Structure of spontaneous periodic deformations in hybrid aligned nematic layers

Periodic deformations, arising spontaneously in hybrid nematic 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 gamma=Wd/k(11) defined for each boundary. The saddle-splay elastic constant k(24) was varied within the limits given by general Ericksen inequalities. The director distributions were calculated. Two structures with different properties were distinguished: one for k(24)<0 (mode 1) and the other for k(24)>0 (mode 2). For given nematic liquid crystal parameters, mode 1 existed when gamma exceeds some critical value. Below this critical gamma, 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 gamma. No upper limit of the gamma range in which mode 1 could exist was found. Mode 2 existed for gamma 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 k(24)>0 was sufficiently small, the gamma range was bounded from below, and a homogeneously planar orientation appeared for low gamma. The visibility of the stripes between crossed polarizers was estimated by calculations of light transmission. In general, the stripes for k(24)<0 turned out to be more distinct than that for k(24)>0.