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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 andn-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 ofn-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.

 

ABSTRACT: Hydration of the amphiphilic diblock oligomer C16H33(CH2CH2O)20OH (C16E20) leads to concentration-dependent formation of micellar body-centered cubic (BCC) and Frank− Kasper A15 lyotropic liquid crystals (LLCs). Quiescent thermal annealing of aqueous LLCs comprising 56−59 wt % C16E20 at 25 °C after quenching from high temperatures established their ability to form short-lived BCC phases, which transform into long-lived, transient Frank−Kasper σ phases en route to equilibrium A15 morphologies on a time scale of months. Here, the frequency and magnitude of applied oscillatory shear show the potential to either dynamically stabilize the metastable BCC phase at low frequencies or increase the rate of formation of the A15 to minutes at high frequencies. Time-resolved synchrotron small-angle X-ray scattering (TR-SAXS) provides in situ characterization of the structures during shear and thermal processing. This work shows that the LLC morphology and order−order phase transformation rates can be controlled by tuning the shear strain amplitude and frequency.