Ion-mediated interactions in suspensions of oppositely charged nanoparticles.

The structure of oppositely charged spherical nanoparticles (polyions), dispersed in ionic solutions with continuous solvent (primitive model), is investigated by Monte Carlo (MC) simulations, within explicit and implicit microion representations, over a range of polyion valences and densities, and microion concentrations. Systems with explicit microions are explored by semigrand canonical MC simulations, and allow density-dependent effective polyion pair potentials v(alphabeta) (eff)(r) to be extracted from measured partial pair distribution functions. Implicit microion MC simulations are based on pair potentials of mean force v(alphabeta) ((2))(r) computed by explicit microion simulations of two charged polyions, in the low density limit. In the vicinity of the liquid-gas separation expected for oppositely charged polyions, the implicit microion representation leads to an instability against density fluctuations for polyion valences mid R:Zmid R: significantly below those at which the instability sets in within the exact explicit microion representation. Far from this instability region, the v(alphabeta) ((2))(r) are found to be fairly close to but consistently more repulsive than the effective pair potentials v(alphabeta) (eff)(r). This is corroborated by additional calculations of three-body forces between polyion triplets, which are repulsive when one polyion is of opposite charge to the other two. The explicit microion MC data were exploited to determine the ratio of salt concentrations c and c(o) within the dispersion and the reservoir (Donnan effect). c/c(o) is found to first increase before finally decreasing as a function of the polyion packing fraction.