Anchoring of a nematic liquid crystal induced by surface grooves: A numerical study

To examine the anchoring energy of a surface with one-dimensional grooves of sinusoidal shape, we carry out numerical calculation of the Frank elastic energy of a nematic cell composed of such a grooved surface and a flat surface. We evaluate the anchoring energy of the grooved surface by carefully eliminating the contribution from a uniform twist deformation in the bulk. When qA 0.2, with q and A being the wave number and the amplitude of the surface groove, we find that the azimuthal-angle dependence of the calculated anchoring energy agrees perfectly with our previous analytical result under the assumption of qA 1. Even when qA 0.6 or 1, we observe an unexpectedly good agreement between the calculated and the analytical anchoring energies, indicating the wide applicability of the analytical anchoring energy in spite of the assumption of qA 1 in its derivation.