Liquid Crystal Elastomers

✍ Scribed by M. Warner, E. M. Terentjev

• Publisher: Oxford University Press
• Year: 2003
• Tongue: English
• Leaves: 422
• Series: International series of monographs on physics 120
• Edition: illustrated edition
• Category: Library

✦ Synopsis

Liquid crystals are fluids with directionality defined. Polymers are long molecules with a shape that can be changed. As a network, polymers form rubber-a soft solid that is locally liquid-like and capable of huge extension. Liquid crystal elastomers area combination of all these curious aspects, but with additional, revolutionary new phenomena-for example, spontaneous shape changes of several hundred percent induced by temperature change, with equally large opto-mechanical responses, shape change without energy cost (Soft elasticity), color change with strain, lasing and photonics, sensitivity to molecular handedness and soft solid ferroelectricity. This book is a primer for liquid crystals, polymers, rubber and elasticity. It then describes the theory and experiment of these remarkable materials for the first time as a monograph. Worked examples are solved so that the reader can become proficient in the field himself. The book is directed at physicists, chemists, material scientists, engineers and applied mathematicians at the graduate level and beyond.

✦ Table of Contents

Contents......Page 12
1 A bird’s eye view of liquid crystal elastomers......Page 16
2.1 Ordering of rod and disc fluids......Page 24
2.2 Nematic order......Page 26
2.3 Free energy and phase transitions of nematics......Page 30
2.4 Molecular theory of nematics......Page 35
2.5 Distortions of nematic order......Page 37
2.6 Transitions driven by external fields......Page 40
2.7 Anisotropic viscosity and dissipation......Page 44
2.8 Cholesteric liquid crystals......Page 48
2.9 Smectic liquid crystals......Page 53
3 Polymers, elastomers and rubber elasticity......Page 62
3.1 Configurations of polymers......Page 63
3.2 Liquid crystalline polymers......Page 67
3.2.1 Shape of liquid crystalline polymers......Page 69
3.2.2 Frank elasticity of nematic polymers......Page 76
3.3 Classical rubber elasticity......Page 77
3.4 Manipulating the elastic response of rubber......Page 82
3.5 Finite extensibility and entanglements in elastomers......Page 85
4.1 Deformation tensor and Cauchy–Green strain......Page 90
4.2 Non-linear and linear elasticity......Page 93
4.3.1 Rotations......Page 98
4.3.2 Shears and their decomposition......Page 99
4.3.3 Square roots and polar decomposition of tensors......Page 105
4.4 Compressibility of rubbery networks......Page 106
5 Nematic elastomers......Page 110
5.1 Structure and examples of nematic elastomers......Page 111
5.2 Stress-optical coupling......Page 114
5.3 Polydomain textures and alignment by stress......Page 116
5.4 Monodomain ‘single-crystal’ nematic elastomers......Page 119
5.4.1 Spontaneous shape changes......Page 121
5.4.2 Nematic photoelastomers......Page 123
5.5 Field-induced director rotation......Page 126
5.6 Applications of liquid crystalline elastomers......Page 130
6.1 Neo-classical theory......Page 135
6.2 Spontaneous distortions......Page 138
6.3 Equilibrium shape of nematic elastomers‡......Page 144
6.4 Photo-mechanical effects......Page 146
6.5 Thermal phase transitions......Page 151
6.6 Effect of strain on nematic order......Page 154
6.7 Mechanical and nematic instabilities......Page 160
6.7.1 Mechanical Freedericks transition......Page 161
6.7.2 The elastic low road......Page 163
6.8 Finite extensibility and entanglements......Page 165
7 Soft elasticity......Page 169
7.1.1 Director rotation without strain......Page 170
7.1.2 Coupling of rotations to pure shear......Page 173
7.2 Soft elasticity......Page 174
7.2.1 Soft modes of deformation......Page 175
7.2.2 Principal symmetric strains and body rotations......Page 179
7.2.3 Forms of the free energy allowing softness......Page 181
7.3.1 A practical method of calculating deformations......Page 182
7.3.2 Stretching perpendicular to the director......Page 184
7.4 Semi-soft elasticity......Page 188
7.4.1 Example: random copolymer networks......Page 189
7.4.2 A practical geometry of semi-soft deformation......Page 190
7.4.3 Experiments on long, semi-soft strips......Page 192
7.4.4 Unconstrained elastomers in external fields......Page 193
7.5 Semi-soft free energy and stress......Page 194
7.6 Thermomechanical history and general semi-softness......Page 198
7.6.1 Thermomechanical history dependence......Page 199
7.6.2 Forms of the free energy violating softness......Page 200
8 Distortions of nematic elastomers......Page 202
8.1 Freedericks transitions in nematic elastomers......Page 203
8.2 Strain-induced microstructure: stripe domains......Page 209
8.3 General distortions of nematic elastomers......Page 216
8.3.1 One-dimensional quasi-convexification......Page 217
8.3.2 Full quasi-convexification......Page 220
8.3.3 Numerical and experimental studies......Page 222
8.4 Random disorder in nematic networks......Page 225
8.4.1 Nematic ordering with quenched disorder......Page 227
8.4.2 Characteristic domain size......Page 228
8.4.3 Polydomain-monodomain transition......Page 231
9 Cholesteric elastomers......Page 235
9.1.1 Intrinsically chiral networks......Page 236
9.1.2 Chirally imprinted networks......Page 237
9.2 Mechanical deformations......Page 242
9.2.1 Uniaxial transverse elongation......Page 243
9.2.2 Stretching along the pitch axis......Page 248
9.3 Piezoelectricity of cholesteric elastomers......Page 251
9.4 Imprinted cholesteric elastomers......Page 257
9.5 Photonics of cholesteric elastomers......Page 260
9.5.1 Photonics of liquid cholesterics......Page 261
9.5.2 Photonics of elastomers......Page 264
9.5.3 Experimental observations......Page 266
9.5.4 Lasing in cholesterics......Page 268
10 Continuum description of nematic elastomers......Page 271
10.1.1 Compressibility effects......Page 272
10.1.2 The limit of linear elasticity......Page 273
10.1.3 The role of nematic anisotropy......Page 275
10.2 Phenomenological theory for small deformations......Page 277
10.3 Strain-induced rotation......Page 280
10.4 Soft elasticity......Page 283
10.4.1 Symmetry arguments......Page 284
10.4.2 The mechanism of soft deformation......Page 286
10.5 Continuum representation of semi-softness......Page 288
10.6 Unconstrained director fluctuations......Page 291
10.7 Unconstrained phonons......Page 294
10.8 Light scattering from director fluctuations......Page 297
11 Dynamics of liquid crystal elastomers......Page 303
11.1 Classical rubber dynamics......Page 304
11.1.1 Rouse model and entanglements......Page 306
11.1.2 Dynamical response of entangled networks......Page 308
11.1.3 Long time stress relaxation......Page 311
11.2 Nematohydrodynamics of elastic solids......Page 313
11.2.1 Viscous coefficients and relaxation times......Page 315
11.2.2 Balance of forces and torques......Page 316
11.2.3 Symmetries and order parameter......Page 318
11.3 Response to oscillating strains......Page 319
11.4 Experimental observations......Page 323
11.4.1 Oscillating shear......Page 324
11.4.2 Steady stress relaxation......Page 328
12.1 Materials and preparation......Page 332
12.1.1 Smectic A elastomers......Page 334
12.1.2 Smectic C and ferroelectric C elastomers......Page 336
12.2.1 Smectic-A elastomers......Page 337
12.2.2 Smectic-C elastomers......Page 341
12.3 A molecular model of Smectic-A rubber elasticity......Page 343
12.3.1 The geometry of affine layer deformations......Page 345
12.3.2 Response to principal deformations......Page 346
12.3.3 General deformations of a SmA elastomer......Page 354
12.4 Instability and CMHH microstructure......Page 355
12.5 Comparison with experiment......Page 357
12.6 Smectic-C rubber elasticity......Page 359
12.6.1 SmC soft deformations......Page 360
12.6.2 SmC deformations with microstructure......Page 363
13.1 Continuum description of smectic A elastomers......Page 365
13.1.1 Relative translations in smectic networks revisited......Page 366
13.1.2 Nematic -strain, -rotation and -smectic couplings......Page 368
13.2 Effective smectic elasticity of elastomers......Page 370
13.3 Effective rubber elasticity of smectic elastomers......Page 375
13.4 Layer elasticity and fluctuations in smectic A elastomers......Page 379
13.5 Layer buckling instabilities: the CMHH effect......Page 386
13.6 Quenched layer disorder and the N-A phase transition......Page 389
13.7 Smectic C and ferroelectric C elastomers......Page 393
References......Page 397
C......Page 408
E......Page 409
L......Page 410
P......Page 411
S......Page 412
T......Page 413
Y......Page 414
C......Page 415
F......Page 416
K......Page 417
M......Page 418
R......Page 419
T......Page 420
W......Page 421
Z......Page 422