Phenomenological theory of smectic-A liquid crystals.

Abstract

A generalization of the Landau--de Gennes phenomenological theory of smectic-A liquid crystals is described. The theory is based on a Landau-Ginzburg free energy that includes local and nonlocal parts. The local part consists of the isotropic-Ising-model free energy and de Gennes's phenomenological free energy of the nematic phase. The nonlocal part is derived from the form of two-body contributions to the free energy in molecular density-functional theories, expanded in gradients of the number density and orientational order parameter. A mean-field approximation to the theory is analyzed by both Landau expansion and by a full numerical solution, involving Fourier-series representations of the number density and an orientational order parameter with an appropriately large number of Fourier coefficients. The main purpose of the analysis is to show that the smectic phase results from the instability of a uniform phase induced by the gradient terms in the free energy, particularly those that couple modulations in the density and orientational order parameter.