Interaction of similarly charged surfaces mediated by nanoparticles

We study the interaction between two like charged surfaces embedded in a solution of oppositely charged multivalent rod-like counterions. The counterions consist of two rigidly bonded point charges, each of valency Z. The strength of the electrostatic coupling increases with increasing surface charge density or valency of the charges. The system is analyzed by employing a self-consistent field theory, which treats the short and long range interactions of the counterions within different approximations. We find that in the weak coupling limit, the interactions are only repulsive. In the intermediate coupling regime, the multivalent rod-like counterions can mediate attractive interactions between the surfaces. For sufficiently long rods, bridging contributes to the attractive interaction. In the strong coupling limit, the charge correlations can contribute to the attractive interactions at short separations between the charged surfaces. Two minima can then appear in the force curve between surfaces.