Numerical method for the equilibrium configurations of a Maier-Saupe bulk potential in a Q-tensor model of an anisotropic nematic liquid crystal

We present a numerical method, based on a tensor order parameter description of a nematic phase, that allows fully anisotropic elasticity. Our method thus extends the Landau-de Gennes Q-tensor theory to anisotropic phases. A microscopic model of the nematogen is introduced (the Maier-Saupe potential in the case discussed in this paper), combined with a constraint on eigenvalue bounds of Q. This ensures a physically valid order parameter Q(i.e., the eigenvalue bounds are maintained), while allowing for more general gradient energy densities that can include cubic nonlinearities, and therefore elastic anisotropy. We demonstrate the method in two specific two dimensional examples in which the Landau-de Gennes model including elastic anisotropy is known to fail, as well as in three dimensions for the cases of a hedgehog point defect, a disclination line, and a disclination ring. The details of the numerical implementation are also discussed. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This study presents a numerical method based on a tensor order parameter description for achieving fully anisotropic elasticity, extending the Landau-de Gennes Q-tensor theory to anisotropic phases. By introducing a microscopic model of the nematogen and a constraint on eigenvalue bounds of Q, physically valid order parameter Q is ensured while allowing for more general gradient energy densities. The method is demonstrated in specific two-dimensional examples and in three dimensions for various defect cases, showing successful results in cases where the Landau-de Gennes model with elastic anisotropy fails.