Polarisation-mediated underscreening from weakly bonded ion clusters
We explore the hypothesis that ions form loosely connected clusters at high ionic strength in aqueous solutions, and that these clusters have relevance to the experimentally observed phenomenon usually referred to as "anomalous underscreening". Cluster formation lowers the ionic strength below its nominal value, slowing the decay of the screening length but not reversing it. Here we focus on an additional contribution, cluster polarisation. We demonstrate that this effect produces longer-ranged repulsive interactions between like-charged surfaces or particles in concentrated salt solutions. We derive an analytical bulk relation in which the entire architecture of a cluster enters through a single quantity, the charge-weighted second moment of its intramolecular charge structure factor, which quantifies the polarisation response of an arbitrary cluster topology. We also make numerical calculations using classical polymer Density Functional Theory, cDFT, for a model based on star-like clusters in which satellite ions are weakly bonded by a harmonic spring to a common central ion. The corona of satellite ions is assumed to be net neutral, since the formation of highly charged clusters would be accompanied by a significant self-energy cost. Using this model, we calculate surface interactions and screening lengths at various overall salt concentrations. We show that, under the assumption that the fraction of ions belonging to clusters increases with salt concentration, one may qualitatively arrive at "anomalous underscreening", i.e., an effective screening length that displays a minimum at an overall (monovalent) salt concentration of about 1 M. Quantitatively, we note that the predicted growth of the screening length beyond this threshold value is weaker than typically found by experimental surface force measurements.