Dodecagonal quasicrystalline order in a diblock copolymer melt

Abstract

Significance: Spherical objects ranging in size from metal atoms to micron-scale colloidal particles to billiard balls tend to form regular close packed arrays with three-dimensional translational symmetry. We show that nearly spherical nanoscale micelles, formed by self-assembled diblock copolymers, spontaneously evolve into a two-dimensional dodecagonal quasicrystal following rapid cooling from the disordered liquid state. This aperiodic arrangement, characterized by rotational symmetry but not translational symmetry, transforms over time into a three-dimensional Frank–Kasper σ phase with local tetrahedral particle packing. This discovery suggests that certain forms of quasicrystalline order are nonequilibrium states generated by kinetically facilitated particle clustering in the supercooled liquid. Redistribution of polymer molecules between micelles through molecular diffusion appears to play a central role in these processes.