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

Abstract

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 $\mathbf{Q}$-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 $\mathbf{Q}$. This ensures a physically valid order parameter $\mathbf{Q}$ (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.

37 pages, 8 figures

References in corpus (3)

• Spontaneous motion in hierarchically assembled active matter
• Introduction to Q-tensor theory
• Anisotropic disclination cores in nematic liquid crystals modelled by a self consistent molecular field theory

Cited by in corpus (5)

• Singularity identification for the characterization of topology, geometry, and motion of nematic disclination lines
• Kinematics and dynamics of disclination lines in three-dimensional nematics
• Equilibrium morphology of tactoids in elastically anisotropic nematics
• A computational study of nematic core structure and disclination interactions in elastically anisotropic nematics
• Approach and rotation of reconnecting topological defect lines in liquid crystal