Charge-TransferCoefficient in the Kinetics of Single-and Multi-electron Transfer Redox Reactions

Single-step single-electron and multi-step multi-electron transfer reactions in neutral and acidic media, respectively, are investigated using a rotating-disk electrode (RDE) assembly as a function of temperature. The estimated kinetic current (<i>i</i>_k) is analyzed using the classical Butler–Volmer (B–V) equation for single-step single-electron transfer reactions and the generalized B–V equation for multi-step multi-electron transfer reactions. The <i>i</i>_k estimated as a function of temperature at very small intervals of overpotential (η) is used to determine the apparent activation enthalpy (Δ<i>H</i>^#) and the pre-exponential factor (<i>A</i>_f) (containing the apparent activation entropy (Δ<i>S</i>^#)) from the Eyring analysis. The trends in the Δ<i>H</i>^# and <i>A</i>_f with η are analyzed. The plots of Δ<i>H</i>^# and <i>A</i>_f as a function of η exhibit the same number of slopes as that of the Tafel plots, corresponding to either a change in the rate-determining step (rds) or a change in the fractional coverage by the adsorbed intermediates in the kinetically operable overpotential range. Consequently, the estimated symmetry factor (β) or charge-transfer coefficient (α) values from both the Tafel and Eyring analyses reach a general consensus and explain the α values greater than 1 for multi-step multi-electron transfer processes. From the η dependence of Δ<i>H</i>^# and Δ<i>S</i>^#, the enthalpic and entropic components of β and α are estimated. Such analysis enhances the understanding of the significance of β and α, aiding the evaluation of the kinetic parameters, the interpretation of the proposed reaction mechanism, and the identification of rds.