Hiding in plain view: Colloidal self-assembly from polydisperse populations

We report small-angle x-ray scattering (SAXS) experiments on aqueous dispersions of colloidal silica with a broad monomodal size distribution (polydispersity 14\%, size $a = 8$ nm). This distribution of sizes was expected to destroy any long-range order of the particles. However, we found ordered states when the particles repelled each other with soft ionic potentials of range $\sim a$. Over a range of volume fractions the particles segregated to build first one, then two distinct sets of colloidal crystals. These dispersions thus demonstrate fractional crystallization and multiple-phase (bcc, Laves AB$_2$, liquid) coexistence. Their remarkable ability to build complex crystal structures from a polydisperse population originates from the intermediate-range nature of interparticle forces, and suggests routes for designing self-assembling colloidal crystals from the bottom-up.