Generalized Rank Two Tensor Statistical Model of the Smectic A state

Abstract

A molecular statistical model for the smectic A phase based on rank two symmetry is developed. The model inter-molecular interaction does not depend critically on the magnitude of the vector joining the molecular centers of mass, as is the case in the McMillan¹-Kobayashi² model, but rather on its orientation relative to the preferred orientation of the molecules. The model predicts a phase diagram similar to that calculated by McMillan.¹ It is an improvement of the McMillan-Kobayashi model because it has two additional features. It is intrinsically stable against three dimensional freezing and predicts a force which keeps the director oriented normal to the smectic layers.