Theory for double potential step chronoamperometry for any potential values at spherical electrodes: Simultaneous determination of the diffusion coefficients of the electroactive species

Abstract

We present a general and explicit analytical solution for double potential step chronoamperometry with any applied potential values ( E 1, E 2) corresponding to a reversible charge transfer process at spherical electrode. This solution is essential to analyze double pulse electrochemical techniques such as RPV and DPV. We consider unequal diffusion coefficients, initial presence of both electroactive species and that the reaction product can dissolve in the electrolytic solution or in the electrode. From the analytical equation obtained it is possible to deduce interesting simplified expressions for some particular cases: both species soluble in the electrolytic solution with equal diffusion coefficients, planar electrodes, ultramicroelectrodes when both species are soluble in the electrolytic solution, and double potential step chronoamperometry with limit current potentials ( E 1 − E ° ′ → − ∞ , E 2 − E ° ′ → + ∞ ). In this last case, when reaction product is not initially present it is pointed that planar electrodes and ultramicroelectrodes cannot be used for determining both diffusion coefficients. This interesting practical consequence can be demonstrated by means of the analytical expression deduced here, which represents a notable advantage in front of numerical results.