Smectic liquid crystals free energy density

The free energy density terms introduced so far are all used in the description of the smectic phases made by rod-like molecules, the electrostatic term (6) being characteristic for the ferroelectric liquid crystals made of chiral rod-like molecules. To describe phases made by bent-core molecules one has to add symmetry allowed terms which include the divergence of the polar director (polarization splay) and coupling of the polar director to the nematic director and the smectic layer normal ... 

We first consider the temperature dependence of the tilt angle 0 of a liquid crystal that exhibits smectic-A and smectic-C. In smectic-A, the tilt angle is zero. The transition from smectic-A to smectic-C is a second-order transition. Below the transition, the tilt angle increases gradually with increasing temperature. The tilt angle, 6, can be used as the order parameter. Near the transition, the free energy density of the system can be expressed in terms of Landau expansion in the powers of 0 [15],... 

---