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 ther mal average of the molecular tilt. The calculation leads to an equatio n of state for the smectic-C phase which is a self-consistent-held equ ation involving the Langevin function of a reduced tilt and a reduced temperature. This molecular-statistical approach of the smectic-C-smec tic-A phase transition is in principle analogous to a ferromagnetic ph ase transition with spin number S --> infinity. An excellent descripti on 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 optica l and by x-ray experiments originate from different moments of the til t angle distribution function and from different interaction parameter s for the mesogenic cores and the complete molecule.