| 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.
for LaTeX users @article{PIlg2012-85,
author = {P. Ilg},
title = {Enhanced Landau–de Gennes potential for nematic liquid crystals from a systematic coarse-graining procedure},
journal = {Phys. Rev. E},
volume = {85},
pages = {061709},
year = {2012}
}
\bibitem{PIlg2012-85} P. Ilg,
Enhanced Landau–de Gennes potential for nematic liquid crystals from a systematic coarse-graining procedure,
Phys. Rev. E {\bf 85} (2012) 061709.PIlg2012-85
P. Ilg
Enhanced Landau–de Gennes potential for nematic liquid crystals from a systematic coarse-graining procedure
Phys. Rev. E,85,2012,061709 |
mk@mat.ethz.ch
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