Dodecagonal quasicrystals of oil-swollen ionic surfactant micelles.

A delicate balance of noncovalent interactions directs the hierarchical self-assembly of molecular amphiphiles into spherical micelles that pack into three-dimensional periodic arrays, which mimic intermetallic crystals. Herein, we report the discovery that adding water to a mixture of an ionic surfactant and n-decane induces aperiodic ordering of oil-swollen spherical micelles into previously unrecognized, aqueous lyotropic dodecagonal quasicrystals (DDQCs), which exhibit local 12-fold rotational symmetry and no long-range translational order. The emergence of these DDQCs at the nexus of dynamically arrested micellar glasses and a periodic Frank-Kasper (FK) σ phase approximant sensitively depends on the mixing order of molecular constituents in the assembly process and on sample thermal history. Addition of n-decane to mixtures of surfactant and water instead leads only to periodic FK A15 and σ approximants with no evidence for aperiodic order, while extended ambient temperature annealing of the DDQC also reveals its transformation into a σ phase. Thus, these lyotropic DDQCs are long-lived metastable morphologies, which nucleate and grow from a stochastic distribution of micelle sizes formed by abrupt segregation of varied amounts of oil into surfactant micelles on hydration. These findings indicate that molecular building block complexity is not a prerequisite for the formation of aperiodic supramolecular order, while also establishing the generic nature of quasicrystalline states across metal alloys and self-assembled micellar materials.