Entropic Assembly of Soft-Matter Quasicrystals

The recent discovery of soft-matter quasicrystals hints at a unique thermodynamic mechanism that gives rise to their stability. In the past, specific interaction potentials have been tailored to stabilize quasicrystals and their approximants in computer simulations. However, such complex interactions are seemingly incompatible with the known properties of soft-matter systems. Here, we explore an entropic mechanism for stabilizing quasicrystals based on maximizing the ability for the system as a whole to sample configuration space. Under certain conditions, this results in the stabilization of a dodecagonal quasicrystal over close-packed crystals for a minimal model system. We demonstrate the generality of this phenomenon by assembling dodecagonal phases in two different micellar systems using tethered nanoparticles as building blocks. In addition to the soft-matter quasicrystals already reported in experiments, we predict that this mechanism can be widely exploited to assemble quasicrystals on the nano and colloidal scale.