Mean Field Theory of Binary Mixtures of Nematic Liquid Crystals

Abstract

Molecular field theory is used to determine the temperature-composition phase diagram and component order parameters of binary mixtures of nematic liquid crystals. A rotationally invariant form of the Maier-Saupe pseudopotential is generalised to two-component mixtures; the parameters of the theory are the ratios of transition temperatures, number densities and isotropic interaction strengths of the pure components. The possibility of induced biaxiality and the effects of an external field are discussed. The model predicts a rich variety of phase behaviour. For dissimilar constituents, coexisting nematic-isotropic and nematic-nematic phases are predicted in agreement with experiment and hard particle theories. In general, the order parameters of the two constituents differ in a given phase; changing the sign of the interspecies interaction term in the pseudopotential results in the appearance of a biaxial solution. This biaxial phase is shown to be unstable however, and, on quenching, is expected to exhibit spinodal decomposition.