Mathematical Framework Underlying the In Situ Electrochemical Diagnosis of Adsorbed Intermediates Formed during Redox Reactions at Electrode Surfaces

Previously, we have presented an electrochemical technique wherein an electroactive tracer species is employed to probe the rate-limiting factors governing redox reactions at an electrode surface. In this technique, the electrode is first held potentiostatically to facilitate a redox process (step 1), and then the potential is released to open circuit conditions (step 2) so as to monitor the time-dependent re-equilibration of the electrode potential in the presence of the tracer. The time-dependent potential response in step 2 has been shown to contain information about diffusion-limited or desorption-limited steps, enabling in situ probing of the electrochemistry at the electrode surface during step 1. In the present contribution, a theoretical model governing the transient response in step 2 is developed for two limiting cases: diffusion-limited and desorption-limited recovery of the electrode potential. Mathematical modeling shows that, during re-equilibration, the step 2 potential transient corresponding to a case where step 1 involves surface adsorbed species which undergo desorption in step 2 exhibits a much longer time constant than that when re-equilibration occurs under diffusion limitations. The mathematical framework presented herein provides a sound fundamental basis for applying the aforementioned technique to studying adsorption-desorption processes during electrochemistry. Also, technique limitations are presented in light of the modeling findings. A technique is presented wherein a tracer redox couple is employed to probe for adsorbed electrochemically-active reaction intermediates.Mathematical modeling is used to quantify the electrode potential transient back to open circuit following redox reactions for a diffusion-limited and a desorption-limited system.In a desorption-limited system, the electrode potential drifts to open circuit slowly compared to a diffusion-limited system. In experiments, such an effect if observed can be suggestive of the presence of adsorbed intermediates.