SmA--SmC^* Phase Transitions in Liquid Crystals

Abstract

For the SmA--SmC^* phase transition in liquid crystals, the free energy can be expanded in powers of two order parameters, namely, the tilt angle \theta and the polarization P, In this free energy, we have taken a nonlinear coupling between P and \theta. We have obtained the temperature dependence of P and \theta by fitting to the experimental data for a single component liquid crystal. We have also studied a binary mixture of liquid crystals under the influence of an applied electric field. Using the same free energy, we have obtained the electric field dependence of tilt angle and concentration dependence of polarization by fitting to the experimental data. For this mixture of liquid crystals, we have also deduced the critical exponents \beta for the polarization, \gamma for the susceptibility and the critical isotherm \delta.