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  • Title: Multiscale approach to nematic liquid crystals via statistical field theory.
    Author: Lu BS.
    Journal: Phys Rev E; 2017 Aug; 96(2-1):022709. PubMed ID: 28950485.
    Abstract:
    We propose an approach to a multiscale problem in the theory of thermotropic uniaxial nematics based on the method of statistical field theory. This approach enables us to relate the coefficients A, B, C, L_{1}, and L_{2} of the Landau-de Gennes free energy for the isotropic-nematic phase transition to the parameters of a molecular model of uniaxial nematics, which we take to be a lattice gas model of nematogenic molecules interacting via a short-ranged potential. We obtain general constraints on the temperature and volume fraction of nematogens for the Landau-de Gennes theory to be stable against molecular orientation fluctuations at quartic order. In particular, for the case of a fully occupied lattice, we compute the values of the isotropic-nematic transition temperature and the order parameter discontinuity predicted by (i) a continuum approximation of the nearest-neighbor Lebwohl-Lasher model and (ii) a Lebwohl-Lasher-type model with a nematogenic interaction of finite range. We find that the predictions of (i) are in reasonably good agreement with known results of Monte Carlo simulation.
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