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

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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

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Nematic liquid crystals
Nematic Liquid Crystal
Order Parameter
Scalar
Temperature
Explicit Bounds
Prediction
Energy Functional
Liquid Crystal
Quantify
Continuum
Tensor
Liquid crystals
Tensors
Moment
Predict
Three-dimensional
Configuration
Dependent
Geometry

Keywords

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

Cite this

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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.",
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Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory. / Majumdar, Apala.

In: European Journal of Applied Mathematics, Vol. 21, No. 2, 30.04.2010, p. 181-203.

Research output: Contribution to journalArticle

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AB - 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.

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