Elastic constants of hard and soft nematic liquid crystals

Abstract

The Frank elastic constants for a nematic liquid crystal have been calculated by computer simulations for a fluid of hard ellipsoids and by the Poniewierski-Stecki method for ellipsoids with and without an attractive square well. Required for the Poniewierski-Stecki method is the direct correlation function c(1,2) and its dependence on the mutual molecular orientations. This was addressed using several models: the Parsons model, a two-term virial expansion, and the PY and HNC theories of Patey et al. In the Parsons model for c(1,2), the derived Frank elastic constants for hard ellipsoids were in agreement with the Poniewierski-Holyst values for hard spherocylinders. However, the agreement with simulation values was less satisfactory, as the simulation values exceeded the Parsons model values and the discrepancy grew with increasing particle asymmetry. The Frank constants, derived using a hard-core potential with an exterior SW (convex peg in a round hole), were in fair agreement with experimental data on prolate and oblate molecules, at the expense of employing overly large-order parameters (characteristic of uniaxial hard particle models). Omitted long-range correlations in the c( 1,2), present even in the hard-body models, is suspected to be the cause of the discrepancy of the simulation and experimental Frank constants with those calculated on the basis of short-range models for c(1,2).