title: Enhanced Landau-de Gennes potential for nematic liquid crystals from a systematic coarse-graining procedure.
abstract: The macroscopic theory of nematics is conveniently described in terms of the phenomenological Landau-de Gennes free energy. Here we show how such an effective free energy can be obtained explicitly from a microscopic model via the help of a systematic coarse-graining procedure. We test our approach for the two- and three-dimensional Lebwohl-Lasher model of nematics. The effective free energy that we obtain is consistent with the phenomenological Landau-de Gennes form for weak orientational ordering and the Maier-Saupe theory of the isotropic-nematic transition. For strong orientational ordering, however, the effective free energy increases rapidly and diverges logarithmically near the fully oriented state. The explicit form for the regularized Landau-de Gennes potential proposed here restricts the order parameter to physical admissible values and reproduces our numerical data accurately.
authors.affiliation: ETH Zürich, Department of Materials, Polymer Physics, HCI H541, CH-8093 Zürich, Switzerland.
authors.forename: Patrick
authors.initials: P
authors.lastname: Ilg
mesh_terms: D003198:Computer Simulation; D004735:Energy Transfer; D050866:Liquid Crystals / Q000737:chemistry*; D008422:Materials Testing / Q000379:methods*; D008956:Models, Chemical; D008958:Models, Molecular