Multidimensional equilibria and their stability in copolymer–solvent mixtures

Karl Glasner, Saulo Orizaga

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This paper discusses localized equilibria which arise in copolymer–solvent mixtures. A free boundary problem associated with the sharp-interface limit of a density functional model is used to identify both lamellar and concentric domain patterns composed of a finite number of layers. Stability of these morphologies is studied through explicit linearization of the free boundary evolution. For the multilayered lamellar configuration, transverse instability is observed for sufficiently small dimensionless interfacial energies. Additionally, a crossover between small and large wavelength instabilities is observed depending on whether solvent–polymer or monomer–monomer interfacial energy is dominant. Concentric domain patterns resembling multilayered micelles and vesicles exhibit bifurcations wherein they only exist for sufficiently small dimensionless interfacial energies. The bifurcation of large radii vesicle solutions is studied analytically, and a crossover from a supercritical case with only one solution branch to a subcritical case with two is observed. Linearized stability of these configurations shows that azimuthal perturbation may lead to instabilities as interfacial energy is decreased.

Original languageEnglish (US)
Pages (from-to)1-12
Number of pages12
JournalPhysica D: Nonlinear Phenomena
StatePublished - Jun 15 2018


  • Block copolymer
  • Concentric domain patterns
  • Multidimensional stability

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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