The Molecular Dynamics of Liquid Crystals

1. A Comparative Survey of the Physical Techniques Used in Studies of Molecular Dynamics.- 1. Introduction.- 2. Molecular Motion in Liquid Crystals.- 3. Spectroscopy in Studies of Molecular Motion.- 4. Applications of Spectroscopy to the Study of Rotational Motion.- 5. Applications to Studies of Translational Diffusion.- 2. On the Description of Ordering in Liquid Crystals.- 1. Introduction.- 2. General Approach.- 3. Purely Positional Order.- 4. Orientational Order.- 5. Positional-Orientational Order in Uniaxial Phases.- 6. Rotameric Molecules.- 3. Diffusion Models for Molecular Motion in Uniaxial Mesophases.- 1. Diffusion Equations.- 2. Solution of the Diffusion Equation.- 3. Diffusion Across Potential Barriers.- 4. Dynamics of Chain Molecules.- 5. Diffusive Coupling with the Solvent.- 4. ESR and Liquid Crystals: Statistical Mechanics and Generalised Smoluchowski Equations.- 1. Introduction.- 2. Rotational and Translational Motion in Ordered Fluids.- 3. Symmetries of the Liquid-Crystalline Potential.- 4. Relative Translational Diffusion: The Pair Correlation Function.- 5. Fluctuating Torques and Slowly Relaxing Local Structures.- 5. Techniques and Applications of Langevin Dynamics Simulations.- 1. Introduction.- 2. Hydrodynamics.- 3. Algorithms and Errors.- 4. Barrier Crossing.- 5. Rotation.- 6. Application to Lipid Bilayers.- 7. Limitations and Extensions of Langevin Dynamics.- 8. Appendix.- 6. An Introduction to the Molecular Dynamics Method and to Orientational Dynamics in Liquid Crystals.- 1. Introduction.- 2. Equations of Motion.- 3. Integration of the Equations of Motion.- 4. Calculation of Static and Dynamic Properties.- 5. General Properties of Orientational Correlation Functions.- 6. Evaluation of Correlation Functions by Molecular Dynamics.- 7. Appendix.- 7. Nuclear Spin Relaxation Formalism for Liquid Crystals.- 1. Introduction.- 2. Spin Dynamics: Density Matrix Description of Relaxation.- 3. Molecular Dynamics.- 4. Cooperative Motion.- 5. Illustrative Experiments.- 6. Summarising Remarks.- 8. Nuclear Spin Relaxation and Molecular Motion in Liquid Crystals.- 1. Introduction.- 2. Experiments and Methods.- 3. Density Operator Theory.- 4. Conclusions.- 9. The Effects of Director Fluctuations on Nuclear Spin Relaxation.- 1. Introduction.- 2. Historical Background.- 3. Theory.- 4. Experiments.- 5. Conclusions.- 10. Nuclear Spin Relaxation Mechanisms in Liquid Crystals Studied By Field Cycling NMR.- 1. Introduction.- 2. Principles and Techniques of Field Cycling NMR.- 3.T1 Relaxation Dispersion in Nematic Mesophases.- 4.T1 Relaxation Dispersion in Smectic Mesophases.- 5. DeuteronT1 Relaxation Dispersion in Methyl Deuteriated MBBA.- 11. Probe Studies of Liquid Crystals.- 1. Introduction.- 2. Orientational Order.- 3. Tools for Molecular Ordering.- 4. Solute-Solvent Interactions.- 5. Interesting Complications.- 6. Conclusions.- 12. ESR and Molecular Motions in Liquid Crystals: Motional Narrowing.- 1. The ESR Spin Hamiltonian: g and A Tensors.- 2. Effective Spin Hamiltonian and Order Parameters.- 3. Spectral Densities and Linewidths.- 4. Rotational Dynamics in Liquid-Crystalline Phases.- 5. Translational Motion in Liquid Crystals.- 13. Thermodynamics of Liquid Crystals and the Relation to Molecular Dynamics: ESR Studies.- 1. Introduction.- 2. Smectic A-Nematic Tricritical Point and Crossover Behaviour.- 3. Universality in Nematic Ordering.- 4. Lipid-Cholesterol Mixtures.- 5. Dynamics: Thermotropics.- 6. Dynamics: Lyotropics.- 14. ESR Studies of Molecular Dynamics at Phase Transitions in Liquid Crystals.- 1. Introduction.- 2. Models of Collective Dynamics: Director Fluctuations.- 3. The Nematic-Isotropic Phase Transition.- 4. The Smectic A-Nematic Phase Transition.- 5. The Dynamic Cluster Model.- 6. Fast versus Slow Collective Motions.- 7. Treatment of Data.- 15. ESR and Slow Motions in Liquid Crystals.- 1. Introduction.- 2. ESR Lineshapes: The Stochastic Liouville Equation.- 3. Methods of Solution: Lanczos and Conjugate Gradient Methods.- 4. Relation to Mori's Method in Statistical Mechanics.- 5. Ordering and Thermodynamics: Behaviour of Large versus Small Probes.- 6. Dynamics in I, N, SA and NR Phases.- 7. Rotational Dynamics in Lyotropics: Lipid Multilayers.- 8. Experimental Techniques: Lineshapes in One and Two Dimensions.- 9. On Fitting the Data.- 16. Raman and IR Fluctuation Spectroscopy of Liquid Crystals.- 1. Introduction.- 2. Determination of Correlation Functions from IR and Raman Lineshapes.- 3. Fluctuation Raman and IR Spectroscopy in Liquid Crystals.- 4. Experimental Results.- 5. Conclusions.- 17. Dielectric Relaxation Behaviour of Liquid Crystals.- 1. Introduction.- 2. Phenomenological Aspects of Dielectric Relaxation.- 3. Measurement of Dielectric Permittivity.- 4. Molecular Aspects of the Dielectric Permittivity.- 5. Experimental Results.- 6. Conclusions.- 18. Neutron Scattering From Liquid Crystals.- 1. Introduction to the Neutron.- 2. Types of Neutron Scattering Experiments.- 3. Coherent and Incoherent Scattering.- 4. Examples of Neutron Diffraction from Liquid Crystals.- 5. Inelastic and Quasi-Elastic Scattering.- 6. Model Incoherent Scattering Laws.- 7. Experiments and Examples of Results.- 19. Molecular Order and Motion in Liquid Crystal Polymers Studied By Pulsed Dynamic NMR.- 1. Introduction.- 2. Experiments and Methods.- 3. Results and Discussion.- 4. Conclusions.- 20. Aggregates of Amphiphiles in Lyotropic Liquid Crystals.- 1. Aggregation of Amphiphiles.- 2. Structure and Aggregates.- 3. Within the Aggregates.- 21. Orientation and Frequency Dependent NMR Relaxation Studies of Bilayer Membranes: Characterisation of the Lipid Motions.- 1. Introduction.- 2. Experiments and Methods.- 3. Results and Discussion.- 4. Conclusions.- 22. Molecular Dynamics in Liquid-Crystalline Systems Studied By Fluorescence Depolarisation Techniques.- 1. Introduction.- 2. Principles of Fluorescence Spectroscopy.- 3. Instrumentation for Fluorescence Spectroscopy.- 4. Principles of Fluorescence Polarisation.- 5. Data Analysis.- 6. Order and Dynamics of DPH and TMA-DPH Molecules in Lipid Bilayer Configurations.- 23. Spectroscopic Studies on Structure and Dynamics of Lyotropic Liquid Crystals: Cubic and Reversed Hexagonal Phases and Lipid Vesicles.- 1. Introduction.- 2. Phase Equilibria and Structural Polymorphism.- 3. Theoretical Aspects on Lipid Self-Assembly.- 4. Nuclear Magnetic Resonance.- 5. Electron Spin Resonance.- 6. Time-Resolved Fluorescence Spectroscopy.- 7. Fluorescence Anisotropy.