Molecular-statistical description of the smectic-A–smectic-C phase transition

A simple molecular-statistical model of the smectic-A--smectic-C phase transition is proposed. Assuming a bilinear mean-field potential, the macroscopic tilt angle is calculated by Boltzmann statistics as a thermal average of the molecular tilt. The calculation leads to an equation of state for the smectic-C phase which is a self-consistent-field equation involving the Langevin function of a reduced tilt and a reduced temperature. This molecular-statistical approach of the smectic-C--smectic-A phase transition is in principle analogous to a ferromagnetic phase transition with spin number S{→}{∞}. An excellent description of experimental tilt angle data for the complete temperature range of the smectic-C phase is achieved with only one or two fit parameters, respectively. Differences between tilt angle data obtained by optical and by x-ray experiments originate from different moments of the tilt angle distribution function and from different interaction parameters for the mesogenic cores and the complete molecule.