A nematic liqiud crystal in contact with a solid substrate is studied by means of the Landau-de Gennes formalism. The free-energy functional is expanded around the bulk nematic order parameter up to the second-order terms. This approximation is used to obtain an explicit condition for the achoring direction in terms of the surface and bulk coupling constants, in a semi-infinite system. Then a finite system is studied and the equilibrium free energy is found as a function of the angular deviation from the anchoring direction and the sample thickness. A geometrical measure of the anchoring strength, resembling the de Gennes extrapolation length, is obtained from the asymptotic behaviour of the free energy for large sample thicknesses.
A.Poniewierski and A.Samborski      PHYSICAL REVIEW E, Vol. 53 , 2436, (1996)