unsaturated Polyester, 682 14.3 Chemorheology of Epoxy Resin, 683 14.4 Chemorheology of Thermosetting Polyurethane, 688 14.5 Summary, 691 Problems, 692 Notes, 693 References, 693 Author Index, 695 Subject Index, 704

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