Extended Donnan-Manning Theory for Selective Ion Partition and Transport in Ion Exchange Membrane

The use of ion exchange membranes (IEMs) for electrochemical ion-ion separation leverages the selectivity of the IEMs toward like-charged species via valence difference and/or other ion-membrane interactions. A mechanistic model that relates selectivity with membrane structural and chemical properties is lacking in the literature. Here, we extend the Manning's counter-ion condensation model for describing ion partition and ion mobility inside IEMs to mixed salts scenarios. We evaluate the extended Donnan-Manning model against experimental data from literature and compare the performance of the Donnan-Manning model to that of the ideal Donnan model and the Donnan-Affinity model. Our analysis shows that, despite its structural complexity, the Donnan-Manning model has less fitting parameters than the Donnan-Affinity model and generally outperforms the two other models in predicting counter-ion and co-ion partition. With the assumption of a higher mobility of condensed ions than that of uncondensed ions, the generalized Manning's model can also predict counter-ion mobility selectivity for cation exchange membranes, but its performance for predicting mobility selectivity for anion exchange membranes is still unsatisfactory.