Topics in Polymer Physics Book

	Dedication
	Preface
Chapter 1	Introduction	1
1.1	Background	1
1.2	Linear Chain Molecules	4
1.2.1	Structure	4
1.2.2	Synthesis	8
1.2.3	Molecular Weight	10
1.3	Network Molecules	15
1.3.1	Structure	15
1.3.2	Synthesis	16
1.3.3	Molecular Weight	16
1.4	Rubber	17
1.4.1	Structure	17
1.4.2	Synthesis	21
1.4.3	Molecular Weight	21
1.5	Multicomponent Systems	21
1.5.1	Copolymers	21
1.5.2	Polyblends	25
1.5.3	Composites	25
1.5.4	Ceramers	26
	References	27
Appendix 1A	Derivation of the Most Probable Distribution	28
	Reference	30
Chapter 2	Statistics of Chain Conformations	31
2.1	Introduction	31
2.2	Small Molecules	31
2.3	Larger Molecules, Statistical Variation of Molecular Conformations	40
2.4	Statistical Segment Model	41
2.5	Generalization to High Polymers	44
2.6	Polymer Chains Containing Two Kinds of Atoms	45
2.7	Model Chains with Restricted Rotation and No Interaction Among the [phi]'s	47
2.8	Rotational Isomeric State (RIS) Approximation	49
2.9	Chains with Interactions between [phi] Values of Neighboring Monomers	51
2.10	Asymmetric Barriers	53
2.11	Comparison with Experiment	56
2.12	Chain End-to-End Distribution Functions	58
2.12.1	One Dimensional Case	58
2.12.2	Extension to a Three Dimensional Chain	61
2.12.3	Extension to Non-Gaussian Case	64
	References	71
Appendix 2A	Statistical Mechanics	73
	References	80
	Statistical Thermodynamics of an Ideal Monatomic Gas	81
Appendix 2B	Vector Analysis	83
2B.1	Vector Addition	83
2.B.2	Scalar Product	84
	Reference	85
Appendix 2C	Radius of Gyration	86
Appendix 2D	Evaluation of (a[subscript m+n] [middle dot] a[subscript m])	92
Appendix 2E	Restricted Rotation with Symmetrical Barrier	99
Appendix 2F	Rotational Isomeric State (RIS) Approximation	103
2F.1	Introduction	103
2F.2	The Conformational Partition Function	104
2E.3	Mean Square Distance	106
	References	107
Appendix 2G	Random Walk of Gaussian Chains	109
	References	113
Appendix 2H	Radius of Gyration, Size and Shape	114
	Definition of	114
	for a Rigid Rod	115
	for a Sphere of Radius R	116
	Determination of from Scattering	117
Chapter 3	Thermodynamics	121
3.1	Introduction	121
3.2	Thermodynamics of Elasticity	121
3.3	Force on a Chain in the Presence of Energy Contributions to Elasticity	129
3.4	Solution Thermodynamics	134
3.4.1	Flory-Huggins Theory	134
3.4.2	Calculation of P[subscript 2]	138
3.3.3	Entropy of Mixing	140
3.5	Polymer Miscibility	145
3.6	Spinodal Decomposition	147
3.7	Heat Capacity	153
3.8	Thermodynamics of Crystallization	154
3.8.1	Polymer Structure - Melting Point	155
3.8.2	Effect of Diluent and Impurities	157
3.8.3	Crystallization Induced by Stretching	164
	References	167
Appendix 3A	Classical Thermodynamics	169
	References	175
Appendix 3B	Heat of Mixing	176
Appendix 3C	Osmotic Pressure	181
Chapter 4	Optics	185
4.1	Introduction	185
4.2	Nature of Electromagnetic Waves	186
4.3	Refraction	187
4.4	Scattering	191
4.4.1	Intensity of Light Scattering for an Isolated Atom or Molecule	194
4.4.2	Effect of the Polarization of Light	195
4.4.3	The Scattering Intensity for a Collection of Scattering Objects	196
4.5	Diffraction	205
4.5.1	The Reciprocal Lattice	205
4.5.2	Interpretation of the Vector Bragg Equation	208
4.5.3	The Distance Between Crystal Planes	209
4.5.4	The Diffraction Phenomenon in One Dimension	211
4.6	Absorption	215
4.7	Fluorescence	216
4.8	Birefringence	218
4.9	Scattering from Inhomogeneous Media	222
4.10	Quasi-elastic Light Scattering	228
4.11	Variation of Scattering with Electric Fields	229
4.12	Non-Linear Optics	230
4.13	Piezo-Electric Materials	232
4.14	Kerr Effect	233
	References	234
Appendix 4A	Depolarization of Scattering	236
Appendix 4B	Scattering from a Collection of Molecules	239
Appendix 4D	The Magnitude of the Reciprocal Vector H	244
Appendix 4E	Orientation Fluctuations	246
Appendix 4F	Scattering from Concentration Fluctuations	249
	Evaluation of ([partial differential alpha]/[partial differential]c)	252
	Evaluation of [-([partial differential mu subscript 1]/[partial differential]c)]	252
	Molecular Weight from Light Scattering	253
	Dealing with Large Molecules	255
	Extensions to Other Kinds of Radiation	256
	Extensions to Concentrated Solution and Bulk Polymers	257
	Effect of Anisotropy and Orientation	257
Appendix 4G	Why Concentration Fluctuations Relate to Molecular Weight	257
	How to Measure the Size of an Elephant	258
	Another Way of Looking at it -	260
Chapter 5	Electrical Properties	263
5.1	Introduction	263
5.2	Dielectrics	264
5.2.1	Dielectric Constant	264
5.2.2	Orientation of permanent dipoles	269
5.2.3	Dielectric Loss	269
5.3	Piezo- and Pyroelectric Effects	272
5.4	Piezo-Electric Coefficient	274
	References	276
Appendix 5A	Lines of Flux	278
5A.1	Electrical Field Strength	278
5A.2	Electric displacement and Flux Density	278
5A.4	The Electrostatic Potential (Voltage)	280
5A.5	The Field between Parallel Plates	280
Appendix 5B	Lorentz Calculation, Internal Field Correction	282
Chapter 6	Spectroscopy	285
6.1	Introduction	285
6.2	General Background	286
6.3	Infrared	288
6.4	Raman	295
6.5	Ultraviolet and Visible	299
6.6	Nuclear Magnetic Resonance	300
6.7	Neutron Inelastic Scattering (NIS)	301
	References	303
Appendix 6A	Fourier Transform Infrared (FTIR)	305
	References	307
Appendix 6B	Normal Coordinate Analysis	308
	References	312
Appendix 6C	Spectrographic Notation	313
Chapter 7	The Rubbery State	314
7.1	Introduction	314
7.2	Force - Extension Relation for Rubbers	316
7.2.1	Simple Case	316
7.2.2	Consideration of Network Crosslinks	318
7.3	Affine Transformation	322
7.4	Uniaxial Stretching at Constant Volume	329
7.5	Biaxial Stretching at Constant Volume	331
7.6	Application to the Inflation of a Balloon	333
7.7	Network Defects - The Relationship between N[subscript c] and v	334
7.8	Effect of Swelling on an Isotropic Network	336
7.9	Elastic Properties of Swollen Rubber	339
7.10	Elasticity of a Sample That is Swollen When Crosslinked	341
7.11	Elasticity of Rubbers at Small Extensions	343
7.12	Guth-Smallwood Equations	347
	References	348
Appendix 7A	Evaluation of Equation 7.30	350
Chapter 8	The Crystalline State	352
8.1	Introduction	352
8.2	Evidence for Crystallinity	354
8.2.1	X-Ray Diffraction	354
8.2.2	Electron Microscopical Observations	358
8.2.3	Optical Microscopy	359
8.2.4	Thermodynamic Transitions	360
8.3	Determination of Degree of Crystalline	361
8.3.1	Density Measurements	361
8.3.2	X-Ray Diffraction	364
8.3.3	Infrared (IR) and Raman	365
8.3.4	Wide Line Nuclear Magnetic Resonance	366
8.3.5	Thermal Measurements	368
8.4	Morphology	369
8.4.1	Electron Microscope	369
i)	The observed pyramidal structure	369
ii)	Moire Patterns	370
i)	Density	370
ii)	nmr	371
iii)	X-ray diffraction	371
iv)	Kinetics	371
8.4.2	Optical Microscopy	372
8.4.3	Liquid Crystals	373
8.5	Mechanisms of Crystallization	375
8.5.1	Nucleation and Growth	375
8.6	Kinetics of Crystallization	376
8.6.1	Temperature Dependence of the Nucleation Rate	376
8.6.2	Nucleation and Growth	379
8.6.3	Experimental Determination of n and k	384
i	Slope-Intercept Method	384
ii	Half-life Method	385
8.6.4	Temperature Dependence of the Rate of Homogeneous Crystallization	386
	References	387
	Glossary of Symbols Arranged by Chapters	389
	Chapter 1	389
	Chapter 2	389
	Chapter 3	392
	Chapter 4	396
	Chapter 5	398
	Chapter 7	402
	Chapter 8	403
	Index	407