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)