Holdings: Polymeric liquids and networks: dynamics and rheology

Polymeric liquids and networks: dynamics and rheology:

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Bibliographic Details
Main Author:	Graessley, William Walter (Author)
Format:	Book
Language:	English
Published:	London [u.a.] Garland Science 2008
Subjects:	Polymer networks Polymer solutions Rheology Polymerlösung Polymeres Netzwerk Rheologie
Online Access:	Inhaltsverzeichnis
Physical Description:	XIX, 801 S. graph. Darst.
ISBN:	9780815341710 0815341717

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adam_text	Contents Dedication Page ................................................................................................................................ v Preface ...................................................................................................................................................xvii Chapter 1 Monomeric Liquid Dynamics ............................................................... 1 1.1 Introduction .............................................................................................. 1 1.2 Molecular Liquids ................................................................................... 3 1.3 Liquid State Transport Coefficients ................................................ 7 1.3.1 Viscosity ........................................................................................ 11 The Arrhenius Equation ......................................................... 13 The Fulcher-Tammann and Williams-Landel-Ferry Equations ....................................................................... 13 Viscosity-Temperature Fits .................................................. 16 1.3.2 Diffusion ....................................................................................... 19 Diffusion Equations ................................................................. 19 Tracer and Self Diffusion ....................................................... 21 1.3.3 Diffusion Measurement Methods ..................................... 24 1.4 The Viscosity-Diffusion Relationship ............................................. 26 1.4.1 A Random Walk Approach ................................................... 27 1.4.2 The Stokes-Einstein Equation .............................................. 28 The Langevin Equation .......................................................... 28 Velocity and Displacement .................................................. 30 Equipartition and Mean Displacement .......................... 30 1.4.3 Orientational Diffusion and Relaxation .......................... 34 1.4.4 Experimental Comparisons ................................................. 35 1.5 Viscoelasticity in Monomeric Liquids ............................................ 39 1.5.1 Modulus ....................................................................................... 41 1.5.2 Relaxation Time ........................................................................ 42 1.5.3 Common Theoretical Forms ............................................... 45 vil Contents Ί .6 The Glass Temperature ........................................................................ 46 1.6.1 Supercooling and Vitrification ........................................... 46 1.6.2 Structural Mixtures .................................................................. 47 1.6.3 Glass Temperature Detection ............................................. 50 Specific Volume ........................................................................ 50 Specific Heat ............................................................................... 51 1.6.4 Effects on Viscosity .................................................................. 52 1.6.5 History Dependence ............................................................... 53 1.7 Analogies and Parallels ......................................................................... 56 1.7.1 Hard Spheres .............................................................................. 56 1.7.2 Colloidal Spheres ...................................................................... 59 1.7.3 Monomeric Spheres ................................................................ 61 1.8 Properties Near the Glass Temperature ....................................... 62 1.8.1 The Strong-Fragile Classification ....................................... 62 1.8.2 Relaxation Time Distribution .............................................. 65 Mechanical Response ............................................................. 66 Electromagnetic Response ................................................... 66 1.8.3 Stokes-Einstein Departures .................................................. 69 Self Diffusion .............................................................................. 70 Tracer Diffusion ......................................................................... 71 Related Phenomena ................................................................ 72 1.8.4 Liquid Heterogeneity .............................................................. 74 A Two-Microstate Interpretation ...................................... 75 A More Detailed Picture ........................................................ 76 1.9 Theories about Vitrification ................................................................ 78 1.10 Free Volume .............................................................................................. 82 Appendix 1.1 Listing and Characteristics of Polymer Species ................................................................................. 87 References .................................................................................................. 93 Chapter 2 Linear Viscoelastidty .................................................................................101 2.1 Polymeric Viscoelasticity .....................................................................101 2.2 Linear Viscoelastic Functions .............................................................103 2.2.1 Stress Relaxation .......................................................................104 2.2.2 Creep and Creep Recovery ..................................................106 2.2.3 Steady-State Oscillatory Response ...................................109 2.2.4 Experimental Aspects .............................................................115 Stress Relaxation .......................................................................115 Creep and Recoil ......................................................................116 Dynamic Compliance and Modulus ...............................116 Contents 2.3 Linear Response Properties ................................................................116 2.3.1 Limits of Linear Response .....................................................117 2.3.2 Boltzmann Superposition .....................................................118 2.3.3 Relationships between Response Functions ................119 Kramers-Kronig Relations .....................................................121 Limiting Functions ...................................................................123 2.3.4 Complex Notation ...................................................................124 2.3.5 Viscoelastic Models .................................................................124 Maxwell ........................................................................................126 Burgers ..........................................................................................128 Davidson-Cole ...........................................................................129 Barlow-Erginsav-Lamb ...........................................................129 2.3.6 Auxiliary Response Functions .............................................130 2.3.7 Linear Viscoelastic Parameters ............................................132 2.3.8 Extensional Deformation ......................................................135 2.4 Temperature Dependence .................................................................136 2.4.1 Time-Temperature Superposition ....................................136 2.4.2 Temperature Shift Factors ....................................................142 2.4.3 Thermorheological Complexity ........................................144 2.5 Flow-Related Properties .......................................................................148 2.5.1 The Terminal Dispersion .......................................................148 2.5.2 Plateau Modulus .......................................................................151 2.5.3 Recoverable Compliance ......................................................156 2.5.4 Zero-Shear Viscosity ................................................................158 2.5.5 Commentary ..............................................................................163 2.6 Molecular Origin of Polymeric Response ....................................164 2.6.1 Conformational Rearrangement .......................................165 2.6.2 Relaxation of Stress .................................................................168 Appendix 2.1 Fourier and Laplace Transforms ........................174 References ..................................................................................................175 Chapter 3 Stress Response to Shear Deformations .....................................179 3.1 Introduction ..............................................................................................179 3.1.1 Contact Forces, Traction, and Stress ..............................180 3.1.2 Elements of Matrix Algebra .................................................189 3.1.3 Reference Frame .......................................................................194 3.2 Conservation of Mass and Momentum .......................................197 3.2.1 Equation of Continuity ..........................................................197 3.2.2 Equation of Motion .................................................................198 Contents 3.2.3 Rheological Considerations................................................. 201 Constitutive Equations ...........................................................201 Pressure .........................................................................................201 Inerţial Effects .............................................................................202 3.3 Simple Shear Deformation .................................................................202 3.3.1 Symmetry Considerations ....................................................204 3.3.2 Equilibrium Stress for Solids ................................................206 3.3.3 Steady-State Stress for Liquids ...........................................207 3.4 Polymeric Liquid Response ................................................................209 3.4.1 Steady-State Properties .........................................................210 Viscosity ........................................................................................211 First Normal Stress Difference ............................................216 Approximate Relationships ..................................................219 Second Normal Stress Difference .....................................225 3.4.2 Start-up and Shut-down Behavior ...................................227 Start-up from Rest ....................................................................228 Relaxation from Steady State .............................................231 3.4.3 Relaxation from Large Step Strains ..................................233 Lodge-Meissner Relation ......................................................234 Strain-Time Factorability ......................................................234 Normal Stress Ratio .................................................................239 3.5 Time-Temperature Superposition ..................................................239 References ..................................................................................................243 Chapter 4 Stress-Deformation Relationships ..................................................247 4.1 Deformation .............................................................................................247 4.1.1 Particle Position .........................................................................248 4.1.2 Particle Displacement .............................................................249 4.1.3 Displacement Gradient Tensor ..........................................251 4.1.4 Cauchy Strain Tensor .............................................................254 4.1.5 Finger Strain Tensor ................................................................257 4.1.6 Other Strain Measures ...........................................................261 Green and Piola Tensors ......................................................261 Deformation Rate Tensor .....................................................261 Infinitesimal Deformation Tensor .....................................264 4.1.7 Reference Frame Rotation ....................................................266 4.1.8 Scalar Invariants ........................................................................267 4.2 Constitutive Considerations ..............................................................268 4.2.1 Incompressibility ......................................................................269 4.2.2 Reference Frame Indifference .............................................271 Contents 4.3 Elastic Response of Solids ...................................................................272 4.3.1 Neo-Hookean Solids ...............................................................273 4.3.2 The Rivlin Equation .................................................................276 4.3.3 Mooney-Rivlin Solids ..............................................................280 4.3.4 Valanis-Landel Formulation .................................................280 4.4 Viscoelastic Response of Liquids ......................................................281 4.4.1 The Lodge Model .....................................................................283 Simple Shear ..............................................................................285 Uniaxial Extension ....................................................................288 Extensional Flow Behavior ...................................................291 Assessment ..................................................................................300 4.4.2 Consistency Tests .....................................................................301 4.5 Strain-Dependent Models ..................................................................303 4.5.1 General KBKZ Properties .......................................................304 4.5.2 Simple Shear Histories ...........................................................304 4.5.3 Factorization ...............................................................................306 4.5.4 Irreversibility ...............................................................................310 Nonlinear Recoil .......................................................................311 Double Step Strain ..................................................................314 References ..................................................................................................316 Chapter 5 Experimental Aspects ...............................................................................319 5.1 Introduction ..............................................................................................319 5.2 Hookean Solids and Newtonian Liquids ......................................325 5.2.1 Simple Shear ..............................................................................326 Hookean Solids ..........................................................................326 Newtonian Liquids ..................................................................330 5.2.2 Uniaxial Extension ....................................................................331 Hookean Solids ..........................................................................331 Poisson Ratio ..............................................................................334 Newtonian Liquids ..................................................................335 5.2.3 Property Measurement ..........................................................337 Shear Modulus ..........................................................................337 Shear Viscosity ...........................................................................339 5.2.4 General Comments .................................................................343 5.3 Simple Shear Rheometry .....................................................................344 5.3.1 Analysis of Rotational Rheometers ...................................344 Concentric Rotating Plates ..................................................346 Concentric Cylinders ..............................................................349 Concentric Cone and Plate .................................................350 Contents 5.3.2 Analysis of Flow-Through Rheometers ...........................354 Capillary Flow ............................................................................355 Annular Flow ..............................................................................359 Slit Flow ........................................................................................361 5.3.3 Weissenberg-Rabinowitsch Procedures .........................363 Capillary Flow ............................................................................363 Slit Flow ........................................................................................366 Concentric Plates .....................................................................367 5.4 Comments on Shear Rheometry .....................................................369 5.4.1 Flow Instabilities .......................................................................370 Edge Instabilities .......................................................................370 Entry Region Vortices .............................................................372 Sharkskin, Slip, and Melt Fracture ....................................373 5.4.2 Instrumental Aspects ..............................................................377 Stiffness and Response Time ...............................................377 Wall Pressure ..............................................................................380 5.4.3 Other Issues ................................................................................382 5.4.4 Summary ......................................................................................383 5.5 Extensional Rheometry ........................................................................384 5.6 Optical Methods .....................................................................................386 5.6.1 Optical Birefringence ..............................................................387 5.6.2 Flow Modeling ..........................................................................390 References ..................................................................................................395 Chapter 6 Flexible-Chain Dynamics .........................................................................399 6.1 Methods and Forces .............................................................................400 6.2 Elastic Dumbbells ...................................................................................403 6.2.1 The Diffusion Equation ..........................................................405 6.2.2 External and Internal Distributions ..................................406 6.2.3 Flow-Induced Effects ..............................................................409 6.2.4 Stress ..............................................................................................411 6.2.5 Flow Properties ..........................................................................415 Relation to the Lodge Model ..............................................416 Association with Observables .............................................416 6.2.6 Extended Formulation ...........................................................418 6.3 The Rouse Model ....................................................................................419 6.3.1 Diffusion and Stress ................................................................421 6.3.2 Diffusion Coefficient ...............................................................423 6.3.3 Viscoelastic Properties ............................................................426 Matrix Diagonalization ..........................................................426 Association with Observables .............................................427 Contents 6.4 The Zimm Model...................................................................................430 6.4.1 Stress and Diffusion ................................................................434 6.4.2 Association with Observables .............................................435 6.4.3 Discussion ....................................................................................437 6.5 Dilute Solution Dynamics ...................................................................440 6.5.1 Linear Response ........................................................................443 Slow Dynamics ..........................................................................443 Excluded Volume Effects .......................................................447 High Frequency Response ....................................................451 6.5.2 Nonlinear Response ................................................................451 Shear Flows .................................................................................451 Stretching Flows .......................................................................454 6.6 Dynamics of Short Chains ..................................................................460 6.6.1 Dynamic Moduli .......................................................................462 6.6.2 Recoverable Compliance ......................................................464 6.6.3 Self Diffusion ..............................................................................465 6.6.4 Monomeric Unit Friction ......................................................468 Appendix 6.1 Integration Formulas for Calculating Averages of Distributions ....................................................................472 References ..................................................................................................474 Chapter 7 Entangled Chain Dynamics ...................................................................479 7.1 Entangled Melts ......................................................................................480 7.1.1 Polarizability and Polarity Aspects ....................................481 Stress-Optical Rule ..................................................................482 Dielectric Methods ..................................................................483 7.1.2 The Plateau Modulus ..............................................................484 7.1.3 The Shifted Rouse Formulation .........................................487 7.2 Reptation and the Tube Model .......................................................488 7.2.1 Doi-Edwards Theory ...............................................................489 7.2.2 Non-Mechanical Dynamics .................................................492 7.2.3 Dynamic-Mechanical Properties .......................................496 Gaussian Networks ..................................................................497 Step Strain Response ..............................................................498 7.3 Linear Viscoelasticity .............................................................................500 7.3.1 Dynamic Properties .................................................................501 7.3.2 Comparisons with Data ........................................................503 7.3.3 Competing Relaxation Mechanisms ...............................509 7.4 Constraint Release ..................................................................................510 7.4.1 Tracer Diffusion .........................................................................511 xiv Contents 7.4.2 Viscoelastic Aspects................................................................. 514 Single Component Properties ............................................514 Tracer Relaxation......................................................................518 7.5 Fluctuations............................................................................................... 520 7.5.1 Viscosity ........................................................................................520 7.5.2 Self Diffusion ..............................................................................527 7.5.3 Nonuniversality .........................................................................531 7.5.4 Simulations ..................................................................................533 7.6 Nonlinear Viscoelastic Properties ....................................................535 7.6.1 Step Shear Strain ......................................................................536 7.6.2 Step Extensional Strain ..........................................................539 7.6.3 Viscometric Functions ............................................................540 7.6.4 Irreversibility ...............................................................................541 7.7 Independent Alignment Approximation .....................................542 7.7.1 Shear Deformation ..................................................................543 7.7.2 Uniaxial Extension ....................................................................546 7.8 Theoretical Additions ............................................................................548 7.8.1 Critique .........................................................................................548 7.8.2 Commentary ..............................................................................550 7.8.3 Convective Constraint Release ...........................................552 Collective Approach ................................................................553 Pairwise junction Approach ................................................554 7.8.4 Comparisons and Discussion ..............................................556 References ..................................................................................................560 Chapter 8 Dynamics of Entangled Solutions ....................................................567 8.1 Introduction ..............................................................................................567 8.2 Friction-Insensitive Properties ...........................................................569 8.2.1 Plateau Modulus G° (φ) .........................................................569 Colby-Rubinstein Theory ......................................................571 Analysis of Data .........................................................................572 Compliance Support ..............................................................576 Entanglement Density Definition .....................................579 8.2.2 Recoverable Compliance β(φ, Μ)..................................... 581 8.2.3 Characteristic Shear Rate γο(φ, Μ).................................... 585 8.2.4 Characteristic Molecular Weight Мс(ф) .........................589 8.2.5 Characteristic Diffusion Dependence Ό(φ) ..................595 8.3 Concentration - Molecular Weight Diagrams ..........................596 8.4 Friction-Dependent Properties .........................................................598 8.4.1 Free Volume Theory ................................................................599 The Williams-Landel-Ferry Form .......................................600 Contents Chain End and Copolymer Effects ...................................602 Diluent Effects ............................................................................603 Homologous Series Data ......................................................605 Solutions .......................................................................................606 8.4.2 Monomeric Tracer Diffusion ...............................................612 8.4.3 Dilute Solutions .........................................................................616 Intrinsic Viscosity ......................................................................617 High Frequency Response ....................................................622 Discussion ....................................................................................623 References ..................................................................................................624 Chapter 9 Dynamics of Nonlinear Chains ...........................................................629 9.1 Long-Chain Branching .........................................................................629 9.1.1 Types of Structural Nonlinearity .......................................631 9.1.2 Plateau Modulus .......................................................................633 9.1.3 Nonlinear Rouse Chains ........................................................635 Linear Chains ..............................................................................637 Symmetric Three-Arm Stars ................................................640 Symmetric ŕ-Arm Stars ..........................................................643 Other Architectures .................................................................644 9.2 Linear Dynamics of Entangled Stars ..............................................644 9.2.1 Viscosity ........................................................................................644 Diluent Effects ............................................................................648 Temperature Effects ................................................................649 9.2.2 Recoverable Compliance ......................................................653 9.2.3 Self Diffusion ..............................................................................657 9.2.4 Thermorheological Complexity ........................................661 9.2.5 Exponential Prefactors ...........................................................663 9.3 Tube Model for Stars ............................................................................666 9.4 Constraint Release Effects for Stars ................................................672 9.4.1 Relaxation in Network Environments .............................672 9.4.2 Tracer Diffusion .........................................................................674 9.4.3 Dynamic Dilution Model ......................................................676 9.4.4 Discussion ....................................................................................681 Compliance Prediction ..........................................................681 Dynamic Dilution Commentary ........................................681 9.5 Hierarchy: H s, Combs and Networks ..........................................682 9.5.1 Dynamic Hierarchy ..................................................................683 Quantitative Aspects ...............................................................685 Terminal Relaxation ................................................................688 9.5.2 Н -Polymers.................................................................................. 690 Contents 9.5.3 Combs ....................................................................................693 9.5.4 Dangling Network Strands ...........................................700 9.6 Nonlinear Viscoelasticity ..................................................................701 9.6.1 Damping Function ...........................................................702 9.6.2 Extensional Behavior ........................................................706 References ...............................................................................................708 Chapter 1 0 Polydispersity Effects ................................................................................713 10.1 Introduction ...........................................................................................713 10.2 Macromolecular Heterogeneity ....................................................714 10.2.1 Averages ................................................................................715 10.2.2 Distribution Functions .....................................................716 10.2.3 Distribution Examples .....................................................718 Exponential Distributions ..............................................718 Branching Distributions ..................................................718 10.3 Molecular Weight Mixtures ............................................................719 10.3.1 Rouse and Tube Model Predictions ..........................721 Rouse Mixing Rules ..........................................................721 Doi-Edwards Mixing Rules ............................................723 10.3.2 Binary Linear-Chain Mixtures ......................................723 10.3.3 Double Reptation ..............................................................734 Binary Mixtures ..................................................................738 Continuous Distributions ...............................................739 Commentary .......................................................................746 The Inverse Problem ........................................................746 10.4 Mixtures of Architectures .................................................................748 10.4.1 Binary Linear-Star Mixtures ..........................................748 10.4.2 Continuous Distributions ...............................................750 10.4.3 Nonlinear Viscoelasticity ................................................757 Shear Thinning ...................................................................757 Strain Hardening ...............................................................758 Discussion .............................................................................761 References ...............................................................................................762 Appendix A Symbols ......................................................................................................................767 Appendix В Acronyms and Abbreviations ............................................................................775 Subject Index ......................................................................................................................................777 Author Index .......................................................................................................................................785
adam_txt	Contents Dedication Page . v Preface .xvii Chapter 1 Monomeric Liquid Dynamics . 1 1.1 Introduction . 1 1.2 Molecular Liquids . 3 1.3 Liquid State Transport Coefficients . 7 1.3.1 Viscosity . 11 The Arrhenius Equation . 13 The Fulcher-Tammann and Williams-Landel-Ferry Equations . 13 Viscosity-Temperature Fits . 16 1.3.2 Diffusion . 19 Diffusion Equations . 19 Tracer and Self Diffusion . 21 1.3.3 Diffusion Measurement Methods . 24 1.4 The Viscosity-Diffusion Relationship . 26 1.4.1 A Random Walk Approach . 27 1.4.2 The Stokes-Einstein Equation . 28 The Langevin Equation . 28 Velocity and Displacement . 30 Equipartition and Mean Displacement . 30 1.4.3 Orientational Diffusion and Relaxation . 34 1.4.4 Experimental Comparisons . 35 1.5 Viscoelasticity in Monomeric Liquids . 39 1.5.1 Modulus . 41 1.5.2 Relaxation Time . 42 1.5.3 Common Theoretical Forms . 45 vil Contents Ί .6 The Glass Temperature . 46 1.6.1 Supercooling and Vitrification . 46 1.6.2 Structural Mixtures . 47 1.6.3 Glass Temperature Detection . 50 Specific Volume . 50 Specific Heat . 51 1.6.4 Effects on Viscosity . 52 1.6.5 History Dependence . 53 1.7 Analogies and Parallels . 56 1.7.1 Hard Spheres . 56 1.7.2 Colloidal Spheres . 59 1.7.3 Monomeric Spheres . 61 1.8 Properties Near the Glass Temperature . 62 1.8.1 The Strong-Fragile Classification . 62 1.8.2 Relaxation Time Distribution . 65 Mechanical Response . 66 Electromagnetic Response . 66 1.8.3 Stokes-Einstein Departures . 69 Self Diffusion . 70 Tracer Diffusion . 71 Related Phenomena . 72 1.8.4 Liquid Heterogeneity . 74 A Two-Microstate Interpretation . 75 A More Detailed Picture . 76 1.9 Theories about Vitrification . 78 1.10 Free Volume . 82 Appendix 1.1 Listing and Characteristics of Polymer Species . 87 References . 93 Chapter 2 Linear Viscoelastidty .101 2.1 Polymeric Viscoelasticity .101 2.2 Linear Viscoelastic Functions .103 2.2.1 Stress Relaxation .104 2.2.2 Creep and Creep Recovery .106 2.2.3 Steady-State Oscillatory Response .109 2.2.4 Experimental Aspects .115 Stress Relaxation .115 Creep and Recoil .116 Dynamic Compliance and Modulus .116 Contents 2.3 Linear Response Properties .116 2.3.1 Limits of Linear Response .117 2.3.2 Boltzmann Superposition .118 2.3.3 Relationships between Response Functions .119 Kramers-Kronig Relations .121 Limiting Functions .123 2.3.4 Complex Notation .124 2.3.5 Viscoelastic Models .124 Maxwell .126 Burgers .128 Davidson-Cole .129 Barlow-Erginsav-Lamb .129 2.3.6 Auxiliary Response Functions .130 2.3.7 Linear Viscoelastic Parameters .132 2.3.8 Extensional Deformation .135 2.4 Temperature Dependence .136 2.4.1 Time-Temperature Superposition .136 2.4.2 Temperature Shift Factors .142 2.4.3 Thermorheological Complexity .144 2.5 Flow-Related Properties .148 2.5.1 The Terminal Dispersion .148 2.5.2 Plateau Modulus .151 2.5.3 Recoverable Compliance .156 2.5.4 Zero-Shear Viscosity .158 2.5.5 Commentary .163 2.6 Molecular Origin of Polymeric Response .164 2.6.1 Conformational Rearrangement .165 2.6.2 Relaxation of Stress .168 Appendix 2.1 Fourier and Laplace Transforms .174 References .175 Chapter 3 Stress Response to Shear Deformations .179 3.1 Introduction .179 3.1.1 Contact Forces, Traction, and Stress .180 3.1.2 Elements of Matrix Algebra .189 3.1.3 Reference Frame .194 3.2 Conservation of Mass and Momentum .197 3.2.1 Equation of Continuity .197 3.2.2 Equation of Motion .198 Contents 3.2.3 Rheological Considerations. 201 Constitutive Equations .201 Pressure .201 Inerţial Effects .202 3.3 Simple Shear Deformation .202 3.3.1 Symmetry Considerations .204 3.3.2 Equilibrium Stress for Solids .206 3.3.3 Steady-State Stress for Liquids .207 3.4 Polymeric Liquid Response .209 3.4.1 Steady-State Properties .210 Viscosity .211 First Normal Stress Difference .216 Approximate Relationships .219 Second Normal Stress Difference .225 3.4.2 Start-up and Shut-down Behavior .227 Start-up from Rest .228 Relaxation from Steady State .231 3.4.3 Relaxation from Large Step Strains .233 Lodge-Meissner Relation .234 Strain-Time Factorability .234 Normal Stress Ratio .239 3.5 Time-Temperature Superposition .239 References .243 Chapter 4 Stress-Deformation Relationships .247 4.1 Deformation .247 4.1.1 Particle Position .248 4.1.2 Particle Displacement .249 4.1.3 Displacement Gradient Tensor .251 4.1.4 Cauchy Strain Tensor .254 4.1.5 Finger Strain Tensor .257 4.1.6 Other Strain Measures .261 Green and Piola Tensors .261 Deformation Rate Tensor .261 Infinitesimal Deformation Tensor .264 4.1.7 Reference Frame Rotation .266 4.1.8 Scalar Invariants .267 4.2 Constitutive Considerations .268 4.2.1 Incompressibility .269 4.2.2 Reference Frame Indifference .271 Contents 4.3 Elastic Response of Solids .272 4.3.1 Neo-Hookean Solids .273 4.3.2 The Rivlin Equation .276 4.3.3 Mooney-Rivlin Solids .280 4.3.4 Valanis-Landel Formulation .280 4.4 Viscoelastic Response of Liquids .281 4.4.1 The Lodge Model .283 Simple Shear .285 Uniaxial Extension .288 Extensional Flow Behavior .291 Assessment .300 4.4.2 Consistency Tests .301 4.5 Strain-Dependent Models .303 4.5.1 General KBKZ Properties .304 4.5.2 Simple Shear Histories .304 4.5.3 Factorization .306 4.5.4 Irreversibility .310 Nonlinear Recoil .311 Double Step Strain .314 References .316 Chapter 5 Experimental Aspects .319 5.1 Introduction .319 5.2 Hookean Solids and Newtonian Liquids .325 5.2.1 Simple Shear .326 Hookean Solids .326 Newtonian Liquids .330 5.2.2 Uniaxial Extension .331 Hookean Solids .331 Poisson Ratio .334 Newtonian Liquids .335 5.2.3 Property Measurement .337 Shear Modulus .337 Shear Viscosity .339 5.2.4 General Comments .343 5.3 Simple Shear Rheometry .344 5.3.1 Analysis of Rotational Rheometers .344 Concentric Rotating Plates .346 Concentric Cylinders .349 Concentric Cone and Plate .350 Contents 5.3.2 Analysis of Flow-Through Rheometers .354 Capillary Flow .355 Annular Flow .359 Slit Flow .361 5.3.3 Weissenberg-Rabinowitsch Procedures .363 Capillary Flow .363 Slit Flow .366 Concentric Plates .367 5.4 Comments on Shear Rheometry .369 5.4.1 Flow Instabilities .370 Edge Instabilities .370 Entry Region Vortices .372 Sharkskin, Slip, and Melt Fracture .373 5.4.2 Instrumental Aspects .377 Stiffness and Response Time .377 Wall Pressure .380 5.4.3 Other Issues .382 5.4.4 Summary .383 5.5 Extensional Rheometry .384 5.6 Optical Methods .386 5.6.1 Optical Birefringence .387 5.6.2 Flow Modeling .390 References .395 Chapter 6 Flexible-Chain Dynamics .399 6.1 Methods and Forces .400 6.2 Elastic Dumbbells .403 6.2.1 The Diffusion Equation .405 6.2.2 External and Internal Distributions .406 6.2.3 Flow-Induced Effects .409 6.2.4 Stress .411 6.2.5 Flow Properties .415 Relation to the Lodge Model .416 Association with Observables .416 6.2.6 Extended Formulation .418 6.3 The Rouse Model .419 6.3.1 Diffusion and Stress .421 6.3.2 Diffusion Coefficient .423 6.3.3 Viscoelastic Properties .426 Matrix Diagonalization .426 Association with Observables .427 Contents 6.4 The Zimm Model.430 6.4.1 Stress and Diffusion .434 6.4.2 Association with Observables .435 6.4.3 Discussion .437 6.5 Dilute Solution Dynamics .440 6.5.1 Linear Response .443 Slow Dynamics .443 Excluded Volume Effects .447 High Frequency Response .451 6.5.2 Nonlinear Response .451 Shear Flows .451 Stretching Flows .454 6.6 Dynamics of Short Chains .460 6.6.1 Dynamic Moduli .462 6.6.2 Recoverable Compliance .464 6.6.3 Self Diffusion .465 6.6.4 Monomeric Unit Friction .468 Appendix 6.1 Integration Formulas for Calculating Averages of Distributions .472 References .474 Chapter 7 Entangled Chain Dynamics .479 7.1 Entangled Melts .480 7.1.1 Polarizability and Polarity Aspects .481 Stress-Optical Rule .482 Dielectric Methods .483 7.1.2 The Plateau Modulus .484 7.1.3 The Shifted Rouse Formulation .487 7.2 Reptation and the Tube Model .488 7.2.1 Doi-Edwards Theory .489 7.2.2 Non-Mechanical Dynamics .492 7.2.3 Dynamic-Mechanical Properties .496 Gaussian Networks .497 Step Strain Response .498 7.3 Linear Viscoelasticity .500 7.3.1 Dynamic Properties .501 7.3.2 Comparisons with Data .503 7.3.3 Competing Relaxation Mechanisms .509 7.4 Constraint Release .510 7.4.1 Tracer Diffusion .511 xiv Contents 7.4.2 Viscoelastic Aspects. 514 Single Component Properties .514 Tracer Relaxation.518 7.5 Fluctuations. 520 7.5.1 Viscosity .520 7.5.2 Self Diffusion .527 7.5.3 Nonuniversality .531 7.5.4 Simulations .533 7.6 Nonlinear Viscoelastic Properties .535 7.6.1 Step Shear Strain .536 7.6.2 Step Extensional Strain .539 7.6.3 Viscometric Functions .540 7.6.4 Irreversibility .541 7.7 Independent Alignment Approximation .542 7.7.1 Shear Deformation .543 7.7.2 Uniaxial Extension .546 7.8 Theoretical Additions .548 7.8.1 Critique .548 7.8.2 Commentary .550 7.8.3 Convective Constraint Release .552 Collective Approach .553 Pairwise junction Approach .554 7.8.4 Comparisons and Discussion .556 References .560 Chapter 8 Dynamics of Entangled Solutions .567 8.1 Introduction .567 8.2 Friction-Insensitive Properties .569 8.2.1 Plateau Modulus G° (φ) .569 Colby-Rubinstein Theory .571 Analysis of Data .572 Compliance Support .576 Entanglement Density Definition .579 8.2.2 Recoverable Compliance β(φ, Μ). 581 8.2.3 Characteristic Shear Rate γο(φ, Μ). 585 8.2.4 Characteristic Molecular Weight Мс(ф) .589 8.2.5 Characteristic Diffusion Dependence Ό(φ) .595 8.3 Concentration - Molecular Weight Diagrams .596 8.4 Friction-Dependent Properties .598 8.4.1 Free Volume Theory .599 The Williams-Landel-Ferry Form .600 Contents Chain End and Copolymer Effects .602 Diluent Effects .603 Homologous Series Data .605 Solutions .606 8.4.2 Monomeric Tracer Diffusion .612 8.4.3 Dilute Solutions .616 Intrinsic Viscosity .617 High Frequency Response .622 Discussion .623 References .624 Chapter 9 Dynamics of Nonlinear Chains .629 9.1 Long-Chain Branching .629 9.1.1 Types of Structural Nonlinearity .631 9.1.2 Plateau Modulus .633 9.1.3 Nonlinear Rouse Chains .635 Linear Chains .637 Symmetric Three-Arm Stars .640 Symmetric ŕ-Arm Stars .643 Other Architectures .644 9.2 Linear Dynamics of Entangled Stars .644 9.2.1 Viscosity .644 Diluent Effects .648 Temperature Effects .649 9.2.2 Recoverable Compliance .653 9.2.3 Self Diffusion .657 9.2.4 Thermorheological Complexity .661 9.2.5 Exponential Prefactors .663 9.3 Tube Model for Stars .666 9.4 Constraint Release Effects for Stars .672 9.4.1 Relaxation in Network Environments .672 9.4.2 Tracer Diffusion .674 9.4.3 Dynamic Dilution Model .676 9.4.4 Discussion .681 Compliance Prediction .681 Dynamic Dilution Commentary .681 9.5 Hierarchy: H's, Combs and Networks .682 9.5.1 Dynamic Hierarchy .683 Quantitative Aspects .685 Terminal Relaxation .688 9.5.2 Н -Polymers. 690 Contents 9.5.3 Combs .693 9.5.4 Dangling Network Strands .700 9.6 Nonlinear Viscoelasticity .701 9.6.1 Damping Function .702 9.6.2 Extensional Behavior .706 References .708 Chapter 1 0 Polydispersity Effects .713 10.1 Introduction .713 10.2 Macromolecular Heterogeneity .714 10.2.1 Averages .715 10.2.2 Distribution Functions .716 10.2.3 Distribution Examples .718 Exponential Distributions .718 Branching Distributions .718 10.3 Molecular Weight Mixtures .719 10.3.1 Rouse and Tube Model Predictions .721 Rouse Mixing Rules .721 Doi-Edwards Mixing Rules .723 10.3.2 Binary Linear-Chain Mixtures .723 10.3.3 Double Reptation .734 Binary Mixtures .738 Continuous Distributions .739 Commentary .746 The Inverse Problem .746 10.4 Mixtures of Architectures .748 10.4.1 Binary Linear-Star Mixtures .748 10.4.2 Continuous Distributions .750 10.4.3 Nonlinear Viscoelasticity .757 Shear Thinning .757 Strain Hardening .758 Discussion .761 References .762 Appendix A Symbols .767 Appendix В Acronyms and Abbreviations .775 Subject Index .777 Author Index .785
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spelling	Graessley, William Walter Verfasser aut Polymeric liquids and networks: dynamics and rheology William W. Graessley London [u.a.] Garland Science 2008 XIX, 801 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Polymer networks Polymer solutions Rheology Polymerlösung (DE-588)4175242-9 gnd rswk-swf Polymeres Netzwerk (DE-588)4307122-3 gnd rswk-swf Rheologie (DE-588)4049828-1 gnd rswk-swf Polymerlösung (DE-588)4175242-9 s Rheologie (DE-588)4049828-1 s DE-604 Polymeres Netzwerk (DE-588)4307122-3 s Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015437418&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Graessley, William Walter Polymeric liquids and networks: dynamics and rheology Polymer networks Polymer solutions Rheology Polymerlösung (DE-588)4175242-9 gnd Polymeres Netzwerk (DE-588)4307122-3 gnd Rheologie (DE-588)4049828-1 gnd
subject_GND	(DE-588)4175242-9 (DE-588)4307122-3 (DE-588)4049828-1
title	Polymeric liquids and networks: dynamics and rheology
title_auth	Polymeric liquids and networks: dynamics and rheology
title_exact_search	Polymeric liquids and networks: dynamics and rheology
title_exact_search_txtP	Polymeric liquids and networks: dynamics and rheology
title_full	Polymeric liquids and networks: dynamics and rheology William W. Graessley
title_fullStr	Polymeric liquids and networks: dynamics and rheology William W. Graessley
title_full_unstemmed	Polymeric liquids and networks: dynamics and rheology William W. Graessley
title_short	Polymeric liquids and networks: dynamics and rheology
title_sort	polymeric liquids and networks dynamics and rheology
topic	Polymer networks Polymer solutions Rheology Polymerlösung (DE-588)4175242-9 gnd Polymeres Netzwerk (DE-588)4307122-3 gnd Rheologie (DE-588)4049828-1 gnd
topic_facet	Polymer networks Polymer solutions Rheology Polymerlösung Polymeres Netzwerk Rheologie
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