Liquid crystal pretilt control by inhomogeneous surfaces
  We consider the pretilt alignment of nematic liquid crystal (LC) on inhomogeneous surface patterns comprising patches of homeotropic or homogeneous alignment domains, with azimuthal anisotropy assumed in the surface plane. We found that the resultant LC pretilt generally increases continuously from the homogeneous limit to the homeotropic limit as the area fraction of the homeotropic region increases from 0 to 1. The variations are qualitatively different depending on how the distance between patches compares to the extrapolation length of the stronger anchoring domain. Our results agree with those previously found in stripped patterns. The present findings may provide useful guidelines for designing inhomogeneous alignment surfaces for variable LC pretilt control - a subject of much technological interest in recent years. 
Jones T. K. Wan, Ophelia K. C. Tsui, Hoi-Sing Kwok, Ping Sheng