Divalent/monovalent cation uptake selectivity in a Nafion cation-exchange membrane: Experimental and modeling studies

The equilibrium uptake of monovalent/divalent cation salt mixtures by a Nafion perfluorosulfonic acid cation-exchange membrane has been investigated using experimental measurements and a theoretical model. Membrane concentrations were determined for Nafion equilibrated in 0.15 M solutions containing Ni2+, CU2+, Ca2+, or Mg2+ with a co-absorbed monovalent cation (Li+, K+, or Cs+). An equilibrium ion absorption model that accounts for ion hydration effects, the dielectric saturation of water molecules in a membrane pore, and the neutralization of tired-charges by ion pairing with divalent cations, was matched to the experimental data. When the extent of ion-pair formation was used as an adjustable parameter, the model predicted accurately both the monovalent and divalent cation concentrations (with an average error of 7.7%). Both theory and experiments showed that the monovalent cation selectivity was in the same order as observed previously during the uptake of monovalent/monovalent cation salt mixtures (i.e. the monovalent cation with the larger hard sphere radius was preferentially absorbed). The computed mobile divalent cation concentration in a Nafion pore was found to be dependent on the extent of monovalent cation absorption. The number of divalent cation/sulfonate fixed-charge-site ion pairs was found to be independent of the divalent cation type, but was controlled by the type and concentration of the co-absorbed monovalent cation. The fraction of ion-paired fixed charges was correlated with the membrane pore concentration of mobile divalent cations via a Frumkin adsorption isotherm.