A Theoretical Study of Smectic Focal Domains

A theoretical study of the c -director and the layer structure in a biaxial smectic focal domain is presented on the basis of a simple elastic theory. A transformation between the Cartesian coordinates and an orthogonal curvilinear system is derived to provide a family of quadratic surface equations representing the Dupin cyclydes. Certain constraints for some of the elastic constants are found to be satisfied in SmC elliptic focal domain to support a uniform molecular alignment corresponding to an equilibrium state. On the other hand, it is shown that there exists no constraint of the elastic constants for biaxial SmA elliptic domain, or a torus domain in SmC phase as well as the biaxial SmA phase. These conclusions are found to be consistent with the experimental findings by Bourdon et al . with SmA and SmC focal domains.