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Introduction to Chain Molecules | p. 1 |
Introduction | p. 1 |
How Big Is Big? | p. 3 |
Molecular Weight | p. 3 |
Spatial Extent | p. 5 |
Linear and Branched Polymers, Homopolymers, and Copolymers | p. 7 |
Branched Structures | p. 7 |
Copolymers | p. 9 |
Addition, Condensation, and Natural Polymers | p. 11 |
Addition and Condensation Polymers | p. 11 |
Natural Polymers | p. 13 |
Polymer Nomenclature | p. 18 |
Structural Isomerism | p. 20 |
Positional Isomerism | p. 20 |
Stereo Isomerism | p. 21 |
Geometrical Isomerism | p. 22 |
Molecular Weights and Molecular Weight Averages | p. 24 |
Number-, Weight-, and z-Average Molecular Weights | p. 25 |
Polydispersity Index and Standard Deviation | p. 26 |
Examples of Distributions | p. 28 |
Measurement of Molecular Weight | p. 31 |
General Considerations | p. 31 |
End Group Analysis | p. 32 |
MALDI Mass Spectrometry | p. 35 |
Preview of Things to Come | p. 37 |
Chapter Summary | p. 38 |
Problems | p. 38 |
References | p. 41 |
Further Readings | p. 41 |
Step-Growth Polymerization | p. 43 |
Introduction | p. 43 |
Condensation Polymers: One Step at a Time | p. 43 |
Classes of Step-Growth Polymers | p. 43 |
First Look at the Distribution of Products | p. 44 |
A First Look at Reactivity and Reaction Rates | p. 46 |
Kinetics of Step-Growth Polymerization | p. 49 |
Catalyzed Step-Growth Reactions | p. 50 |
How Should Experimental Data Be Compared with Theoretical Rate Laws? | p. 52 |
Uncatalyzed Step-Growth Reactions | p. 53 |
Distribution of Molecular Sizes | p. 55 |
Mole Fractions of Species | p. 56 |
Weight Fractions of Species | p. 58 |
Polyesters | p. 60 |
Polyamides | p. 64 |
Stoichiometric Imbalance | p. 67 |
Chapter Summary | p. 71 |
Problems | p. 71 |
References | p. 76 |
Further Readings | p. 76 |
Chain-Growth Polymerization | p. 77 |
Introduction | p. 77 |
Chain-Growth and Step-Growth Polymerizations: Some Comparisons | p. 77 |
Initiation | p. 79 |
Initiation Reactions | p. 80 |
Fate of Free Radicals | p. 81 |
Kinetics of Initiation | p. 82 |
Photochemical Initiation | p. 84 |
Temperature Dependence of Initiation Rates | p. 85 |
Termination | p. 86 |
Combination and Disproportionation | p. 86 |
Effect of Termination on Conversion to Polymer | p. 88 |
Stationary-State Radical Concentration | p. 89 |
Propagation | p. 90 |
Rate Laws for Propagation | p. 91 |
Temperature Dependence of Propagation Rates | p. 92 |
Kinetic Chain Length | p. 94 |
Radical Lifetime | p. 96 |
Distribution of Molecular Weights | p. 99 |
Distribution of i-mers: Termination by Disproportionation | p. 99 |
Distribution of i-mers: Termination by Combination | p. 102 |
Chain Transfer | p. 104 |
Chain Transfer Reactions | p. 105 |
Evaluation of Chain Transfer Constants | p. 106 |
Chain Transfer to Polymer | p. 108 |
Suppressing Polymerization | p. 109 |
Chapter Summary | p. 110 |
Problems | p. 110 |
References | p. 114 |
Further Readings | p. 115 |
Controlled Polymerization | p. 117 |
Introduction | p. 117 |
Poisson Distribution for an Ideal Living Polymerization | p. 118 |
Kinetic Scheme | p. 119 |
Breadth of the Poisson Distribution | p. 122 |
Anionic Polymerization | p. 126 |
Block Copolymers, End-Functional Polymers, and Branched Polymers by Anionic Polymerization | p. 129 |
Block Copolymers | p. 129 |
End-Functional Polymers | p. 133 |
Regular Branched Architectures | p. 135 |
Cationic Polymerization | p. 137 |
Aspects of Cationic Polymerization | p. 138 |
Living Cationic Polymerization | p. 140 |
Controlled Radical Polymerization | p. 142 |
General Principles of Controlled Radical Polymerization | p. 142 |
Particular Realizations of Controlled Radical Polymerization | p. 144 |
Atom Transfer Radical Polymerization (ATRP) | p. 144 |
Stable Free-Radical Polymerization (SFRP) | p. 145 |
Reversible Addition-Fragmentation Transfer (RAFT) Polymerization | p. 146 |
Polymerization Equilibrium | p. 147 |
Ring-Opening Polymerization (ROP) | p. 150 |
General Aspects | p. 150 |
Specific Examples of Living Ring-Opening Polymerizations | p. 152 |
Poly(ethylene oxide) | p. 152 |
Polylactide | p. 153 |
Poly(dimethylsiloxane) | p. 154 |
Ring-Opening Metathesis Polymerization (ROMP) | p. 155 |
Dendrimers | p. 156 |
Chapter Summary | p. 160 |
Problems | p. 161 |
References | p. 163 |
Further Readings | p. 163 |
Copolymers, Microstructure, and Stereoregularity | p. 165 |
Introduction | p. 165 |
Copolymer Composition | p. 166 |
Rate Laws | p. 166 |
Composition versus Feedstock | p. 168 |
Reactivity Ratios | p. 170 |
Effects of r Values | p. 171 |
Relation of Reactivity Ratios to Chemical Structure | p. 173 |
Resonance and Reactivity | p. 175 |
A Closer Look at Microstructure | p. 179 |
Sequence Distributions | p. 180 |
Terminal and Penultimate Models | p. 183 |
Copolymer Composition and Microstructure: Experimental Aspects | p. 185 |
Evaluating Reactivity Ratios from Composition Data | p. 185 |
Spectroscopic Techniques | p. 188 |
Sequence Distribution: Experimental Determination | p. 190 |
Characterizing Stereoregularity | p. 193 |
A Statistical Description of Stereoregularity | p. 196 |
Assessing Stereoregularity by Nuclear Magnetic Resonance | p. 200 |
Ziegler-Natta Catalysts | p. 205 |
Single-Site Catalysts | p. 208 |
Chapter Summary | p. 211 |
Problems | p. 212 |
References | p. 216 |
Further Readings | p. 216 |
Polymer Conformations | p. 217 |
Conformations, Bond Rotation, and Polymer Size | p. 217 |
Average End-to-End Distance for Model Chains | p. 219 |
The Freely Jointed Chain | p. 220 |
The Freely Rotating Chain | p. 221 |
Hindered Rotation Chain | p. 222 |
Characteristic Ratio and Statistical Segment Length | p. 223 |
Semiflexible Chains and the Persistence Length | p. 225 |
Persistence Length of Flexible Chains | p. 227 |
Worm-Like Chains | p. 228 |
Radius of Gyration | p. 230 |
Spheres, Rods, and Coils | p. 234 |
Distributions for End-to-End Distance and Segment Density | p. 235 |
Distribution of the End-to-End Vector | p. 236 |
Distribution of the End-to-End Distance | p. 239 |
Distribution about the Center of Mass | p. 240 |
Self-Avoiding Chains: A First Look | p. 241 |
Chapter Summary | p. 242 |
Problems | p. 242 |
References | p. 244 |
Further Readings | p. 245 |
Thermodynamics of Polymer Solutions | p. 247 |
Review of Thermodynamic and Statistical Thermodynamic Concepts | p. 247 |
Regular Solution Theory | p. 249 |
Regular Solution Theory: Entropy of Mixing | p. 249 |
Regular Solution Theory: Enthalpy of Mixing | p. 251 |
Flory-Huggins Theory | p. 254 |
Flory-Huggins Theory: Entropy of Mixing by a Quick Route | p. 255 |
Flory-Huggins Theory: Entropy of Mixing by a Longer Route | p. 255 |
Flory-Huggins Theory: Enthalpy of Mixing | p. 257 |
Flory-Huggins Theory: Summary of Assumptions | p. 258 |
Osmotic Pressure | p. 258 |
Osmotic Pressure: General Case | p. 259 |
Number-Average Molecular Weight | p. 261 |
Osmotic Pressure: Flory-Huggins Theory | p. 263 |
Phase Behavior of Polymer Solutions | p. 264 |
Overview of the Phase Diagram | p. 265 |
Finding the Binodal | p. 268 |
Finding the Spinodal | p. 269 |
Finding the Critical Point | p. 270 |
Phase Diagram from Flory-Huggins Theory | p. 271 |
What's in [chi]? | p. 275 |
[chi] from Regular Solution Theory | p. 275 |
[chi] from Experiment | p. 276 |
Further Approaches to [chi] | p. 278 |
Excluded Volume and Chains in a Good Solvent | p. 280 |
Chapter Summary | p. 283 |
Problems | p. 284 |
References | p. 287 |
Further Readings | p. 288 |
Light Scattering by Polymer Solutions | p. 289 |
Introduction: Light Waves | p. 289 |
Basic Concepts of Scattering | p. 291 |
Scattering from Randomly Placed Objects | p. 292 |
Scattering from a Perfect Crystal | p. 292 |
Origins of Incoherent and Coherent Scattering | p. 293 |
Bragg's Law and the Scattering Vector | p. 294 |
Scattering by an Isolated Small Molecule | p. 296 |
Scattering from a Dilute Polymer Solution | p. 298 |
The Form Factor and the Zimm Equation | p. 304 |
Mathematical Expression for the Form Factor | p. 305 |
Form Factor for Isotropic Solutions | p. 306 |
Form Factor as qR[subscript g][Right Arrow]0 | p. 307 |
Zimm Equation | p. 307 |
Zimm Plot | p. 308 |
Scattering Regimes and Particular Form Factors | p. 312 |
Experimental Aspects of Light Scattering | p. 314 |
Instrumentation | p. 316 |
Calibration | p. 317 |
Samples and Solutions | p. 319 |
Refractive Index Increment | p. 319 |
Chapter Summary | p. 320 |
Problems | p. 321 |
References | p. 325 |
Further Readings | p. 325 |
Dynamics of Dilute Polymer Solutions | p. 327 |
Introduction: Friction and Viscosity | p. 327 |
Stokes' Law and Einstein's Law | p. 330 |
Viscous Forces on Rigid Spheres | p. 331 |
Suspension of Spheres | p. 332 |
Intrinsic Viscosity | p. 334 |
General Considerations | p. 334 |
Mark-Houwink Equation | p. 336 |
Measurement of Viscosity | p. 341 |
Poiseuille Equation and Capillary Viscometers | p. 341 |
Concentric Cylinder Viscometers | p. 345 |
Diffusion Coefficient and Friction Factor | p. 346 |
Tracer Diffusion and Hydrodynamic Radius | p. 347 |
Mutual Diffusion and Fick's Laws | p. 348 |
Dynamic Light Scattering | p. 354 |
Hydrodynamic Interactions and Draining | p. 357 |
Size Exclusion Chromatography (SEC) | p. 360 |
Basic Separation Process | p. 361 |
Separation Mechanism | p. 365 |
Two Calibration Strategies | p. 367 |
Limitations of Calibration by Standards | p. 367 |
Universal Calibration | p. 368 |
Size Exclusion Chromatography Detectors | p. 369 |
RI Detector | p. 369 |
UV-Vis Detector | p. 370 |
Light Scattering Detector | p. 371 |
Viscometer | p. 372 |
Chapter Summary | p. 372 |
Problems | p. 373 |
References | p. 378 |
Further Readings | p. 379 |
Networks, Gels, and Rubber Elasticity | p. 381 |
Formation of Networks by Random Cross-Linking | p. 381 |
Definitions | p. 381 |
Gel Point | p. 383 |
Polymerization with Multifunctional Monomers | p. 386 |
Calculation of the Branching Coefficient | p. 387 |
Gel Point | p. 388 |
Molecular-Weight Averages | p. 389 |
Elastic Deformation | p. 392 |
Thermodynamics of Elasticity | p. 394 |
Equation of State | p. 394 |
Ideal Elastomers | p. 396 |
Some Experiments on Real Rubbers | p. 397 |
Statistical Mechanical Theory of Rubber Elasticity: Ideal Case | p. 398 |
Force to Extend a Gaussian Chain | p. 400 |
Network of Gaussian Strands | p. 402 |
Modulus of the Gaussian Network | p. 403 |
Further Developments in Rubber Elasticity | p. 406 |
Non-Gaussian Force Law | p. 406 |
Front Factor | p. 407 |
Network Defects | p. 408 |
Mooney-Rivlin Equation | p. 409 |
Swelling of Gels | p. 410 |
Modulus of a Swollen Rubber | p. 411 |
Swelling Equilibrium | p. 412 |
Chapter Summary | p. 414 |
Problems | p. 416 |
References | p. 418 |
Further Readings | p. 418 |
Linear Viscoelasticity | p. 419 |
Basic Concepts | p. 419 |
Stress and Strain | p. 421 |
Viscosity, Modulus, and Compliance | p. 421 |
Viscous and Elastic Responses | p. 422 |
Response of the Maxwell and Voigt Elements | p. 423 |
Transient Response: Stress Relaxation | p. 423 |
Transient Response: Creep | p. 425 |
Dynamic Response: Loss and Storage Moduli | p. 426 |
Dynamic Response: Complex Modulus and Complex Viscosity | p. 429 |
Boltzmann Superposition Principle | p. 430 |
Bead-Spring Model | p. 432 |
Ingredients of the Bead-Spring Model | p. 432 |
Predictions of the Bead-Spring Model | p. 434 |
Zimm Model for Dilute Solutions, Rouse Model for Unentangled Melts | p. 439 |
Phenomenology of Entanglement | p. 444 |
Rubbery Plateau | p. 444 |
Dependence of M[subscript e] on Molecular Structure | p. 447 |
Reptation Model | p. 450 |
Reptation Model: Longest Relaxation Time and Diffusivity | p. 451 |
Reptation Model: Viscoelastic Properties | p. 453 |
Reptation Model: Additional Relaxation Processes | p. 456 |
Aspects of Experimental Rheometry | p. 458 |
Shear Sandwich and Cone and Plate Rheometers | p. 458 |
Further Comments about Rheometry | p. 459 |
Chapter Summary | p. 460 |
Problems | p. 461 |
References | p. 464 |
Further Readings | p. 464 |
Glass Transition | p. 455 |
Introduction | p. 455 |
Definition of a Glass | p. 455 |
Glass and Melting Transitions | p. 466 |
Thermodynamic Aspects of the Glass Transition | p. 468 |
First-Order and Second-Order Phase Transitions | p. 469 |
Kauzmann Temperature | p. 471 |
Theory of Gibbs and DiMarzio | p. 472 |
Locating the Glass Transition Temperature | p. 474 |
Dilatometry | p. 474 |
Calorimetry | p. 476 |
Dynamic Mechanical Analysis | p. 478 |
Free Volume Description of the Glass Transition | p. 479 |
Temperature Dependence of the Free Volume | p. 480 |
Free Volume Changes Inferred from the Viscosity | p. 481 |
Williams-Landel-Ferry Equation | p. 483 |
Time-Temperature Superposition | p. 486 |
Factors that Affect the Glass Transition Temperature | p. 491 |
Dependence on Chemical Structure | p. 491 |
Dependence on Molecular Weight | p. 492 |
Dependence on Composition | p. 492 |
Mechanical Properties of Glassy Polymers | p. 496 |
Basic Concepts | p. 496 |
Crazing, Yielding, and the Brittle-to-Ductile Transition | p. 498 |
Role of Chain Stiffness and Entanglements | p. 501 |
Chapter Summary | p. 504 |
Problems | p. 505 |
References | p. 508 |
Further Readings | p. 508 |
Crystalline Polymers | p. 511 |
Introduction and Overview | p. 511 |
Structure and Characterization of Unit Cells | p. 513 |
Classes of Crystals | p. 513 |
X-Ray Diffraction | p. 515 |
Examples of Unit Cells | p. 518 |
Thermodynamics of Crystallization: Relation of Melting Temperature to Molecular Structure | p. 521 |
Structure and Melting of Lamellae | p. 526 |
Surface Contributions to Phase Transitions | p. 526 |
Dependence of T[subscript m] on Lamellar Thickness | p. 527 |
Dependence of T[subscript m] on Molecular Weight | p. 530 |
Experimental Characterization of Lamellar Structure | p. 532 |
Kinetics of Nucleation and Growth | p. 536 |
Primary Nucleation | p. 537 |
Crystal Growth | p. 539 |
Morphology of Semicrystalline Polymers | p. 545 |
Spherulites | p. 545 |
Nonspherulitic Morphologies | p. 548 |
Kinetics of Bulk Crystallization | p. 551 |
Avrami Equation | p. 552 |
Kinetics of Crystallization: Experimental Aspects | p. 556 |
Chapter Summary | p. 561 |
Problems | p. 562 |
References | p. 565 |
Further Readings | p. 565 |
Appendix | p. 567 |
Series Expansions | p. 567 |
Summation Formulae | p. 568 |
Transformation to Spherical Coordinates | p. 569 |
Some Integrals of Gaussian Functions | p. 570 |
Complex Numbers | p. 572 |
Index | p. 575 |
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