| Summary: | This Thesis is dedicated to computer simulation investigations of the phase behaviour of binary and ternary liquid crystals mixtures represented using the LebwohlLasher lattice model. The binary mixture is studied in the Canonical and Semi Grand Canonical Ensembles over a comprehensive set of temperatures, concentrations and the relative coupling constants. The ternary mixture is studied in the Canonical Ensemble only, over a comprehensive set of temperatures and concentrations and single set of coupling constants. In order to determine the boundaries between different phase regions in the Canonical Ensemble, the thermal and concentration dependencies of three different observabIes are used. The first observable is the potential energy of the system, the second is the second rank orientational order parameter and the third is the short-range radial distribution function. The long-range radial distribution function and the system snapshots are used as auxiliary observables. In order to determine the phase boundaries in the Semi Grand Canonical Ensemble, the concentration dependence of the chemical potential is used. The order parameter is also used as an auxiliary observable in order to establish the symmetries of the phases on each side of the various coexistence regions encountered. Some features of the phase diagram (e.g. phase re-entrance) are shown to be difficult to determine in the Canonical Ensemble, whereas other features (e.g. the boundary between two phase coexistence regions) are difficult to determine in the Semi Grand Canonical Ensemble. The remaining data from both ensembles are found to be in good agreement. As well as homogeneous nematic (N) and isotropic (I) phases, regions of N + I and N + N phase coexistence are identified. For mixtures of similar particle types, two distinct coexistence regions are found, but as the particle types are made increasingly dissimilar, these two regions are found to coalesce. This leads to a distortion of the I-N transition temperature curve away from the behaviour predicted by classical ideal mixing rules. The ternary mixture results show further departures from ideal mixing behaviour, while maintaining consistency with the data obtained from the equivalent binary systems. Also, unexpectedly, the cooperative ordering and phase separating of the intermediate particle type takes place at the same temperature for all concentrations considered. Overall, the results from ternary mixtures provide a focus for future work into the phase behaviour of multi-component and poly-disperse mesogenic systems.
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