Current efficiency of an ion-exchange membrane: Effect of piecewise continuous fixed charge distribution

The current efficiency eta for the transport of ions through an ion-exchang e membrane is analyzed theoretically. In particular, the effect of discreti zing the fixed charges contained in the membrane into charged intervals on eta is investigated. We show that if the applied current density I is low, a membrane with a continuous linear fixed charge distribution has a higher eta than a membrane with evenly distributed charged intervals, and the larg er the number of charged intervals the lower the eta. If I is high, a membr ane with randomly distributed charged intervals may have a higher eta than that of a membrane with a continuous linear fixed charge distribution. It c an be inferred that, as far as raising eta is concerned, distributing fixed charges discretely and/or randomly in a membrane has no practical advantag e.