Thermodynamic Model of Ferroelectric Chiral Smectic C* Liquid Crystals

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Abstract
A thermodynamic model of the ferroelectric SmC* phase, based on an extended Landau expansion of the free-energy density, is presented. We discuss how the signs of the parameters entering the model are depending on whether the pitch of the helix is right-handed or left-handed and whether the compound is of the (+) or (-) type in regard to the sign of the polarization. With the introduced Landau expansion as a basis, we derive the equations governing the behaviour of the tilt, polarization, pitch, dielectric susceptibility and heat capacity of the system. We show that by rewriting the equations into dimensionless form, we can transform the original set of eleven parameters in the Landau expansion into a new set, consisting of six dimensionless parameters and five scaling factors. The six dimensionless parameters are the only ones which enter the calculations of the quantities mentioned above, i.e. we need six dimensionless parameters to describe the temperature dependence of the five basic quantities of the system. By solving the governing equations we investigate the influence of the parameters on the behaviour of the system. We show that, concerning the calculation of tilt and polarization, only three paremeters have to be taken into account under reasonable assumptions. Furthermore we show, that the behaviour of the ratio polarization/tilt versus tilt-squared is determined by one parameter only. It is also shown that our model predicts, for large enough tilt, a sign reversal of the polarization. Finally a simple relation is derived, connecting the Goldstone mode part of the dielectric susceptibility lo the quantities polarization, tilt and pitch. This relation is verified as well by numerical calculations as by comparison to experimental data.