Computer simulation studies of anisotropic systems. IX. The Maier—Saupe theory for nematic liquid crystals and the molecular field approximation

Abstract

The first real test of the molecular field approximation employed in the Maier—Saupe theory of nematic liquid crystals was provided by the Lebwohl—Lasher Monte-Carlo simulation of an idealized lattice model. However the system employed in the simulation is not uniquely consistent with the Maier—Saupe theory and so does not provide an unambiguous test of the molecular field approximation. We describe here three new lattice models which are also compatible with the theory and report the temperature dependence of the internal energy, heat capacity and the second-rank orientational order parameter determined using the Monte-Carlo technique. In addition the second- and fourth-rank orientational pair correlation functions were also evaluated at selected temperatures for one of the models. All of the results are compared with the predictions of the Maier—Saupe theory. We find that the validity of the molecular field approximation improves as the coordination number and the range of the anisotropic pair potential employed in the model increase. This improvement is especially evident for the nematic—isotropic transition temperature although the agreement with the order parameter at the transition is not so impressive and that for the entropy of transition is poor.