Beyond the Butler–Volmer equation. Curved Tafel slopes from steady-state current–voltage curves

Abstract

We report the discovery and analysis of curved Tafel slopes from the electrochemical reduction of hexamminecobalt(III) under steady-state conditions. In order to confirm the existence of the curvature, random assemblies of carbon microelectrodes (RAMt electrodes) were employed to obtain experimental data over more than three orders of magnitude, without significant double layer charging currents and without ohmic distortion. Since the rate-determining step in the reduction reaction is electron transfer, and no ligand substitution reactions occur on the timescale of experiments, the curvature of the Tafel plot is attributed to the dependence of the symmetry factor on electrode potential.

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

“…A change in Tafel slope with potential can then be interpreted as a change in reaction mechanism. However, potential-dependent Tafel slopes have been observed for relatively simple redox processes [12][13][14][15]. Variation with electrode potential is also consistent with the Marcus theory (MT) of (heterogeneous) electron transfer [5,6].…”

“…The Marcus symmetry factor however varies linearly with the applied potential. To derive the entropic component, we first evaluate the activation entropy at constant overpotential (the intrinsic activation entropy) from Equation (7) (15) where S λ = −∂λ/∂T is the reorganisation entropy. S λ is a central parameter in the MT of electron transfer.…”

Giving physical insight into the Butler–Volmer model of electrode kinetics: Part 2 – Nonlinear solvation effects on the voltammetry of heterogeneous electron transfer processes

“…2 it can be concluded that the nonlinear solvation model predicts a potential-dependent transfer coefficient giving rise to curved Tafel plots. Experimental confirmation of this behavior was first documented by Savéant et al for the electroreduction of nitrocompounds [45], and later by Fletcher et al for the electroreduction of hexamminecobalt(III) at carbon microdisc electrodes [46] and by several authors for different electroactive self-assembled monolayers [6,[47][48][49].…”

A comparison of Marcus–Hush vs. Butler–Volmer electrode kinetics using potential pulse voltammetric techniques

“…Notable efforts have been made to theoretically and experimentally reveal the differences between the Butler-Volmer and Marcus-Hush kinetic models in the description and analysis of the electrochemical response [12][13][14][15][16][17][18][19][20][21][22][23][24]. It is theoretically predicted that significant discrepancies between both models exists in the case of slow charge transfer processes, which affects the values of kinetic parameters extracted.…”