Equilibrium ion partitioning between aqueous salt solutions and inhomogeneous ion exchange membranes

This study investigates the ability of a recently proposed thermodynamic framework (i.e., Donnan/Manning model) to quantify equilibrium ion partitioning between aqueous salt solutions and inhomogeneous (i.e., phase separated) ion exchange membranes. Two inhomogeneous cation exchange membranes (CEMs) and one homogeneous anion exchange membrane (AEM), which served as a basis for comparison, were synthesized via free radical polymerization. Surface characterization of the membranes via cryogenic scanning electron microscopy revealed the inhomogeneous structure of the CEMs and the reasonably homogeneous structure of the AEM. Equilibrium ion concentrations in membranes equilibrated with NaCl, KCl, or MgCl₂ solutions were experimentally measured. The experimental results were interpreted via a thermodynamic model based on Donnan theory and Manning's counter-ion condensation theory. The framework predicted NaCl partitioning in the AEM, presumably due to its reasonably homogeneous structure, but failed to predict NaCl partitioning in the CEMs when the Manning parameter, ξ, was calculated assuming a homogeneous membrane. For the inhomogeneous CEMs, the Manning parameter was used as an adjustable constant, which was extracted from the NaCl sorption results. Remarkably, the value of ξ obtained from the NaCl sorption results accurately predicted KCl and MgCl₂ sorption in the two CEMs over the entire salt concentration range considered.