Critical reexamination of Berreman's theory on surface anchoring

We critically reexamine well-known Berreman's theory [Phys. Rev. Lett. 28, 1683 (1972)] on the anchoring of a nematic liquid crystal due to its elastic distortions induced by a sinusoidally grooved surface. We put emphasis on the effect of azimuthal distortions of the director n and the contribution of saddle-splay surface elasticity characterized by K24. We give a correct calculation of the anchoring energy and show that Berreman's theory gives a correct result only when K1=K2 and K24=0, where K1 and K2 are the splay and twist elastic constants, respectively. We also present our preliminary numerical attempts to evaluate the anchoring energy of a surface with square patterns and compare the anchoring energy calculated numerically with an analytical one obtained by a direct extension of our theoretical argument on one-dimensional parallel grooves.