Abstract

A mesoscopic tiling pattern with twelvefold symmetry has been observed in a three-component polymer system composed of polyisoprene, polystyrene, and poly(2-vinylpyridine) which forms a star-shaped terpolymer, and a polystyrene homopolymer blend. TEM images reveal a nonperiodic tiling pattern covered with equilateral triangles and squares, their triangle/square number ratio of 2.3 ($\approx 4/\sqrt{3}$), and a microbeam X-ray diffraction pattern shows dodecagonal symmetry. The same kind of quasicrystalline structures have been found for metal alloys (-0.5 nm), chalcogenides (-2 nm), and liquid crystals(-10 nm). The present result (-50 nm) confirms the universal nature of dodecagonal quasicrystals over several hierarchical length scales.