Geoffrey R. Luckhurst

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 Moris 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.

Non-symmetric dimeric liquid crystals. The preparation and properties of the α-(4 -cyanobiphenyl-4'-yloxy )-ω-(4-n-alkylanilinebenzylidene-4'-oxy )alkanes

Abstract Six series of a family of non-symmetric dimers, the α-(4-cyanobiphenyl-4′-yloxy)-ω-(4-n-alkylanilinebenzylidene-4′-oxy)alkanes, have been prepared. In three of the series, the number of methylene groups in the flexible alkyl spacer has been varied from 3 to 12 while the terminal alkyl chain is held constant at either 2, 6 or 10. In the remaining series, the effect of increasing the terminal chain length has been studied by holding the spacer length constant at 3, 4 or 5 methylene units while varying the length of the terminal chain from 0 to 10 carbon atoms. The phase behaviour and transitional properties of these series have been investigated using optical microscopy and differential scanning calorimetry, while the structures of the mesophases have been studied using X-ray diffraction on both powder and aligned samples. This study has revealed novel phase behaviour involving intercalated smectic phases stabilized by the mixed mesogenic group interaction. We have identified the first examples of ...

Smectogenic dimeric liquid crystals. The preparation and properties of the α,ω-bis(4-n-alkylanilinebenzylidine-4′-oxy)alkanes

Abstract Eleven series of dimeric liquid crystals, namely the α,ω-bis(4-n-alkylanilinebenzylidine-4′-oxy)alkanes, have been synthesized and their transitional properties characterized. The number of methylene groups in the flexible core was varied from one to twelve while the length of the terminal alkyl chains was increased from a methyl group to a decyl substituent. The rich smectic polymorphism of this family of compounds was studied using X-ray diffraction and polarizing microscopy; it includes several examples of rare phase transitions, for example, smectic F-smectic A and crystal G-isotropic, as well as novel modulated hexatic phases based on a two dimensional lattice. The transitional properties of a given series, where the length of the terminal chain is held constant while the length and parity of the flexible spacer is varied, exhibit a pronounced alternation. For example, the entropy change at the nematic-isotropic transition exhibits a strong alternation and this has been interpreted in terms ...

Biaxial nematic liquid crystals: fact or fiction?

Mesogenic molecules invariably deviate from the cylindrical symmetry usually assumed for them. One consequence of this is that, in addition to the ubiquitous uniaxial nematic phase, there should also be a biaxial nematic phase. For this there are three different principal components of a second rank tensorial property, such as the magnetic susceptibility, as opposed to two for a uniaxial phase. Each of these components is associated with a separate director; the three directors correspond to the directions about which three orthogonal axes set in the molecule tend to be aligned. Although the existence of the biaxial nematic phase was predicted over 30 years ago it was not until 10 years later that the first claim to have found this phase appeared. This system was, in fact, a lyotropic liquid crystal. Surprisingly, the search for a thermotropic biaxial nematic has proved to be especially challenging. This review is concerned with the thermotropic materials for which a biaxial nematic have now been claimed. Of particular importance is the technique used to establish the symmetry of the nematic phase and it is suggested that deuterium NMR spectroscopy is a powerful method with which to determine this. However, the biaxial nematics claimed to be formed by certain compounds are shown by NMR to have uniaxial symmetry. The reasons why the biaxial nematic phase proves to be so elusive are explored using molecular field theory and used to inform the design of thermotropic mesogens which are likely to form this phase.

The Preparation and Properties of the α,ω-bis(4,4′-Cyanobiphenyloxy)Alkanes: Nematogenic Molecules with a Flexible Core

Abstract The first twelve members of the homologous series of α,ω-bis(4,4′-cyanobiphenyloxy) alkanes have been synthesised. The compounds are nematogenic, although the mesophases for the first and third members of the series are monotropic. Both the nematic-isotropic transition temperature and the entropy of transition exhibit a pronounced dependence on the length of the flexible core; this is analogous to that found for main chain thermotropic liquid crystal polymers.

Computer simulation studies of anisotropic systems. XXX. The phase behavior and structure of a Gay–Berne mesogen

The Gay–Berne potential is proving to be a valuable model with which to investigate the behavior of liquid crystals using computer simulation techniques. The potential contains four independent parameters which control the anisotropy in the attractive and repulsive interactions. The choice of these parameters is not straightforward and it would seem that those employed in some simulations are not strictly appropriate for mesogenic rodlike molecules. Here we report a detailed computer simulation study of Gay–Berne particles interacting via a potential parametrized to reflect the anisotropic forces based on a fit to a realistic mesogenic molecule. The behavior of the phases and the transitions between them have been investigated for a system of 2000 particles using isothermal–isobaric Monte Carlo simulations. At low pressures, this Gay–Berne mesogen exhibits isotropic, smectic A and smectic B phases but, as the pressure is increased, so a nematic phase is added to the sequence. The nature of the phase trans...

A shape model for molecular ordering in nematics

An explicit form for the orientating potential acting in uniaxial liquid crystal phases is derived, by analogy with the surface anchoring potential which determines the orientation of macroscopic anisometric particles. The surface of a molecule is determined by describing the molecule as an assembly of van der Waals spheres. The model is successfully applied to predict the ordering tensors for a variety of systems, namely, solutions in nematic solvents of small and rigid probes, or relatively long n-alkanes with many degrees of internal freedom, and pure nematogens formed by aromatic cores attached to flexible chains.

Computer simulation studies of anisotropic systems. XXI: Parametrization of the Gay-Berne potential for model mesogens

The Gay-Berne potential is proving to be of considerable value in computer simulation studies of liquid crystals. However, the parameters employed in the potential were chosen by comparison with that for a line of four Lennard-Jones centres; they may not, therefore, be appropriate for mesogenic molecules. To see if this is the case we have estimated the parameters in the Gay-Berne potential by comparison with the site-site potential constructed for p-terphenyl, which has a molecular structure typical of many mesogens. Unlike the Gay-Berne potential the site-site potential is biaxial, and a method for projecting out this biaxiality is proposed. The resultant uniaxial model has then been used to obtain values for the parameters occurring in the Gay-Berne potential. These are found to differ significantly from those proposed originally; they are, we believe, more appropriate for investigations of the behaviour of liquid crystals. Our own molecular dynamics simulations, based on the new parametrization, revea...

An enhanced odd-even effect of liquid crystal dimers Orientational order in the α,ω-bis(4′-cyanobiphenyl-4-yl)alkanes

Abstract The odd-even behaviour observed for liquid crystal dimers has been predicted to be a sensitive function of the geometry of the link joining the mesogenic groups to the flexible spacer. Here we report the synthesis of two cyanobiphenyl dimers with methylene links, together with a determination of their transitional properties. In particular we have probed their orientational order via the major and biaxial orientational order parameters of a solute molecule, anthracene-d 10, using NMR spectroscopy. For comparison we have also determined the corresponding quantities for the cyanobiphenyl dimers with ether links. The enhanced odd-even effect observed for the methylene linked dimers relative to those with ether links is in good accord with theory.

Computer simulation studies of anisotropic systems

The Lebwohl-Lasher model of a nematogen provides a simple system with which to study the order-disorder transition and to examine the properties of the nematic phase. We have investigated the model containing 203 particles over a small temperature range characteristic of that for real nematogens using the Monte Carlo method to evaluate the internal energy, the heat capacity and the second rank orientational order parameter. Our results are in reasonable agreement with those of other simulations and are compared with the predictions of theories based on a cluster expansion of the free energy. The temperature dependence of the order parameter is used to investigate the validity of the singlet orientational distribution function predicted by the Maier-Saupe theory. The potential of mean torque is found to be linear in the order parameter as required by the theory although the orientational free energy is in error. The simulated properties are in reasonable but not complete accord with those of a real nematog...