Structure of spontaneous periodic deformations in hybrid aligned nematic layers

Periodic deformations, arising spontaneously in hybrid nernatic layers were investigated numerically. So called splay stripes, which appear when the surface anchoring energy of the planar alignment was greater than that of the homeotropic alignment, were considered. Conical degeneration of the anchoring is assumed. The role of the layer thickness d and the anchoring strength W was studied by means of the dimensionless control parameter γ=Wdlk₁₁ defined for each boundary. The saddle-splay elastic constant k₂₄ was varied within the limits given by general Ericksen inequalities. The director distributions were calculated. Two structures with different properties were distinguished: one for k₂₄<0 (mode 1) and the other for k₂₄>0 (mode 2). For given nematic liquid crystal parameters, mode 1 existed when γ exceeds some critical value. Below this critical γ, the director distortion decayed and the spatial period simultaneously diverged to infinity. As a result mode 1 disappeared and the homogeneously planar orientation was realized. The width of the stripes also increased infinitely for high γ. No upper limit of the γ range in which mode 1 could exist was found. Mode 2 existed for γ ranging from 0 to a certain critical value. Above this limit the periodic structure was replaced by the homogeneous hybrid alignment as a consequence of an infinite increase of the stripes' width. When k₂₄>0 was sufficiently small, the γ range was bounded from below, and a homogeneously planar orientation appeared for low γ. The visibility of the stripes between crossed polarizers was estimated by calculations of light transmission. In general, the stripes for k₂₄<0 turned out to be more distinct than that for k₂₄>0.