Theory of ion-transfer kinetics at a viscous immiscible liquid/liquid interface by means of the Langevin equation

In the ion-transfer kinetic model at the immiscible liquid/liquid interface presented here, the transfer of an ion is controlled by an activation energy and velocity of the ion in the viscous interface. The model was enlightened by the insufficient agreement of the potential dependence of the experimental transfer coefficient with the Butler equation and by a loss of a reasonable physical meaning in the activationless kinetic theory based on the Nernst-Planck equation. The velocity of the large spherical ion in this model was driven by the desolvation energy, the energy of overcoming the interfacial tension between the two liquids, the electrostatic energy in the double layer, and the thermal fluctuation. It is retarded by the viscous force, as expressed by the Langevin equation. The activation energy resulted from the first three energies. The kinetic equation was derived from the expressions for the velocity and the activation energy through the Boltzmann's distribution equation. It could elucidate both properties of the activation control and of the viscous control. The equilibrium condition did not lead to the Nernst equation because the frictional energy should be compensated with the potential difference between the two phases. The logarithmic forward rate constant was approximately linear with the potential difference. However, the theory could not explain quantitatively the non-linearity observed experimentally for small non-spherical anions. Copyright (C) 1996 Elsevier Science Ltd