Landau–de Gennes theory of wetting and orientational transitions at a nematic-liquid–substrate interface

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Abstract
The surface phases of a nematic liquid in the presence of a smooth substrate are studied using Landau–de Gennes theory. The alignment of the nematic director is restricted to be either parallel or perpendicular to the substrate, although methods of treating more general structures are indicated. We describe extensions and a synthesis of earlier studies which obtained analytic solutions of the theory in certain limits, including surface-induced biaxiality, to determine the domains of wetting by planar and homeotropic nematic films as well as by the isotropic phase, as a function of surface-interaction parameters. The relation of wetting to orientational transitions in the surface-induced bulk alignment is discussed. The ‘‘parabolic approximation’’ recently introduced in related contexts is used to obtain solutions of the theory in more general circumstances where exact analytic solutions are precluded. It is found that, for realistic values of the ratio of model elastic constants, complete wetting by planar nematic films exhibits ‘‘reentrant’’ behavior and does not occur for arbitrarily strong substrate potentials. We argue that this outcome is not an artifact of the parabolic approximation, despite several deficiencies of the method. The relevance to experimental studies of nematic-liquid–substrate interfaces is described.