Dielectric relaxation and rotational viscosity of a ferroelectric liquid crystal mixture

The dielectric permittivities have been measured over a wide temperature range of a ferroelectric liquid crystal mixture having low spontaneous polarization in its smectic-${\mathit{C}}^{\mathrm{*}}$ (Sm-${\mathit{C}}^{\mathrm{*}}$) and smectic-A (Sm-A) phases on planar alignment. The measuring electric field is parallel to the layer plane. In this particular geometry of the cell, the well-known Goldstone relaxation mode has been observed in the Sm-${\mathit{C}}^{\mathrm{*}}$ phase. Due to very low spontaneous polarization of molecules of this sample, we could not observe any soft mode in the Sm-${\mathit{C}}^{\mathrm{*}}$ phase even very near the Sm-${\mathit{C}}^{\mathrm{*}}$–Sm-A transition temperature. The soft mode, however, is observed at the transition and a few degrees above the transition temperature. In addition to the soft mode and the Goldstone mode, we have observed another high frequency relaxation mode in both smectic phases. The dielectric strength as well as the corresponding relaxation frequencies of the modes have been calculated. The Goldstone mode rotational viscosity has been determined using evaluation models from dielectric results.