Nonlinear Polymer Rheology

Integrating latest research results and characterization techniques, this book helps readers understand and apply fundamental principles in nonlinear polymer rheology. The author connects the basic theoretical framework with practical polymer processing, which aids practicing scientists and engineers to go beyond the existing knowledge and explore new applications. Although it is not written as a textbook, the content can be used in an upper undergraduate and first year graduate course on polymer rheology. Describes the emerging phenomena and associated conceptual understanding in the field of nonlinear polymer rheology Incorporates details on latest experimental discoveries and provides new methodology for research in polymer rheology Integrates latest research results and new characterization techniques like particle tracking velocimetric method Focuses on the issues concerning the conceptual and phenomenological foundations for polymer rheology Has a companion website for readers to access with videos complementing the content within several chapters

Auteur

SHI-QING WANG, PhD, is Kumho Professor of Polymer Science at the University of Akron. He has been teaching at the university level for more than 28 years and has over 150 peer reviewed publications. Dr. Wang is a reviewer for many journals and a Fellow of both the American Physical Society (APS) and American Association for the Advancement of Science (AAAS).

Texte du rabat
Polymers are long string-like molecules. At high molecular weights, the long molecules are heavily intertwined, leading to unique viscoelastic behavior due to chain entanglement. Under large deformation, entangled polymers show a rich variety of nonlinear rheological responses including strain localization. Nonlinear Polymer Rheology offers new, significant insights to students and research professionals. All aspects of nonlinear polymer rheology are described within one common framework. The author explains why yielding, i.e., the transition from elastic response to irreversible deformation (flow), always takes place when entangled polymeric liquids are subjected to a variety of different forms of large deformation. Integrating latest research results and characterization techniques, Nonlinear Polymer Rheology helps readers understand and apply basic principles of nonlinear polymer rheology. The book connects the theoretical framework with practical polymer processing, aiding practicing scientists and engineers to go beyond existing knowledge and explore innovative applications.

Contenu
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 KelvinVoigt 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 StressStrain 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 KirkwoodRiseman 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 StokesEinstein 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 TimeTemperature 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 ...