Nematic liquid crystals : from Maier-Saupe to a continuum theory
We define a continuum energy functional in terms of the mean-field Maier-Saupe free energy, that describes both spatially homogeneous and inhomogeneous systems. The Maier-Saupe theory defines the main macroscopic variable, the Q-tensor order parameter, in terms of the second moment of a probabil...
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| Format: | Journal article |
| Published: |
2009
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| Summary: | We define a continuum energy functional in terms of the mean-field Maier-Saupe free energy, that describes both spatially homogeneous and inhomogeneous systems. The Maier-Saupe theory defines the main macroscopic variable, the Q-tensor order parameter, in terms of the second moment of a probability distribution function. This definition requires the eigenvalues of Q to be bounded both from below and above. We define a thermotropic bulk potential which blows up whenever the eigenvalues tend to these lower and upper bounds. This is in contrast to the Landau-de Gennes theory which has no such penalization. We study the asymptotics of this bulk potential in different regimes and discuss phase transitions predicted by this model. |
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