Low-symmetry sphere packings of simple surfactant micelles induced by ionic sphericity.

Supramolecular self-assembly enables access to designer soft materials that typically exhibit high-symmetry packing arrangements, which optimize the interactions between their mesoscopic constituents over multiple length scales. We report the discovery of an ionic small molecule surfactant that undergoes water-induced self-assembly into spherical micelles, which pack into a previously unknown, low-symmetry lyotropic liquid crystalline Frank-Kasper σ phase. Small-angle X-ray scattering studies reveal that this complex phase is characterized by a gigantic tetragonal unit cell, in which 30 sub-2-nm quasispherical micelles of five discrete sizes are arranged into a tetrahedral close packing, with exceptional translational order over length scales exceeding 100 nm. Varying the relative concentrations of water and surfactant in these lyotropic phases also triggers formation of the related Frank-Kasper A15 sphere packing as well as a common body-centered cubic structure. Molecular dynamics simulations reveal that the symmetry breaking that drives the formation of the σ and A15 phases arises from minimization of local deviations in surfactant headgroup and counterion solvation to maintain a nearly spherical counterion atmosphere around each micelle, while maximizing counterion-mediated electrostatic cohesion among the ensemble of charged particles.