2016-04-042016-04-042012Rojas-Gómez, O.A. y Romero Enrique, J.M. (2012). Generalized Berreman's model of the elastic surface free energy of a nematic liquid crystal on a sawtoothed substrate. Physical Review E - Statistical, 86 (4), 041706-1-041706-10.1539-3755http://hdl.handle.net/11441/39437In 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 achievedapplication/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttp://dx.doi.org/10.1103/PhysRevE.86.041706https://idus.us.es/xmlui/handle/11441/39437