Variational problems and modeling of ferroelectricity in chiral smectic C liquid crystals

This article deals with modeling and analysis of chiral smectic C liquid crystals and their ferroelectric phases. The polarization field plays an important role in the problem. The total energy of the smectic C* contains the Oseen-Frank free energy of the nematic, together with smectic terms quadratic in the second order gradient,,; of the complex wave function describing smectic layering, and expression for the surface energy. In addition, the polar self-interaction is taken into account, together with the electrostatic energy associated with an external electric field. The case of spatial variable electric fields is also addressed. Stability properties of the solutions are discussed to determine the interplay between the surface and electric energy terms. The physically relevant boundary conditions of the admissible fields bring out analogies to the problems of vortex tubes and vortex sheets in fluid mechanics.