Perturbation Theory for Nematic Liquid Crystals of Axially Symmetric Molecules: II. Effect of Quadrupolar Forces

Abstract

A statistical mechanical perturbation theory, that derives from the work of Singh and Singh, is applied to analyse the influence of quadrupole interaction on a variety of thermodynamic properties of nematic liquid crystals. Numerical evaluations are done for a model system in which molecules are assumed to interact via a pair potential having both repulsive and attractive parts. The repulsive interaction is represented by a repulsion between hard spherocylinders. The attractive potential, a function of only the centre of mass distance and the relative orientation between the two molecules, is represented approximately by the isotropic dispersion and anisotropic quadrupole interaction between two asymmetric molecules. The properties of the reference system and the first order perturbation term are calculated by assuming that an angle-dependent range parameter scales the pair correlation function such that it decouples the orientational degrees of freedom from the translational one. The functional form and the density dependence of the effective one-body orientational potential is discussed. It is found that the thermodynamic properties for the nematic-isotropic transition are highly sensitive to the form of effective one-body orientational potential. The influence of pressure on the stability, ordering and thermodynamic functions for the NI transition is analysed and found to be in accordance with the experimental observation.