Av. Sokirko et Fh. Bark, DIFFUSION-MIGRATION TRANSPORT IN A SYSTEM WITH BUTLER-VOLMER KINETICS, AN EXACT SOLUTION, Electrochimica acta, 40(12), 1995, pp. 1983-1996
Steady one-dimensional electrolysis of a metal salt in a system with a
supporting electrolyte is considered. The electrolyte in the system i
nvestigated is made up of three ionic species, one of which takes part
in the electrode reactions. Attention is restricted to the quite comm
on cases where the transfer coefficient in the Butler-Volmer law for t
he electrode kinetics is 1/2. For reasons of algebriac simplicity, the
main part of the paper deals with the special case with two species o
f cations of charge numbers 2 and 1, respectively, and one species of
anions of charge number 1. However, all results are easily generalized
to any set of charge numbers. In the special case of a binary electro
type, an exact explicit simple expression is computed for the polariza
rion curve. Also the drops in ohmic potential, concentration overpoten
tial in the electrolyte and the surface overpotentials. are computed a
s functions of the electric current density. In the general case with
three ionic species, an exact expression for the polarization curve is
given in implicit form. In the limiting case of the polarization curv
e and the aforementioned parts of the difference in potential between
the electrodes. For the diffusion layer configuration, and explicit ex
pression for the polarization curve is computed for a system with arbi
trary charge numbers and a more general form of the Butler-Volmer law.