Splay-bend periodic deformation in nematic liquid crystal slabs

We predict a two-dimensional splay-bend periodic deformation in a nematic slab with homeotropic boundary conditions. The nematic director modulation is induced by surface contributions in the elastic energy, which are linear in the deformation tensor. The instability appears only if the surface anchoring energy strength is small enough, and if the two surfaces are different. The wave vector of the stripe modulation is proportional to the thickness of the nematic slab. The order of magnitude of the surface elastic constants relevant to the linear elastic terms in the deformation tensor, and the critical value of the anchoring energy, less than or similar to10(-6) J/m(2), to observe the instability are discussed.