title: Generalized Berreman's model of the elastic surface free energy of a nematic liquid crystal on a sawtoothed substrate.
abstract: In this paper we present a generalization of Berreman's model for the elastic contribution to the surface free-energy density of a nematic liquid crystal in presence of a sawtooth substrate which favors homeotropic anchoring as a function of the wave number of the surface structure q, the tilt angle α, and the surface anchoring strength w. In addition to the previously reported nonanalytic contribution proportional to -q ln q, due to the nucleation of disclination lines at the wedge bottoms and apexes of the substrate, the next-to-leading contribution is proportional to q for a given substrate roughness, in agreement with Berreman's predictions. We characterize this term, finding that it has two contributions: the deviations of the nematic director field with respect to a reference field corresponding to the isolated disclination lines and their associated core free energies. Comparison with the results obtained from the Landau-de Gennes model shows that our model is quite accurate in the limit wL>1, when strong anchoring conditions are effectively achieved.
authors.affiliation: Departamento de Física Atómica, Molecular y Nuclear, Area de Física Teórica Universidad de Sevilla, Apartado de Correos 1065, 41080 Sevilla, Spain.
authors.forename: O A
authors.initials: OA
authors.lastname: Rojas-Gómez
authors.forename: J M
authors.initials: JM
authors.lastname: Romero-Enrique