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, Ox + e velence Red, between an electrode and a redox couple, the Butler-Volmer formalism predicts that the operative heterogeneous rate constant, k_(red) (cm s~(-1)) for reduction (or k_(ox) for oxidation) increases without limit as an exponential function of -alpha (E - E~(0)) for reduction (or (1 - alpha)(E - E~(0)) for oxidation), where E is the applied electrode potential, alpha (approx1/2) is the transfer coefficient and E~(0) is the formal potential. The Marcus-Hush formalism, as exposited by Chidsey (Chidsey, C. E. D. Science 1991, 215, 919), predicts that the value of k_(red) or k_(ox) limits at sufficiently large values of -(E - E~(0)) or (E - E~(0)). The steady-state currents at an inlaid disk electrode obtained for a redox species in solution were computed using both formalisms with the Oldham-Zoski approximation (Oldham, K. B.; Zoski, C. G. J. Electroanal. Chem. 1988, 256, 11). Significant differences are noted for the two formalisms. When k~(0)r_(0)/D is sufficiently small (k~(0) is the standard rate constant, r_(0) is the radius of the disk electrode, and D is the diffusion coefficient of the redox species), the Marcus-Hush formalism effects a limiting current that can be significantly smaller than the mass transport limited current. This is easily explained in terms of the limiting values of k_(red) and k_(ox) predicted by the Marcus-Hush formalism. The experimental conditions that must be met to effect significant differences in behavior are discussed; experimental conditions that effect virtually identical behavior are also discussed. As a caveat for experimentalists, applications of the Butler-Volmer formalism to systems that are more properly described using the Marcus-Hush formalism are shown to yield incorrect values of k~(0) and meaningless values of alpha, which serves only as a fitting parameter.