Multilayered equilibria in a density functional model of copolymer-solvent mixtures

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)1593-1620
Number of pages28
JournalSIAM Journal on Mathematical Analysis
Volume49
Issue number2
DOIs
StatePublished - 2017

Keywords

  • Copolymer mixture
  • Free boundary problem
  • Pattern formation

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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