Isotropic-symmetry-breaking bifurcations in a class of liquid-crystal models

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Abstract
The isotropic-symmetry-breaking bifurcations occurring in a class of liquid-crystal models describing particles with the symmetry of rectangular slabs are studied. The model free-energy functional employed is appropriate to both the mean-field treatment of anisotropic dispersion forces and the Onsager approximation for hard anisometric particles. The symmetry of the bifurcating solutions to the stationary-phase equations is classified in terms of the eigenvalues of the effective pair interaction. Explicit conditions are derived for systems exhibiting crossover behavior between rodlike and platelike ordering. The results are applied to the question of the existence of biaxial phases in systems of uniaxial particles, and to two models for nonaxially symmetric particles: the hard spheroplatelet fluid and the Straley model.

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