Effective pair potential between charged nanoparticles at high volume fractions

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^f. Still, the determination of w^f is difficult mainly because it depends on the colloidal density, ϕ. Here we propose to calculate w^f 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.