Nanoparticle Superlattices as Quasi-Frank-Kasper Phases

I show that all phases reported experimentally in binary nanoparticle superlattices can be described as networks of disclinations in an ideal lattice of regular tetrahedra. A set of simple rules is provided to identify the different disclination types from the Voronoi construction, and it is shown that those disclinations completely screen the positive curvature of the ideal tetrahedral lattice. In this way, this study provides a generalization of the well-known Frank-Kasper phases to binary systems consisting of two types of particles, and with a more general type of disclinations, i.e., quasi-Frank-Kasper phases. The study comprises all strategies in nanoparticle self-assembly, whether driven by DNA or hydrocarbon ligands, and establishes the universal tendency of superlattices to develop icosahedral order, which is facilitated by the asymmetry of the particles. Besides its interest in predicting nanoparticle self-assembly, I discuss the implications for models of the glass transition, micelles of diblock polymers, and dendritic molecules, among many others.