Temperature Dependence of the Heterogeneous Ferrous‐Ferric Electron Transfer Reaction Rate: Comparison of Experiment and Theory

Abstract

We describe experiments on the temperature dependence of the rate of the ferrous-ferric electron transfer reaction at a gold electrode and compare them with a detailed molecular dynamics simulation which is used to predict the rate. We find from the experiments that the temperature dependence of the rate has the Arrhenius form over the temperature range from 25 to 275~ and that the transfer coefficient is independent of temperature in this range. The molecular dynamics simulations are used in two ways to extract activation energies and transfer coefficients for comparison with experiment. In one of these methods, we assume parabolic dependence of the energies for the product and reactant in a reaction coordinate which is not specified a priori. In the other method, we use a quantum mechanical calculation extrapolated from the very short molecular dynamics time scale to times characteristic of the electron transfer rate. The assumption of parabolic dependence of the energies gives an estimate for the activation energy which is consistent with experiment. The transfer coefficient calculated using this assumption is also consistent with experiment. The activation energy and the transfer coefficient from the quantum mechanical calculation are both lower than the experimental values. The quantum mechanical method, together with a molecular orbital calculation of the electron transfer matrix element, permits a theoretical estimate of the absolute value of the rate, which is also compared with the experimental result. These results show that the ferrous-ferric reaction, which is a single-step outer-sphere charge-transfer reaction, follows the classical Butler-Volmer equation at temperatures up to 275~ and that earlier results on other reactions giving a temperature dependent transfer coefficient are likely to arise from elementary steps other than outer-sphere charge transfer.

The temperature dependence of the symmetry factor for a model Fe3+(aq)/Fe2+(aq) redox half reaction

“…All numerical studies of ferrous-ferric electron transfer agree that the symmetry factor β = 1/2 at rG 0 = 0 with the expected linear dependence on thermodynamic driving force [36,37,[39][40][41][42]. Temperature effects have been investigated as well and were also found to be consistent with the MT [16,20,21]. These calculations were, however, carried out under constant overpotential.…”

“…For parabolic free-energy curves, the reorganisation energy λ is the same for all reaction free energies μ and therefore also its temperature derivative S λ . The potential dependence of the intrinsic activation entropy Equation (15) is again proportional to μ (16) and vanishes at zero overpotential. The potential dependence of ‡S • μ is more complicated.…”

“…For example, when enthalpic effects dominate (β H β S ), Tafel slopes (Equation (3)) are expected to vary linearly with temperature which is the commonly observed behaviour. However, anomalous temperature dependence of the Tafel slope has been found not only for complex reactions [29][30][31][32] but also for simple outer-sphere electron-transfer processes [11,16]. An extreme anomalous effect would be a temperature-independent Tafel slope.…”

Interfacial Bond-Breaking Electron Transfer in Mixed Water–Ethylene Glycol Solutions: Reorganization Energy and Interplay between Different Solvent Modes

“…The environmental reorganization was found to be strongly asymmetric (the effect of the asymmetric intramolecular reorganization on the activation barrier of interfacial electron transfer reactions was thoroughly investigated in work 51 ), that is, λ⃗ s and λ⃖ s values differ significantly; the asymmetry parameter v = λ⃗ s / λ⃖ s ranges from 0.2 to 1.2. The average values (λ s ) were computed using the formula: 39,40 …”

Molecular Dynamic Simulations in Interfacial Electrochemistry

“…Following earlier work by Warshel, [171][172][173] Halley and Hautman 174 and Curtiss et al 175 presented an approximate numerical scheme to calculate the nonadiabatic electron transfer rate under the above conditions. The method is based on solving Eq.…”