The effect of the sample thickness on the collective modes in ferroelectric liquid crystals

Complex permittivity epsilon* has been studied in the vicinity of the SmA-S mC* phase transition for samples 6, 12, 25, 50, and 100 mu m thick. In the studied frequency range of (10(1) - 10(6)) Hz the relaxation of collective modes, namely the soft, Goldstone and/or "thickness" modes, occurs. From th e frequency dependence of epsilon* the relaxation frequency, f(r) and diele ctric strength, Delta epsilon, of these modes are determined in dependence of temperature and the sample thickness. Results are discussed on the basis of a phenomenological theory taking into account surface interactions.