Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory

Research output: Contribution to journalArticle

75 Citations (Scopus)

Abstract

We study equilibrium liquid crystal configurations in three-dimensional geometries, within the continuum Landau-de Gennes theory. We obtain explicit bounds for the equilibrium scalar order parameters in terms of the temperature and material-dependent constants. We explicitly quantify the temperature regimes where the Landau-de Gennes predictions match and the temperature regimes where the Landau-de Gennes predictions do not match the probabilistic second-moment definition of the Q-tensor order parameter. The regime of agreement may be interpreted as the regime of validity of the Landau-de Gennes theory since the Landau-de Gennes theory predicts large values of the equilibrium scalar order parameters – larger than unity, in the low-temperature regime. We discuss a modified Landau-de Gennes energy functional which yields physically realistic values of the equilibrium scalar order parameters in all temperature regimes.
Original languageEnglish
Pages (from-to)181-203
Number of pages23
JournalEuropean Journal of Applied Mathematics
Volume21
Issue number2
Early online date25 Feb 2010
DOIs
Publication statusPublished - 30 Apr 2010

Keywords

  • nematic liquid crystals
  • order parameters
  • equilibrium configurations
  • Landau–De Gennes theory

Fingerprint Dive into the research topics of 'Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory'. Together they form a unique fingerprint.

Cite this