Spatially localized structures in diblock copolymer mixtures

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10 Scopus citations


Above the critical temperature for the order-disorder transition, diblock copolymer melts have been observed to exhibit localized structures that exist within the homogeneous mixture. This paper uses an Ohta-Kawasaki-type density functional to explore this regime. Spatially localized peak-shaped equilibria are studied in one, two, and three dimensions, corresponding to amphiphilic bilayers, cylindrical micelles, and spherical micelles, respectively. A combination of rigorous estimates, asymptotic analysis, and numerical computation is used to characterize solutions and the regime where they exist. The interaction of superpositions of these solutions is studied by a perturbation analysis and shows how steady multipeak configurations can be achieved. Evidence is found for a secondary bifurcation slightly below the spinodal instability threshold, beyond which self-replication phenomena are observed. Dynamics in two dimensions are also illustrated, suggesting other mechanisms for instability and growth.

Original languageEnglish (US)
Pages (from-to)2045-2074
Number of pages30
JournalSIAM Journal on Applied Mathematics
Issue number6
StatePublished - 2010


  • Density functional theory
  • Diblock copolymer
  • Micelle
  • Self-replication

ASJC Scopus subject areas

  • Applied Mathematics


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