The Molecular Dynamics of Liquid Crystals

Liquid-crystalline phases are now known to be formed by an ever growing range of quite diverse materials, these include those of low molecular weight as well as the novel liquid-crystalline polymers, such phases can also be induced by the addition of a solvent to amphiphilic systems leading to lyotropic liquid crystals. Irrespective of the structure of the constituent molecules these numerous liquid-cl)'Stailine phases are characterised by their long range orientational order. In addition certain phases exhibit elements of long range positional order. Our understanding, both experimental and theoretical, at the molecular level of the static behaviour of these fascinating and important materials is now well advanced. In contrast the influence of the long range order; both orientational and positional, on the molecular dynamics in liquid Cl)'Stais is less well understood. In an attempt to address this situation a NATO Advanced Study Institute devoted to liquid ctystal dynamics was held at n Ciocco, Barga, Italy in September 1989. This brought together experimentalists and theoreticians concerned with the various dynamical processes occurring in all liquid crystals. The skills of the participants was impressively wide ranging; they spanned the experimental techniques used in the study of molecular dynamics, the nature of the systems investigated and the theoretical models employed to understand the results. While much was learnt it was also recognised that much more needed to be done in order to advance our understanding of molecular dynamics in liquid Cl)'Stais.

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.