Topics In Polymer Physics

By: Joseph Powers, Richard S Stein

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Paperback | 10 March 2006

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This book can serve as an introduction to students interested in learning the techniques used in developing mathematical models of physical phenomenon in polymers; or it can furnish the background information to the experienced professional desiring to broaden his/her knowledge of polymers. The senior author presented material in this book to students interested in learning the fundamental mathematics underlying many areas of polymer physics and in lectures to audiences with varying backgrounds in polymer physics. Too many times, the basic equations are presented in final form from either lack of space or the assumption that the derivation is widely disseminated and does not require repetition. A wide variety of topics are covered, from the statistical physics and thermodynamics of polymers, to the optical and electrical behavior of polymers, as well as spectroscopy techniques for polymers.A website for the book is available at the URL: web.mac.com/rsstein1/iWebThis contains pages describing the book, the authors, information about important polymer scientists, links to additional material, book corrections, and recent developments.

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Dedication	p. v
Preface	p. vii
Introduction	p. 1
Background	p. 1
Linear Chain Molecules	p. 4
Structure	p. 4
Synthesis	p. 8
Molecular Weight	p. 10
Network Molecules	p. 15
Structure	p. 15
Synthesis	p. 16
Molecular Weight	p. 16
Rubber	p. 17
Structure	p. 17
Synthesis	p. 21
Molecular Weight	p. 21
Multicomponent Systems	p. 21
Copolymers	p. 21
Polyblends	p. 25
Composites	p. 25
Ceramers	p. 26
References	p. 27
Derivation of the Most Probable Distribution	p. 28
Reference	p. 30
Statistics of Chain Conformations	p. 31
Introduction	p. 31
Small Molecules	p. 31
Larger Molecules, Statistical Variation of Molecular Conformations	p. 40
Statistical Segment Model	p. 41
Generalization to High Polymers	p. 44
Polymer Chains Containing Two Kinds of Atoms	p. 45
Model Chains with Restricted Rotation and No Interaction Among the [phi]'s	p. 47
Rotational Isomeric State (RIS) Approximation	p. 49
Chains with Interactions between [phi] Values of Neighboring Monomers	p. 51
Asymmetric Barriers	p. 53
Comparison with Experiment	p. 56
Chain End-to-End Distribution Functions	p. 58
One Dimensional Case	p. 58
Extension to a Three Dimensional Chain	p. 61
Extension to Non-Gaussian Case	p. 64
References	p. 71
Statistical Mechanics	p. 73
References	p. 80
Statistical Thermodynamics of an Ideal Monatomic Gas	p. 81
Vector Analysis	p. 83
Vector Addition	p. 83
Scalar Product	p. 84
Reference	p. 85
Radius of Gyration	p. 86
Evaluation of (a[subscript m+n] [middle dot] a[subscript m])	p. 92
Restricted Rotation with Symmetrical Barrier	p. 99
Rotational Isomeric State (RIS) Approximation	p. 103
Introduction	p. 103
The Conformational Partition Function	p. 104
Mean Square Distance	p. 106
References	p. 107
Random Walk of Gaussian Chains	p. 109
References	p. 113
Radius of Gyration, Size and Shape	p. 114
Definition of <r[superscript 2 subscript q]>	p. 114
<r[superscript 2 subscript q]> for a Rigid Rod	p. 115
<r[superscript 2 subscript q]> for a Sphere of Radius R	p. 116
Determination of <r[superscript 2 subscript q]> from Scattering	p. 117
Thermodynamics	p. 121
Introduction	p. 121
Thermodynamics of Elasticity	p. 121
Force on a Chain in the Presence of Energy Contributions to Elasticity	p. 129
Solution Thermodynamics	p. 134
Flory-Huggins Theory	p. 134
Calculation of P[subscript 2]	p. 138
Entropy of Mixing	p. 140
Polymer Miscibility	p. 145
Spinodal Decomposition	p. 147
Heat Capacity	p. 153
Thermodynamics of Crystallization	p. 154
Polymer Structure - Melting Point	p. 155
Effect of Diluent and Impurities	p. 157
Crystallization Induced by Stretching	p. 164
References	p. 167
Classical Thermodynamics	p. 169
References	p. 175
Heat of Mixing	p. 176
Osmotic Pressure	p. 181
Optics	p. 185
Introduction	p. 185
Nature of Electromagnetic Waves	p. 186
Refraction	p. 187
Scattering	p. 191
Intensity of Light Scattering for an Isolated Atom or Molecule	p. 194
Effect of the Polarization of Light	p. 195
The Scattering Intensity for a Collection of Scattering Objects	p. 196
Diffraction	p. 205
The Reciprocal Lattice	p. 205
Interpretation of the Vector Bragg Equation	p. 208
The Distance Between Crystal Planes	p. 209
The Diffraction Phenomenon in One Dimension	p. 211
Absorption	p. 215
Fluorescence	p. 216
Birefringence	p. 218
Scattering from Inhomogeneous Media	p. 222
Quasi-elastic Light Scattering	p. 228
Variation of Scattering with Electric Fields	p. 229
Non-Linear Optics	p. 230
Piezo-Electric Materials	p. 232
Kerr Effect	p. 233
References	p. 234
Depolarization of Scattering	p. 236
Scattering from a Collection of Molecules	p. 239
The Magnitude of the Reciprocal Vector H	p. 244
Orientation Fluctuations	p. 246
Scattering from Concentration Fluctuations	p. 249
Evaluation of ([partial differential alpha]/[partial differential]c)	p. 252
Evaluation of [-([partial differential mu subscript 1]/[partial differential]c)]	p. 252
Molecular Weight from Light Scattering	p. 253
Dealing with Large Molecules	p. 255
Extensions to Other Kinds of Radiation	p. 256
Extensions to Concentrated Solution and Bulk Polymers	p. 257
Effect of Anisotropy and Orientation	p. 257
Why Concentration Fluctuations Relate to Molecular Weight	p. 257
How to Measure the Size of an Elephant	p. 258
Another Way of Looking at it -	p. 260
Electrical Properties	p. 263
Introduction	p. 263
Dielectrics	p. 264
Dielectric Constant	p. 264
Orientation of permanent dipoles	p. 269
Dielectric Loss	p. 269
Piezo- and Pyroelectric Effects	p. 272
Piezo-Electric Coefficient	p. 274
References	p. 276
Lines of Flux	p. 278
Electrical Field Strength	p. 278
Electric displacement and Flux Density	p. 278
The Electrostatic Potential (Voltage)	p. 280
The Field between Parallel Plates	p. 280
Lorentz Calculation, Internal Field Correction	p. 282
Spectroscopy	p. 285
Introduction	p. 285
General Background	p. 286
Infrared	p. 288
Raman	p. 295
Ultraviolet and Visible	p. 299
Nuclear Magnetic Resonance	p. 300
Neutron Inelastic Scattering (NIS)	p. 301
References	p. 303
Fourier Transform Infrared (FTIR)	p. 305
References	p. 307
Normal Coordinate Analysis	p. 308
References	p. 312
Spectrographic Notation	p. 313
The Rubbery State	p. 314
Introduction	p. 314
Force - Extension Relation for Rubbers	p. 316
Simple Case	p. 316
Consideration of Network Crosslinks	p. 318
Affine Transformation	p. 322
Uniaxial Stretching at Constant Volume	p. 329
Biaxial Stretching at Constant Volume	p. 331
Application to the Inflation of a Balloon	p. 333
Network Defects - The Relationship between N[subscript c] and v	p. 334
Effect of Swelling on an Isotropic Network	p. 336
Elastic Properties of Swollen Rubber	p. 339
Elasticity of a Sample That is Swollen When Crosslinked	p. 341
Elasticity of Rubbers at Small Extensions	p. 343
Guth-Smallwood Equations	p. 347
References	p. 348
Evaluation of Equation 7.30	p. 350
The Crystalline State	p. 352
Introduction	p. 352
Evidence for Crystallinity	p. 354
X-Ray Diffraction	p. 354
Electron Microscopical Observations	p. 358
Optical Microscopy	p. 359
Thermodynamic Transitions	p. 360
Determination of Degree of Crystalline	p. 361
Density Measurements	p. 361
X-Ray Diffraction	p. 364
Infrared (IR) and Raman	p. 365
Wide Line Nuclear Magnetic Resonance	p. 366
Thermal Measurements	p. 368
Morphology	p. 369
Electron Microscope	p. 369
The observed pyramidal structure	p. 369
Moire Patterns	p. 370
Density	p. 370
nmr	p. 371
X-ray diffraction	p. 371
Kinetics	p. 371
Optical Microscopy	p. 372
Liquid Crystals	p. 373
Mechanisms of Crystallization	p. 375
Nucleation and Growth	p. 375
Kinetics of Crystallization	p. 376
Temperature Dependence of the Nucleation Rate	p. 376
Nucleation and Growth	p. 379
Experimental Determination of n and k	p. 384
Slope-Intercept Method	p. 384
Half-life Method	p. 385
Temperature Dependence of the Rate of Homogeneous Crystallization	p. 386
References	p. 387
Glossary of Symbols Arranged by Chapters	p. 389
Chapter 1	p. 389
Chapter 2	p. 389
Chapter 3	p. 392
Chapter 4	p. 396
Chapter 5	p. 398
Chapter 7	p. 402
Chapter 8	p. 403
Index	p. 407
Table of Contents provided by Ingram. All Rights Reserved.

Topics In Polymer Physics

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