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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
2.8. Conclusions, 39
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
3.8. Conclusions, 58
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
4.7. Conclusions, 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
5.5. Conclusions, 98
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
6.8. Conclusions, 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
7.4. Conclusions, 144
References, 144
Further Reading, 145
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
8.7. Conclusions, 163
References, 164
Further Reading, 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
9.6. Conclusions, 183
References, 183
Further Reading, 184
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
10.6. Conclusions, 209
References, 210
Further Reading, 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. Plastic Deformation, 218
11.3.2.1. Compression Behavior, 218
11.3.2.2. Relations with j3 Relaxation Motions, 218
11.3.3. Micromechanisms of Deformation and Relations with
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. Plastic Deformation, 219
11.4.2.1. Compression Behavior, 219
11.4.2.2. Relations with /3 Relaxation Motions, 219
11.4.3. Micromechanisms of Deformation and Relations with
j3 Relaxation Motions, 220
11.4.4. Fracture, 220
CONTENTS xiii
11.5. Conclusions, 221
References, 221
Further Reading, 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. Plastic Deformation, 224
12.1.2.1. Compression Behavior, 224
12.1.2.2. Relation with p Relaxation Motions, 224
12.1.3. Micromechanisms of Deformation and Relations with
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
12.4. Conclusions, 227
References, 228
Further Reading, 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
13.5. Conclusions, 239
References, 239
Further Reading, 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
14.4. Conclusions, 250
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
15.3. Conclusions, 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
17.5. Conclusions, 279
References, 280
Further Reading, 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
18.5.1. Particle Cavitation, 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
18.7. Conclusions, 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
19.4.1. Particle Cavitation, 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
19.6. Conclusions, 309
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
20.1.3.1. Young Modulus, 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
20.2.2.2. Young Modulus, 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
20.3. Conclusions, 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
21.5. Conclusions, 338
References, 338
Further Reading, 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
23.2.3.1. Young Modulus, 363
23.2.3.2. Stress-Strain Behavior, 364
23.2.3.3. Fracture Behavior, 365
23.3. Conclusions, 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