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Multilayered Equilibria in a Density Functional Model of Copolymer-solvent Mixtures

This paper considers a free energy functional and corresponding free boundary problem for multilayered structures which arise from a mixture of a block copolymer and a weak solvent. The free boundary problem is formally derived from the limit of large solvent/polymer segregation and intermediate segregation between monomer species. A change of variables based on Legendre transforms of the effective bulk energy is used to explicitly construct a family of equilibrium solutions. The second variation of the effective free energy of these solutions is shown to be positive. This result is used to show more generally that equilibria are local minimizers of the free energy.

Identiferoai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/624087
Date25 April 2017
CreatorsGlasner, Karl
ContributorsUniv Arizona, Dept Math
PublisherSIAM PUBLICATIONS
Source SetsUniversity of Arizona
LanguageEnglish
Detected LanguageEnglish
TypeArticle
Rights© 2017, Society for Industrial and Applied Mathematics
Relationhttp://epubs.siam.org/doi/10.1137/16M1066129

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