Microscopic origin of spontaneous polarization in ferroelectric SC* liquid crystals

The origin of spontaneous polarization in the ferroelectric smectic C* phase is investigated within a mean-field microscopic model which describes the coupling between the tilt of molecules from the normal to the smectic layers and the rotation of a molecule around its long axis. The mean-field potential is studied which takes into account a chiral polar and a non-chiral quadrupolar biasing of the rotation of molecules around the molecular long axes. Each molecule is characterized by three transverse molecular axes: the chiral axis which turns parallel to the macroscopic C₂ axis at small tilts, the polar axis in the direction of the transverse dipole moment and the quadrupolar axis which tends to be parallel to the C₂ axis at very large tilts. A numerical analysis of the model shows that there are four different types of spontaneous polarization dependent on the temperature, including the sign-reversal type. The influence of three microscopic parameters, i.e. two angles between the three characteristic axes and the relative strength of the chiral versus the non-chiral biasing, on the type of spontaneous polarization is investigated. The relationship between the microscopic and the equivalent Landau model is established and discussed.