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UBC Theses and Dissertations

Nematic phases in fluids of biaxial particles Reid, Andrew Charles Edmund


The investigation of the possible uniaxial phases of a fluid of biaxial particles undertaken by Bergersen, Palffy-Muhoray and Dunmur forms the starting point for further research into the full range of possible phases of such a fluid. A generalization of their interaction model, free from constraints having to do with interaction details, retaining only the biaxial symmetry, is used in the mean-field approximation to explore the range of possible orientationally-ordered phases for such a system. This model is an equilibrium model which does not include dynamic effects. The basic inter-particle interaction is abstract, having the correct symmetry for biaxial particles, and is the most general biaxial interaction constructable from lowest-order scalar invariants. The self-consistent equations resulting from this formulation are obtained in the mean-field approximation and therefore retain both the symmetry and the generality at the cost of exact numerical correctness. Four order parameters are identified, corresponding (within a numerical factor) to those found by Straley and Freiser, as well as those of Bergersen et al. The phase diagram of a fluid of biaxial particles, then, is mapped out in terms of the behavior of these order parameters, as indicated by the self-consistent equations, as a function of three anisotropy parameters and the temperature. The primary method of analysis is iteration of the self-consistent equations obtained from differentiating the free energy. Numerical results are obtained for the location of the phase boundaries, and the temperature dependence of the order parameters in various phases.

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