On the Validity of the Maier-Saupe Theroy of the Nematic Transition

Abstract

The Maier-Saupe theory of the nematic phase transition can be viewed as arising from two basic assumptions: a kind of induced-dipole induced-dipole interaction and the neglect of the effect of orientational interactions on postional correlations. The theory makes the further assumption of the validity of the molecular field approximation for the orientational interactions. We have asked if the first-order transition predicted by Maier and Saupe is just an artificial consequence of the molecular field approximation. To answer this question, we have constructed a model based on the same two assumptions. These are augmented by the further assumptions of discretization of space and discretization of molecular orientations and by the replacement of a rotationally invariant interaction with one having a preferred axis. The latter replacement is analogous to replacing the Heisenberg model for spin systems with the Ising model. By imbedding the present model and the Maier-Saupe theory within the same sequence of variational bounds on the grand potential, it is argued that the present model is superior. It is shown that this model has no first-order phase transition, although the molecular field approximation, when applied to this model, agian gives such a transition. It is therefore proposed that the failure to find a first-order transition points to a breakdown in one of the two basic assumptions.