Accounting for ion pairing effects on sulfate salt sorption in cation exchange membranes

Ion exchange membranes (IEMs) are frequently used in water treatment and electrochemical applications, with their ion separation properties largely governed by equilibrium ion partitioning between a membrane and contiguous solution. Despite an expansive literature on IEMs, the influence of electrolyte association (i.e., ion pairing) on ion sorption remains relatively unexplored. In this study, salt sorption in two commercial cation exchange membranes equilibrated with 0.01-1.0 M MgSO₄ and Na₂SO₄ is investigated experimentally and theoretically. Association measurements of salt solutions using conductometric experiments and the Stokes-Einstein approximation show significant concentrations of ion pairs in MgSO₄ and Na₂SO₄ relative to those in simple electrolytes (i.e., NaCl), which is consistent with prior studies of sulfate salts. The Manning/Donnan model, developed and validated for halide salts in previous studies, substantially underpredicts sulfate sorption measurements, presumably due to ion pairing effects not accounted for in this established theory. These findings suggest that ion pairing can enhance salt sorption in IEMs due to partitioning of reduced valence species. By reformulating the Donnan and Manning models, a theoretical framework for predicting salt sorption in IEMs that explicitly considers electrolyte association is developed. Remarkably, theoretical predictions of sulfate sorption are improved by over an order of magnitude by accounting for ion speciation. In some cases, good quantitative agreement is observed between theoretical and experimental values for external salt concentrations between 0.1 and 1.0 M using no adjustable parameters.