Characteristic cylindrical microphase-separated structures have been found for three ABC star-shaped terpolymers. The samples are composed of polystyrene (S), polyisoprene (I), and poly(2vinylpyridine) (P); their volume ratios of I:

The structure-preserving finite difference schemes for the one dimensional Cahn-Hilliard equation with dynamic boundary conditions are studied. A dynamic boundary condition is a sort of transmission condition that includes the time derivative, namely, it is itself a time evolution equation. The Cahn-Hilliard equation with dynamic boundary conditions is well-treated from various viewpoints. The standard type consists of a dynamic boundary condition for the order parameter, and the Neumann boundary condition for the chemical potential. Recently, Goldstein-Miranville-Schimperna proposed a new type of dynamic boundary condition for the Cahn-Hilliard equation. In this article, numerical schemes for the problem with these two kinds of dynamic boundary conditions are introduced. In addition, a mathematical result on the existence of a solution for the scheme with an error estimate is also obtained for the former boundary condition.

Several hierarchical nanophase-separated structures have been observed for a series of ABC star-shaped terpolymers by transmission electron microscopy (TEM) and electron computerized tomography (3D-TEM). The seven terpolymers synthesized are composed of polyisoprene (I), polystyrene (S), and poly(2-vinylpyridine) (P), their volume fraction ratios of I:S:P are 1:1:X, where X equals 0.2, 0.4, 0.7, 1.2, 1.9, 3.0, and 4.9, respectively, and additional four samples were prepared by blending each two parent terpolymers. From morphological observation by TEM and tomography, a terpolymer with X of 0.2 shows lamellar structure with spheres at the interface, those with X ranging from 0.4 to 1.9 show cylindrical structures with twodimensional tiling, while those with X of 3.0 and 4.9 show hierarchical cylinders-inlamella structure. Two the other terpolymer samples with X of 7.9 and 10 were produced by blending a P homopolymer with the terpolymer I 1.0 S 1.0 P 4.9 , and they both exhibited columnar piled disk cylinders in P matrix. From the comparison of the present results with the predictions by the Monte-Carlo simulation, it was confirmed that the observed nanophase-separated structures of the ISP star-shaped terpolymers are mostly in good agreement with the prediction.

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