ミクロ相分離のモルフォロジーとダイナミクス

概要

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Micro-phase separation of diblock copolymer melts have become an excellent model system for studying fundamental phenomena associated with molecular self-assembly. We deal with the gradient system derived from the free-energy functional of nonlocal type and focus on the morphological analysis of the periodic 3D structures obtained by the simulations. We have numerically confirmed that "balanced scaling law", i.e., a morphology is attained where two competing terms are balanced, is valid for the functional in the singular limit which is consistent with the theoretical results by Ren and Wei[19]. This view point allows us to demonstrate the mechanism behind the appearance of the gyroid minimizers in terms of some geometrical measures. We also apply computational homology to characterize the complex morphology during the phase transition dynamics. Our topological characterization points to the transient perforated lamellar state in the lamellar-hexagons transition and the t^<-1> law of the Betti number in the late stage of phaseordering process.
日本応用数理学会の論文
2005-09-27