Interaction between like-charged colloidal spheres in electrolyte solutions.

How colloidal particles interact with each other is one of the key issues that determines our ability to interpret experimental results for phase transitions in colloidal dispersions and our ability to apply colloid science to various industrial processes. The long-accepted theories for answering this question have been challenged by results from recent experiments. Herein we show from Monte-Carlo simulations that there is a short-range attractive force between identical macroions in electrolyte solutions containing divalent counterions. Complementing some recent and related results by others, we present strong evidence of attraction between a pair of spherical macroions in the presence of added salt ions for the conditions where the interacting macroion pair is not affected by any other macroions that may be in the solution. This attractive force follows from the internal-energy contribution of counterion mediation. Contrary to conventional expectations, for charged macroions in an electrolyte solution, the entropic force is repulsive at most solution conditions because of localization of small ions in the vicinity of macroions. Both Derjaguin-Landau-Verwey-Overbeek theory and Sogami-Ise theory fail to describe the attractive interactions found in our simulations; the former predicts only repulsive interaction and the latter predicts a long-range attraction that is too weak and occurs at macroion separations that are too large. Our simulations provide fundamental "data" toward an improved theory for the potential of mean force as required for optimum design of new materials including those containing nanoparticles.