Computational and experimental determination of electrochemical standard rate constant from cyclic voltammetry: insights into <i>α</i> + <i>β</i> ≠ 1 systems

In this work an in-depth examination of the soluble-soluble electrochemical system is presented, focusing on the challenge of accurately describing redox kinetics when the cathodic and anodic transfer coefficients do not necessarily sum to unity (<i>α</i> + <i>β</i> ≠ 1). A detailed approach that combines simulation calculations with experimental testing through cyclic voltammetry (CV) was employed. Kinetic curves with interpolation equations were established for the determination of the electrochemical standard heterogeneous rate constant (<i>k</i> ⁰). These kinetic curves illustrate the relationship between the difference in anodic and cathodic cyclic voltammetric peak potentials (Δ<i>E</i> _p), the cathodic charge transfer coefficient (<i>α</i>), and <i>k</i> ⁰. Interpolation equations were derived for both cases, when <i>α</i> + <i>β</i> = 1 and when <i>α</i> + <i>β</i> ≠ 1, allowing a more comprehensive treatment of electron transfer kinetics, and additional kinetic curves were added. Experimental validation of these theoretical kinetic results was carried out by analyzing CVs for the electro-oxidation of ferrocyanide yielding a <i>k</i> ⁰ value of (4.76 ± 0.49) × 10^-6 m s^-1 with an average deviation between theoretical and experimental Δ<i>E</i> _p of 0.024 ± 0.014 V. The close alignment between the theoretical voltammograms and experimental results highlights the reliability of the model and marks a significant step forward in accurately characterizing electrochemical reaction kinetics.