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 bias electric field we have been able to measure the soft mode 2 ^∘{}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 {β}, 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 values 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 TC has been determined from the dielectric results. The deviation between the TC determined experimentally and the TC observed from texture studies is around 0.3 ^∘{}C for the ferroelectric liquid-crystal mixture studied in this paper. {} 1996 The American Physical Society.