Current-induced concentration polarization of interfaces between non-ideally perm-selective ion-exchange media and electrolyte solutions

In non-ideally perm-selective ion-exchange media and/or nano-porous/nano-channel systems, ion transport numbers depend on the salt concentration. Under conditions of current-induced polarization, this concentration changes considerably close to the membrane surface or nano-/micro-interface. It is well known that the value of limiting current is controlled (among other things) by the difference of counter-ion transport numbers between the membrane and solution. Thus, a natural question arises about what value of concentration has to be used in the estimates of the difference of transport numbers and, thus, of limiting current. At first glance, it appears that one should use the value of salt concentration occurring at the polarized interface. If this were correct, there would be a positive feedback in the process of concentration polarization making the latter self-sustaining. This communication shows that, rather surprisingly, the limiting current is controlled by the counter-ion transport number taken at the salt concentration occurring at the “opposite” membrane side where the salt concentration goes up (in the limiting case of dominant diffusion resistance of membrane as compared to the unstirred layer). Accordingly, the positive feedback does not occur. Besides, the limiting current can considerably depend on the stirring conditions close to the “back” membrane surface, which has not been generally recognized previously and can be important for the experimental practice. This result has been obtained via explicit solution of the ion-transport problem in the membrane phase.