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Dilution of nematic surface potentials: statics

The weak anchoring of a nematic liquid crystal is further illuminated by studying the consequences of finite-range surface torques. It is shown that the actual decay law of a diluted surface potential has little influence on either the equilibrium profile and the saturation field, provided that the range of the potential is small compared to the surface extrapolation length. This appears as a possible way to extend the conventional Rapini-Papoular model without altering its predictions away from the boundary. The net advantage of a dilution model is to better understand surface phenomena, which indeed pertain to a thin boundary layer.