Multicomponent Space-Charge Transport Model for Ion-Exchange Membranes with Variable Pore Properties

A multicomponent space-charge transport model for an ion-exchange membrane composed of cylindrical pores with a variable radius and/or a variable wall charge density has been developed and tested for the Donnan dialysis separation of aqueous Cs+/Pb2+ and Na+/Pb2+ mixtures with a Nafion 117 cation-exchange membrane. Model equations for ion and water transport take into account ion/fixed-charge site electrostatic interactions, electric-field-induced water dipole orientation, ion-hydration free-energy changes during ion partitioning, concentration-dependent transport parameters, and ion-pair formation between absorbed Pb2+ and the membrane fixed charges. An excellent match of theory with experimental concentration vs time and water flow vs time data was achieved using pores with a constant radius and a repeating high/low square-wave surface charge distribution (where the low surface charge was a consequence of ion pairing). The model could not reproduce Donnan dialysis transport data when (1) the pore radius...