Effective electrostatic interactions in colloid-nanoparticle mixtures

Interparticle interactions and bulk properties of colloidal suspensions can be substantially modified by the addition of nanoparticles. Extreme asymmetries in size and charge between colloidal particles and nanoparticles present severe computational challenges to molecular-scale modeling of such complex systems. We present a statistical mechanical theory of effective electrostatic interactions that can greatly ease large-scale modeling of charged colloid-nanoparticle mixtures. By applying a sequential coarse-graining procedure, we show that a multicomponent mixture of charged colloids, nanoparticles, counterions, and coions can be mapped first onto a binary mixture of colloids and nanoparticles and then onto a one-component model of colloids alone. In a linear-response approximation, the one-component model is governed by a single effective pair potential and a one-body volume energy, whose parameters depend nontrivially on nanoparticle size, charge, and concentration. To test the theory, we perform molecular dynamics simulations of the two-component and one-component models and compute structural properties. For moderate electrostatic couplings, colloid-colloid radial distribution functions and static structure factors agree closely between the two models, validating the sequential coarse-graining approach. Nanoparticles of sufficient charge and concentration enhance screening of electrostatic interactions, weakening correlations between charged colloids and destabilizing suspensions, consistent with experiments.