Understanding the molecular differences in partitioning of higher- and lower-valent counterions in densely charged cation exchange membranes

Abstract

Optimizing metal ion recycling necessitates a fundamental understanding of competitive multivalent ion sorption in ion exchange membranes, particularly at the molecular scale. Here, we develop a molecular theory to systematically quantify sorption forces driving the partitioning of counterions with distinct valencies (e.g., trivalent/monovalent and trivalent/divalent pairs). Unlike prior studies, we resolve spatially dependent sorption forces under the landscape of condensation phenomena, revealing how dielectric, electrical, and osmotic forces synergistically govern competitive ion partitioning. Decoupling the molecular-level mobile ion sorption mechanisms demonstrates that Donnan and dielectric effects modulate macroscale partitioning trends. Strikingly, at the polymer-chain level, condensed trivalent counterions remain largely invariant to bulk solution concentration changes, mostly equilibrating in that state. Our theory is validated against data, successfully replicating global partitioning equilibria between binary salt solutions and membranes while predicting condensed-phase ion fractions. Collectively, this work establishes a chain-to-membrane multilevel framework that bridges macroscopic sorption behavior with molecular interactions, offering predictive insights for tailoring ion exchange membranes, for instance, in rare metal recovery.