Interaction between like-charged colloidal spheres in electrolyte solutions

How colloidal particles interact with each other is one of the key issues t hat determines our ability to interpret experimental results for phase tran sitions in colloidal dispersions and our ability to apply colloid science t o various industrial processes. The long-accepted theories for answering th is question have been challenged by results from recent experiments. Herein we show from Monte-Carlo simulations that there is a short-range attractiv e force between identical macroions in electrolyte solutions containing div alent counterions. Complementing some recent and related results by others, we present strong evidence of attraction between a pair of spherical macro ions in the presence of added salt ions for the conditions where the intera cting macroion pair is not affected by any other macroions that may be in t he solution, This attractive force follows from the internal-energy contrib ution of counterion mediation. Contrary to conventional expectations, for c harged macroions in an electrolyte solution, the entropic force is repulsiv e at most solution conditions because of localization of small ions in the vicinity of macroions. Both Derjaguin-Landau-Verwey-Overbeek theory and Sog ami-Ise theory fail to describe the attractive interactions found in our si mulations; the former predicts only repulsive interaction and the latter pr edicts a long-range attraction that is too weak and occurs at macroion sepa rations that are too large. Our simulations provide fundamental "data" towa rd an improved theory for the potential of mean force as required for optim um design of new materials including those containing nanoparticles.