Quasiperiodic Ordering of Minimally Hydrated Ionic Surfactant Micelles*

Minimally hydrated surfactant micelles, by analogy to hard spheres, pack into high-symmetry body-centered cubic, face-centered cubic and hexagonally closest-packed structures. Recently, hydrated dianionic surfactant micelles were shown to self-assemble into low-symmetry Frank-Kasper (FK) σ and A15 morphologies. These FK phases are well-known periodic approximants of dodecagonal quasicrystals (DDQC), which possess 12-fold rotational symmetry yet lack translational symmetry. We report the formation of a well-ordered DDQC formed by oil-swollen aqueous dispersions of alkylphosphonate surfactants. Our studies show that the DDQC formation is strongly path dependent, and that different processing approaches to the same final composition instead yield periodic σ and A15 approximants. These findings coupled with the observations of irreversible thermal transformation of the DDQC into a σ phase suggest the metastability of these soft quasicrystals. This discovery illustrates avenues to tune the subtle free-energy balance prevalent among complex micellar phases and exemplifies the universality of quasiperiodic order in soft matter self-assembly.