Goldstone mode and soft mode at the smectic-A–smectic-C/emph>phase transition studied by dielectric relaxation

The complex dielectric constant has been measured in a room-temperature ferroelectric liquid-crystal mixture. We have resolved the experimental data into the Goldstone mode and the soft mode and for each mode determined the dielectric strength and the corresponding relaxation frequency. The results are compared with the dielectric strength calculated using the extended Landau type of free-energy density proposed by Žekš [Mol. Cryst. Liq. Cryst. 114, 259 (1984)], and it is shown that this calculation is able to describe the experimental data well. We have shown that by reasonable assumptions we can derive a simple relation between the Goldstone-mode contribution to the dielectric susceptibility (${\chi }_2$) and the polarization ($P_0$), tilt (${\mathrm{theta}}_0$), and pitch (p) of the system: ${\mathrm{\chi }}_2$=(${\mathrm{P}}_0$p${\mathit{theta}}_0$ ${)}^2$/${8\mathrm{K}}_3$ ${\mathrm{\pi }}^2$), where $K_3$ is a bend nematic curvature elastic constant. We also predict, on theoretical grounds, a small peak of the dielectric strength to exist at $T_c$.