  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.
