Theory and simulation of the confined Lebwohl-Lasher model.

We discuss the Lebwohl-Lasher model of nematic liquid crystals in a confined geometry, using Monte Carlo simulation and mean-field theory. A film of material is sandwiched between two planar, parallel plates that couple to the adjacent spins via a surface strength ε(s). We consider the cases where the favored alignments at the two walls are the same (symmetric cell) or different (asymmetric cell). In the latter case, we demonstrate the existence of a single phase transition in the slab for all values of the cell thickness. This transition has been observed before in the regime of narrow cells, where the two structures involved correspond to different arrangements of the nematic director. By studying wider cells, we show that the transition is in fact the usual isotropic-to-nematic (capillary) transition under confinement in the case of antagonistic surface forces. We show results for a wide range of values of film thickness and discuss the phenomenology using a mean-field model.

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.