Liquid crystal elastomers / M. Warner and E. M. Terentjev.

Format:

Book

Author/Creator:

Warner, Mark, 1952-2021.

Contributor:

Terentjev, E. M. (Eugene Michael)

Series:

International series of monographs on physics (Oxford, England) ; 120.

International series of monographs on physics ; 120

Language:

English

Subjects (All):

Liquid crystals.

Elastomers.

Physical Description:

xiv, 407 pages : illustrations ; 24 cm.

Place of Publication:

Oxford : Clarendon Press ; New York : Oxford University Press, 2003.

Summary:

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.

Contents:

1 A bird's eye view of liquid crystal elastomers 1

2 Liquid crystals 8

2.1 Ordering of rod and disc fluids 8

2.2 Nematic order 10

2.3 Free energy and phase transitions of nematics 14

2.4 Molecular theory of nematics 19

2.5 Distortions of nematic order 21

2.6 Transitions driven by external fields 24

2.7 Anisotropic viscosity and dissipation 28

2.8 Differences between liquid and solid nematics 32

3 Polymers, elastomers and rubber elasticity 35

3.1 Configurations of polymers 36

3.2 Liquid crystalline polymers 40

3.2.1 Shape of liquid crystalline polymers 42

3.2.2 Frank elasticity of nematic polymers 49

3.3 Classical rubber elasticity 50

3.4 Manipulating the elastic response of rubber 55

3.5 Finite extensibility and entanglements in elastomers 58

4 Classical elasticity 63

4.1 Deformation tensor and Cauchy

Green strain 63

4.2 Non-linear and linear elasticity 66

4.3 Geometry of deformations and rotations 71

4.3.1 Rotations 71

4.3.2 Shears and their decomposition 72

4.3.3 Square roots and polar decomposition of tensors 78

4.4 Compressibility of rubbery networks 79

5 Nematic elastomers 83

5.1 Structure and examples of nematic elastomers 84

5.2 Stress-optical coupling 87

5.3 Polydomain textures and alignment by stress 89

5.4 Monodomain 'single-crystal' nematic elastomers 93

5.4.1 Spontaneous shape changes 94

5.4.2 Nematic photoelastomers 96

5.5 Strain-induced director rotation 98

5.6 Applications of liquid crystalline elastomers 102

6 Nematic rubber elasticity 107

6.1 Neo-classical theory 107

6.2 Spontaneous distortions 110

6.3 Equilibrium shape of nematic elastomers 116

6.4 Photo-mechanical effects 118

6.5 Thermal phase transitions 124

6.6 Effect of strain on nematic order 127

6.7 Mechanical and nematic instabilities 131

6.7.1 Mechanical Freedericks transition 134

6.7.2 The elastic low road 136

6.8 Finite extensibility and entanglements 137

7 Soft elasticity 142

7.1 Director anchoring to the bulk 143

7.1.1 Director rotation without strain 143

7.1.2 Coupling of rotations to pure shear 146

7.2 Soft elasticity 147

7.2.1 Soft modes of deformation 148

7.2.2 Soft symmetric strain, body rotations and principal extensions 152

7.2.3 Forms of the free energy allowing softness 153

7.3 Optimal deformations 155

7.3.1 A practical method of calculating deformations 155

7.3.2 Stretching perpendicular to the director 157

7.4 Semi-soft elasticity 161

7.4.1 Example: random copolymer networks 161

7.4.2 A practical geometry of semi-soft deformations 163

7.5 Semi-soft free energy and stress 165

7.6 Thermomechanical history and general semi-softness 170

7.6.1 Thermomechanical history dependence 170

7.6.2 Forms of the free energy violating softness 172

8 Distortions of nematic elastomers 174

8.1 Freedericks transitions in nematic elastomers 175

8.2 Strain induced microstructure: stripe domains 181

8.3 General distortions of nematic elastomers 187

8.3.1 One-dimensional quasi-convexification 188

8.3.2 Full quasi-convexification 191

8.3.3 Numerical and experimental studies 193

8.4 Random disorder in nematic networks 196

8.4.1 Characteristic domain size 198

8.4.2 Polydomain-monodomain transition 200

9 Cholesteric elastomers 205

9.1 Cholesteric liquid crystals 206

9.2 Cholesteric networks 210

9.2.1 Intrinsically chiral networks 210

9.2.2 Chirally imprinted networks 212

9.3 Mechanical deformations 216

9.3.1 Uniaxial transverse elongation 218

9.3.2 Stretching along the pitch axis 222

9.4 Piezoelectricity of cholesteric elastomers 225

9.5 Imprinted cholesteric elastomers 231

9.6 Photonics of cholesteric elastomers 235

9.6.1 Photonics of liquid cholesterics 236

9.6.2 Photonics of elastomers 238

9.6.3 Experimental observations of elastomer photonics 240

9.6.4 Lasing in cholesterics 243

10 Continuum theory of nematic elastomers 245

10.1 From molecular theory to continuum elasticity 246

10.1.1 Compressibility effects 246

10.1.2 The limit of linear elasticity 247

10.1.3 The role of nematic anisotropy 249

10.2 Phenomenological theory for small deformations 251

10.3 Strain-induced rotation 254

10.4 Soft elasticity 258

10.4.1 Symmetry arguments 258

10.4.2 The mechanism of soft deformation 260

10.5 Continuum representation of semi-softness 263

10.6 Unconstrained director fluctuations 266

10.7 Unconstrained rubbery network phonons 269

10.8 Light scattering from director fluctuations 273

11 Dynamics of liquid crystal elastomers 281

11.1 Classical rubber dynamics 282

11.1.1 Rouse model and entanglements 284

11.1.2 Dynamical response of entangled networks 287

11.1.3 Long time stress relaxation 289

11.2 Nematohydrodynamics of elastic solids 291

11.2.1 Viscous coefficients and relaxation times 293

11.2.2 Balance of forces and torques 294

11.2.3 Symmetries and order parameter 296

11.3 Response to oscillating strains 297

11.4 Experimental observations 300

11.4.1 Oscillating shear 302

11.4.2 Steady stress relaxation 307

12 Smectic elastomers 310

12.1 Materials and preparation 312

12.2 Smectic A liquids 316

12.3 Continuum description of smectic A elastomers 319

12.3.1 Relative translations in smectic networks 320

12.3.2 Nematic -strain, -rotation and -smectic couplings 322

12.4 Effective smectic elasticity of elastomers 324

12.5 Effective rubber elasticity of smectic elastomers 329

12.6 Layer elasticity and fluctuations in smectic A elastomers 335

12.7 Layer buckling instabilities: the Helfrich-Hurault effect 342

12.8 Quenched layer disorder and the N-A phase transition 346

12.9 Smectic C and ferroelectric C* elastomers 350

A Nematic order in elastomers under strain 357

B Biaxial soft elasticity 364

C Stripe microstructure 368

D Couple-stress and Cosserat elasticity 375

E Expansion at small deformations and rotations 380.

Notes:

Includes bibliographical references and index.

ISBN:

0198527675

OCLC:

55214646