Archimedean Tiling Patterns of ABC Star-Shaped Terpolymers Studied by Microbeam Small-Angle X-ray Scattering

Characteristic cylindrical structures formed by ABC star-shaped terpolymers were investigated by microbeam small-angle X-ray scattering (SAXS) in addition to transmission electron microscopy (TEM). The polymer samples are composed of polyisoprene (I), polystyrene (S), and poly(2-vinylpyridine) (P); their volume ratios for I:S:P are 1:1:X, where X equals 0.7, 1.2, 1.3, and 1.9. The spotlike diffraction patterns were observed by microbeam SAXS due to scattering from a small number of ordered grains in the polymer samples, where the exact packing manners of the cylinders, or their lattice constants, have been clarified. In short, it has been found that the cross-sectional patterns of these tilings have the features of four Archimedean tiling patterns, i.e., (6.6.6), (4.8.8), (3.3.4.3.4), and (4.6.12). All the four SAXS patterns are quite consistent with the structural observation by TEM with regard to the crystallographic data.