McMillan Theory of Binary Smectic Mixtures

Abstract

The molecular field theory of the smectic A phase, developed by McMillan, is extended to binary smectic mixtures. Expressions for the orientation-dependent mean field potential of each component are derived. Besides the interaction terms of the pure components, two additional parameters appear. These mixed parameters describe the interaction forces between particles of different species. The composition dependences of the transition temperatures are determined from the free energies. The possible existence of a two-phase region is neglected. By suitable choices of the interaction parameter set, it is possible to predict induced phases. If all interaction parameters satisfy the geometric mean rule, the mixture will be an ideal one, exhibiting linear phase transition lines. Because of the coupling between the smectic order and the nematic order, the transition lines of both phases are correlated. By fitting an experimental phase diagram we are able to determine the unknown values of the mixed interaction parameters.