Contents
Introduction ................................................. xiii
Chapter 1 Introduction .......................................... 1
1.1 Molecular Nature of Polymers ...................... 1
1.2 Polymeric Structure ............................... 6
1.2.1 Chemical Microstructure ..................... 7
1.2.2 Chemical Macrostructure .................... 10
1.2.3 Rotational States .......................... 10
1.3 Polymeric Properties ............................. 12
1.3.1 Species Dependence ......................... 13
1.3.2 Architectural Dependence ................... 14
Viscosity .................................. 14
Viscoelastic behavior ...................... 16
1.4 Macromolecular Heterogeneity ..................... 17
1.4.1 Averages ................................... 18
1.4.2 Distribution Functions ..................... 20
Exponential distribution ................... 21
Distributions from branching and
scission ................................... 22
Empirical distribution functions ........... 25
1.5 Molecular Simulations ............................ 27
Chapter 2 Molecular Liquids .................................... 29
2.1 Microscopic Origin of Liquid Properties .......... 35
2.1.1 Intermolecular Forces ...................... 35
2.1.2 Terminology ................................ 38
2.1.3 Statistical Thermodynamics ................. 40
2.1.4 Pair Distributions and Intermolecular
Energy ..................................... 43
2.1.5 Principles of Elastic Scattering ........... 46
2.1.6 The Structure Factor ....................... 52
2.2 Liquid Structure and Properties .................. 55
2.2.1 Scattering by Pure Liquids ................. 55
2.2.2 The van der Waals Liquid ................... 59
2.2.3 Hard Sphere Liquids ........................ 61
2.3 Generalized van der Waals Theory ................. 63
2.3.1 The Longuet-Higgins and Widom Model ........ 64
2.3.2 Cell Models ................................ 66
2.3.3 Lattice Models ............................. 67
2.3.4 Reduced Equations of State ................. 69
2.3.5 Cohesive Energy and Internal Pressure ...... 70
Chapter 3 Molecular Mixtures ................................... 77
3.1 Thermodynamics of Liquid Mixtures ................ 77
3.2 Liquid-Liquid Phase Behavior ..................... 83
3.3 Molecular Aspects of Mixing ...................... 89
3.4 Simple Mixtures .................................. 94
3.4.1 Properties of the Interaction Parameter .... 96
3.4.2 Phase Behavior ............................. 98
3.4.3 Observations .............................. 100
3.5 Regular Mixtures ................................ 103
3.5.1 Commentary ................................ 105
3.5.2 Volume Change on Mixing ................... 107
3.6 The Free Volume Effect .......................... 109
3.6.1 Modified FOV Theory ....................... 111
3.6.2 The Free Volume Interaction Parameter ..... 114
3.6.3 Commentary ................................ 116
Chapter 4 The Random Coil Model ............................... 121
4.1 Random Walks .................................... 123
4.1.1 Average End-to-End Distance ............... 124
4.1.2 Radius of Gyration ........................ 125
4.2 Polymer Chains .................................. 128
4.2.1 Locally Restricted Conformations .......... 129
4.2.2 Step Length Definitions ................... 132
4.3 Nonlinear Molecules ............................. 136
4.3.1 Branched Chains ........................... 137
4.3.2 Macrocycles ............................... 140
4.4 Random Coil Asymmetry ........................... 142
4.5 Conformational Distributions .................... 142
4.5.1 The End-to-End Vector Distribution ........ 143
4.5.2 The Gaussian Form ......................... 147
4.5.3 Mass Distribution for Gaussian Coils ...... 148
4.6 Properties of Random Coil Ensembles ............. 149
4.6.1 Mechanical Properties ..................... 149
4.6.2 Thermodynamic Properties .................. 150
4.7 Scattering Properties ........................... 152
4.7.1 Form Factors .............................. 152
Random coil molecules ..................... 154
Pair distributions ........................ 155
General properties ........................ 156
4.7.2 Structure Factors ......................... 158
One-component systems ..................... 159
Two-component systems ..................... 160
Incompressible mixtures ................... 160
Chapter 5 Dilute Solution Characterization .................... 167
5.1 Thermodynamic Characterization Methods .......... 167
5.1.1 Osmotic Pressure .......................... 168
5.1.2 Light Scattering .......................... 171
Fundamentals .............................. 172
Dilute solutions .......................... 175
Scattering method comparisons ............. 182
5.2 Dynamic Characterization Methods ................ 184
5.2.1 Dynamic Light Scattering .................. 185
5.2.2 Viscometry ................................ 189
5.3 Chromatographic Methods ..................... 192
5.3.1 Size Exclusion Chromatography ............. 192
5.3.2 Multidetector Methods ..................... 197
Chapter 6 Dilute Solution Properties .......................... 203
6.1 Intramolecular Interactions ..................... 203
6.1.1 Excluded Volume ........................... 204
Pervaded volume and self-concentration .... 206
Self-exclusion ............................ 208
6.1.2 Hydrodynamic Interaction .................. 217
6.2 Linear Polymers ................................. 222
6.2.1 Limiting Size Ratios ...................... 223
6.2.2 Expansion Factors ......................... 224
6.2.3 Good Solvent Master Curves ................ 227
Master curve forms ........................ 231
Onset molecular weights ................... 232
6.3 Branched and Macrocyclic Polymers ............... 235
6.3.1 Lightly Branched Model Structures ......... 237
Regular stars ............................. 237
Rings ..................................... 239
H-Polymers ................................ 243
Combs ..................................... 243
6.3.2 Lightly Branched Statistical Structures ... 247
6.3.3 Highly Branched Structures ................ 249
Daoud-Cotton model ........................ 251
Many-arm star properties .................. 254
Colloidal analogies ....................... 255
6.4 Concentration Regimes ........................... 257
Chapter 7 Polymer Solutions ................................... 265
7.1 Coil Size Beyond Overlap ........................ 266
7.1.1 Chain Dimensions in Polymer Melts ......... 266
7.1.2 Chain Dimensions in Semidilute
Solutions ................................. 269
Excluded volume screening ................. 269
Concentration dependence .................. 273
Semidilute-concentrated crossover ......... 274
Observations .............................. 276
7.2 Osmotic Pressure Beyond Overlap ................. 278
7.2.1 Flory-Huggins Predictions ................. 280
7.2.2 Scaling Analysis .......................... 283
7.2.3 Experimental Observations ................. 284
7.3 Scattering Beyond Overlap ....................... 286
7.3.1 Correlation Length ........................ 286
7.3.2 The Random Phase Approximation ............ 293
7.3.3 Interpretation Alternatives ............... 295
7.3.4 Branch-Induced Ordering ................... 296
7.4 The Interaction Parameter ....................... 297
7.4.1 Evaluation of X ........................... 298
Vapor composition and sorption ............ 298
Osmometry ................................. 299
Inverse chromatography .................... 300
Scattering ................................ 300
7.4.2 Interpretation of X ....................... 304
Free volume effects ....................... 306
Impact on dilute solutions ................ 312
Athermal solutions ........................ 313
7.5 Liquid-Liquid Phase Behavior .................... 314
7.5.1 Upper Critical Behavior ................... 314
7.5.2 Lower Critical Behavior ................... 320
7.5.3 Scattering and Criticality ................ 323
7.5.4 The Cinzburg Criterion .................... 329
Chapter 8 Polymer Blends ...................................... 341
8.1 Molecular Interactions .......................... 343
8.2 Isotopic Blends ................................. 347
8.2.1 Isotopic Interactions ..................... 348
Experimental aspects ...................... 349
8.2.2 Temperature Dependence of
the Interactions .......................... 352
8.2.3 Some Properties of Xhd .................... 355
8.3 Polyolefin Blends ............................... 356
8.3.1 Measurements .............................. 357
8.3.2 Observations .............................. 359
8.3.3 Solubility Parameters ..................... 364
Molecular considerations .................. 367
PVT measurements .......................... 369
Simulations ............................... 372
8.3.4 Interaction Properties .................... 375
Temperature dependence .................... 375
Pressure dependence ....................... 377
Molecular weight dependence ............... 378
Composition dependence .................... 379
8.3.5 Irregular Blends .......................... 381
8.4 Hydrocarbon Polymer Blends ...................... 385
8.4.1 Inter-Family Blends ....................... 388
8.4.2 Intra-Family Blends ....................... 389
8.4.3 Commentary ................................ 391
8.5 Blends of Copolymers ............................ 393
8.5.1 Sequencing Effects ........................ 393
8.5.2 Mean Composition Effects .................. 394
8.6 Blends with Specific Associations ............... 399
Chapter 9 Network Structure and Elasticity .................... 409
9.1 Equal Reactivity and Random Linking ............. 411
9.1.1 Network Connectivity ...................... 413
9.1.2 Strand Dimensions ......................... 418
9.1.3 Linking Statistics ........................ 418
9.2 Structurally Related Observables ................ 420
9.2.1 Pre-Gelation Region ....................... 421
9.2.2 The Gel Curve ............................. 423
9.3 Elasticity-Related Properties ................... 427
9.3.1 Active Junctions and Strands .............. 428
9.3.2 Topological and Dynamics-Related
Properties ................................ 431
9.3.3 Architectural Characterization ............ 435
9.4 General Considerations on
Network Elasticity .............................. 436
9.5 The Affine Network .............................. 441
9.5.1 The Logarithmic Contribution .............. 443
9.5.2 Effects of Temperature and
Volume Change ............................. 445
9.5.3 Network Pressure .......................... 446
9.6 The Phantom Network ............................. 447
9.7 The Entangled Network ........................... 452
9.7.1 Modulus Magnitude ......................... 453
9.7.2 Experimental Tests ........................ 456
9.7.3 Comments .................................. 466
Chapter 10 Network Properties ................................. 471
10.1 Stress-Strain Behavior ........................ 472
10.1.1 The Mooney-Rivlin Form ................. 476
10.1.2 Swelling and Supercoiling Effects ...... 479
10.1.3 The Ferry-Kan Formulation .............. 487
10.2 Swelling Equilibrium .......................... 490
10.3 Thermoelasticity .............................. 501
10.4 Observations on Networks ...................... 508
10.4.1 Microscopic Features ................... 509
Orientational correlations ............. 509
Neutron scattering ..................... 509
10.4.2 Macroscopic Features ................... 514
10.5 Modeling Uncrossability ....................... 514
10.5.1 Topological Classification ............. 519
10.5.2 Slip-Links ............................. 522
10.5.3 Constrained Junction Models ............ 524
10.5.4 Tube Models ............................ 524
Affine models .......................... 526
Constant mesh density models ........... 527
Empirical models ....................... 528
Nonaffine models ....................... 528
Tube model comparisons ................. 530
10.5.5 Commentary ............................. 530
Appendix A—Symbols ............................................ 537
Subject Index ................................................. 543
Author Index .................................................. 549
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