Implications of Marcus−Hush Theory for Steady-State Heterogeneous Electron Transfer at an Inlaid Disk Electrode

摘要

For an outer-sphere heterogeneous electron transfer, Oxne Red, between an electrode and a redox couple, thenButler Volmer formalism predicts that the operative het-nerogeneous rate constant, kred (cm s 1) for reduction (ornkox for oxidation) increases without limit as an exponen-ntial function of (E E0) for reduction (or (1 )(EnE0) for oxidation), where E is the applied electrodenpotential, (~1/2) is the transfer coefficient and E0 isnthe formal potential. The Marcus Hush formalism, asnexposited by Chidsey (Chidsey, C. E. D. Science 1991,n215, 919), predicts that the value of kred or kox limits atnsufficiently large values of (E E0)or(E E0). Thensteady-state currents at an inlaid disk electrode obtainednfor a redox species in solution were computed usingnboth formalisms with the Oldham Zoski approximationn(Oldham, K. B.; Zoski, C. G. J. Electroanal. Chem. 1988,n256, 11). Significant differences are noted for the twonformalisms.When k0r0/D is sufficiently small (k0 is thenstandard rate constant, r0 is the radius of the disknelectrode, and D is the diffusion coefficient of the redoxnspecies), the Marcus Hush formalism effects a limit-ning current that can be significantly smaller than thenmass transport limited current. This is easily explainednin terms of the limiting values of kred and kox predictednby the Marcus Hush formalism. The experimentalnconditions that must be met to effect significant differ-nences in behavior are discussed; experimental condi-ntions that effect virtually identical behavior are alsondiscussed. As a caveat for experimentalists, applica-ntions of the Butler Volmer formalism to systems thatnare more properly described using the Marcus Hushnformalism are shown to yield incorrect values of k0 andnmeaningless values of , which serves only as a fittingnparameter.