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Multiscale approach to nematic liquid crystals via statistical field theory.
- Source :
-
Physical review. E [Phys Rev E] 2017 Aug; Vol. 96 (2-1), pp. 022709. Date of Electronic Publication: 2017 Aug 15. - Publication Year :
- 2017
-
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.
Details
- Language :
- English
- ISSN :
- 2470-0053
- Volume :
- 96
- Issue :
- 2-1
- Database :
- MEDLINE
- Journal :
- Physical review. E
- Publication Type :
- Academic Journal
- Accession number :
- 28950485
- Full Text :
- https://doi.org/10.1103/PhysRevE.96.022709