Multilayered Equilibria in a Density Functional Model of Copolymer-solvent Mixtures
AffiliationUniv Arizona, Dept Math
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CitationMultilayered Equilibria in a Density Functional Model of Copolymer-solvent Mixtures 2017, 49 (2):1593 SIAM Journal on Mathematical Analysis
Rights© 2017, Society for Industrial and Applied Mathematics
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AbstractThis 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.
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