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 |
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2009
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| _version_ | 1797079457943519232 |
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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 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. |
| first_indexed | 2024-03-07T00:46:09Z |
| format | Journal article |
| id | oxford-uuid:84b96285-1f6c-49bb-871d-446d3ea7d217 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:46:09Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:84b96285-1f6c-49bb-871d-446d3ea7d2172022-03-26T21:52:56ZNematic liquid crystals : from Maier-Saupe to a continuum theoryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:84b96285-1f6c-49bb-871d-446d3ea7d217Mathematical Institute - ePrints2009Ball, JMajumdar, A 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. |
| 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 |