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  • Title: Enhanced Landau-de Gennes potential for nematic liquid crystals from a systematic coarse-graining procedure.
    Author: Ilg P.
    Journal: Phys Rev E Stat Nonlin Soft Matter Phys; 2012 Jun; 85(6 Pt 1):061709. PubMed ID: 23005116.
    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.
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