On the Elastic Free Energy Expression of Biaxial Smectic Liquid Crystals

In this work, a complete expression of the elastic free energy of the biaxial smectics is derived within a quadratic expansion in terms of the spatial derivatives of the biaxial tensor order parameter. It is found that there exist 25 non-chiral terms, 5 of which are found to eventually be reduced as surface contributions, and 5 chiral terms in bulk elastic energy. In a uniform helicoidal state with a flat layer structure, the helical pitch is expressed as a function of the molecular tilt angle and the microscopic order parameters related to the uniaxial and biaxial molecular orderings. According to the present result, the temperature dependence of the helical pitch in SmC * or SmC A * phase is found to result from an anisotropy of the elastic constants concerned with the molecular orientation and the biaxial molecular ordering.