Classical Density Functional Treatment of Polydisperse Polarizable Clusters

Ion clustering has been proposed as a mechanism leading to the peculiar "anomalous underscreening" phenomenon seen for electrostatic interactions between charged surfaces immersed in concentrated electrolytes. These interactions have been measured using the Surface Force Apparatus, according to which there are strong repulsive interactions between like-charged surfaces, with a range that increases upon further addition of salt, above some threshold concentration. A common suggestion is that ionic aggregates, if they form in sufficient numbers, will reduce the concentration of free ions and thereby increase the nominal Debye length. In previous work, we investigated a cluster model using classical Density Functional Theory (cDFT) and a polymer-like description of the ion clusters. These clusters were monodisperse and of either a linear or branched architecture, and a fixed charge sequence along the chains. In this work, we generalize the cDFT to treat "living polymers" with variable chain lengths and charge arrangements along the chain. This approach allows clusters to become polarized by the presence of charged surfaces, manifested by like-charged bonding. We find that even with a small degree of like-charged bonding a full equilibrium treatment of our model predicts only weak repulsion between like-charged surfaces. When a global constraint is applied so that the charged surfaces are neutralized only by the dissociated ions, while the clusters contribute overall zero charge, even a very small fraction of clustering ions generate strong and long-ranged forces. Moreover, if the cluster fraction increase substantially upon the addition of further salt, then the strength of the surface forces will also increase, although the range remains roughly constant.