Mesoscopic Archimedian Tiling Patterns in ABC Star-Shaped Terpolymers

Microphase-separated structures formed by ABC star-shaped terpolymers were investigated by transmission electron microscopy (TEM), electron tomography (3D-TEM), and small-angle X-ray scattering (SAXS). The samples are composed of polystyrene (S), polyisoprene (I) and poly(2-vinylpyridine) (P), their volume ratios of I:S:P are 1:1:X, where 0.2$<$X$<$4.9. From morphological observations by TEM, it was found that ISP stars show characteristic cylindrical structures when X is within the range 0.7$\mathbin{\lower.3ex\hbox{$\buildrel<\over {\smash{\scriptstyle=}\vphantom{_x}}$}} $X$\mathbin{\lower.3ex\hbox{$\buildrel<\over {\smash{\scriptstyle=}\vphantom{_x}}$}} $1.9. By the careful investigation of the ISP stars by TEM and 3D-TEM, it was confirmed that the cross-sections of cylindrical structures of four samples show two-dimensional tiling patterns consisting of regular polygons, that is, [6.6.6], [4.8.8], [3.3.4.3.4], and [4.6.12], which are families of the Archimedian tiling patterns. Furthermore the SAXS patterns of four samples are quite consistent with structural observation of TEM.