Extension of McMillan's model to liquid crystals of disc-like molecules

Abstract

McMillan's mean field model of smectic A is extended so that the translational order parameter is now periodic in two dimensions. The theory is developed for a face-centered rectangular lattice composed of liquid-like columns, taking the molecular cores to be circular discs normal to the columnar axes but with an asymmetrical disposition of the chains. When the axial ratio b/a =square root 3, the rectangular lattice reduces to a hexagonal one and the theory becomes essentially identical to that. proposed very recently by Feldkamp , Handschy and Clark. When b/a = square root 3 or departs from it only slightly, it turns out that 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 McMillanls theory, the phase diagram is in broad agreement with the trends exhibited by the hexa-n-alkoxybenzoates of triphenylene. For higher values of b/a the theory predicts a columnar-smectic A transition as well. The new smectic A phase is biaxial. The possibility of such a phase occurring in real systems is discussed briefly.