Consequences of a potential-dependent transfer coefficient in ac voltammetry and in coupled electron–proton transfer for attached redox couples

The Marcus density-of-states model for simple electron transfer predicts that the transfer coefficient is dependent on overpotential. The nature of the potential dependence is a function of the reorganization energies associated with oxidation and reduction processes. A fifth-order polynomial expression accurately yields the potential dependence of the transfer coefficient and the resulting curved Tafel plots. With this polynomial expression, the effects of the potential-dependent transfer coefficient are examined for two cases, ac voltammetry of an attached redox molecule with simple electron transfer and the kinetic behavior of the 1-electron/1-proton redox system. Simulations of ac voltammograms indicate that the effects are minor and that ac voltammetry is poorly suited for determination of the reorganization energy of the redox molecule. In the coupled electron–proton redox case, the effects are marked. As expected, the apparent standard rate constant decreases dramatically at pH values between the pKa values of the two oxidation states. More surprisingly, the simulated Tafel plots exhibit asymmetry between the anodic and cathodic branches depending on the pH. The path of electron transfer from the oxidized to the reduced species (electron–proton or proton–electron) at a fixed pH depends on the electrode potential.