Uniform theory of V-shape characteristics

The purpose of this article is to develop a simple theory for V-shape in (A)FLC materials. This is the so-called “uniform” theory, which means that the director orientations are assumed to be independent of the depth into the liquid crystal. V-shape requires a strong polar interaction with the alignment layers. However this cannot be incorporated in the uniform theory, but it was shown in the literature that it can be represented, at least qualitatively, by a fictitious negative non-polar interaction coefficient. It is first shown how extremely simple the FLC-V-shape can be explained analytically. For AFLC-V-shape, we need a smectic layer interaction energy described by an antiferroelectric term A and a quadrupolar term Q. It is shown that if A > 2Q the return of the Ferroelectric up-state to the splayed state at the tip of the V is antiferroelectric, and if A < 2Q it is ferroelectric. The analytical results are confirmed by a non-uniform computer simulation. These models do not contain the possibility of...