Current efficiency of an ion-selective membrane: Effect of fixed charge distribution

Abstract

The effect of fixed charge distribution, C3, in an ion-selective membrane on its current efficiency, £b, is investigated. An intuitive parameter M2, which is a measure for the nature of C3, is proposed, and three families of fixed charge distribution, including linear, exponential, and trigonometric, are examined. Under the condition that the total amount of fixed charges is constant, M2 has the positive maximum M2max if all fixed charges are near the right membrane-liquid interface, and the negative minimum M2min if all fixed charges are near the left membrane-liquid interface. Any other type of fixed charge distribution has an M2 value between these two extremes, and if C3 is uniform, M2 = 0. It is found that £b is closely related to M2. In other words, the latter can be used to predict the former. We show that: (i) the value of £b for M2 < 0 is smaller than that for M2 = 0; (ii) if M2 > 0, the variation of £b as a function of M2 has a maximum; (iii) if M2 < 0, £b decreases with the increase in current density and reverse is true for M2 > 0, and (iv) if M2 = 0, £b is independent of applied current density.