The role of the order parameter in a liquid crystalline phase transition

Abstract

The question of what the role is of the long-range orientational order parameter, S, in a liquid crystalline phase transition, in particular, the nematic to isotropic transition, is here considered. An analytical calculation of S as a function of temperature T for a Lebwohl-Lasher orientational potential and a semi-analytical calculation of S for a Maier-Saupe potential are presented. Also, the distribution function f(θ) is found to have the form of a Dirac-Delta function in the perfectly ordered state for which S = 1.