Model-Free Kinetic Data Analysis Using Massive Dynamic Impedance Data Sets
Authors: Sacci Robert L , Harrington David A. 
Published: February 2020

Dynamic Electrochemical Impedance Spectroscopy (dEIS) enables the collection of impedance data sets continuously as a slow-sweep cyclic voltammogram is carried out. Provided that careful baseline corrections are carried before the Fourier analysis of the multisine signal and the lowest frequency is not too low for the chosen sweep rate (typically 1 Hz at 2 mV s-1), then it may be shown that the impedance data is valid, for example by the Kramers-Kronig transformation [1]. The method can measure the dynamic state of the surface, and the correlation with the voltammetric features, such as integrated charges or subtle changes in the peak shape, assists in the interpretation.

The enormous amount of data produced, e.g., spectra every 1 mV over 3 V for a voltammetry cycle, is daunting in terms of data analysis (and required disk space), but this is solved to some extent by automated batch fitting to equivalent circuits. However, the large data density offers the possibility to deduce the form of the rate law in a model-free kinetic data analysis, rather than the more usual propose-mechanism—fit—reject--modify cycle of identifying reaction mechanisms. This cycle frequently fails because (1) many standard assumptions are oversimplified, and (2) the real behaviour may be outside known models. Consider the surface reaction step that is key in many small molecule oxidation mechanisms,

                             OH(ads) + CO(ads) → CO2 + H+ + e- + 2(site)     rate = kθ
OH·
θ
CO

The rate law is written as a product of coverages, θ,  in the most common, but oversimplified, Langmuir (mass-action) form. An unrealistically high maximum coverage of one adsorbate per metal site is typically assumed. There is controversy over whether this proceeds by random collisions between mobile adsorbed species, or at the edge of islands of the adsorbed species (nucleation-collision-growth kinetics). This debate hinges on the surface diffusion rate, and it needs to be remembered that these are extremes. Interactions between adsorbed species are sometimes modeled by the Frumkin isotherm, which is only approximate. Adsorption of OH and mass transport of CO typically involve approximations. Anion adsorption can be significant in these types of reactions, but is usually not explicitly invoked. This type of complexity thwarts conventional kinetic analysis. 

We illustrate an alternative method, applied here to the simpler case of the oxide formation and reduction on polycrystalline Pt and Pd. The kinetics are characterized by seeking (i) the net rate of production of the adsorbed species as a function of both coverage and potential, r(θ,E), and (ii) the current density as a function of these variables, j(θ,E). Under the very generic assumption that these rates are some (unknown) function of coverage times some function of potential times some function of bulk concentration (mass transport being fast for this system), we can show that the experimental quantity R
ct times the voltammetry current density must be the function of the potential divided by its derivative with respect to potential. Integration of this ratio with potential at constant coverage and concentration then shows (for this system) that the data obeys the Tafel relationship and enables extraction of the transfer coefficient without assuming any functional form for the coverage and concentration functions. Similar tests may be devised to determine the latter functions, and in this way, the rate law may be deduced directly from the data.

[1] R.L. Sacci, F. Seland and D.A. Harrington, Dynamic Electrochemical Impedance Spectroscopy for Electrocatalytic Reactions, Electrochim. Acta., 131 (2014) 13-19.

* Present address, Oak Ridge National Laboratory