Blinov Structure and Properties of Liquid Crystals

2011
ISBN: 978-90-481-8829-1
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 439 Seiten, eBook

This book by Lev M. Blinov is ideal to guide researchers from their very first encounter with liquid crystals to the level where they can perform independent experiments on liquid crystals with a thorough understanding of their behaviour also in relation to the theoretical framework. Liquid crystals can be found everywhere around us. They are used in virtually every display device, whether it is for domestic appliances of for specialized technological instruments. Their finely tunable optical properties make them suitable also for thermo-sensing and laser technologies. There are many monographs written by prominent scholars on the subject of liquid crystals. The majority of them presents the subject in great depth, sometimes focusing on a particular research aspect, and in general they require a significant level of prior knowledge. In contrast, this books aims at an audience of advanced undergraduate and graduate students in physics, chemistry and materials science. The book consists of three parts: the first part, on structure, starts from the fundamental principles underlying the structure of liquid crystals, their rich phase behaviour and the methods used to study them; the second part, on physical properties, emphasizes the influence of anisotropy on all aspects of liquid crystals behaviour; the third, focuses on electro-optics, the most important properties from the applications standpoint. This part covers only the main effects and illustrates the underlying principles in greater detail. Professor Lev M. Blinov has had a long carrier as an experimentalist. He made major contributions in the field of ferroelectric mesophases. In 1985 he received the USSR state prize for investigations of electro-optical effects in liquid crystals for spatial light modulators. In 1999 he was awarded the Frederiks medal of the Soviet Liquid Crystal Society and in 2000 he was honoured with the G. Gray silver medal of the British Liquid Crystal Society. He has held many visiting academic positions in universities and laboratories across Europe and in Japan.

Zielgruppe

Research

Autoren/Hrsg.

Blinov, Lev M.

Inhaltsverzeichnis

1;Epigraph;8
2;Foreword;10
3;Contents;14
4;Chapter 1: Introductory Notes;20
4.1;References;23
5;Part I: Structure of Liquid Crystals;24
5.1;Chapter 2: Symmetry;25
5.1.1;2.1 Point Group Symmetry;25
5.1.1.1;2.1.1 Symmetry Elements and Operations;25
5.1.1.2;2.1.2 Groups;28
5.1.1.3;2.1.3 Point Groups;30
5.1.1.4;2.1.4 Continuous Point Groups;32
5.1.2;2.2 Translational Symmetry;33
5.1.3;References;36
5.2;Chapter 3: Mesogenic Molecules and Orientational Order;37
5.2.1;3.1 Molecular Shape and Properties;37
5.2.1.1;3.1.1 Shape, Conformational Mobility and Isomerization;37
5.2.1.2;3.1.2 Symmetry and Chirality;39
5.2.1.3;3.1.3 Electric and Magnetic Properties;40
5.2.2;3.2 Intermolecular Interactions;42
5.2.3;3.3 Orientational Distribution Functions for Molecules;46
5.2.3.1;3.3.1 Molecules with Axial Symmetry;47
5.2.3.2;3.3.2 Lath-Like Molecules;50
5.2.4;3.4 Principal Orientational Order Parameter (Microscopic Approach);51
5.2.5;3.5 Macroscopic Definition of the Orientational Order Parameter;53
5.2.5.1;3.5.1 Tensor Properties;53
5.2.5.2;3.5.2 Uniaxial Order;54
5.2.5.3;3.5.3 Macroscopic Biaxiality;56
5.2.6;3.6 Apparent Order Parameters for Flexible Chains;57
5.2.7;References;57
5.3;Chapter 4: Liquid Crystal Phases;59
5.3.1;4.1 Polymorphism Studies;59
5.3.1.1;4.1.1 Polarized Light Microscopy;59
5.3.1.2;4.1.2 Differential Scanning and Adiabatic Calorimetry (DSC and AC);60
5.3.1.3;4.1.3 X-Ray Analysis;61
5.3.2;4.2 Main Calamitic Phases;62
5.3.2.1;4.2.1 Nematic Phase;62
5.3.2.2;4.2.2 Classical Smectic A Phase;63
5.3.2.3;4.2.3 Special SmA Phases;64
5.3.2.4;4.2.4 Smectic C Phase;66
5.3.2.5;4.2.5 Smectic B;67
5.3.3;4.3 Discotic, Bowl-Type and Polyphilic Phases;68
5.3.4;4.4 Role of Polymerization;69
5.3.5;4.5 Lyotropic Phases;71
5.3.6;4.6 General Remarks on the Role of Chirality;73
5.3.7;4.7 Cholesterics;75
5.3.7.1;4.7.1 Intermolecular Potential;75
5.3.7.2;4.7.2 Cholesteric Helix and Tensor of Orientational Order;76
5.3.7.3;4.7.3 Tensor of Dielectric Anisotropy;77
5.3.7.4;4.7.4 Grandjean Texture;79
5.3.7.5;4.7.5 Methods of the Pitch Measurements;80
5.3.8;4.8 Blue Phases;81
5.3.9;4.9 Smectic C* Phase;83
5.3.9.1;4.9.1 Symmetry, Polarization and Ferroelectricity;83
5.3.9.2;4.9.2 Helical Structure;84
5.3.10;4.10 Chiral Smectic A*;86
5.3.10.1;4.10.1 Uniform Smectic A*;86
5.3.10.2;4.10.2 TGB Phase;86
5.3.11;4.11 Spontaneous Break of Mirror Symmetry;87
5.3.12;References;90
5.4;Chapter 5: Structure Analysis and X-Ray Diffraction;92
5.4.1;5.1 Diffraction Studies and X-Ray Experiment;92
5.4.1.1;5.1.1 General Consideration;92
5.4.1.2;5.1.2 X-Ray Experiment;93
5.4.2;5.2 X-Ray Scattering;94
5.4.2.1;5.2.1 Scattering by a Single Electron;94
5.4.2.2;5.2.2 Scattering by Two Material Points;96
5.4.2.3;5.2.3 Scattering by a Stack of Planes (Bragg Diffraction);97
5.4.2.4;5.2.4 Amplitude of Scattering for a System of Material Points;98
5.4.2.5;5.2.5 Scattering Amplitude for an Atom;100
5.4.3;5.3 Diffraction on a Periodic Structure;101
5.4.3.1;5.3.1 Reciprocal Lattice;101
5.4.3.2;5.3.2 Intensity of Scattering;103
5.4.3.3;5.3.3 Form Factor and Structure Factor;104
5.4.4;5.4 Fourier Transforms and Diffraction;105
5.4.4.1;5.4.1 Principle;105
5.4.4.2;5.4.2 Example: Form Factor of a Parallelepiped;106
5.4.4.3;5.4.3 Convolution of Two Functions;108
5.4.4.4;5.4.4 Self-Convolution;110
5.4.5;5.5 X-Ray Diffraction by Crystals;111
5.4.5.1;5.5.1 Density Function and Structure Factor for Crystals;112
5.4.5.1.1;5.5.1.1 Density Function;112
5.4.5.1.2;5.5.1.2 The Structure Factor;112
5.4.5.2;5.5.2 A Crystal of a Finite Size;113
5.4.6;5.6 Structure of the Isotropic and Nematic Phase;114
5.4.6.1;5.6.1 Isotropic Liquid;114
5.4.6.2;5.6.2 Nematic Phase;116
5.4.7;5.7 Diffraction by Smectic Phases;118
5.4.7.1;5.7.1 Smectic A;118
5.4.7.2;5.7.2 Landau-Peierls Instability;119
5.4.7.2.1;5.7.2.1 Displacement and Free Energy;119
5.4.7.2.2;5.7.2.2 Stability of Crystallographic Lattices of Different Dimensionality;121
5.4.7.3;5.7.3 ``Bond´´ Orientational Order in a Single Smectic Layer and Hexatic Phase;122
5.4.7.4;5.7.4 Three-Dimensional Smectic Phases;123
5.4.7.4.1;5.7.4.1 Uniaxial Orthogonal;123
5.4.7.4.2;5.7.4.2 Biaxial Orthogonal;125
5.4.7.4.3;5.7.4.3 Biaxial Tilted;125
5.4.8;References;126
5.5;Chapter 6: Phase Transitions;128
5.5.1;6.1 Landau Approach;128
5.5.2;6.2 Isotropic Liquid-Nematic Transition;132
5.5.2.1;6.2.1 Landau-De Gennes Equation;132
5.5.2.2;6.2.2 Temperature Dependence of the Nematic Order Parameter;133
5.5.2.3;6.2.3 Free Energy;135
5.5.2.4;6.2.4 Physical Properties in the Vicinity of the N-Iso Transition;136
5.5.3;6.3 Nematic-Smectic A Transition;138
5.5.3.1;6.3.1 Order Parameter;138
5.5.3.2;6.3.2 Free Energy Expansion;139
5.5.3.3;6.3.3 Weak First Order Transition;141
5.5.3.3.1;6.3.3.1 Role of Higher Order Fourier Components;142
5.5.3.3.2;6.3.3.2 Interaction of Two Order Parameters;143
5.5.3.4;6.3.4 Re-entrant Phases;144
5.5.4;6.4 Smectic A-Smectic C Transition;145
5.5.4.1;6.4.1 Landau Expansion;145
5.5.4.2;6.4.2 Influence of External Fields;146
5.5.5;6.5 Dynamics of Order Parameter;147
5.5.5.1;6.5.1 Landau-Khalatnikov Approach;147
5.5.5.2;6.5.2 Relaxation Rate;147
5.5.6;6.6 Molecular Statistic Approach to Phase Transitions;150
5.5.6.1;6.6.1 Entropy, Partition Function and Free Energy;150
5.5.6.1.1;6.6.1.1 Entropy;150
5.5.6.1.2;6.6.1.2 Partition Function and Free Energy;152
5.5.6.2;6.6.2 Equations of State for Gas and Liquid;153
5.5.6.2.1;6.6.2.1 Ideal Gas of Spherical Particles;153
5.5.6.2.2;6.6.2.2 Equation of State for a Dense Gas or a Liquid;155
5.5.7;6.7 Nematic-Isotropic Transition (Molecular Approach);157
5.5.7.1;6.7.1 Interaction Potential and Partition Function;157
5.5.7.2;6.7.2 Onsager´s Results;158
5.5.7.3;6.7.3 Mean Field Approach for the Nematic Phase;160
5.5.7.3.1;6.7.3.1 Interaction Potential and Partition Function;160
5.5.7.3.2;6.7.3.2 Maier-Saupe Theory;163
5.5.8;References;164
6;Part II: Physical Properties;166
6.1;Chapter 7: Magnetic, Electric and Transport Properties;167
6.1.1;7.1 Magnetic Phenomena;167
6.1.1.1;7.1.1 Magnetic Anisotropy;167
6.1.1.2;7.1.2 Diamagnetism;168
6.1.1.2.1;7.1.2.1 Single Electron;168
6.1.1.2.2;7.1.2.2 Molecules;169
6.1.1.3;7.1.3 Paramagnetism and Ferromagnetism;171
6.1.1.3.1;7.1.3.1 Paramagnetism;171
6.1.1.3.2;7.1.3.2 Ferromagnetism;172
6.1.2;7.2 Dielectric Properties;173
6.1.2.1;7.2.1 Permittivity of Isotropic Liquids;173
6.1.2.1.1;7.2.1.1 Dielectric Spectrum;173
6.1.2.1.2;7.2.1.2 Local Field, Clausius-Mossotti and Onsager Equations;173
6.1.2.2;7.2.2 Static Dielectric Anisotropy of Nematics and Smectics;177
6.1.2.2.1;7.2.2.1 Maier-Meier Theory;177
6.1.2.2.2;7.2.2.2 SmA Phase and the Role of the Positional Order;180
6.1.2.2.3;7.2.2.3 Smectic C Case;181
6.1.2.3;7.2.3 Dipole Dynamics of an Isotropic Liquid;181
6.1.2.3.1;7.2.3.1 Dipole Relaxation;181
6.1.2.3.2;7.2.3.2 Debye and Cole-Cole Diagrams;184
6.1.2.4;7.2.4 Frequency Dispersion of epsi|| and epsi in Nematics;186
6.1.2.4.1;7.2.4.1 Relaxation Modes;186
6.1.2.4.2;7.2.4.2 Dual Frequency Addressing;188
6.1.3;7.3 Transport Properties;188
6.1.3.1;7.3.1 Thermal Conductivity;188
6.1.3.2;7.3.2 Diffusion;190
6.1.3.3;7.3.3 Electric Conductivity;192
6.1.3.3.1;7.3.3.1 Mobility of Ions;192
6.1.3.3.2;7.3.3.2 Ion Concentration;193
6.1.3.3.3;7.3.3.3 Current-Voltage Curve for Thin Cells;194
6.1.3.3.4;7.3.3.4 Frequency Dependence of Ionic Conductivity;197
6.1.3.3.5;7.3.3.5 Conductivity due to Dielectric Losses;198
6.1.3.3.6;7.3.3.6 Space Charge Relaxation;200
6.1.3.3.7;7.3.3.7 Measurements of Anisotropy epsia (omega) and sigmaa(omega);202
6.1.3.3.8;7.3.3.8 Characteristic Times Related to the Discussed Phenomena (Resume);202
6.1.4;References;203
6.2;Chapter 8: Elasticity and Defects;204
6.2.1;8.1 Tensor of Elasticity;204
6.2.1.1;8.1.1 Hooke´s Law;204
6.2.1.2;8.1.2 Stress, Strain and Elasticity Tensors;205
6.2.1.2.1;8.1.2.1 Stress Tensor;205
6.2.1.2.2;8.1.2.2 Strain Tensor;206
6.2.1.2.3;8.1.2.3 Tensor of Elasticity;208
6.2.2;8.2 Elasticity of Nematics and Cholesterics;209
6.2.2.1;8.2.1 Elementary Distortions;209
6.2.2.1.1;8.2.1.1 Specific Features of Elasticity of Nematics;209
6.2.2.1.2;8.2.1.2 Elementary Distortions;210
6.2.2.1.3;8.2.1.3 Curvature Distortion Tensor;211
6.2.2.2;8.2.2 Frank Energy;212
6.2.2.2.1;8.2.2.1 Elasticity Tensors;212
6.2.2.2.2;8.2.2.2 Elastic Energy of the Conventional Nematic for n||z;213
6.2.2.2.3;8.2.2.3 Frank Formula;214
6.2.2.3;8.2.3 Cholesterics and Polar Nematics;215
6.2.2.3.1;8.2.3.1 Cholesterics;215
6.2.2.3.2;8.2.3.2 Polar Nematics;216
6.2.3;8.3 Variational Problem and Elastic Torques;216
6.2.3.1;8.3.1 Euler Equation;216
6.2.3.2;8.3.2 Application to a Twist Cell;218
6.2.3.3;8.3.3 ``Molecular Field´´ and Torques;220
6.2.3.4;8.3.4 Director Fluctuations;221
6.2.4;8.4 Defects in Nematics and Cholesterics;224
6.2.4.1;8.4.1 Nematic Texture and Volterra Process;224
6.2.4.1.1;8.4.1.1 Textures;224
6.2.4.1.2;8.4.1.2 Volterra Process;225
6.2.4.2;8.4.2 Linear Singularities in Nematics;226
6.2.4.2.1;8.4.2.1 Disclination Strength;226
6.2.4.2.2;8.4.2.2 The Director Field Around Disclination;227
6.2.4.2.3;8.4.2.3 Energy of a Disclination;229
6.2.4.3;8.4.3 Point Singularities and Walls;230
6.2.4.3.1;8.4.3.1 Point Singularities in the Bulk (Hedgehogs);230
6.2.4.3.2;8.4.3.2 Point Singularities at the Surfaces (Boodjooms);231
6.2.4.3.3;8.4.3.3 Walls;232
6.2.4.4;8.4.4 Defects in Cholesterics;233
6.2.4.4.1;8.4.4.1 Singular tau- and lambda-Lines in the Planar Texture;233
6.2.4.4.2;8.4.4.2 Defects in the Polygonal or Fingerprint Textures;234
6.2.5;8.5 Smectic Phases;235
6.2.5.1;8.5.1 Elasticity of Smectic A;235
6.2.5.1.1;8.5.1.1 Free Energy;235
6.2.5.1.2;8.5.1.2 Wave-Like Distortion;237
6.2.5.2;8.5.2 Peierls Instability of the SmA Structure;239
6.2.5.3;8.5.3 Defects in Smectic A;241
6.2.5.3.1;8.5.3.1 Steps and Dislocations;241
6.2.5.3.2;8.5.3.2 Cylinders, Tores, Hedgehogs;242
6.2.5.3.3;8.5.3.3 Focal-Conics;242
6.2.5.4;8.5.4 Smectic C Elasticity and Defects;243
6.2.5.4.1;8.5.4.1 Elastic Energy;243
6.2.5.4.2;8.5.4.2 Defects in Smectics C;244
6.2.6;References;246
6.3;Chapter 9: Elements of Hydrodynamics;247
6.3.1;9.1 Hydrodynamic Variables;247
6.3.2;9.2 Hydrodynamics of an Isotropic Liquid;248
6.3.2.1;9.2.1 Conservation of Mass Density;248
6.3.2.2;9.2.2 Conservation of Momentum Density;249
6.3.2.2.1;9.2.2.1 Ideal Liquid;249
6.3.2.2.2;9.2.2.2 Viscous Liquid;251
6.3.2.3;9.2.3 Navier-Stokes Equation;252
6.3.3;9.3 Viscosity of Nematics;253
6.3.3.1;9.3.1 Basic Equations;253
6.3.3.2;9.3.2 Measurements of Leslie coefficients;256
6.3.3.2.1;9.3.2.1 Laminar Shear Flow;256
6.3.3.2.1.1;Geometry (a), nz = 1 (Director Perpendicular to the Shear Plane);257
6.3.3.2.1.2;Geometry (b), nx = 1 (Director in the Shear Plane Parallel to the Velocity of Upper Plate);258
6.3.3.2.1.3;Geometry (c), ny = 1 (Director in the Shear Plane Perpendicular to the Upper Plate Velocity);258
6.3.3.2.2;9.3.2.2 Poiseuille Flow in Magnetic Field;259
6.3.3.2.3;9.3.2.3 Capillary Flow and Determination of a2 and a3;260
6.3.3.2.4;9.3.2.4 Determination of gamma1;262
6.3.4;9.4 Flow in Cholesterics and Smectics;264
6.3.4.1;9.4.1 Cholesterics;264
6.3.4.1.1;9.4.1.1 Shear;264
6.3.4.1.1.1;Geometry I, h||x, s_yx = v_y/x||h and vh;264
6.3.4.1.1.2;Geometry II, h||z, s_yx = v_y/ x h and v h;265
6.3.4.1.1.3;Geometry III, h||y, s_yx = v_y/ x||h, and v||h;265
6.3.4.1.2;9.4.1.2 Permeation Effect;265
6.3.4.2;9.4.2 Smectic A Phase;267
6.3.4.2.1;9.4.2.1 Flow and Viscosity;267
6.3.4.2.2;9.4.2.2 Undulation Instability;269
6.3.5;References;269
6.4;Chapter 10: Liquid Crystal - Solid Interface;270
6.4.1;10.1 General Properties;270
6.4.1.1;10.1.1 Symmetry;270
6.4.1.2;10.1.2 Surface Properties of a Liquid;271
6.4.1.2.1;10.1.2.1 Surface Tension;271
6.4.1.2.2;10.1.2.2 Adsorption;272
6.4.1.2.3;10.1.2.3 Wetting;273
6.4.1.3;10.1.3 Structure of Surface Layers;273
6.4.1.3.1;10.1.3.1 Surface Induced Change in the Orientational Order Parameter;274
6.4.1.3.2;10.1.3.2 Surface-Induced Smectic Ordering;277
6.4.1.3.3;10.1.3.3 Polar Surface Order and Surface Polarization;279
6.4.1.3.3.1;Ionic Polarization;280
6.4.1.3.3.2;Dipolar Polarization;280
6.4.1.3.3.3;Ordoelectric (Quadrupolar) Polarization;281
6.4.2;10.2 Surface Energy and Anchoring of Nematics;284
6.4.2.1;10.2.1 Easy Axis;284
6.4.2.2;10.2.2 Variational Problem;285
6.4.2.3;10.2.3 Surface Energy Forms;287
6.4.2.4;10.2.4 Extrapolation Length;288
6.4.3;10.3 Liquid Crystal Alignment;290
6.4.3.1;10.3.1 Cells;290
6.4.3.2;10.3.2 Alignment;291
6.4.3.2.1;10.3.2.1 Planar Homogeneous and Tilted Alignment;291
6.4.3.2.2;10.3.2.2 Homeotropic Alignment;292
6.4.3.2.3;10.3.2.3 Multistable Alignment;292
6.4.3.3;10.3.3 Berreman Model;293
6.4.4;References;295
7;Part III: Electro-Optics;296
7.1;Chapter 11: Optics and Electric Field Effects in Nematic and Smectic A Liquid Crystals;297
7.1.1;11.1 Optical Properties of Uniaxial Phases;297
7.1.1.1;11.1.1 Dielectric Ellipsoid, Birefringence and Light Transmission;297
7.1.1.1.1;11.1.1.1 Dielectric Ellipsoid;297
7.1.1.1.2;11.1.1.2 Extraordinary Index of a Birefringent Layer;298
7.1.1.1.3;11.1.1.3 Light Ellipticity;300
7.1.1.1.3.1;Case 1 Corresponds to the So-Called lambda/4 Plate;301
7.1.1.1.3.2;Case 2 Corresponds to the lambda Plate;302
7.1.1.1.4;11.1.1.4 Light Transmission (Cell Between Polarizers);302
7.1.1.1.5;11.1.1.5 Measurements of Birefringence of Nematics;303
7.1.1.1.6;11.1.1.6 Twist Structure;305
7.1.1.2;11.1.2 Light Absorption and Linear Dichroism;306
7.1.1.2.1;11.1.2.1 Extinction Index, Absorption Coefficient, Optical Density;306
7.1.1.2.2;11.1.2.2 Linear Dichroism;308
7.1.1.2.3;11.1.2.3 Kramers - Kronig Relations;309
7.1.1.3;11.1.3 Light Scattering in Nematics and Smectic A;311
7.1.1.3.1;11.1.3.1 Isotropic Phase;312
7.1.1.3.2;11.1.3.2 Nematic Phase;313
7.1.1.3.2.1;Case A: f || no||z and f deltan;314
7.1.1.3.2.2;Case B: f n0;314
7.1.1.3.3;11.1.3.3 Smectic A Phase;315
7.1.2;11.2 Frederiks Transition and Related Phenomena;316
7.1.2.1;11.2.1 Field Free Energy and Torques;316
7.1.2.2;11.2.2 Experiments on Field Alignment of a Nematic;318
7.1.2.3;11.2.3 Theory of Frederiks Transition;319
7.1.2.3.1;11.2.3.1 Simplest Model;320
7.1.2.3.2;11.2.3.2 Threshold Condition;321
7.1.2.4;11.2.4 Generalizations of the Simplest Model;324
7.1.2.4.1;11.2.4.1 Electric Field Case;324
7.1.2.4.2;11.2.4.2 Anisotropy of Elastic Properties;325
7.1.2.4.3;11.2.4.3 Oblique Field or Tilted Alignment;325
7.1.2.4.4;11.2.4.4 Weak Anchoring;325
7.1.2.4.5;11.2.4.5 Break of Anchoring;326
7.1.2.5;11.2.5 Dynamics of Frederiks Transition;327
7.1.2.6;11.2.6 Backflow Effect;328
7.1.2.7;11.2.7 Electrooptical Response;330
7.1.2.7.1;11.2.7.1 Splay-Bend Distortions;330
7.1.2.7.2;11.2.7.2 Twist and Supertwist Effects;333
7.1.2.7.3;11.2.7.3 Guest-Host Effect;333
7.1.3;11.3 Flexoelectricity;334
7.1.3.1;11.3.1 Flexoelectric Polarization;334
7.1.3.1.1;11.3.1.1 Dipolar and Quadrupolar Flexoelectricity;334
7.1.3.1.2;11.3.1.2 A Hybrid Cell;337
7.1.3.1.3;11.3.1.3 Measurements of Pf;338
7.1.3.2;11.3.2 Converse Flexoelectric Effect;339
7.1.3.2.1;11.3.2.1 Uniform Distortion;339
7.1.3.2.2;11.3.2.2 Electrooptical Properties;342
7.1.3.2.3;11.3.2.3 Dynamics of the Flexoelectric Effect;343
7.1.3.3;11.3.3 Flexoelectric Domains;344
7.1.4;11.4 Electrohydrodynamic Instability;346
7.1.4.1;11.4.1 The Reasons for Instabilities;346
7.1.4.2;11.4.2 Carr-Helfrich Mode;348
7.1.4.2.1;11.4.2.1 The Instability Threshold in the Simplest Model;349
7.1.4.2.2;11.4.2.2 Behaviour Above the Threshold;351
7.1.5;Reference;352
7.2;Chapter 12: Electro-Optical Effects in Cholesteric Phase;354
7.2.1;12.1 Cholesteric as One-Dimensional Photonic Crystal;354
7.2.1.1;12.1.1 Bragg Reflection;354
7.2.1.1.1;12.1.1.1 Experimental Data;354
7.2.1.1.2;12.1.1.2 The Simplest Model;356
7.2.1.2;12.1.2 Waves in Layered Medium and Photonic Crystals;358
7.2.1.2.1;12.1.2.1 Hill and Mathieu Equations;358
7.2.1.2.2;12.1.2.2 One Dimensional Photonic Band-Gap Structure (Modelling);360
7.2.1.3;12.1.3 Simple Analytical Solution for Light Incident Parallel to the Helical Axis;362
7.2.1.3.1;12.1.3.1 Wave Equations;362
7.2.1.3.2;12.1.3.2 Dispersion Relation;363
7.2.1.3.3;12.1.3.3 Rotation of Linearly Polarised Light;366
7.2.1.3.4;12.1.3.4 Waveguide Regime;367
7.2.1.4;12.1.4 Other Important Cases;367
7.2.1.4.1;12.1.4.1 Cholesteric Slab of Finite Thickness;367
7.2.1.4.2;12.1.4.2 Oblique Incidence of Light;367
7.2.1.4.3;12.1.4.3 Diffraction and Scattering;368
7.2.2;12.2 Dielectric Instability of Cholesterics;369
7.2.2.1;12.2.1 Untwisting of the Cholesteric Helix;369
7.2.2.1.1;12.2.1.1 De Gennes-Meyer Model for Field Induced Cholesteric-Nematic Transition;369
7.2.2.1.2;12.2.1.2 Topological Limitation;372
7.2.2.2;12.2.2 Field Induced Anharmonicity and Dynamics of the Helix;375
7.2.2.3;12.2.3 Instability of the Planar Cholesteric Texture;377
7.2.3;12.3 Bistability and Memory;381
7.2.3.1;12.3.1 Naive Idea;381
7.2.3.2;12.3.2 Berreman-Heffner Model;382
7.2.3.2.1;12.3.2.1 A Cell and Free Energy;382
7.2.3.2.2;12.3.2.2 Backflow and Director Relaxation;384
7.2.3.2.3;12.3.2.3 Topological Problem and Trap States;384
7.2.3.3;12.3.3 Bistability and Field-Induced Break of Anchoring;386
7.2.4;12.4 Flexoelectricity in Cholesterics;387
7.2.5;References;389
7.3;Chapter 13: Ferroelectricity and Antiferroelectricity in Smectics;391
7.3.1;13.1 Ferroelectrics;391
7.3.1.1;13.1.1 Crystalline Pyro-, Piezo- and Ferroelectrics;391
7.3.1.1.1;13.1.1.1 Polarization Catastrophe in Liquids and Solids;391
7.3.1.1.2;13.1.1.2 Pyro-, Piezo- and Ferroelectrics;392
7.3.1.1.3;13.1.1.3 Simplest Description of a Proper Ferroelectric;394
7.3.1.2;13.1.2 Ferroelectric Cells with Non-ferroelectric Liquid Crystal;396
7.3.1.2.1;13.1.2.1 Meyer´s Discovery;396
7.3.1.2.2;13.1.2.2 Goldstone Mode and Helicity of the Structure;398
7.3.1.2.3;13.1.2.3 Smectic C* Phase and Criteria for Ferroelectricity;399
7.3.1.2.4;13.1.2.4 Surface Stabilised Ferroelectric Cells;400
7.3.1.3;13.1.3 Phase Transition SmA*-SmC*;402
7.3.1.3.1;13.1.3.1 Simplification;402
7.3.1.3.2;13.1.3.2 Soft Mode for Smectic A*-Smectic C* Transition;403
7.3.1.3.3;13.1.3.3 Goldstone and Soft Modes in Sm C* Phase;406
7.3.1.3.4;13.1.3.4 Measurements of Landau Expansion Coefficients;407
7.3.1.4;13.1.4 Electro-Optic Effects in Ferroelectric Cells;408
7.3.1.4.1;13.1.4.1 Electroclinic Effect in SmA;408
7.3.1.4.2;13.1.4.2 Helix Distortion and Deformed Helix Ferroelectric effect;410
7.3.1.4.3;13.1.4.3 Frederiks Transition and Clark-Lagerwall Bistability;413
7.3.1.5;13.1.5 Criteria for Bistability and Hysteresis-Free Switching;417
7.3.1.5.1;13.1.5.1 Cells with No Insulating Layers;417
7.3.1.5.2;13.1.5.2 Role of Aligning Layers in Bistability;418
7.3.1.5.3;13.1.5.3 V-Shape Effect;420
7.3.2;13.2 Introduction to Antiferroelectrics;420
7.3.2.1;13.2.1 Background: Crystalline Antiferroelectrics and Ferrielectrics;420
7.3.2.2;13.2.2 Chiral Liquid Crystalline Antiferroelectrics;423
7.3.2.2.1;13.2.2.1 Discovery and Polymorphism;423
7.3.2.2.2;13.2.2.2 Molecular Interactions;424
7.3.2.2.3;13.2.2.3 Models;426
7.3.2.2.4;13.2.2.4 Electric Field Switching;430
7.3.2.3;13.2.3 Polar Achiral Systems;433
7.3.2.3.1;13.2.3.1 The Problem;433
7.3.2.3.2;13.2.3.2 Achiral Ferroelectrics;434
7.3.2.3.3;13.2.3.3 Achiral Antiferroelectrics;435
7.3.2.3.4;13.2.3.4 Ferro- and Antiferroelectric Compounds Based on the Bent-Shape Molecules;437
7.3.3;References;439
8;Index;442