Polymeric quasicrystal: mesoscopic quasicrystalline tiling in ABC star polymers

Abstract

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 (approximately equal to 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 (approximately 0.5 nm), chalcogenides (approximately 2 nm), and liquid crystals (approximately 10 nm). The present result (approximately 50 nm) confirms the universal nature of dodecagonal quasicrystals over several hierarchical length scales.