Dodecagonal quasicrystalline order in a diblock copolymer melt

We report the discovery of a dodecagonal quasicrystalline state (DDQC) in a sphere (micelle) forming poly(isoprene-b-lactide) (IL) diblock copolymer melt, investigated as a function of time following rapid cooling from above the order-disorder transition temperature (T-ODT = 66 degrees C) using small-angle X-ray scattering (SAXS) measurements. Between T-ODT and the order-order transition temperature T-OOT = 42 degrees C, an equilibrium body-centered cubic (BCC) structure forms, whereas below T-OOT the Frank-Kasper sigma phase is the stable morphology. At T < 40 degrees C the supercooled disordered state evolves into a metastable DDQC that transforms with time to the sigma phase. The times required to form the DDQC and sigma phases are strongly temperature dependent, requiring several hours and about 2 d at 35 degrees C and more than 10 and 200 d at 25 degrees C, respectively. Remarkably, the DDQC forms only from the supercooled disordered state, whereas the sigma phase grows directly when the BCC phase is cooled below T-OOT and vice versa upon heating. A transition in the rapidly supercooled disordered material, from an ergodic liquid-like arrangement of particles to a nonergodic soft glassy-like solid, occurs below similar to 40 degrees C, coincident with the temperature associated with the formation of the DDQC. We speculate that this stiffening reflects the development of particle clusters with local tetrahedral or icosahedral symmetry that seed growth of the temporally transient DDQC state. This work highlights extraordinary opportunities to uncover the origins and stability of aperiodic order in condensed matter using model block polymers.