By: Paulo Teixeira
At: Faculdade de Ciências, Ed. C8, 8.2.06
Low-molecular-weight liquid crystals are typically modelled as collections of either hard rods or hard discs. However, small, flexible molecules known as tetrapodes also exhibit liquid crystalline phases, including the elusive biaxial nematic phase [1,2]. This is a consequence of the interplay between conformational and packing entropies: the molecules are able to adopt an anisometric stable conformation that allows then to pack more efficiently into orientationally ordered mesophases. Previous theoretical studies of such systems have been presented , but in order to capture the essential physics of the process, we introduce a minimal model which permits a clear detailed analysis. In our model a particle can exist in one of two states, corresponding to a prolate and an oblate spheroid. The energies of these two states differ by a prescribed amount Δε; and the two conformers are in chemical equilibrium. The interactions between the particles are described by the hard Gaussian Overlap Model  and we investigate the phase behaviour using a second-virial (Onsager) approach, which has been successfully applied to binary mixtures of plate-like and rod-like particles . We use both bifurcation analysis and a numerical minimisation of the free energy to show that, for additive particle shapes, (i) there is no stable biaxial phase even for Δε=0 (although there is a metastable biaxial phase in the same density range as the stable uniaxial phase); (ii) the isotropic-to-nematic transition is into either one of two degenerate uniaxial phases, rod-rich or plate-rich. We confirm that even a small amount of shape non-additivity may stabilise the biaxial nematic phase.
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