Rigorous Analysis of Reversible Faradaic Depolarization Processes in the Electrokinetics of the Metal/Electrolyte Solution Interface

Abstract

The bipolar faradaic depolarization of the interface metal/solution is examined for the situation in which the transversal electron transfer is limited by mass transfer of the components of a reversible redox couple. Transversal diffusion of the electroactive species to and from the surface and lateral convective mass transport, resulting from a pressure gradient applied along the surface, are taken into account. The analysis first focuses on the case in which the lateral electric field required for bipolar behavior is externally applied through the solution. Numerical analysis of the intrinsic nonlinear coupling between the convective-diffusion equation and the Poisson equation for finite currents allows derivation of the spatial distribution of the potential and the concentration profiles of the electroactive species. The corresponding distribution of the local faradaic current density along the metallic surface and the ensuing overall bipolar current are obtained. Characteristics of the conductivity curves, bipolar current versus applied field, are given for different sets of electric and hydrodynamic parameters. Then, on the basis of these results, the analysis of bipolar faradaic depolarization process is extended to electrokinetic phenomena, in particular streaming potential.

Induced-charge electrokinetic phenomena

“…(The system then resembles two electrochemical cells in series.) Under direct current conditions, Duval et al [97,98,99,100] have shown that Faradaic reactions with a known redox couple can alter the electrokinetic 11 response of the metal surface, and the groups of Crooks and Tallerek [101,102,103] have shown how water and buffer reactions can lead to electric field gradient focusing of charged analytes, due to the spatially dependent electrophoretic velocity near the bipolar electrode. It would be interesting to extend the models in these papers to include diffuse-layer effects on reaction rates (the generalized Frumkin correction to the Butler-Volmer equation [104,105]) and apply them to AC forcing of the bipolar electrode with a DC bias, or other examples of ICEO phenomena described above.…”

Electrokinetics of the amphifunctional metal/electrolyte solution interface in the presence of a redox couple

“…Calculation of the corresponding zeta-potential may be performed using the classical linear Helmholtz-Smoluchowski (H-S) equation [22][23][24][25]. If the solution between the two conducting surfaces contains a redox couple, and a lateral potential is either externally applied in the solution across the cell [26] or generated by tangential hydrodynamic flow [12,19], faradaic depolarization takes place. The potential distribution in the thin solution layer adjacent to the surfaces leads to reduction of Ox at one side of the surface and oxidation of R at the other.…”

“…The steady state streaming current, generated upon application of a pressure gradient P , is balanced by the countercurrent, which now contains an electronic contribution. The resulting streaming potential ϕ str is defined by the H-S equation, extended with a bipolar conductance term [19] ε 0 ε r ζ P η…”

“…Rigorous estimation of I f requires numerical treatment of the coupled Nernst-Planck equation, describing the lateral convective and transversal diffusive transports of the Ox/R species, and the Poisson equation, which relates the potential and local faradaic current distributions in the solution. The theory reported in [19] is valid for steady state situations under the assumption that there is a sufficiently large excess of indifferent ions over the reversible redox species (as assumed in Section 3) to render the latter insignificant for the DL composition. I f is a function of a, K L , and the redox concentrations c * Ox , c * R .…”

“…Using newly developed, rigorous theory accounting for the nonlinearity of the lateral electric field as generated in streaming potential measurements [19], determination of the ζ potentials corresponding to the data in [12] is carried out. The results are discussed in connection with the validity of the hypothesis of electrochemical reversibility for the redox-active species under the convective conditions encountered in the electrokinetic experiments.…”