Revisiting McMillan's theory of the smectic A phase

We consider the full solution of McMillan's molecular model of the smectic A phase within the mean-field approximation, expressing the free energy (or the effective one-particle mean-field energy) of the model in terms of an infinite set of orientational and translational order parameters. The general formalism reduces to the usual McMillan theory (hereafter referred to as McMillan's approximation) when second- and higher-order harmonics in the Fourier expansion are neglected, which leads to a description of the smectic phase in terms of the leading order parameters. The effects of such a truncation on the location of the tricritical nematic-smectic A point have been previously considered by Longa (1986 J. Chem. Phys. 85 2974). A quantitative analysis to assess the relative importance of the neglected terms in the description of the smectic phase and its various transitions is reported. It is shown that McMillan's approximation underestimates both orientational and translational order, and leads to values of the transition entropies smaller than those resulting from the full expansion.