Anchoring transitions and periodic deformations in nematic slabs

Elastic energy terms linear in the deformation tensor can appear in an ultrathin layer at the interface of a nematic liquid crystal with a substrate. These Lifchitz invariant like terms can destroy an initially uniform alignment. In particular, they can induce modulated structures. The instability towards a periodic deformation of the nematic director can occur only if the anchoring energy is lower, and the elastic constant of the Lifchitz term is larger than well-defined critical values. The present phenomenological model accounts for experimental observations where a homeotropic slab undergoes, upon cooling, a tilt transition followed by a structural transition towards a stripe texture