Liquid crystals of disc-like molecules

Abstract

Liquid crystals of disc-like molecules fall into two distinct structural types, the columnar and the nematic. The columnar phase in its simplest form consists of discs stacked a periodically in columns, the different columns constituting a two-dimensional array, whereas the nematic phase is an orientationally ordered arrangement of discs without any long-range translational order. After a brief review of the structures of the various mesophases, two topics are considered in somewhat greater detail., (i) An extension of McMillan's mean field model of smectic A to liquid crystals of disc-like molecules. The translational order is now assumed to be periodic in two dimensions. Calculations show that when the lattice is hexagonal, or departs from it only slightly, the transition from the columnar to the isotropic phase may take place either directly or via a nematic phase, depending on the model potential parameters a. Interpreting a to be a measure of the chain lengths as in McMillan's model, the theoretical phase diagram is shown to be in broad agreement with the experimental trends. As the asymmetry of the lattice is increased the theory predicts the occurrence of a smectic A phase as well. The new smectic A phase is biaxial. (ii) A theoretical study of fluctuations in the columnar liquid crystal. It is shown that the Frank elasticity of the liquid-like columns stabilizes the two-dimensional order, a result that was in fact envisaged by Peierls and Landau in the 1930s. The mean- square fluctuation of the lattice as well as the Debye-Waller factor show a certain dependence on the linear dimensions of the sample.