The Archimedean tiling (3 2 .4.3.4) is a regular but complex polygonal assembly of equilateral triangles and squares. This tiling pattern with mesoscopic repeating distance has been found for an ABC star-branched three-component polymer composed of polyisoprene, polystyrene, and poly(2-vinylpyridine). In this structure the environment of a molecule splits into multiple sites and two microdomains with different sizes and shapes are formed for one component. This complexity is the first observation in complex polymer systems and can lead to a new type of mesoscale self-organization. The tiling pattern has been observed for the other materials on much shorter length-scale; therefore, the experimental fact observed in the present study is demonstrating that the complexity is universal over different hierarchies.

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.