Dielectric response of ferroelectric∗_C liquid crystals in a bias electric field

Abstract

The dielectric response of the ferroelectric chiral smectic C phase in a bias electric field is studied theoretically within the Landau model using the constant amplitude approximation. It is argued that the response consists of two modes, one of which is related to the unwinding of the helix (the unwinding mode), whereas the other mode is associated with the distortion of the polarization distribution at constant pitch of the helix (the Goldstone mode). The relaxation frequency of the unwinding mode (fu), which is inversely proportional to the square of the sample dimension along the helical axis, is estimated to be of the order of 10⁻⁴Hz for a sample of length l≈ 1 mm along the helical axis. Consequently, in dielectric experiments performed usually at frequencies higher than fu, only the Goldstone mode contribution is detected. In this way, we can explain the behaviour of the measured static dielectric susceptibility which goes to zero as the critical field is approached from below, although the model predicts that the total static dielectric susceptibility, being a sum of the Goldstone mode and the unwinding mode contribution, diverges at the critical field.