The Landau-de Gennes approach revisited : A minimal self-consistent microscopic theory for spatially inhomogeneous nematic liquid crystals

We design a novel microscopic mean-field theory of inhomogeneous nematic liquid crystals formulated entirely in terms of the tensor order parameter field. It combines the virtues of the Landau-de Gennes approach in allowing both the direction and magnitude of the local order to vary, with a self-consistent treatment of the local free-energy valid beyond the small order parameter limit. As a proof of principle, we apply this theory to the well-studied problem of a colloid dispersed in a nematic liquid crystal by including a tunable wall coupling term. For the two-dimensional case, we investigate the organization of the liquid crystal and the position of the point defects as a function of the strength of the coupling constant.