← back to Research


水中の脂質や界面活性剤などの両親媒性分子は二重膜を形成し,空間を二つの入り組んだ共連続な部分空間に分割する.分子密度が高ければ膜は数学的によく知られた周期的極小曲面(Gyroid (G), Diamond (D), Primitive (P))を形成し,得られる構造は共連続立方相とよばれる.極小曲面や定曲率曲面の話題は数学の最前線でもある!




最近,G相を形成するAC 対称なABC線形トリブロック共重合体にAとCのホモポリマーを混合し,その量を増やすにつれてD相,P相へとリオトロピック転移することが研究室のシミュレーションから示唆された.


A Zoo of Tricontiuous Structures

Biological amphiphilies (lipids) or synthetic surfactants in aqueous solutions self-assemble to bilayers centered on the multiply connected surface dividing the space into two interpenetrating "bicontinuous" subspaces. At high concentration of lipids or surfactants, these bilayers can organize cubic phases based on mathematically well-known minimal surfaces: Schoen-Luzatti gyroid (G), Schwarz diamond (D), and Schwarz primitive (P). Interestingly, these mathematical surfaces abound in biological cells such as the endoplasmic reticulum, the mitochondrion and the nucleus of certain cells. These self-assembling structures have attracted much attention of mathematicians, physicists, chemists, biologists, and nanotechnology engineers. The gyroid phases have been frequently found in high polymeric block copolymer systems as well. Moreover, in plastic technologies, high polymeric bicontinuous systems are thought to be promising candidates of future technologies like photonic crystals. The problem is that only the gyroid phase has been found in most block copolymer systems: Why not non-gyroid phase? Is there any systematic route to find non-gyroid cubic phases in high polymeric systems? Using Monte Carlo lattice simulation technique, we present numerical evidences of the formation of gyroid and non-gyroid "tricontinuous" cubic phases in high polymeric systems of ABC/A/C triblock copolymer and homopolymer blends. With increasing the volume fraction of homopolymer, a remarkable minimal surface sequence G→D→P is observed, which is common to certain surfactant systems. The results indicate that the ABC triblock copolymer system with/without blending homopolymer is a zoo of tricontinuous phases, suitable for comparative studies of these phases. Numerical prediction of morphology in high polymeric systems has just begun such as our recent Monte Carlo study on complex ABC and ABCD star copolymers. From movies, which you can download, you can feel that simulation study will change the mode of polymer science.