Behavior of the Goldstone mode in smectic-C* phase and the soft mode in the smectic-C* and smectic-A* phases of a ferroelectric liquid-crystal mixture

The complex dielectric permittivity has been measured as a function of temperature, and the bias electric field for a ferroelectric liquid-crystal mixture having low spontaneous polarization. By applying the I,ias electric field we have been able to measure the soft mode 2 degrees C inside the smectic-C* phase. From the experimental results, relaxation frequency and dielectric strength of the Goldstone mode in the Sm-C* phase and soft mode in the smectic-C* and smectic-A* phases have been determined. The parameter beta, which determines the importance of biquadratic coupling compared to the bilinear coupling of extended Landau model near to the transition temperature in the Sm-C* phase, has been determined from known valuer of spontaneous polarization and tilt angles at various temperatures. The experimental results have been compared to those of numerically calculated values and a good agreement between the results has been obtained. The Sm-C*-Sm-A* transition temperature T-C has been determined from the dielectric results. The deviation between the T-C determined experimentally and the T-C observed from texture studies is around 0.3 degrees C for the ferroelectric liquid-crystal mixture studied in this paper.