Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory
We define a continuum energy functional that effectively interpolates between the mean-field Maier-Saupe energy and the continuum Landau-de Gennes energy functional and can describe both spatially homogeneous and inhomogeneous systems. In the mean-field approach the main macroscopic variable, the Q-...
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| Format: | Conference item |
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2010
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| _version_ | 1797094040608440320 |
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| author | Ball, J Majumdar, A |
| author_facet | Ball, J Majumdar, A |
| author_sort | Ball, J |
| collection | OXFORD |
| description | We define a continuum energy functional that effectively interpolates between the mean-field Maier-Saupe energy and the continuum Landau-de Gennes energy functional and can describe both spatially homogeneous and inhomogeneous systems. In the mean-field approach the main macroscopic variable, the Q-tensor order parameter, is defined in terms of the second moment of a probability distribution function. This definition imposes certain constraints on the eigenvalues of the Q-tensor order parameter, which may be interpreted as physical constraints. We define a thermotropic bulk potential which blows up whenever the eigenvalues of the Q-tensor order parameter approach physically unrealistic values. As a consequence, the minimizers of this continuum energy functional have physically realistic order parameters in all temperature regimes. We study the asymptotics of this bulk potential and show that this model also predicts a first-order nematic-isotropic phase transition, whilst respecting the physical constraints. In contrast, in the Landau-de Gennes framework the Q-tensor order parameter is often defined independently of the probability distribution function, and the theory makes physically unrealistic predictions about the equilibrium order parameters in the low-temperature regime. Copyright © Taylor and Francis Group, LLC. |
| first_indexed | 2024-03-07T04:08:36Z |
| format | Conference item |
| id | oxford-uuid:c70d5bc2-a21f-4672-ae0b-d73493f331cb |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:08:36Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:c70d5bc2-a21f-4672-ae0b-d73493f331cb2022-03-27T06:42:19ZNematic Liquid Crystals: From Maier-Saupe to a Continuum TheoryConference itemhttp://purl.org/coar/resource_type/c_5794uuid:c70d5bc2-a21f-4672-ae0b-d73493f331cbSymplectic Elements at Oxford2010Ball, JMajumdar, AWe define a continuum energy functional that effectively interpolates between the mean-field Maier-Saupe energy and the continuum Landau-de Gennes energy functional and can describe both spatially homogeneous and inhomogeneous systems. In the mean-field approach the main macroscopic variable, the Q-tensor order parameter, is defined in terms of the second moment of a probability distribution function. This definition imposes certain constraints on the eigenvalues of the Q-tensor order parameter, which may be interpreted as physical constraints. We define a thermotropic bulk potential which blows up whenever the eigenvalues of the Q-tensor order parameter approach physically unrealistic values. As a consequence, the minimizers of this continuum energy functional have physically realistic order parameters in all temperature regimes. We study the asymptotics of this bulk potential and show that this model also predicts a first-order nematic-isotropic phase transition, whilst respecting the physical constraints. In contrast, in the Landau-de Gennes framework the Q-tensor order parameter is often defined independently of the probability distribution function, and the theory makes physically unrealistic predictions about the equilibrium order parameters in the low-temperature regime. Copyright © Taylor and Francis Group, LLC. |
| spellingShingle | Ball, J Majumdar, A Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory |
| title | Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory |
| title_full | Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory |
| title_fullStr | Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory |
| title_full_unstemmed | Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory |
| title_short | Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory |
| title_sort | nematic liquid crystals from maier saupe to a continuum theory |
| work_keys_str_mv | AT ballj nematicliquidcrystalsfrommaiersaupetoacontinuumtheory AT majumdara nematicliquidcrystalsfrommaiersaupetoacontinuumtheory |