Shape of the nematic-isotropic interface in conditions of partial wetting

A nematic liquid crystal in contact with a solid substrate is studied in the partial wetting regime. Both a mesoscopic Landau-de Gennes theory and a macroscopic effective interface Hamiltonian approach are considered. A generalized Young equation for the balance of forces at the three-phase contact line is derived, which takes into account corrections due to distortions of the nematic director field. It is also shown that the asymptotic form of the separation of the nematic-isotropic interface from the substrate has a logarithmic correction to the usual linear behaviour. The characteristic length scale of this correction is given by the ratio K/(2σ_NI), where K and σ_NI are the average elastic constant and the nematic-isotropic surface tension, respectively, and is of the order of a few hundred angstroms. Then, a simple form of an effective interface Hamiltonian is proposed, and results consistent with the predictions of the Landau-de Gennes theory are obtained. It is shown, in the framework of this macroscopic approach, that the line tension associated with the contact line remains finite, when the thermodynamic limit is taken, if the anchoring at both the nematic-substrate and the nematic-isotropic interfaces is homeotropic. However, in the case of different anchoring directions, the line tension diverges logarithmically with the system size.