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Elastic Anchoring Energy Related to Orientational Order Parameter of Nematic Liquid Crystal

The elastic strain energy density of liquid crystal molecules in the vicinity of the interface between a solid surface and nematic liquid crystal is investigated. The elastic strain energy density for various surface topographies is related analytically to the orientational order parameter by assuming a Gaussian distribution of liquid crystal molecules around the director along the direction of the periodic grooves on the substrate. From the measured orientational order parameter in the surface region and the analytical relation, we determine quantitatively the elastic strain energy density of the surface induced nematic liquid crystal.