A nematic liqiud crystal in contact with a solid substrate is studied by
means of the Landaude Gennes formalism. The freeenergy functional is expanded
around the bulk nematic order parameter up to the secondorder 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 semiinfinite 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.
