Analysis of nonlocal electrostatic effects in chiral smectic C liquid crystals

We present modeling and analysis of smectic C phases of liquid crystals capable of sustaining spontaneous polarization. The layered liquid crystals are also assumed to be chiral. We study minimization of the total energy subject to electrostatic constraints. In order to determine mathematically and physically relevant boundary conditions, we appeal to the analogy between the current problem and the vorticity in fluids. We place a special emphasis on the nonlocal and self-energy effects arising from spontaneous polarization. We discuss examples pertaining to the electric field created by the liquid crystal in dielectric medium, and also to the possible role of a domain shape as an energy reduction mechanism.