Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory
By Apala Majumdar. European journal of applied mathematics, 2008
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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.
Subfields: Ecology, Evolution, Behavior and Systematics, Electronic, Optical and Magnetic Materials, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/470fcc00ac582cb8c98227d2467ecd45df07332d
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Citations in the corpus
- Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory (2010, background): “temeratures quite close to the nematic-isotropic transition temperature [ 10 ].”
- Energy Dissipation and Regularity for a Coupled Navier–Stokes and Q-Tensor System (2010, unknown): “ ∂ Q ζδ∂ Q − δαβ d ∂ λQ ∂ Q +L∂ (Q αγ∆Q γβ−∆Q Q ) ∂γuγ = 0 (6) in Rd, d= 2,3. 2 We also need to assume from now on that c>0 (7) This assumption is necessary from a modelling point of view (see [20],[21] ) so that the energy F (see next section, relation (8)) is bounded from below, and it is als”