Liquid crystal smectic-A phases and issues of geometry

Abstract

A simple density functional theory (DFT) is applied to an analysis of the isotropic, nematic and smectic-A phase transitions in single component systems comprised of hard convex bodies. In the chosen DFT, the exact orientation dependent second virial coefficient is used together with an approximation due to Parsons which subsumes some of the three, four, etc., body correlations. The reported calculations are performed for particles with varying shapes: an ellipsoid, a spherocylinder and an ‘ellipo-cylinder’ (a geometry intermediate between an ellipsoid and a spherocylinder). Transition densities are calculated for the first order isotropic to nematic transition and for the second order nematic to smectic-A transition. The wavelength associated with the smectic period is also determined. Both the perfectly aligned and the orientationally unconstrained nematic phases are considered as precursors of the smectic phase. The hard ellipsoid undergoes transition (in the aligned and freely rotating systems) from t...