Electrical Properties of Polymers

Electrical Properties of Polymers......Page 1
Dedication......Page 2
Preface......Page 3
Contents......Page 8
1.1. DIPOLES......Page 17
Contents......Page 0
1.2. ELECTRIC POTENTIALS ARISING FROM AN ISOLATED DIPOLE......Page 18
1.3. POINT DIPOLE......Page 19
1.4. FIELD OF AN ISOLATED POINT DIPOLE......Page 20
1.5. FORCE EXERTED ON A DIPOLE BY AN EXTERNAL ELECTRIC FIELD......Page 21
1.6. DIPOLE-DIPOLE INTERACTION......Page 22
1.7. TORQUES ON DIPOLES......Page 23
1.8. DIPOLE MOMENT AND DIELECTRIC PERMITTIVITY. MOLECULAR VERSUS MACROSCOPIC PICTURE......Page 24
1.9. LOCAL FIELD. THE DEBYE STATIC THEORY OF DIELECTRIC PERMITTIVITY......Page 26
1.10. DRAWBACK OF THE LORENTZ LOCAL FIELD......Page 29
1.11. DIPOLE MOMENT OF A DIELECTRIC SPHERE IN A DIELECTRIC MEDIUM......Page 30
1.12. ACTUAL DIPOLE MOMENTS, DEFINITION AND STATUS......Page 34
1.13. DIRECTING FIELD AND THE ONSAGER EQUATION......Page 36
1.14. STATISTICAL THEORIES FOR STATIC DIELECTRIC PERMITTIVITY. KIRKWOOD’S THEORY......Page 39
1.15. FROHLICH’S STATISTICAL THEORY......Page 43
1.16. DISTORTION POLARIZATION IN THE KIRKWOOD AND FROHLICH THEORIES......Page 45
Properties of the Legendre Polynomials......Page 47
Frohlich alternative calculations for the polarization of a dielectric sphere in an infinite medium......Page 48
The Polarization of an Ellipsoid......Page 52
Important Formulae in SI Units......Page 54
Problem 1......Page 55
Problem 2......Page 56
Problem 3......Page 57
Problem 4......Page 59
Problem 5......Page 60
Problem 7......Page 62
Problem 8......Page 63
Problem 9......Page 64
Problem 10......Page 65
REFERENCES......Page 66
2.1. BROWNIAN MOTION......Page 67
2.2. BRIEF ACCOUNT OF EINSTEIN’S THEORY OF BROWNIAN MOTION......Page 68
2.3. LANGEVIN TREATMENT OF BROWNIAN MOTION......Page 69
2.4. CORRELATION FUNCTIONS......Page 70
2.5. MEAN- SQUARE DISPLACEMENT OF A BROWNIAN PARTICLE......Page 71
2.6. FLUCTUATION-DISSIPATION THEOREM......Page 72
2.7. SMOLUCHOWSKI EQUATION......Page 73
2.8. ROTATIONAL BROWNIAN MOTION......Page 74
2.9. DEBYE THEORY OF RELAXATION PROCESSES......Page 77
2.10. DEBYE EQUATIONS FOR THE DIELECTRIC PERMITTIVITY......Page 79
2.11. MACROSCOPIC THEORY OF THE DIELECTRIC DISPERSION......Page 81
2.12. DIELECTRIC BEHAVIOR IN TIME-DEPENDENT ELECTRIC FIELDS......Page 82
2.13. DISSIPATED ENERGY IN POLARIZATION......Page 85
2.14. DISPERSION RELATIONS......Page 86
2.15. ENERGY DISSIPATION AND THE DEBYE PLATEAU......Page 87
2.16. INERTIAL EFFECTS......Page 88
2.17. LANGEVIN EQUATION FOR THE DIPOLE VECTOR......Page 90
2.18. DIFFUSIVE THEORY OF DEBYE AND THE ONSAGER MODEL......Page 93
2.19. RELATIONSHIP BETWEEN MACROSCOPIC DIELECTRIC AND MECHANICAL PROPERTIES......Page 95
2.20. STATISTICAL MECHANICS AND LINEAR RESPONSE......Page 96
2.21. RELATIONSHIP BETWEEN THE FREQUENCY- DEPENDENT PERMITTIVITY AND THE AUTOCORRELATION FUNCTION FOR DIPOLE MOMENTS......Page 101
2.22. EXTENSION TO POLARIZABLE DIPOLES......Page 104
2.23. MACROSCOPIC AND MICROSCOPIC CORRELATION FUNCTIONS......Page 105
2.24. COMPLEX POLARIZABILITY......Page 108
2.25. DISPERSION RELATIONS CORRESPONDING TO THE POLARIZABILITY. A NEW VERSION OF THE FLUCTUATION^ DISSIPATION THEOREM......Page 109
2.26. FLUCTUATIONS IN A SPHERICAL SHELL......Page 111
2.27. DIELECTRIC FRICTION......Page 117
2.28. RESONANCE ABSORPTION......Page 122
2.29. MEMORY FUNCTIONS......Page 124
2.30. FIRST-ORDER MEMORY FUNCTION AND MACROSCOPIC RELAXATION TIME......Page 130
2.31. MODE COUPLING THEORIES......Page 133
Problem 1......Page 135
Problem 3......Page 136
Problem 4......Page 137
REFERENCES......Page 139
3.1. THERMODYNAMICS OF IRREVERSIBLE PROCESSES......Page 141
3.2. DIELECTRIC RELAXATION IN THE FRAMEWORK OF LIT......Page 142
3.3. MAXWELL EQUATIONS......Page 143
3.4.1. Conservation of Mass......Page 144
3.4.3. Conservation of Linear Momentum......Page 145
3.4.4. Conservation of Energy......Page 147
3.4.5. Internal Energy Equation......Page 149
3.5. ENTROPY EQUATION......Page 150
3.6. RELAXATION EQUATION......Page 155
3.7. CORRELATION AND MEMORY FUNCTIONS......Page 157
3.8.2. Balance Equations......Page 160
3.8.3. Entropy Equation......Page 162
3.9. DIELECTRIC SUSCEPTIBILITIES AND PERMITTIVITIES......Page 165
3.10. GENERALIZATION AND SPECIAL CASES......Page 168
3.11. MEMORY FUNCTION......Page 169
3.12. NORMAL MODE ABSORPTION......Page 170
APPENDIX......Page 176
Problem 1......Page 178
Problem 2......Page 179
Problem 3......Page 183
Problem 4......Page 184
Problem 5......Page 185
Problem 6......Page 186
REFERENCES......Page 189
4.1. MEASUREMENT SYSTEMS IN THE TIME DOMAIN......Page 191
4.2. MEASUREMENT SYSTEMS IN THE FREQUENCY DOMAIN......Page 194
4.3.1. Basic Immittance Functions......Page 197
4.3.2. Series and Parallel RC Networks......Page 198
4.3.3. Mixed Circuit. Debye Equations......Page 199
4.4.1. Retardation Time Spectra......Page 202
4.4.2. Cole-Cole Equation......Page 204
4.4.3. Fuoss-Kirkwood Equation......Page 208
4.4.4. Davidson-Cole Equation......Page 209
4.4.5. Havriliak-Negami Equation......Page 210
4.4.6. Jonscher Model......Page 212
4.4.7. Hill Model......Page 213
4.4.8. KWW Model......Page 214
4.4.9. Dissado-Hill Model......Page 215
4.4.10. Friedrich Model......Page 216
4.4.11. Model of Metzler, Schick, Kilian, and Nonnenmacher......Page 218
4.4.12. Biparabolic Model......Page 219
4.5.1. Electrets......Page 221
4.5.3. Microscopic Mechanisms and Applications of TSD Currents......Page 222
4.5.4. Basic Equations for Dipolar Depolarization......Page 223
4.5.5. Isothermal Measurements......Page 225
4.5.6. Thermal Windowing......Page 230
4.5.7. Thermostimulated Depolarization Currents Versus Conventional Dielectric Measurements......Page 231
Edge Corrections......Page 232
Single- Surface Interdigital Electrode......Page 239
Problem 1......Page 243
Problem 2......Page 245
Problem 3......Page 246
Problem 4......Page 249
Problem 5......Page 252
Problem 6......Page 253
Problem 7......Page 254
REFERENCES......Page 256
5.1. INTRODUCTION......Page 259
5.2. DIPOLE MOMENTS OF GASES......Page 260
5.3. DIPOLE MOMENTS OF LIQUIDS AND POLYMERS......Page 261
5.4. EFFECT OF THE ELECTRIC FIELD ON THE MEAN- SQUARE DIPOLE MOMENT......Page 264
5.5. EXCLUDED VOLUME EFFECTS......Page 267
5.6. DIPOLE MOMENTS FOR FIXED CONFORMATIONS......Page 268
5.7. AVERAGE VALUES OF u2......Page 271
5.8. ROTATIONAL STATES AND CONFORMATIONAL ENERGIES......Page 272
5.9 DIPOLE AUTOCORRELATION COEFFICIENT OF POLYMERS......Page 275
5.10. DETERMINATION OF CONFORMATIONAL ENERGIES......Page 276
REFERENCES......Page 279
6.1. INTRODUCTION......Page 281
6.2. BIREFRINGENCE: BASIC PRINCIPLES......Page 282
6.3. ELECTRIC BIREFRINGENCE......Page 283
6.4. INDUCED DIPOLE MOMENTS AND POLARIZABILITY......Page 284
6.5. ORIENTATION FUNCTION OF RIGID RODS......Page 286
6.6. EVALUATION OF mK FOR POLYMER CHAINS......Page 289
6.7. REALISTIC MODEL FOR THE EVALUATION OF mK IN FLEXIBLE POLYMERS......Page 290
6.8. VALENCE OPTICAL SCHEME......Page 295
6.9. COMPUTATION OF mK BY THE RIS MODEL......Page 297
Problem 1......Page 302
Problem 3......Page 303
Problem 4......Page 306
REFERENCES......Page 307
7.1. INTRODUCTION......Page 309
7.2.1. Force Fields......Page 310
7.2.2. Integration Algorithms and Trajectories......Page 312
7.2.3. Computation Time Savings......Page 318
7.3. TRAJECTORIES OF MOLECULES IN PHASE SPACE AND COMPUTING TIME......Page 319
7.4. DETERMINATION OF THE TIME^ DIPOLE CORRELATION COEFFICIENT......Page 325
REFERENCES......Page 335
8.1. INTRODUCTION......Page 337
8.2. PHENOMENOLOGICAL DIELECTRIC RESPONSE IN THE TIME DOMAIN......Page 338
8.3. DIELECTRIC RESPONSE IN THE FREQUENCY DOMAIN......Page 341
8.4. DIELECTRIC RELAXATION MODULUS IN THE TIME AND FREQUENCY DOMAINS......Page 343
8.5. KRONIG-KRAMERS RELATIONSHIPS......Page 346
8.6. ANALYTICAL EXPRESSIONS FOR THE DIELECTRIC PERMITTIVITY AND DIELECTRIC RELAXATION MODULUS IN THE TIME AND FREQUENCY DOMAINS ( SEE ALSO SECTION 4.4.1)......Page 348
8.7. LOCAL AND COOPERATIVE DYNAMICS: BASIC CONCEPTS......Page 351
8.8. RESPONSES OF GLASS FORMERS ABOVE TO PERTURBATION FIELDS IN A WIDE INTERVAL OF FREQUENCIES......Page 353
8.9. BROADBAND DIELECTRIC SPECTROSCOPY OF SUPERCOOLED POLYMERS......Page 356
8.10. TEMPERATURE DEPENDENCE OF THE STRETCH EXPONENT FOR THE a-RELAXATION......Page 363
8.11. TEMPERATURE DEPENDENCE OF SECONDARY RELAXATIONS......Page 364
8.12. TEMPERATURE DEPENDENCE OF THE a-RELAXATION......Page 365
8.13. DIELECTRIC STRENGTH AND POLARITY......Page 367
8.14. SEGMENTAL MOTIONS......Page 368
8.15. LONG-TIME RELAXATION DYNAMICS......Page 370
8.16. TIME-DIPOLE CORRELATION FUNCTION FOR POLYMERS OF TYPE A......Page 374
8.17. NORMAL RELAXATION TIME FOR POLYMERS HAVING TYPE A AND TYPE AB DIPOLES......Page 375
8.18.1. Rouse Model......Page 376
8.18.2. Zimm Model......Page 379
8.19. NORMAL MODE RELAXATION TIME FOR MELTS AND CONCENTRATED SOLUTIONS OF POLYMERS HAVING TYPE A AND TYPE AB DIPOLES......Page 381
8.20. SCALING LAWS FOR THE DIELECTRIC NORMAL MODE OF SEMI- DILUTE SOLUTIONS OF POLYMERS HAVING EITHER TYPE A OR TYPE AB DIPOLES......Page 383
8.21. RELATION BETWEEN MOLECULAR DIMENSIONS AND RELAXATION STRENGTH FOR TYPE A POLYMERS......Page 384
REFERENCES......Page 386
9.1. INTRODUCTION......Page 389
9.2. MOLECULAR MODELS ASSOCIATED WITH A SINGLE RELAXATION TIME......Page 390
9.3. DYNAMICS OF SECONDARY DIELECTRIC RELAXATION IN TWO- SITE MODELS......Page 396
9.4. COALESCENT ab-PROCESS......Page 398
9.5. RELAXATION OF OF N SEGMENTS IN A CHAIN: DYNAMIC ROTATIONAL ISOMERIC STATE MODEL (DRIS)......Page 399
9.6. PROBABILITY OF ROTATIONAL STATES AT EQUILIBRIUM......Page 400
9.7. CONFORMATIONAL TRANSITION RATES......Page 401
9.8. INDEPENDENT CONFORMATIONAL TRANSITIONS......Page 402
9.9. PAIRWISE DEPENDENT CONFORMATIONAL TRANSITIONS......Page 405
9.11. RELAXATION TIMES......Page 408
9.12. MOTION OF A SINGLE BOND......Page 409
9.13.1. Local Main Chain Motions......Page 413
9.13.2. Motions of Side Groups About Their Link to the Main Backbone......Page 414
9.13.5. Secondary Relaxations in Semicrystalline Polymers......Page 415
Problem 1......Page 416
Problem 2......Page 419
Problem 3......Page 420
REFERENCES......Page 422
10.1. INTRODUCTION......Page 424
10.2. ORIENTATION FUNCTION......Page 425
10.3. DECAY FUNCTION......Page 426
10.4. BUILDUP ORIENTATION FUNCTION......Page 427
10.5. PULSED FIELDS......Page 429
10.6. DISPERSION OF THE BIREFRINGENCE IN SINE WAVE FIELDS......Page 431
Problem 1......Page 435
REFERENCES......Page 440
11.1. INTRODUCTION: LIQUID CRYSTAL GENERALITIES......Page 441
11.2. TENSORIAL DIELECTRIC PROPERTIES OF ANISOTROPIC MATERIALS......Page 448
11.3. MACROSCOPIC ORDER PARAMETER......Page 451
11.4. MICROSCOPIC ORDER PARAMETER......Page 452
11.5. DIELECTRIC SUSCEPTIBILITIES......Page 456
11.6. HIGH-FREQUENCY RESPONSE......Page 457
11.7. STATIC DIELECTRIC PERMITTIVITIES......Page 459
11.8. SMECTIC PHASES......Page 463
11.9. DYNAMIC DIELECTRIC PERMITTIVITY. INTERNAL FIELD FACTORS......Page 470
11.10. DIELECTRIC RELAXATIONS IN NEMATIC UNIAXIAL MESOPHASES......Page 471
APPENDIX A......Page 482
APPENDIX B......Page 486
APPENDIX C......Page 490
Problem 1......Page 494
Problem 2......Page 497
Problem 3......Page 498
Problem 5......Page 502
Problem 6......Page 504
Problem 7......Page 505
Problem 8......Page 507
Problem 9......Page 508
Problem 10......Page 509
REFERENCES......Page 510
12.1. INTRODUCTION......Page 513
12.2. BASIC CONCEPTS......Page 514
12.3. THERMODYNAMICS......Page 516
12.4. PIEZOELECTRICITY......Page 518
12.5. PYROELECTRICITY......Page 522
12.6. PIEZOELECTRIC AND PYROELECTRIC POLYMERS......Page 523
12.7. PIEZOELECTRICITY EFFECT AND SYMMETRY......Page 528
12.8. PIEZOELECTRIC AND PYROELECTRIC MECHANISMS......Page 537
12.9. PIEZOELECTRICITY AND PYROELECTRICITY IN POLAR POLYMERS......Page 540
12.10. UNIAXIALLY ORIENTED, OPTICALLY ACTIVE POLYMERS......Page 541
12.11. FERROELECTRIC LIQUID CRYSTALLINE POLYMERS......Page 542
12.12. MEASUREMENTS OF PIEZOELECTRIC CONSTANTS......Page 547
12.13. RELATION BETWEEN THE REMNANT POLARIZATION AND THE PIEZOELECTRIC CONSTANTS IN FERROELECTRIC POLYMERS......Page 549
12.14. FERROELECTRIC COMPOSITES......Page 551
REFERENCES......Page 557
13.1. INTRODUCTION......Page 559
13.2. BASIC PRINCIPLES OF HARMONIC GENERATION IN CRYSTALS......Page 560
13.3. SECOND HARMONIC GENERATION AND COHERENCE LENGTH......Page 561
13.5. NONLINEAR POLARIZATION IN POLYMERS......Page 564
13.6. POLING PROCESS......Page 568
13.7. RELATION BETWEEN HYPERPOLARIZABILITY AND SECOND- ORDER SUSCEPTIBILITY IN UNIAXIALLY POLED ORIENTED POLYMERS......Page 569
13.8. POLING DECAY......Page 572
13.9. DETERMINATION OF x(2)ijk SUSCEPTIBILITIES......Page 574
13.10. MEASUREMENT OF THE ELECTROOPTIC EFFECT......Page 576
13.11. GUIDELINES FOR DESIGNING NLO POLYMER SYSTEMS......Page 578
13.12. POLYMER SYSTEMS WITH NLO PROPERTIES......Page 580
REFERENCES......Page 588
14.1. INTRODUCTION......Page 591
14.2. CHEMICAL STRUCTURE AND CONDUCTING CHARACTER......Page 592
14.3. ROUTES OF SYNTHESIS OF CONJUGATED POLYMERS......Page 593
14.3.1. Electropolymerization......Page 600
14.4. ENERGY GAPS IN CONDUCTING POLYMERS......Page 604
14.5. DOPING PROCESSES......Page 609
14.6. CHARGE TRANSPORT......Page 612
14.7. METALLIC CONDUCTIVITY......Page 616
14.9. OPTICAL DIELECTRIC PERMITTIVITY AND CONDUCTIVITY......Page 618
14.10. APPLICATIONS OF SEMICONDUCTOR POLYMERS......Page 620
14.11. CONDUCTING POLYMERS......Page 624
14.12. POLYMERS FOR RECHARGEABLE BATTERIES......Page 626
Problem......Page 629
REFERENCES......Page 632
References Related to Fig. 14.7......Page 637