Perturbation Theroy for Nematic Liquid Crystals of Axially Symmetric Molecules: Properties of a Trial System

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Abstract
A statistical mechanical perturbation theory for the equilibrium properties of nematic liquid crystals is presented in which the reference potential function is non-spherical and consists of the short-range rapidly varying repulsive part of the pair potential. Calculations are made for a trial system in which molecules are assumed to interact via a pair potential which has repulsive part represented by a repulsion between hard spherocylinders and an attractive part which is function of only r 12 and Ω12 (r 12 is the center of mass distance and Ω12 the relative orientation between the two molecules), and represent approximately the interaction arising from dispersion interaction between two asymmetric molecules. Assuming that the pair correlation function g(r l2, Ω12) for a fluid of hard spherocylinders scales as g[r 12/D(Ω12] where D(Ω12) is angle-dependent range parameter the properties of the reference system and the first order perturbation term are evaluated. The agreement found between the calculated values of the compressibility factor for isotropic phase of fluids of hard spherocylinders and the values obtained from machine simulations is excellent. The functional form and the density dependence of the effective one-body orientational potential ψ(Ω) is discussed in detail. It is shown that the nematic-isotropic transition properties are very sensitive to the form of ψ(Ω). The biaxial symmetry of the low temperature smectic phase of N-(4-n-hexyloxybenzylidene)-4-n-hexylaniline is demonstrated through observation of the deuterium NMR resonance of CDCl3 probe molecules dissolved in this phase. The biaxial ordering is revealed in the observed powder spectrum as well as in a complete rotation study of a uniformly aligned sample.