Biaxial Nematic Liquid Crystals : Theory, Simulation and Experiment.

Cover -- Contents -- About the Editors -- List of Contributors -- Preface -- Chapter 1 Introduction -- 1.1 Historical Background -- 1.2 Freiser Theory -- 1.3 Nematic Order Parameters -- 1.4 Nematic Tensor Order Parameters -- 1.5 Theoretical Phase Diagrams -- 1.6 Landau-de Gennes Theory -- 1.7 Computer Simulation -- 1.8 Other Theoretical Issues -- 1.9 Applications -- 1.10 Characterisation -- 1.11 Lyotropic and Colloidal Systems -- 1.12 Molecular Design -- References -- Chapter 2 Biaxial Nematics: Order Parameters and Distribution Functions -- 2.1 Introduction -- 2.2 The Cartesian Language -- 2.2.1 Order Parameters -- 2.2.2 Molecular Symmetry -- 2.2.3 Measurement -- 2.3 The Spherical Tensor Language -- 2.3.1 The Order Parameters of Biaxial Molecules in a Uniaxial Phase -- 2.3.2 Molecular Symmetry -- 2.3.3 Measurement -- 2.4 Extension to Biaxial Nematics -- 2.4.1 Orientational Order Parameters -- 2.4.2 Systems with D2h Point Group Symmetry -- 2.4.3 Measurement of the Order Parameters -- 2.4.4 Systems with C2h Point Group Symmetry and Their Order Parameters -- 2.4.5 Systems with C2h Point Group Symmetry: The Cartesian Language -- 2.5 Fourth-Rank Order Parameters -- 2.6 The Singlet Orientational Distribution Function -- 2.7 Appendices -- 2.7.1 Point Group Symmetry and the Associated Symmetry Operations -- 2.7.2 Legendre Polynomials, Modified Spherical Harmonics and Wigner Rotation Matrices -- Acknowledgements -- References -- Chapter 3 Molecular Field Theory -- 3.1 Introduction -- 3.2 General Mathematical Theory -- 3.2.1 Two-Particle Hamiltonian -- 3.2.2 Ensemble Potentials -- 3.2.3 Molecular Field Approximation -- 3.2.4 Variational Principles -- 3.2.5 Local Stability Criterion -- 3.3 Non-Polar Molecules -- 3.3.1 Quadrupolar Hamiltonians -- 3.3.2 Phase Transitions -- 3.3.3 Universal Phase Diagram -- 3.3.4 Steric Effects -- 3.4 Polar Molecules.

3.4.1 Dipolar Fluids -- 3.4.2 Dipolar Hamiltonian -- 3.4.3 Condensed Polar Phases -- References -- Chapter 4 Hard Particle Theories -- 4.1 Introduction -- 4.2 Theoretical Approaches -- 4.3 Board-Like Models -- 4.4 Bent-Core Models -- 4.5 Rod-Plate Mixtures -- 4.6 Conclusions and Speculations -- Acknowledgements -- References -- Chapter 5 Landau Theory of Nematic Phases -- 5.1 Introduction -- 5.2 Symmetry of Biaxial Nematics and Primary Order Parameters -- 5.3 Landau Expansion -- 5.3.1 Generic NU-I Phase Transition -- 5.3.2 Generic NB-NU and NB-I Phase Transitions -- 5.3.3 Role of Coupling between Nematic Order Parameters -- 5.3.4 Landau-de Gennes Expansion in Terms of the Alignment Tensor -- 5.4 Conclusion -- Acknowledgements -- References -- Chapter 6 Computer Simulations of Biaxial Nematics -- 6.1 Introduction -- 6.2 Order Parameters -- 6.3 Model Potentials and Applications -- 6.3.1 Lattice Models -- 6.3.2 Atomistic Models -- 6.3.3 Molecular Models -- 6.4 Conclusion -- Acknowledgements -- 6.5 Appendices -- 6.5.1 Quaternions -- 6.5.2 Angular Momentum Operator -- 6.5.3 Kinematic and Dynamic Equations of Rotational Motion -- 6.5.4 Propagator/Integrator of Rotational Equations of Motion -- 6.5.5 Gradient of the Biaxial Gay-Berne Potential -- 6.5.6 Torques of the Biaxial Gay-Berne Potential -- References -- Chapter 7 Continuum Theory of Biaxial Nematic Liquid Crystals -- 7.1 Introduction -- 7.2 Continuum Model and Energies -- 7.2.1 The Elastic Energy -- 7.2.2 The Magnetic and Electric Energies -- 7.2.3 The Total Energy -- 7.3 Dynamic Equations -- 7.3.1 Balance Laws -- 7.3.2 The Viscous Stress -- 7.3.3 The Dynamic Equations -- 7.3.4 Euler Angle Description -- 7.3.5 A Simple Shear Flow -- 7.4 Equilibrium Equations -- 7.4.1 The Equilibrium Equations -- 7.4.2 Alignment Induced by a Magnetic Field -- 7.5 Conclusion -- References.

Chapter 8 The Alignment of Biaxial Nematics -- 8.1 Introduction -- 8.2 Alignment by an External Electric or Magnetic Field -- 8.3 Surface Alignment -- 8.3.1 Macroscopic Description -- 8.3.2 Molecular Scale Description -- 8.4 Flow Alignment -- 8.5 Lower Symmetry Biaxial Nematics and Hierarchical Domain Structures -- Acknowledgements -- References -- Chapter 9 Applications -- 9.1 Introduction -- 9.1.1 Materials Considerations -- 9.1.2 Surface Alignment -- 9.2 Thin-Film Electro-Optic Devices -- 9.2.1 Minor-Director In-Plane Switching Devices -- 9.2.2 Electric Field-Induced Biaxiality Effects -- 9.2.3 Planar Biaxial Nematic Devices -- 9.2.4 Twist Effects in Biaxial Nematics and Biaxial Pi-Cells -- 9.2.5 Bistable Biaxial Nematic Devices -- 9.2.6 Spontaneous Chirality Effects -- 9.3 Non-Device Applications of Biaxial Nematic Liquid Crystals -- 9.3.1 Optical Compensation Films -- 9.4 Conclusion -- References -- Chapter 10 Characterisation -- Chapter 11 Lyotropic Systems -- 11.1 Introduction -- 11.2 Phase Diagrams -- 11.3 The Potassium Laurate-Decanol-Water Mixture: A Working Example -- 11.4 The Intrinsically Biaxial Micelles Model -- 11.5 Theoretical Reconstruction of the Lyotropic Nematic Phase Diagram: a Landau-Like Approach -- 11.6 Conclusions -- Acknowledgements -- References -- Chapter 12 Colloidal Systems -- 12.1 Introduction -- 12.2 Onsager Theory and Extensions -- 12.3 Special Features of Colloids and Colloidal Liquid Crystals -- 12.4 Biaxiality in Mixtures of Rods and Plates -- 12.5 Particles with Inherent Biaxial Shape -- 12.6 Concluding remarks -- References -- Chapter 13 Thermotropic Systems: Biaxial Nematic Polymers -- 13.1 Introduction -- 13.2 Main-Chain Liquid Crystal Polymers -- 13.3 Side-Chain Liquid Crystal Polymers -- 13.4 Comparison of Attachment Geometries - Influence of Molecular Dynamics and Molecular Shape -- 13.5 Conclusion.

References -- Chapter 14 Low Molar Mass Thermotropic Systems -- 14.1 Preamble -- 14.2 Introduction and General Considerations -- 14.3 Single Component -- 14.3.1 Biaxial Board-Shaped Mesogens -- 14.3.2 V-Shaped Nematogens -- 14.3.3 Multipodes -- 14.4 Mixtures -- 14.5 Concluding Remarks -- References -- Chapter 15 Final Remarks -- References -- Index -- Supplemental Images -- EULA.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.