We report small-angle x-ray scattering experiments on aqueous dispersions of colloidal silica with a broad monomodal size distribution (polydispersity, 14%; size, 8 nm). Over a range of volume fractions, the silica particles segregate 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 it suggests routes for designing self-assembling colloidal crystals from the bottom up.

Monte-Carlo simulations and small-angle x-ray scattering experiments were used to determine the phase diagram of aqueous dispersions of titratable nano-colloids with a moderate size polydispersity over a broad range of monovalent salt concentrations, 0.5 mM ≤ cs ≤ 50 mM and volume fractions, φ. Under slow and progressive increase in φ, the dispersions freeze into a face-centered-cubic (fcc) solid followed unexpectedly by the formation of a body centered cubic (bcc) phase before to melt in a glass forming liquid. The simulations are found to predict very well these observations. They suggest that the stabilization of the bcc solid at the expense of the fcc phase at high φ and cs results from the interaction (charge) polydispersity and vibrational entropy. arXiv:1909.02774v1 [cond-mat.soft]

A good understanding and determination of colloidal interactions is paramount to comprehend and model the thermodynamic and structural properties of colloidal suspensions. In concentrated aqueous suspensions of colloids with a titratable surface charge, this determination is, however, complicated by the density dependence of the effective pair potential due to both the many-body interactions and the charge regulation of the colloids. In addition, colloids generally present a size distribution which results in a virtually infinite combination of colloid pairs. In this paper we develop two methods and describe the corresponding algorithms to solve this problem for arbitrary size distributions. An implementation in Nim is also provided. The methods, inspired by the seminal work of Torres et al., are based on a generalization of the cell and renormalized jellium models to polydisperse suspensions of spherical colloids with a charge regulating boundary condition. The latter is described by the one-pK-Stern model. The predictions of the models are confronted to the equations of state of various commercially available silica dispersions. The renormalized Yukawa parameters (effective charges and screening lengths) are also calculated. The importance of size and charge polydispersity as well as the validity of these two models are discussed in light of the results. arXiv:1807.09542v1 [cond-mat.soft]

Simulations of charged colloidal dispersions are technically challenging. One possible workaround consists in reducing the system to the colloids only, whose interactions are described through an effective pair potential, w. Still, the determination of w is difficult mainly because it depends on the colloidal density, ϕ. Here we propose to calculate w from simulations of a pair of colloids placed in a cubic box with periodic boundary conditions. The variation in ϕ is mimicked by an appropriate change in the concentration of counterions neutralized by an homogeneous background charge. The method is tested at the level of the primitive model. A good description of the structure of the colloidal dispersion is obtained in the low and high coupling regimes, even at high ϕ (≈30%). Furthermore, the method can easily be used in popular molecular simulation program packages and extended to non-spherical objects.