Phase diagram of nematic polymer monolayers with the Onsager interaction potential

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dc.contributor.authorZhou, Hong
dc.contributor.authorWang, Hongyun
dc.contributor.departmentDepartment of Applied Mathematics
dc.date2010
dc.date.accessioned2014-04-23T20:35:25Z
dc.date.available2014-04-23T20:35:25Z
dc.date.issued2010
dc.descriptionJournal of Computational and Theoretical Nanoscience, 7, 738-755, 2010en_US
dc.descriptionThe article of record as published may be found at http://dx.doi.org/10.1166/jctn.2010.1417en_US
dc.description.abstractWe present an asymptotic study on the phase diagram of two-dimensional nematic liquid crystal polymer monolayers with the Onsager intermolcular potential. In contrast to the case of Maier-Saupe interaction potential where there is only one nematic branch. For small polymer concentration is increased, nematic branches appear one by one, starting with the first nematic branch. The polymer orientation distribution of the first nematic branch has a two fold rotational symmetry, the second branch has a four fold rotational symmetry, the third branch has a six fold rotational symmetry, and so on. To determine the stability of these nematic branches, we derive an asymptotic expression of free energy for each nematic branch. We find that free energies of all nematic branches are lower than that of the isotropic state, the first nematic branch has the lowest free energy among all branches. To further investigate the stability and meta-stability, we carry out asymptotic analysis of the free energy when each nematic state is perturbed. We conclude that (1) the isotropic branch is stable until the first nematic branch appears (2) the first nematic branch is stable, and (3) the isotropic branch (after the appearance of the first nematic branch) and all other nematic branches are unstable when perturbed by the leading Fourier mode in the first nematic branch. We also present a spectrum numerical method for calculating nematic branches and free energies. The spectrum method yields results that are accurate up to the computer precision. All of asymptotic results are confirmed by numerical results obtained with the spectrum method.en_US
dc.identifier.citationPhase diagram of nematic polymer monolayers with the Onsager interaction potential (with H. Wang) , Journal of Computational and Theoretical Nanoscience, 7, 738-755, 2010
dc.identifier.urihttps://hdl.handle.net/10945/40953
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.subject.authorNematic Polymersen_US
dc.subject.authorPhase Diagramen_US
dc.subject.authorIsotropic-Nematic Phase Transitionen_US
dc.subject.authorOnsager Intermolecular Potentialen_US
dc.subject.authorMaier-Saupe Intermolecular Potentialen_US
dc.subject.authorSmoluchowski Equationen_US
dc.subject.authorFree Energy of a Polymer Ensembleen_US
dc.subject.authorStability of an Equilibrium Stateen_US
dc.titlePhase diagram of nematic polymer monolayers with the Onsager interaction potentialen_US
dspace.entity.typePublication
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