An extension of the McMillan theory to a bilayer smectic A phase with long range antiferroelectric order

Abstract

Here an extension of the McMillan theory to describe both a monolayer smectic A phase with short range antiferroelectric order and a bilayer smectic A phase with long range antiferroelectric order in polar liquid crystals is proposed. In a molecular field approximation the single particle pseudopotential and self consistent equations which determine the usual orientational and translational order parameters and a new order parameter taking into account the antiferroelectric character of a bilayer smectic A structure are derived from a modified pair potential. The regions of existence for the isotropic, nematic, as well as both monolayer and bilayer smectic A phases together with the transitional characteristics are determined by numerical solution of the self consistent equations. In addition the temperature dependence of all the order parameters is determined. These results are compared with those from experiment.