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

Cody D. Schimming, Jorge Viñals, Shawn W. Walker

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish (US)
Article number110441
JournalJournal of Computational Physics
Volume441
DOIs
StatePublished - Sep 15 2021

Bibliographical note

Funding Information:
C.D. Schimming acknowledges financial support by NSF DMR-1838977.J. Vi?als acknowledges financial support by NSF DMR-1838977.S.W. Walker acknowledges financial support by the NSF DMS-1555222 (CAREER).

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

  • Defects
  • Finite element method
  • Landau-de Gennes
  • Liquid crystals
  • Singular bulk potential

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