Japan Journal of Industrial and Applied Mathematics

, Volume 27, Issue 2, pp 175–190

Morphological characterization of the diblock copolymer problem with topological computation

Original Paper Area 1

DOI: 10.1007/s13160-010-0014-9

Cite this article as:
Teramoto, T. & Nishiura, Y. Japan J. Indust. Appl. Math. (2010) 27: 175. doi:10.1007/s13160-010-0014-9


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.


Double gyroidMicrophase separationThe Betti number

Copyright information

© The JJIAM Publishing Committee and Springer 2010

Authors and Affiliations

  1. 1.Chitose Institute of Science and TechnologyChitoseJapan
  2. 2.Research Institute of Electronic ScienceHokkaido UniversitySapporoJapan