Spatial Correlations in Nematic Liquid Crystals

Abstract

Liquid crystals are liquids. At such densities, spatial correlations between molecules are expected to play an important role in the determination of their collective and phase transition properties. At short range, these correlations are quite anisotropic as a result of anisotropic intermolecular repulsions. We recall a molecular potential model that takes into account anisotropic forces. We show how spatial correlations are accounted for in the “orientationally averaged pair correlations” approximation (OAPC) to affect the macroscopic properties of nematic liquid crystals. We then perform a cell model calculation in which both the molecular orientational distribution and the spatial distribution about lattice sites are determined self-consistently, by solving coupled Euler-Lagrange equations which minimize the free energy. Numerical work is carried out for a simple potential without anisotropicters. We are able to determine the potential parameters which reproduce earlier OAPC results. Such an exercise illustrates how the cell approximation works and provides us with a theoretical framework for introducing anisotropic forces and pair correlations into later work. It is hoped that the latter would help remove some of the serious discrepancies between molecular theories and esperiment.

Work supported in part by the National Science Foundation through Grant No. DMR-8008816.