Calculation of the tilt angle and susceptibility as functions of temperature and the electric field close to the Sm A – Sm C* transition in C7

Abstract

Smectic A-Smectic C * transition in the ferroelectric liquid crystal (C7) is studied as functions of the electric field and the temperature. By expanding the free energy in terms of the tilt angle ϴ (smectic C * phase) and the polarization P with a linear coupling between ϴ and P (Pϴ) in the mean field theory, the tilt angle is calculated as a function of the electric field (ϴ vs. E) at constant temperatures with respect to the transition temperature for C7 using the observed data from the literature. Also, by extracting the tilt angle from the observed electric displacements at various temperatures (at constant field strength), the inverse tilt angle susceptibility (χ ఏ ିଵ ) derived from the free energy, is fitted to the observed data for the dielectric constant and the fitted parameters are determined. Our calculated ϴ and χ ఏ show that the mean field theory explains adequately the observed behavior of the Smectic A-Smectic C * transition in the liquid crystals C7.