Simple model for the polarization reversal current in a ferroelectric liquid crystal

The spontaneous ferroelectric polarization in the chiral smectic-C phase can be measured by monitoring the dynamic response to a changing electric field. A model for the system is presented and analyzed for the two cases of square-wave and sinusoidal voltage applied to a ``bookshelf geometry'' sample, where the smectic layers are oriented relative to the glass plates as books are to a shelf. The model gives a good description for the observed polarization reversal current and yields the rotational viscosity and one effective elastic constant in addition to the spontaneous polarization. Relations between these parameters and the width of the observed hysteresis loop are derived as well as relations for the contribution of the ferroelectric polarization to the permittivity. The model is applied in evaluating data from measurements on the substance MBRA-8 [2-hydroxy-4(2-methyl-butyloxy)-benzylidene-4-p-n-octyl-aniline].