A rigorous derivation of mean-field models for diblock copolymer melts

Barbara Niethammer, Yoshihito Oshita

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We study the free boundary problem describing the micro phase separation of diblock copolymer melts in the regime that one component has small volume fraction such that micro phase separation results in an ensemble of small balls of one component. Mean-field models for the evolution of a large ensemble of such spheres have been formally derived in Glasner and Choksi (Physica D, 238:1241-1255, 2009), Helmers et al. (Netw Heterog Media, 3(3):615-632, 2008). It turns out that on a time scale of the order of the average volume of the spheres, the evolution is dominated by coarsening and subsequent stabilization of the radii of the spheres, whereas migration becomes only relevant on a larger time scale. Starting from the free boundary problem restricted to balls we rigorously derive the mean-field equations in the early time regime. Our analysis is based on passing to the homogenization limit in the variational framework of a gradient flow.

Original languageEnglish
Pages (from-to)273-305
Number of pages33
JournalCalculus of Variations and Partial Differential Equations
Volume39
Issue number3
DOIs
Publication statusPublished - Mar 8 2010

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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