The Mathematical Institute, University of Oxford, Eprints Archive

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

Majumdar, Apala (2009) Equilibrium order parameters of nematic liquid
crystals in the Landau-De Gennes theory.
Not specified . (Submitted)

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Abstract

We study equilibrium liquid crystal configurations in three-dimensional domains, 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 don’t 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.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:812
Deposited By:Dr M. Stoll
Deposited On:24 Sep 2009 13:32
Last Modified:24 Sep 2009 13:32

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