Solitons in Liquid Crystals

Solitons are a well-known and intriguing aspect of nonlinear behavior in a continuous system such as a fluid: a wave propagates through the medium without distortion. Liquid crystals are highly ordered systems without a rigid, long-range structure. Solitons in liquid crystals (sometimes referred to as "walls") have a wide variety of remarkable properties that are becoming important for practical applications such as electroluminescent display. This book, the first review of the subject to be published, contains not only surveys of the existing literature, but presents new results as well.

Contenu

1 Introduction.- 1.1 Liquid Crystal Phases.- 1.2 Solitons in Liquid Crystals.- References.- 2 Solitons and Field Induced Solitons in Liquid Crystals.- 2.1 Introduction.- 2.2 Solitons.- 2.2.1 Origin and Definition.- 2.2.2 A Brief History.- 2.3 Soliton Equations.- 2.3.1 Korteweg-deVries Equation.- 2.3.2 Nonlinear Schrödinger Equation.- 2.3.3 Sine-Gordon Equation.- 2.3.4 Fisher Equation.- 2.3.5 The Damped ?4Equation.- 2.3.6 Other Equations.- 2.4 Constructing Soliton Equations.- 2.5 Methods of Solving Soliton Equations.- 2.5.1 Inverse Scattering Method.- 2.5.2 Bäcklund Transformation.- 2.5.3 Hirota Method.- 2.5.4 Perturbation.- 2.5.5 Numerical Method.- 2.5.6 Experimental Simulation.- 2.6 Formation of Solitons.- 2.7 Magnetic Field Induced Solitons in Nematics.- 2.7.1 Early Works.- 2.7.2 Nematics Under Tilted Magnetic Fields.- 2.8 Electric Field Induced Solitons in Liquid Crystals.- 2.9 Conclusions.- References.- 3 Solitons in Shearing Liquid Crystals.- 3.1 Introduction.- 3.2 Steady Uniform Shear I: One-Dimensional Case.- 3.2.1 Equations of Motion.- 3.2.2 Classification of Solitons.- 3.2.3 Single Solitons.- 3.2.4 Multisolitons.- 3.2.5 Energy Dissipation.- 3.2.6 Transmitted Light Intensity.- 3.2.7 Flexoelectric Solitons.- 3.2.8 Spatiotemporal Distribution of Directors.- 3.2.9 Experimental Situation.- 3.3 Steady Uniform Shear II: Boundary Effects.- 3.3.1 Director Equation of Motion.- 3.3.2 Steady States.- 3.3.3 Numerical Soliton Solutions.- 3.3.4 Analytic Soliton Solutions.- 3.3.5 Relaxation Processes.- 3.4 Unsteady Uniform Shear.- 3.4.1 Multiple Scale Analysis.- 3.4.2 Perturbed Solitons.- 3.5 Steady Nonuniform Shear I: Linear Cell.- 3.5.1 Theory of Pressure Gradient Induced Solitons.- 3.5.2 Experimental Results in Linear Cells.- 3.5.3 Perturbed Solitons Under Spatially Varying Shear.- 3.6 Steady Nonuniform Shear II: Radial Cell.- 3.6.1 Torsional Shear Flow.- 3.6.2 Radial Poiseuille Flow.- 3.6.3 Experiments in Radial Cells.- 3.7 Conclusions.- References.- 4 Some Nonlinear Problems in Anisotropic Systems.- 4.1 Introduction.- 4.2 Nonlinear Aspects of Static Properties of Liquid Crystals.- 4.2.1 Nonlinearities Associated with the Freedericksz Transition.- 4.2.2 Escape into the Third Dimension.- 4.3 Nonlinear Macroscopic Dynamics of Liquid Crystals.- 4.3.1 Dynamics of Line Defects in Nematic Liquid Crystals.- 4.3.2 Moving Wall Fronts in Helielectric Liquid Crystals.- 4.3.3 An Exact Solitary Wave Solution for ?a< 0.- 4.3.4 Biological Significance of Chirality.- 4.3.5 Nonlinear Aspects of Liquid Crystals in Flow.- 4.4 Perspectives.- 4.5 Conclusions.- References.- 5 Solitary Waves in Ferroelectric Liquid Crystals.- 5.1 Introduction.- 5.2 Equations of Motion in One Dimension.- 5.2.1 Solving the Equation of Motion.- 5.3 Wave Fronts in Infinite Systems.- 5.3.1 Computer Simulations.- 5.3.2 Marginal Stability.- 5.3.3 Analytic Solution for the Metastable-Stable Case.- 5.3.4 Summary.- 5.4 Director Reorientation in Finite Domains with Fixed Boundaries.- 5.4.1 Thick Cells with a Helix.- 5.4.2 Thin Cells with Splay.- 5.4.3 Computer Simulations.- 5.5 Structures with Finite Interface Energies.- 5.5.1 Introduction.- 5.5.2 One-Dimensional Structures.- 5.5.3 Two-Dimensional Structures.- 5.6 Conclusions.- References.- 6 Frustrated Smectics.- 6.1 Introduction.- 6.2 The Physics of Polar Smectics.- 6.2.1 Intrinsic Incommensurability of Coexisting Modulations.- 6.2.2 Phenomenological Theory of Frustrated Smectics.- 6.2.3 Solitons in the Model of Frustrated Smectics.- 6.2.4 Connection with Experiments.- 6.3 Electric Properties of the Incommensurate Smectics.- 6.3.1 Intrinsic Ferroelectricity of Incommensurate Smectics.- 6.3.2 Distortion of the Modulated Smectic Structure by an Electric Field.- 6.3.3 Longitudinal Ferroelectricity.- 6.3.4 Conclusions.- 6.4 Escape from Incommensurability.- 6.4.1 Two-Dimensional Lockin of the Wavevectors.- 6.4.2 Theoretical Phase Diagrams with 2D Antiphases.- 6.4.3 Including Higher Order Harmonics in kx.- 6.5 Conclusions.- References.- 7 Soft Walls and Orientational Singularities in Two-Dimensional Liquid Crystal Films.- 7.1 Background.- 7.2 Experimental Techniques.- 7.3 Soft Tilt Director Walls in Ferroelectric Smectic C* Films.- 7.4 Characteristic Orientational Singularities in Tilted Hexatic Films.- 7.5 Concluding Remarks.- References.- 8 Charged Twist Walls in Nematic Liquid Crystals.- 8.1 Introduction.- 8.2 Experiment.- 8.3 Model.- 8.4 Conclusions.- References.- 9 Localized Instabilities in the Convection of Nematic Liquid Crystals.- 9.1 Introduction.- 9.2 Localized Instabilities in the Evolution to the Chaotic State.- 9.3 Theoretical Model: The Amplitude Equation.- 9.4 Convective Instabilities in Nematics Under A.C. Electric Fields.- 9.5 Sequence of Homogeneous Stationary States.- 9.6 Topology of Dislocations.- 9.7 Experimental Techniques.- 9.8 Nucleation of Dislocations in the Convective Rolls.- 9.9 Phase Propagation and Localization of a Convective Structure.- 9.10 Propagation of Solitary Rolls.- References.- 10 Solitons and Commensurate-Incommensurate Phase Transitions in Ferroelectric Smectics.- 10.1 Introduction.- 10.2 Condensation of Solitons.- 10.2.1 Soliton and Soliton Lattices of the Sine-Gordon Equation.- 10.2.2 Cholesteric-Nematic Phase Transition.- 10.2.3 Flexoelectric Instability of the Nematic Phase.- 10.3 The Chiral Smectic C-Smectic CPhase Transition.- 10.3.1 Chiral Smectic CPhase Under an Electric Field.- 10.3.2 Interaction Between Solitons.- 10.3.3 Multisolitons and Soliton Lattices.- 10.3.4 Phase Transition of Instability Type.- 10.3.5 Effect of Magnetic Field.- 10.4 Incommensurate and Rippled Phases Without Lifshitz Invariant.- 10.4.1 Rippled Phase.- 10.4.2 Phase Transitions Between Smectic APhases.- 10.5 Summary.- References.- Author Index.