  Interparticle interactions and bulk properties of colloidal suspensions can
be substantially modified by 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 nano particle 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.

Soft Condensed Matter;Materials Science;Statistical Mechanics