Surface-groove-induced azimuthal anchoring of a nematic liquid crystal: Berreman's model reexamined

To account for azimuthal surface anchoring of a nematic liquid crystal, Berreman [Phys. Rev. Lett. 28, 1683 (1972)] proposed a simple model attributing the surface anchoring to the elastic distortion of the liquid crystal induced by the grooves of a surface. He showed that the surface anchoring energy is proportional to sin(2)phi, with phi being the angle between the director at infinity and the direction of the surface grooves. We argue that his assumption of negligibly small azimuthal distortion of the nematic is not valid. Proper treatment of the azimuthal distortion reveals that the Berreman's model should yield a surface anchoring energy proportional to sin(4)phi. This implies that surface grooves alone cannot contribute to the surface anchoring coefficient in the usual Rapini-Papoular sense.