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POLYMER MATERIALS

Macroscopic Properties and Molecular Interpretations

JEAN LOUIS HALARY

FRAMBOISE LAUPRETRELUCIEN MONNERIE

©WILEYA JOHN WILEY & SONS, INC., PUBLICATION

CONTENTS

PREFACE

LIST OF SYMBOLS

Introduction to Polymer Materials

1.1. Chronological Landmarks for Polymers, 1

1.2. The Polymer Chain, 2

1.3. The Key Points of Polymer Synthesis, 2

1.3.1. Step Polymerization, 3

1.3.2. Chain Polymerization, 3

1.3.3. Controlled Polymerizations, 4

1.3.4. Ziegler-Natta and Metallocene Polymerizations, 5

1.3.5. Synthesis of Copolymers, 5

1.3.6. Polymer Cross-Linking, 7

1.3.7. The Molecular Weight Distribution, 8

1.3.8. Conclusion, 8

1.4. Major Polymers, 8

1.5. The Lightness of Polymer Materials, 8

1.6. Main Mechanical Aspects of Polymer Materials, 11

1.7. Comprehensive Survey of the Polymer Mechanical Behaviors, 11

Further Reading, 12

PARTI

1 The Four Classes of Polymer Materials

1.1. The Young Modulus, 15

1.2. Un-Cross-Linked Amorphous Polymers, 15

1.3. Semicrystalline Thermoplastics, 17

1.4. Thermosetting Polymers, 17

1.5. Cross-Linked Elastomers, 18

1.6. Conclusions, 19

CONTENTS

The Macromolecular Chain in the Amorphous Bulk Polymer: Static

and Dynamic Properties

2.1. Conformational Statistics of Isolated Polymer Chains, 21

2.1.1. Freely Jointed Chain, 21

2.1.2. Freely Rotating Chain, 22

2.1.3. Chain with Symmetrically Restricted Internal Rotation, 22

2.1.4. Equivalent Kuhn Chain, 23

2.2. Conformational Energy Calculations, 24

2.2.1. Conformational Energy of Model Molecules, 24

2.2.2. Conformational Energy Maps, 25

2.2.3. NMR Investigation of Polymer Conformations, 27

2.3. Global Properties of an Isolated Chain, 27

2.3.1. Rotational Isomers, Statistical Weights, and Calculation

of (R2), 28

2.3.2. Construction of an Isolated Chain According to the

Monte-Carlo Method, 28

2.4. Chain Conformations in Bulk Amorphous Polymers, 28

2.4.1. Experimental Investigation by Neutron Scattering, 28

2.4.2. Computer Modeling of an Amorphous Cell, 28

2.5. Local Dynamics of Isolated Chains, 30

2.5.1. Conformational Jumps in Linear Alkanes and AliphaticChains, 30

2.5.2. Molecular Dynamics of Isolated Chains, 32

2.5.3. Cooperative Kinematics Technique, 33

2.6. Local Dynamics of a Polymer Chain in Solution, 34

2.6.1. Experimental Investigation by 13C NMR, 35

2.6.2. Molecular Modeling of Local Chain Dynamics in Solution, 35

2.7. Local Dynamics in Bulk Polymers, 37

2.7.1. Investigation by BC NMR, 37

2.7.2. Molecular Modeling of Local Chain Dynamics in PolymerMelts, 37


References, 39

Further Reading, 40

The Glass Transition

3.1. Experimental Studies, 41

3.1.1. Temperature Dependence of the Specific Volume, 41

3.1.2. Differential Scanning Calorimetry Investigation, 41

3.1.3. Mechanical Observation of the Glass Transition, 42

3.1.3.1. The Young Modulus, 42

3.1.3.2. Dynamic Mechanical Analysis, 42

3.2. Molecular Origin of the Glass Transition Temperature, 43

3.2.1. Cooperative Motions of the Main-Chain Bonds, 44

3.2.2. Time (or Frequency)-Temperature Equivalence, 44

3.3. Overview of the Glass Transition Temperature Theories, 45

3.3.1. The Gibbs-Di Marzio Thermodynamic Theory, 46

3.3.2. Dynamic Free Volume, 47

3.3.3. Computer Simulations, 50

3.3.4. Physical Aging, 51

3.4. Effect of the Polymer Architecture on the Glass Transition

Temperature, 52

3.4.1. Molecular Weight, 52

3.4.2. Ring and Branches, 53

3.4.3. Cross-Links, 53

3.5. Effect of the Polymer Chemical Structure on the Glass

Transition Temperature, 54

3.6. Glass Transition of Random Copolymers, 54

3.7. Glass Transition of Polymer/Plasticizer Blends, 57

3.7.1. Polymer/Plasticizer Blends, 57

3.7.2. Tg Dependence on Plasticizer Content, 57


References, 58

Further Reading, 58

Secondary Relaxations in Amorphous Polymers 59

4.1. Experimental Evidences of a Secondary Relaxation, 59

4.1.1. Dynamic Mechanical Analysis, 59

4.1.1.1. A Simple Example: The /Relaxation of

Poly(cyclohexyl methacrylate), 59

4.1.1.2. A More Complex Example: The Relaxation of

Poly(ethylene terephthalate), 61

4.1.2. Dielectric Analysis, 61

4.1.3. Relaxation Map, 61

4.2. Identification of the Motions that Are Responsible for the

Secondary Relaxations, 61

4.2.1. High-Resolution Solid-State 13C NMR, 62

4.2.1.1. Some General Principles, 62

4.2.1.2. Example of the /Relaxation of Poly(cyclohexyl

methacrylate), 63

4.2.1.3. Example of the /3 Relaxation of Poly(ethyleneterephthalate), 64

4.2.2. 2H NMR of Selectively Deuterated Compounds, 66

4.2.3. Comparison of Results Obtained from the Different

Techniques, 66

4.2.4. Use of Antiplasticizers, 67

4.3. Motional Cooperativity Associated with Secondary Relaxations, 67

4.3.1. Starkweather Approach, 68

4.3.2. Nature of the Motional Cooperativity, 69

4.3.2.1. Intermolecular Cooperativity, 69

4.3.2.2. Intramolecular Cooperativity, 69

4.4. Secondary Relaxations of Poly(methyl methacrylate) and Some

of Its Random Copolymers, 69

4.4.1. PMMA, 69

4.4.1.1. Low-Temperature Secondary Relaxations of PMMA, 69

4.4.1.2. DMA and Dielectric Relaxation Evidences of

the )3 Relaxation of PMMA, 69

4.4.1.3. Identification of Local Motions Responsible for

the ft Relaxation of PMMA, 70

4.4.1.4. Information Derived from Molecular Modeling, 71

4.4.2. Methyl Methacrylate-co-A^-cyclohexylmaleimide Random

Copolymers, 72

4.4.3. Methyl Methacrylate-co-Af-methylglutarimide Random

Copolymers, 73

viii CONTENTS

4.5. Secondary Relaxation of Neat and Antiplasticized Bisphenol-A

Polycarbonate, 75

4.5.1. Characterization by Dynamic Mechanical Analysis and

Dielectric Relaxation, 75

4.5.2. Identification of Motions, 75

4.5.3. Nature of the Motional Cooperativity, 76

4.5.3.1. Influence of Hydrostatic Pressure, 76

4.5.3.2. Effect of Small-Molecule Antiplasticizers, 76

4.5.3.3. Molecular Modeling, 77

4.6. Secondary Relaxations in Neat and AntiplasticizedAryl-Aliphatic Epoxy Resins, 78

4.6.1. Characterization of the ji Relaxation and Motional

Cooperativity, 80

4.6.2. Identification of Local Motions Involved in the /5Relaxation, 81

4.6.3. Characterization of the p Secondary Relaxation of

Antiplasticized Epoxy Networks, 82

4.6.4. Local Motions in Antiplasticized Epoxy Networks, 82

4.6.5. Intermolecular Cooperativity of the fi Relaxation

Motions in Neat and Antiplasticized Epoxy Networks, 83


References, 84

Further Reading, 84

5 Entanglements in Bulk Un-Cross-Linked Polymers 85

5.1. Concept of Entanglement, 85

5.2. Experimental Determinations of Me, 87

5.2.1. From the Rubbery Plateau, 87

5.2.1.1. Young Modulus, 87

5.2.1.2. Dynamic Shear Modulus, 87

5.2.2. From the Viscosity in the Flow Region, 88

5.2.2.1. Characterization of the Newtonian Viscosity, 88

5.2.2.2. Physical Meaning of Viscosity, 89

5.2.2.3. Molecular Weight Dependence of the Newtonian

Viscosity, 89

5.3. Theoretical Overview of Chain Dynamics, 90

5.3.1. The Rouse Model, 90

5.3.2. de Gennes Reptation Model, 92

5.3.3. The Doi-Edwards Model, 94

5.4. Relationships Between Entanglements and Polymer Chemical

Structure, 95

5.4.1. Values of the Molecular Weight Between Entanglements, 95

5.4.2. Entanglement Density, 95

5.4.3. Number of Bonds Between Entanglements, 96

5.4.4. Number of Equivalent Bonds Between Entanglements, 96

5.4.5. The Example of Random Copolymers, 96


References, 99

Further Reading, 99

6 Semicrystalline Polymers 101

6.1. Experimental Evidence of Semicrystalline State, 101

6.1.1. Wide-Angle X-Ray Scattering (WAXS), 101

CONTENTS ix

6.1.1.1. Principle of the Technique, 101

6.1.1.2. Experimental Observations, 101

6.1.2. Differential Scanning Calorimetry (DSC), 103

6.1.2.1. Observations and Preliminary Interpretations, 103

6.1.2.2. Crystalline Fraction, 104

6.2. Crystalline Structure of Polymers, 104

6.2.1. Chain Conformation within the Crystalline Cell, 104

6.2.1.1. Planar Zigzag, 105

6.2.1.2. Helical Conformation, 106

6.2.2. Computer Modeling of a Crystalline Cell, 107

6.2.3. Crystalline Polymorphism, 108

6.3. Morphology of Semicrystalline Polymers, 108

6.3.1. Isolated Lamellae, 109

6.3.2. Organization of the Lamellae Formed by Crystallizationfrom Polymer Solutions, 110

6.3.3. Crystallization from Bulk Polymers, 110

6.3.3.1. Fringed Micelles, 110

6.3.3.2. Spherulites, 111

6.3.4. Morphologies Resulting from Specific Processing

Conditions, 112

6.3.4.1. Tram-Crystallization, 112

6.3.4.2. Strain-Induced Crystallization of

Un-Cross-Linked Polymers, 112

6.3.4.3. Strain-Induced Crystallization of Elastomer

Networks, 113

6.4. Crystallization Kinetics, 113

6.4.1. Primary Crystallization, 113

6.4.2. General Avrami Equation, 115

6.4.3. Growth Theories, 115

6.4.4. Secondary Crystallization, 115

6.5. Melting Temperature of Crystalline Domains, 116

6.5.1. Melting of a Crystal of Infinite Size, 116

6.5.2. Melting of a Crystalline Lamella of Finite Size, 116

6.5.3. Multiple Melting, 116

6.5.4. Effect of Chain Ends, 118

6.6. Influence of the Polymer Chemical Structure, 118

6.6.1. Chemical Structure Conditions for Crystallization, 118

6.6.2. Effect of the Chemical Structure on the MeltingTemperature, 120

6.7. Glass Transition of Semicrystalline Polymers, 120

6.7.1. Macroscopic Approach, 120

6.7.2. Molecular Investigation, 121


References, 122

Further Reading, 122

PART II 123

7 Elastic and Hyperelastic Behaviors 125

7.1. Definition and Physical Origin of an Elastic Behavior, 125

7.1.1. Definition, 125

7.1.2. Physical Origin, 125

CONTENTS

7.2. Enthalpic Elasticity (True Elasticity), 128

7.2.1. Stress-Strain Curve, 128

7.2.2. States of Stress and Strain, 128

7.2.3. Expression of Hooke's Law in Terms of Elastic Constants, 129

7.2.4. Expression of Hooke's Law in Terms of Compliances, 130

7.2.5. Expression of Hooke's Law in the Case of SimpleLoadings, 130

7.3. Entropic Elasticity (Hyperelasticity or Rubber Elasticity), 132

7.3.1. Force-Extension Curve, 132

7.3.2. Entropic Deformation of a Polymer Coil, 133

7.3.3. Conditions for Entropic Elasticity, 134

7.3.4. Molecular Theories of Network Entropic Elasticity, 134

7.3.4.1. The Affine Model, 134

7.3.4.2. The Phantom Network Model, 136

7.3.4.3. Comparison of Affine and Phantom Models with

Experimental Results, 137

7.3.4.4. The Constrained Junction Fluctuation Model, 138

7.3.4.5. Chain Confinement in a Tube and SlidingEntanglements, 139

7.3.5. The Mooney-Rivlin Equation, 141

7.3.6. Micromechanical Model of a Tri-dimensional Network, 142

7.3.7. Elastic Behavior at Large Strain, 143

7.3.8. Non-elastic Behavior at Large Strain, 143


References, 144


Linear Viscoelastic Behavior

8.1. Introduction and Definitions, 147

8.2. Transient Mechanical Measurements, 148

8.2.1. Creep Tests, 148

8.2.2. Stress Relaxation Test, 149

8.3. Dynamic Mechanical Tests, 149

8.3.1. Definition of Dynamic Descriptors, 149

8.3.2. Typical Viscoelastic Behavior, 151

8.4. Analogical Mechanical Models, 151

8.4.1. Kelvin-Voigt and Maxwell Analogical Models, 151

8.4.2. Generalized Kelvin-Voigt and Maxwell Models, 152

8.5. Time (or Frequency)-Temperature Equivalence Principle, 154

8.5.1. Formal Expressions of the Equivalence Principle, 154

8.5.2. Master Curves, 155

8.5.3. Relevance of Master Curves, 155

8.6. Examples ofViscoelastic Behavior, 156

8.6.1. Creep Behavior of PS Near Tg, 156

8.6.2. Stress Relaxation Behavior of PS Near Ts, 157

8.6.3. Dynamic Mechanical Behavior of PS Near Ts, 157

8.6.4. Analysis of the aT/n Shift Factors in the Tg Region, 158

8.6.5. Behavior of Entangled Polymers on the Rubbery Plateau, 160

8.6.6. Behavior of Glassy Polymers in the SecondaryRelaxation Range, 161


References, 164


CONTENTS xi

9 Anelastic and Viscoplastic Behaviors 165

9.1. Investigation of Stress-Strain Curves, 165

9.1.1. Uniaxial Compression Test; Temperature and Strain Rate

Effects, 165

9.1.2. Shear Test and Hydrostatic Pressure Effect, 167

9.1.3. Uniaxial Tensile Test and Brittle-Ductile Transition, 169

9.2. Yield Criteria, 169

9.2.1. Tresca and von Mises Yield Criteria for Metallic Materials, 170

9.2.1.1. Tresca Criterion, 170

9.2.1.2. von Mises Criterion, 170

9.2.2. Plasticity Criteria for Polymer Materials, 171

9.3. Molecular Interpretation of Yielding, 173

9.3.1. Role of a and /? Molecular Motions, 174

9.3.2. The Ree-Eyring Model, 174

9.3.3. The Robertson Model, 176

9.4. Specific Behavior in the Viscoplastic Range, 178

9.4.1. Observed Behavior Under Compression, 178

9.4.2. Plastic Instability in Tension, 179

9.5. Inhomogeneous Plastic Deformation of Semicrystalline Polymers, 181


References, 183


10 Damage and Fracture of Solid Polymers 185

10.1. Micromechanisms of Deformation, 185

10.1.1. Shear Bands, 185

10.1.2. Crazes, 186

10.1.2.1. Craze Morphology, 186

10.1.2.2. Mechanisms of Craze Initiation, Growth, and

Breakdown, 187

10.1.2.3. Crazes Formed Under a Chemical Environment

(Stress-Cracking), 189

10.1.2.4. Role of Chain Entanglements in the Craze

Formation, 190

10.1.2.5. Correlation Between the Nature of the Stress

Field and the Craze Formation, 191

10.1.2.6. Competition Between Shear Banding and

Crazing, 192

10.1.3. Interaction Between Shear Banding and Crazing, 193

10.1.4. Specific Damage of Semicrystalline Polymers, 194

10.2. Fracture Mechanics, 196

10.2.1. The Crack Opening Modes, 196

10.2.2. Definition of Plane Stress and Plane Strain Conditions, 196

10.2.3. Revisiting the Brittle-Ductile Transition, 196

10.2.4. Brittle Fracture Criteria, 197

10.2.4.1. The Griffith Criterion, 197

10.2.4.2. The Irwin Criterion, 199

10.2.4.3. Correlation Between G,c and Kk, 200

10.2.5. Plastic Zone at the Crack Tip, 200

10.2.6. The Dugdale Criterion, 201

10.3. G,c and Klc Determinations and Values, 201

10.3.1. Principles of Determination of Gk and K!c, 202

10.3.2. Experimental Tests, 203

xii CONTENTS

10.3.2.1. Compact Tension and Three-Point Bending, 203

10.3.2.2. Other Fracture Tests, 204

10.3.2.3. Conditions for G,c and Kk Determination, 204

10.3.2.4. Crack Tip Blunting, 204

10.3.3. Gk and Kk Values, 205

10.3.3.1. Typical Values at Room Temperature, 205

10.3.3.2. Effect of Test Temperature, 206

10.3.3.3. Dependence of Gk and Kk on Crack

Propagation Rate, 206

10.3.3.4. Dependence of Gk and Klc on PolymerMolecular Weight, 206

10.4. Fatigue Fracture, 207

10.4.1. Experimental Tests, 207

10.4.2. The Wholer Curve, 207

10.4.3. The Paris Expression, 208

10.5. Molecular Approach of Fracture Behavior, 208


References, 210


PART III

11 Mechanical Properties of Poly(Methyl Methacrylate) and Some of

Its Random Copolymers

11.1. Poly(Methyl Methacrylate), 213

11.1.1. j3 Secondary Relaxation, 213

11.1.2. Plastic Deformation, 214

11.1.2.1. Compression Behavior, 214

11.1.2.2. Molecular Interpretation of Plastic

Deformation and Relation with /J Relaxation

Processes, 215

11.1.3. Micromechanisms of Deformation and Relations with

j8 Relaxation Processes, 216

11.1.4. Micromechanisms of Fracture and Relations with

/3 Relaxation Processes, 216

11.2. Methyl Methacrylate-co-maleimide Random Copolymers, 216

11.3. Methyl Methacrylate-co-7V-cycohexylmaleimide Random

Copolymers, 217

11.3.1. Secondary Relaxations, 217



11.3.2.2. Relations with j3 Relaxation Motions, 218


fi Relaxation Processes, 218

11.3.4. Fracture, 219

11.4. Methyl Methacrylate-co-N-methylglutarimide Random

Copolymers, 219

11.4.1. f} Relaxation, 219



11.4.2.2. Relations with /3 Relaxation Motions, 219


j3 Relaxation Motions, 220

11.4.4. Fracture, 220

CONTENTS xiii


References, 221


12 Mechanical Properties of Bisphenol-A Polycarbonate 223

12.1. Neat BPA-PC, 223

12.1.1. p Secondary Relaxation, 223



12.1.2.2. Relation with p Relaxation Motions, 224


the {} Relaxation, 225

12.1.4. Micromechanisms of Fracture and Relations with

the /} Relaxation, 226

12.2. Antiplasticized BPA-PC, 227

12.2.1. Antiplasticizers, 227

12.2.2. Yielding and Fracture of Antiplasticized BPA-PC and

Relations with the P Relaxation, 227

12.3. Other Tough Polymers, 227


References, 228


13 Mechanical Properties of Epoxy Resins 229

13.1. Synthesis of Epoxy Resins, 229

13.2. Molecular Mobility in the Solid State, 230

13.2.1. Secondary Relaxations, 230

13.2.1.1. p Relaxation in Neat Epoxy Resins, 230

13.2.1.2. p Relaxation in Antiplasticized EpoxyResins, 232

13.2.1.3. Effect of p Relaxation on Young Modulus

at 25°C, 233

13.2.2. a Relaxation, 233

13.2.2.1. Effect of Chemical Structure, 233

13.2.2.2. Effect of Cross-Link Density, 233

13.3. Plastic Behavior, 233

13.3.1. Yielding Behavior of Neat Epoxy Resins, 233

13.3.1.1. Comparison with the Ree-Eyring Model, 234

13.3.1.2. Comparison with the Robertson Model, 234

13.3.1.3. Effect of Chemical Structure, 234

13.3.2. Yielding of Antiplasticized Epoxy Resins, 235

13.4. Fracture Behavior, 236

13.4.1. Deformation Micromechanisms, 236

13.4.2. Different Fracture Types, 236

13.4.2.1. Stable Brittle Fracture, 236

13.4.2.2. Unstable Semi-brittle Fracture, 236

13.4.2.3. Stable Ductile Fracture, 238

13.4.3. Effect of Yield Stress, 238

13.4.4. Effect of Chemical Structure and Cross-Link Densityon Toughness, 238


References, 239


xiv CONTENTS

14 Polyethylene and Ethylene-a-olefin Copolymers 241

14.1. Synthesis and Structural Characteristics of PE and Random

Ethylene-a-olefin Copolymers, 241

14.1.1. Radical Polymerization, 241

14.1.2. Ziegler-Natta-Catalyzed Polymerization, 241

14.1.3. Metallocene-Catalyzed Polymerization, 243

14.2. Morphology, 244

14.2.1. HDPE, 244

14.2.2. Ethylene-a-olefin Copolymers Resulting from

Metallocene Catalysis, 245

14.2.2.1. Influence of the Degree of Branching, 245

14.2.2.2. Influence of the Branch Length, 245

14.2.3. Ethylene-a-olefin Copolymers Resulting from

Ziegler-Natta Catalysis, 246

14.2.4. Free-Radical LDPEs, 247

14.3. Mechanical Properties, 247

14.3.1. Mechanical Relaxations, 247

14.3.2. Stress-Strain Behavior, 248

14.3.3. Plastic Behavior, 248


References, 250

15 High-Modulus Thermoplastic Polymers 251

15.1. High-Modulus PE, 251

15.1.1. Extensibility Limit of an Entangled Chain in a Gel, 252

15.1.2. Processing Techniques of Ultra-High-Molecular-Weight

Polyethylene, 253

15.1.2.1. Gel Spinning, 253

15.1.2.2. Cold Drawing, 253

15.1.3. Orientation Characterization, 253

15.1.4. UHMWPE Properties, 254

15.1.4.1. Chain Orientation, 254

15.1.4.2. Tensile Modulus, 254

15.1.4.3. Crystalline Morphology, 255

15.2. High-Modulus Polymers Obtained from MesomorphousPolymers, 255

15.2.1. Main Mesophases, 255

15.2.2. Lyotropic Polymers, 255

15.2.2.1. PPTA, 255

15.2.2.2. Other Lyotropic Polymers, 257

15.2.3. Thermotropic Polymers, 259

15.2.3.1. Chemical Structures, 259

15.2.3.2. Properties, 260


References, 261

PART IV 263

16 Mechanical Tests for Studying Impact Behavior 265

16.1. Mechanical Tests, 265

16.1.1, Impact Tests, 265

16.1.2. High-Speed Test, 266

CONTENTS xv

16.2. Fracture Behaviors of Toughened Polymers, 266

16.2.1. Brittle Fracture, 267

16.2.2. Semi-brittle Fracture, 267

16.2.3. Ductile Fracture, 268

16.2.3.1. Stable-Unstable Ductile Fracture, 268

16.2.3.2. Stable Ductile Fracture, 268

16.2.4. Crack Tip Blunting, 269

16.2.5. Comment on Fracture Characterization by K,c and Glc, 269

References, 269

17 High-Impact Polystyrene 271

17.1. HIPS Synthesis, 271

17.2. Characteristic Behaviors and Observations, 272

17.2.1. Temperature Dependence of Toughness and Fracture

Types, 272

17.2.2. Stress-Strain Curves at Low Strain Rate and Sample

Aspect, 273

17.2.3. Observation of Damaged HIPS, 273

17.3. Effect of the Main Parameters, 274

17.3.1. PB Content, 274

17.3.2. Particle Volume Fraction, 274

17.3.3. Particle Size, 274

17.3.4. Brittle-Ductile Behavior of Polymer Matrix, 275

17.4. Toughening Mechanisms, 276

17.4.1. Stress Intensification, 276

17.4.2. Elastomer Particle Behavior, 277

17.4.2.1. Pure Elastomer Particle, 277

17.4.2.2. Elastomer Particles with PS Occlusions, 277

17.4.2.3. Optimal Morphology of Elastomer Particles, 277

17.4.3. Craze Initiation and Particle Size, 277

17.4.4. Arrest of Craze Propagation, 278

17.4.4.1. Arrest by Particles, 278

17.4.4.2. Arrest by Shear Bands, 278

17.4.4.3. Comment on Rigid Particles, 279

17.4.5. Temperature Dependence of Toughening, 279


References, 280


18 Toughened Poly(Methyl Methacrylate) 281

18.1. Elaboration of RT-PMMA, 281

18.1.1. Synthesis of Elastomer Particles, 281

18.1.2. Blending with PMMA Matrix, 282

18.2. Low Strain Rate Behaviors and Observations, 282

18.2.1. Tensile Stress-Strain Curves, 282

18.2.2. Young Modulus, 282

18.2.3. Yield Stress, 283

18.2.4. Particle Cavitation, 283

18.2.5. Fracture, 285

18.2.5.1. Effect of Particle Volume Fraction and

Temperature, 285

18.2.5.2. Crack Tip Damage, 285

xvi CONTENTS

18.3. High Strain Rate Behaviors and Observations, 286

18.3.1. High-Speed Fracture, 287

18.3.2. Impact Strength, 287

18.3.2.1. Effect of Particle Size, 287

18.3.2.2. Effect of Particle Volume Fraction, 287

18.3.2.3. Observation of the Damaged Zone, 288

18.3.2.4. Effect of Temperature, 288

18.4. Toughening Mechanism, 289

18.4.1. Single-Particle Cavitation, 289

18.4.2. Particle Cavitation and Matrix Yielding, 291

18.4.3. Cavitation Diagram for a Shear Yielding Matrix, 292

18.4.4. Cavitation Diagram for Matrix Yielding by Shearingand Crazing, 294

18.4.5. Mechanical Interactions Between Particles, 295

18.4.6. Spatial Development of Cavitation. Dilatation Bands, 295

18.5. Consequences of Toughening Mechanisms on Formulation and

Behavior of RT-PMMA, 295


18.5.2. Cavitation and Plastic Deformation of the Matrix, 296

18.5.3. Particle Volume Fraction, 296

18.5.4. Temperature Effect, 296

18.5.5. Strain Rate Effect, 296

18.5.6. Comparison with PS Toughening, 296

18.6. Analysis of the Dependence of Toughening on Temperatureand Strain Rate, 297

18.6.1. Temperature Dependence, 297

18.6.2. Compared Dependences of Temperature and

Strain Rate, 298


References, 298

19 Toughened Aliphatic Polyamides

19.1. Polyamide-Elastomer Blends, 301

19.2. Low Strain Rate Behavior, 302

19.2.1. Young Modulus, 302

19.2.2. Yield Stress, 302

19.2.3. Volume Change Under Strain, 302

19.2.4. Dilatation Bands, 302

19.2.5. Crack Tip Damage, 303

19.3. Impact Behavior and Observations, 303

19.3.1. Typical Results, 303

19.3.2. Effect of Particle Size, 304

19.3.3. Effect of Particle Volume Fraction, 304

19.3.4. Effect of Interparticle Distance, 305

19.3.5. Effect of Elastomer Type, 306

19.4. Toughening Mechanisms, 306


19.4.2. Matrix Shear Yielding. Effect of Temperature and

Interparticle Distance, 307

19.4.3. Analysis of the Interparticle Distance Effect, 308

19.5. Toughening by Block Copolymers, 308


References, 309

20 Toughened Epoxy Resins

20.1. Toughening by Elastomer Particles, 311

20.1.1. In Situ Synthesis of Elastomer Particles, 311

20.1.2. Preformed Particles, 312

20.1.3. Characteristics of Elastomer-Toughened Epoxy Resins, 313


20.1.3.2. Yield Stress, 313

20.1.4. Fracture Behavior of Toughened Epoxy Resins, 313

20.1.4.1. Different Fracture Types, 313

20.1.4.2. Damage Observation of Toughened EpoxyResins, 314

20.1.4.3. Effect of the Particle Size, 317

20.1.4.4. Effect of Particle Content, 317

20.1.4.5. Effect of the Cross-Link Density of

the Epoxy Resin, 318

20.1.5. Toughening Mechanism by Elastomer Particles, 318

20.1.5.1. Particle Cavitation, 318

20.1.5.2. Matrix Plastic Deformation, 319

20.1.5.3. Critical Interparticle Distance, 319

20.2. Toughening of Epoxy Resins by Thermoplastic Polymers, 320

20.2.1. Thermoplastic Polymer Incorporation, 320

20.2.2. Characteristics of Thermoplastic-Toughened EpoxyResins, 321

20.2.2.1. Glass Transition Temperature, 321


20.2.2.3. Yield Stress, 321

20.2.2.4. Fracture Behavior, 321

20.2.3. Toughening Mechanisms of Epoxy Resins by

Thermoplastic Polymers, 322


References, 322

PART V

21 Chemically Cross-Linked Elastomers

21.1. Main Chemically Cross-Linked Elastomers, 327

21.1.1. Dienic Polymers and Random Copolymers, 327

21.1.1.1. 1,4 and 1,2 Linkages of Dienic Elastomers, 329

21.1.1.2. Natural Rubber, 329

21.1.1.3. Synthetic Polyisoprene, 331

21.1.1.4. Polybutadienes, 331

21.1.1.5. Random (Styrene-co-butadiene)Copolymers, 331

21.1.1.6. Random (Acrylonitrile-co-butadiene)Copolymers, 331

21.1.1.7. Butyl Rubber, 331

21.1.1.8. Ethylene Propylene Diene Monomer, 331

21.1.2. Silicone Polymers, 332

21.2. Fracture Testing Techniques for Elastomers, 332

21.2.1. Single-Edge Crack, 332

21.2.2. Pure Shear, 333

21.2.3. Trouser Tear Testing, 333

xviii CONTENTS

21.3. Fracture of Noncrystallizing Elastomers, 333

21.3.1. Uniaxial Tensile Fracture, 333

21.3.1.1. Fracture Envelope, 334

21.3.1.2. Fracture and Viscoelasticity, 334

21.3.2. Fracture Energy, 336

21.3.2.1. Fracture Energy Surface, 336

21.3.2.2. Fracture Energy and Hysteresis, 336

21.3.2.3. Fatigue Crack Propagation, 336

21.4. Natural Rubber, 337

21.4.1. Fracture Envelope, 337

21.4.2. Fracture Energy and Hysteresis, 337

21.4.3. Crack Propagation, 337


References, 338


22 Reinforcement of Elastomers by Fillers 339

22.1. Different Fillers and Their Characterization, 339

22.1.1. Filler Morphology, 339

22.1.1.1. Carbon Black Fillers, 339

22.1.1.2. Silica Fillers, 341

22.1.2. Characterization of Filler Surface, 341

22.1.3. Filler Dispersion in Elastomer, 342

22.2. Characteristics of the Filler-Elastomer System, 343

22.2.1. Bound Elastomer, 343

22.2.2. Glassy Elastomer Layer at the Filler Surface, 344

22.2.3. Occluded Elastomer, 344

22.2.4. Filler Network Percolation, 345

22.3. Improvement of Elastomer Properties by Fillers, 345

22.4. Analysis of Elastic Modulus, 346

22.4.1. Mechanical Models for Structureless Filler Particles, 346

22.4.1.1. Spherical Particles, 346

22.4.1.2. Ellipsoid and Rod-Like Particles, 346

22.4.2. Semiempirical Models for Structured Aggregated Particles, 347

22.4.3. Strain Amplification, 347

22.4.4. Glassy Layer at the Filler Surface, 347

22.5. Specific Energy Dissipation of Filled Elastomers, 347

22.5.1. Payne Effect, 348

22.5.1.1. Manifestations of the Payne Effect, 348

22.5.1.2. Temperature Dependence, 348

22.5.1.3. Analysis of the Payne Effect, 349

22.5.1.4. Interpretation of the Payne Effect, 350

22.5.2. Mullins Effect, 352

22.5.2.1. Manifestations of the Mullins Effect, 352

22.5.2.2. Analysis of the Mullins Effect, 353

22.5.2.3. Interpretation of the Mullins Effect, 354

22.6. Fracture Behavior, 355

22.6.1. Fracture Envelope, 355

22.6.2. Fracture Energy Surface, 356

22.6.3. Fracture Energy, 356

29,6A. Crack Propagation, 356

ions, 357

357

eading, 358

23 Thermoplastic Elastomers

23.1. Triblock Copolymers with Immiscible Blocks, 359

23.1.1. Synthesis, 359

23.1.2. Morphology, 360

23.1.3. Glass Transition, 360

23.1.4. Mechanical Properties, 361

23.2. Multi-block Copolymers, 361

23.2.1. Main Multi-block Thermoplastic Elastomers, 361

23.2.2. Morphologies and Crystallinity, 363

23.2.2.1. PBT-PTMG Copolymers, 363

23.2.2.2. PA-12-PTMG Copolymers, 363

23.2.2.3. Polyurethane Copolymers, 363

23.2.3. Mechanical Properties, 363


23.2.3.2. Stress-Strain Behavior, 364

23.2.3.3. Fracture Behavior, 365


References, 365

Appendix: Problems

A.l. Conformations of PP and PMMA (Part I), 367

A.l.l. Analysis of PP Dyads, 367

A.l.2. Conformational Energy Calculations for PMMA, 367

A.1.3. Triad Analysis, 368

A.2. PET (Part I), 370

A.2.1. Conformations of the PET Chain, 370

A.2.2. Crystallization of PET, 371

A.2.3. Entanglements in Neat PET, 372

A.3. Glass Transition Temperature of Polybutadienes (Part I), 373

A.3.1. Effect of PB Configurations on Tg, 373

A.3.2. Effect of PB Configurations on Ta, 373

A.3.3. Effect of PB Molecular Weight on Ts, 374

A.3.4. Tss of Star-PBs, 374

A.4. PA-6,6 (Parts I and II), 374

A.4.1. The As-Received Commercial Polymer, 375

A.4.2. Influence of Moisture Uptake on the Relaxational

Behavior of PA-6,6 at 1Hz, 375

A.4.3. Frequency Dependence of the Relaxations in Dry and

Wet PA-6,6, 376

A.4.4. Tensile Behavior of a PA-6,6 Textile Yarn, 376

A.5. PMMA/PVDF Blends (Parts I and II), 377

A.5.1. Blends of PVDF and PMMA-A, 377

A.5.2. Mechanical Behavior of the PVDF/PMMA-A Blends, 378

A.5.3. Comparison of PVDF/PMMA-A and PVDF/PMMA-I

Blends, 378

A.6. Blends of Polystyrene and Poly(Dimethylphenylene Oxide)(Parts I and II), 379

A.6.1. Glass Transition of PS/PDMPO Blends, 379

A.6.2. Plastic Behavior of PS/PDMPO Blends in

Compression, 380

A.7. Bisphenol-A Polycarbonate and Tetramethyl Bisphenol-A

Polycarbonate (Part III), 381

A.7,1. Stress Relaxation in BPA-PC, 382

A.7.2. a and j3 Relaxations of the BPA-PC/TMPC Blends, 383

XX CONTENTS

A.7.3. Comparative Study of the Fracture Behavior of

BPA-PC and TMPC, 384

A.8. Semiaromatic Polyamides (Part III), 384

A.8.1. Physical States of QI and QT Polymers, 384

A.8.2. Stress-Strain Behavior of QI and QT, 385

A.8.3. Fracture Behavior of QI and QI03T07, 386

A.9, ABS (Part IV), 386

A.9.1. Mechanisms, 387

A.9.2. Effect of the AN Content in the Grafted Shell and

SAN Matrix, 387

A.10. Rubber Toughened Polyvinyl Chloride) (RT-PVC) (Part IV), 388

A.10.1. Light Scattering and Volume Change, 388

A.10.2. Effect of the Particle Core Size, 389

A.10.3. Effect of the Loading Rate, 389

A.10.4. Effect of the Morphology, 390

A.ll. Determination of the Molecular Weight Between Cross-Links

in Rubbery Networks (Parts II and V), 390

A.11.1. Analysis of Stress-Strain Data in Vulcanized

Elastomers, 390

A.11.2. Swelling of Cross-Linked Elastomers in Solvents, 391

A.12. Neat and Silica-Filled SBRs (Part V), 393

A.12.1. Neat SBR, 393

A.12.2. Stress-Strain Behavior, 393

A.12.3. Analysis of the Chain Orientation, 393

A.12.4. Silica-Filled SBR, 394

A.12.5. Analysis of the Chain Orientation, 394

A.12.6. Investigation of the Stress-Strain Dependence, 394

A.12.7. Analysis of the Nonlinear Behavior Under DynamicShear, 394

A.12.8. Investigation of Successive Stretchings, 395

INDEX

polymer materials - gbv · contents themacromolecular chainintheamorphousbulk polymer:static...

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