Foot-of-the-wave analysis (FOWA), developed by Savéant and Costentin, has been an useful approach to estimate reaction rates of electrocatalytic reactions upon benchmarking the electrochemical mechanisms. In practice, the “foot” of an electrocatalytic cyclic voltammogram (CV), typically between the onset potential and E_cat/2 (where, E_cat is the peak potential of the catalytic CV), is chosen to fit with an appropriate FOWA equation for the analysis. The resulting curve is further fitted linearly to obtain the slope value and finally, the rate constant can be extracted for the electrocatalytic reaction. These reaction rates can also be related to the turnover frequencies (TOFs) of the electrocatalytic reactions of interest.

However, the selection of FOWA equations are different depending on the electrochemical mechanisms Our efforts to design website to perform FOWA focus on the most commonly reported electrocatalytic mechanism in the literature, such as EECC and ECEC, where E and C denote electron transfer step and the first chemical (most often, proton transfer) step of a multi-steps electrocatalytic reactions. We use the following FOWA equation for these mechanisms as reported by Savéant and coworkers.

where i is the catalytic current, i_p is the non-catalytic Faradaic current of the second redox couple, R is the universal gas constant, T is the temperature, n is the number of electron transfer processes per catalyst, F is the Faraday constant, v is the scan rate in V/s, TOF_max is the maximum turnover frequency, E is the applied potential, and E_redox is the potential where the catalyst undergoes a mechanistic redox process in the absence of a substrate or the potential for the redox couple at which catalytic turnover occurs.

Figure 1. An example of an ideal electrocatalytic CV under pure kinetic condition, typically called “S-shape” CV. FOWA performed on such CVs provide the K_FOWA that estimate the maximum TOF (TOF_max) of the reaction.

Figure 2. An example of a non-ideal “S-shape” CV but FOWA still can be performed considering E_redox = E_cat/2 (in Eq. 1) as the potentials at E_cat/2 are comparable considering both i_cat/2 values (red and blue).

Tafel plots help to benchmark the performance of molecular electrocatalysts for a particular reaction of interest by comparing the turnover frequencies (TOF) and overpotentials in logarithm scale. We use the following Tafel equation for the catalytic Tafel plot where turnover frequency (TOF) is described as a function of overpotential (η) as reported by Savéant and coworkers.

where TOFmax is the maximum turnover frequency calculated by FOWA, F is Faraday’s constant, R is the ideal gas constant, T is temperature in K, E°_A/B is the thermodynamic standard potential, E_cat/2 is the potential where catalytic current is at half maximum, and η is the overpotential in V.