The phenomenon of anchoring in the nematic liquid crystal-amorphous substrate system is considered and model independent definitions of the surface nematic director, the surface tension and the anchoring energy coefficient are proposed. Then the Landau-de Gennes model of the system is studied for a specific choice of the surface parameters, which leads to a continuous homeotropic-conical ancoring transition. The free energy as a function of the director at a distance l from the surface is found. It is shown that its form is different in two regions of the temperature-distance plane separated by the line of a Frederiks transition. The asymptotic behavior of the free energy for large l and for infinitesimal deviations of the director from the anchoring direction is studied. It is found that the asymptotic formula holds also in the vicinity of the anchoring transition. Finally, the results of numerical studies of the Landau-de Gennes model are compared with the predictions of a simple phenomenological model.
A.Poniewierski and A.Samborski         LIQUID CRYSTAL, Vol. 23 ,377 (1997)