Ion transport dependence on the ion pairing/solvation competition in cation-exchange membranes

Effect of ion-pairing on ion partitioning at equilibrium and on transport properties is studied by means of the Poisson-Nernst-Planck (PNP) equations. Owing to the low electrolyte solution relative permittivity (εS) and the high ion density in the membrane, the excess terms of the chemical potential must be computed. In this aim, the density functional theory and the binding mean sphere approximation were used in order to extend the PNP equations and to compute the association constant. The counter-ion/fixed-charge-group pairing and the counter-ion/co-ion one were examined. In the case of monovalent fixed charge, the total density of co-ion and the free one decreases with εS owing to the solvation contribution. So that it induces a decrease of the membrane system conductivity. If the counter-ion/co-ion pairing is considered, the free co-ion density and the conductivity increase when εS reaches small values. However in the ohmic regime, this dependence of the conductivity towards the free co-ion density is not always fulfilled.