Molecular Theory of Liquid Crystals Including Anisotropic Repulsion

Abstract

We summarize in this report our progress on constructing a molecular theory for liquid crystals using models which include anisotropic intermolecular forces. In terms of cylindrically symmetric non-chiral molecules, whose pairwise interactions depend on the scalars r _ij , and , this means the introduction of terms explicitly into the formulation of the Hamiltonian. In the mean field treatment, such terms contribute nothing to the nematic phase. In a more sophis ticated theory such as our OAPC, to be described below, such terms in the Hamiltonian bring with them non-trivial mathematical complications and significant physical effects. In the OAPC (orientational averaged pair correlation) theory, liquid structures are brought into consideration through methods well known from the theory of classical liquids, while the orientaional order is treated in a mean-field-like manner. The physical basis for such a theory is obvious: at liquid crystalline densities one can hardly justify the neglect of short-range spatial correlations. In earlier work involving one of the authors, OAPC was applied to models whose Hamiltonians depend on r _ij and . Certain improvements on the calculation of isotropicnematic transition properties over mean field theories were seen. The discrepancies that remain can probably be traced to the neglect of the anisotropic terms. We have now succeeded to work out the mathematics for models including potentials, find ways to related the associate potential parameters to the parameters describing soft-core cylindrical molecules, determine changes in the calculated results for cases of weak anisotropic forces, and build up computer programs for solving integral equations that govern cases of strong anisotropic repulsions.