Polymeric Quasicrystal: Mesoscopic Quasicrystalline Tiling in ABC Star Polymers

A mesoscopic tiling pattern with 12-fold 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. Transmission electron microscopy images reveal a nonperiodic tiling pattern covered with equilateral triangles and squares, their triangle/square number ratio of 2.3 (≈4/√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.