Equation of state for nematic liquid crystals

Abstract

Taking the point of view that a nematic is an ordinary simple liquid, whose anisotropic properties can be treated in terms of perturbation theory, an equation of state for nematic liquid crystals is derived, based on both anisotropic repulsion between (slightly) nonspherical molecular hard cores and anisotropic attractive forces. The spatial order in the liquid is, in a first approximation, thought to be determined by a hardsphere repulsion. The orientational ordering is considered to result from the effect of the eccentricity of the molecular hard core and the superimposed attractive interaction, both of which are taken into account by means of perturbation theory. A molecular field approximation and, in order to account for short-range orientational correlations, a two-site cluster approximation, are both applied to the orientational molecular coordinates. Expressions for the equilibrium thermodynamics quantities are derived. Extensive numerical model calculations are reported and compared with experimental data for $p$-azoxyanisole (PAA) and the results of Cotter. As a special case an equation of state for the Maier-Saupe model (spherical molecules) is presented. If short-range orientational order is taken into account, quantitative agreement with the experimental data for PAA can be obtained.