A molecular field theory of smectic A liquid crystals

A molecular theory for smectic A liquid crystals is described which starts from an expression for the internal energy in terms of the orientational and translational order parameters. This expression is used to determine the single particle distribution function by invoking the molecular field approximation. The relationship of this model to the McMillan theory of smectic A liquid crystals which contains an additional mixed order parameter is explained. The predictions of our theory have been explored for a wide range of the strength parameters occurring in it. The phase diagram which contains isotropic, nematic, smectic A and plastic crystal phases has been constructed and the properties of the smectic A-nematic transition evaluated in detail; these include the second order transition temperatures and tricritical point, the entropy of transition and the change in the order parameters. Such properties, which have been determined both numerically and analytically, are found to be in good agreement with the predictions of McMillan's theory for a wide range of the strength parameters. Finally the analytic results for the smectic A-nematic transition are used to show that this molecular theory cannot on its own, account for the observation of re-entrant nematic and smectic A phases. However we show that re-entrant polymorphism is possible if the strength parameters are allowed to vary with temperature.