Revisiting McMillan’s theory of the smectic A phase

Abstract

We consider the full solution of McMillan’s molecular model of the smectic A phase withinthe mean-field approximation, expressing the free energy (or the effective one-particlemean-field energy) of the model in terms of an infinite set of orientational and translationalorder parameters. The general formalism reduces to the usual McMillan theory (hereafterreferred to as McMillan’s approximation) when second- and higher-order harmonics in theFourier expansion are neglected, which leads to a description of the smectic phase in termsof the leading order parameters. The effects of such a truncation on the location of thetricritical nematic–smectic A point have been previously considered by Longa(1986 J. Chem. Phys. 85 2974). A quantitative analysis to assess the relativeimportance of the neglected terms in the description of the smectic phase andits various transitions is reported. It is shown that McMillan’s approximationunderestimates both orientational and translational order, and leads to values ofthe transition entropies smaller than those resulting from the full expansion.