Current Efficiency of Ion-Selective Membranes: Effects of Local Electroneutrality and Donnan Equilibrium

The current efficiency, E, of the transport of ions through an ion-penetrable, charged membrane is investigated. Two assumptions often made in the literature, namely, local electroneutrality and Donnan equilibrium, are discussed quantitatively. We show that, if the concentration of fixed charges, C 3, is sufficiently high, the former is appropriate except for the region near the liquid−membrane interface. The deviation from local electroneutrality is alleviated if Donnan equilibrium can be assumed. In general, if C 3 is low, the local electroneutrality is unsatisfactory. Typically, assuming local electroneutrality will overestimate E to an extent on the order of 10% for a high C 3 and 30% for a low C 3 . If C 3 is high, the effect of fixed charge distribution on E is marginal, regardless of whether Donnan equilibrium is satisfied. It is significant, however, for the case where C 3 is low. For a fixed total amount of fixed charges, linear fixed charge distribution leads to a higher E than sinusoidal fixed charge distribution.