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arXiv · 2002.11855

Computational molecular field theory for nematic liquid crystals

Cody D. Schimming·Jorge Viñals
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Abstract

Nematic liquid crystals exhibit configurations in which the underlying ordering changes markedly on macroscopic length scales. Such structures include topological defects in the nematic phase and tactoids within nematic-isotropic coexistence. We discuss a computational study of inhomogeneous configurations that is based on a field theory extension of the Maier-Saupe molecular model of a uniaxial, nematic liquid crystal. A tensor order parameter is defined as the second moment of an orientational probability distribution, leading to a free energy that is not convex within the isotropic-nematic coexistence region, and that goes to infinity if the eigenvalues of the order parameter become non-physical. Computations of the spatial profile of the order parameter are presented for an isotropic-nematic interface in one dimension, a tactoid in two dimensions, and a nematic disclination in two dimensions. We compare our results to those given by the Landau de-Gennes free energy for the same configurations and discuss the advantages of such a model over the latter.

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Cody D. Schimming, Jorge Viñals. 2020-02-27. Computational molecular field theory for nematic liquid crystals. https://doi.org/10.1103/physreve.101.032702

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