Morphological characterization of the diblock copolymer problem with topological computation

Takashi Teramoto, Yasumasa Nishiura

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

Abstract

Our subject is the diblock copolymer problem in a three-dimensional space. Using numerical simulations, the double gyroid and orthorhombic morphologies are obtained as energy minimizers. By investigating the geometric properties of these bicontinuous morphologies, we demonstrate the underlying mechanism affecting the triply periodic energy minimizers in terms of a balanced scaling law. We also apply computational homology to their characterization during the dynamics of morphology transition. Our topological approaches detect the morphology of transient perforated layers as they transition from layers to cylinders, and the t-1 law of the Betti number in the phase ordering process.

Original languageEnglish
Pages (from-to)175-190
Number of pages16
JournalJapan Journal of Industrial and Applied Mathematics
Volume27
Issue number2
DOIs
Publication statusPublished - 2010 Sep

Keywords

  • Double gyroid
  • Microphase separation
  • The Betti number

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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