Morphological characterization of the diblock copolymer problem with topological computation

• Published in: Japan journal of industrial and applied mathematics Vol. 27; no. 2; pp. 175 - 190
• Main Authors: Teramoto, Takashi, Nishiura, Yasumasa
• Format: Journal Article
• Language: English
• Published: Japan Springer Japan 01.09.2010; Springer Nature B.V
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematics; Mathematics and Statistics; Original Paper; Microphase separation; Double gyroid; The Betti number
• ISSN: 0916-7005; 1868-937X
• 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.