Some mathematical aspects of the micro-phase separation in diblock copolymers

Yasumasa Nishiura, Isamu Ohnishi

Research output: Contribution to journalArticlepeer-review

116 Citations (Scopus)

Abstract

A free energy functional of nonlocal type is considered that was originally introduced to describe the micro-phase separation of diblock copolymer. A mathematical framework is given to the issues of the scaling law for stationary states and the governing equation of morphology. The scaling law is equivalent to finding a nice rescaling in order to have a well-defined limiting interfacial problem which is free from the interfacial thickness and the total chain length of copolymer, and the associated stationary problem becomes a morphology equation that governs the configuration of final patterns. Although the steady patterns become finer and finer in our scaling limit due to the mesoscopic nature, a possible rigorous approach is presented to stability and morphological selection problems for them.

Original languageEnglish
Pages (from-to)31-39
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Volume84
Issue number1-2
DOIs
Publication statusPublished - 1995 Jun 15
Externally publishedYes

ASJC Scopus subject areas

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

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