ANCHORING OF NEMATIC LIQUID-CRYSTALS AT A SOLID SUBSTRATE

A nematic liquid 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 conditio n for the anchoring direction in terms of the surface and bulk couplin g constants, in a semi-infinite system. Then a finite system is studie d and the equilibrium free energy is found as a function of the angula r deviation from the anchoring direction and the sample thickness. A g eometrical measure of the anchoring strength, resembling the de Gennes extrapolation length, is obtained from the asymptotic behavior of the free energy for large sample thicknesses.