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

APALA MAJUMDAR

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84 Scopus citations

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 (US)
Pages (from-to)181-203
Number of pages23
JournalEuropean Journal of Applied Mathematics
Volume21
Issue number2
DOIs
StatePublished - 2010
Externally publishedYes

ASJC Scopus subject areas

  • Applied Mathematics

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