Molecular models for the smectic A-smectic C phase transition in a system of biaxial molecules

A molecular theory of the smectic A-smectic C transition in a system of biaxial molecules is developed in the mean-field approximation. The influence of molecular biaxiality on the transition is considered in detail and it is demonstrated how the biaxial order parameters are induced by the tilt. It is shown that the ordering of biaxial molecules of low symmetry in the smectic C phase is generally described by ten independent orientational order parameters, and there exist three different tilt angles which specify the tilt of three ordering tensors. The order parameters are calculated numerically as functions of temperature for two models of biaxial molecules: molecules with two principal axes and molecules with a pair of off-center transverse dipoles. A substantial difference between the three tilt angles is found, which makes impossible a strict definition of a unique director in the smectic C phase. It is also shown that biaxial interactions may lead to an anomalously weak layer contraction in the smectic C phase. Finally, it is demonstrated that the smectic A-smectic C phase transition may be directly driven by biaxial intermolecular interactions. In this case, the tilt of long molecular axes is not a primary order parameter, and its temperature dependence is very different from convention.