Rate constant for ion transfer in inhomogeneous media at the interface of immiscible electrolytes

An expression for the impedance due to ion transfer across the interface of immiscible electrolyte solutions (ITIES) is derived, assuming a continuous change of the ionic resolvation energy across an interfacial layer. The model is analogous to the Goldman constant field approximation. The result is practically identical to the one obtained assuming an activated step occurs during the transfer, i.e., the classical Butler-Volmer relationship, so that the standard rate constant k(0) in the Butler-Volmer theory is replaced by the quantity D/delta, where D is the average diffusion coefficient of the transferring ion inside the interfacial layer and delta is the thickness of the interfacial layer. At potentials close to the standard transfer potential, the apparent charge-transfer coefficient alpha takes the value of 1/2. Combination of the charge-transfer impedance and an inner layer capacitance in parallel gives a complete semicircle in an impedance plot, characteristic of a parrallel RC circiut.