Orientational instability of a lyotropic nematic liquid crystal layer

The problem of periodic domain initiation in a thin lyotropic nematic liquid crystal layer is studied. This layer has a planar director initial orientation, but the anchoring energy is minimized by the homeotropic one. The periodic structures with the perpendicular to the director wave vector exist during the director reorientation process from the planar orientation to the homeotropic one when the reorientation wave front appears. It is shown that the divergent terms of the Frank orientation elasticity energy plays an important role in this effect. The saddle-splay Frank constant and the anisotropic anchoring energy coefficient are estimated.