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We study the phase behavior of a nematic liquid crystal confined between aflat substrate with strong anchoring and a patterned substrate whose structureand local anchoring strength we vary. By first evaluating an effective surfacefree energy function characterizing the patterned substrate we derive anexpression for the effective free energy of the confined nematic liquidcrystal. Then we determine phase diagrams involving a homogeneous state inwhich the nematic director is almost uniform and a hybrid aligned nematic statein which the orientation of the director varies through the cell. Directminimization of the free energy functional were performed in order to test thepredictions of the effective free energy method. We find remarkably goodagreement between the phase boundaries calculated from the two approaches. Inaddition the effective energy method allows one to determine the energybarriers between two states in a bistable nematic device.

Effective free energy method for nematic liquid crystals in contact with structured substrates