A theory for the liquid-crystalline phase behavior of the Gay–Berne model

Abstract

A simple yet reasonably accurate perturbation theory for the Gay–Berne model, capable of describing the uniform isotropic and nematic phases, as well as the layered smectic-A phase, is presented. The theory, in line with a previously proposed theory, is based on a perturbative scheme, but the reference system, a hard Gaussian overlap model, is treated using the nonlocal approximation of Somoza and Tarazona. This approximate scheme, which reduces to the well-known decoupling approximation for nematics, is a simple generalization of the decoupling approximation designed to include smectic structures. The attractive free energy is calculated using a mean-field approximation. Underestimation of the attractive energy implied by this approximation is alleviated by introducing some scale factors, set to reproduce the critical point and two triple points involving the smectic phase. The choice of scale factors, which is valid for a particular set of molecular parameters, is shown to reproduce accurately the phase diagram corresponding to other parameter values. The theory is used to examine the global liquid-crystalline phase behavior of the Gay–Berne model, paying particular attention to the effect of the anisotropy attraction parameter κ′ on the location of the various phase boundaries. Comparison of the results with the available computer simulations for this system indicates that the theory leads to qualitatively correct predictions. The theory could be useful to predict the phase behavior of realistic systems with respect to molecular elongation and energy anisotropy.