Rojas-Gómez OA, Romero-Enrique JM. Generalized Berreman's model of the elastic surface free energy of a nematic liquid crystal on a sawtoothed substrate.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012;
86:041706. [PMID:
23214602 DOI:
10.1103/physreve.86.041706]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2012] [Revised: 10/05/2012] [Indexed: 06/01/2023]
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.
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