STOCHASTIC CONTRIBUTION TO THE ANCHORING ENERGY - DEVIATION FROM THE RAPINI-PAPOULAR EXPRESSION

The effect of a stochastic contribution to the surface energy, coming from the direct interaction between an orienting film and a solid subs trate, is considered. It is shown that in the hypothesis in which the nematic liquid crystal orientation coincides with the film orientation , the well known Rapini-Papoular expression for the anisotropic part o f the surface energy is modified. More precisely the anchoring strengt h, connected with the square of the sine of the deformation angle, is renormalized. Furthermore, there appears an additional contribution, p roportional to the fourth power of the same quantity, whose coefficien t is equal in modulus and opposite in sign. The physical origin of the considered effect is connected with the elastic contribution to the s urface energy of the film.