Use of Bayesian Inference for Parameter Recovery in DC and AC Voltammetry

Abstract

We describe the use of Bayesian inference for quantitative comparison of voltammetric methods for investigating electrode kinetics. We illustrate the utility of the approach by comparing the information content in both DC and AC voltammetry at a planar electrode for the case of a quasi‐reversible one electron reaction mechanism. Using synthetic data (i. e. simulated data based on Butler‐Volmer electrode kinetics for which the true parameter values are known and to which realistic levels of simulated experimental noise have been added), we are able to show that AC voltammetry is less affected by experimental noise (so that in effect it has a greater information content then the corresponding DC measurement) and hence yields more accurate estimates of the experimental parameters for a given level of noise. Significantly, the AC approach is shown to be able to distinguish higher values of the rate constant. The results of using synthetic data are then confirmed for an illustrative case of experimental data for the [Fe(CN)6]3−/4− process.

Models and Their Limitations in the Voltammmetric Parameterization of the Six‐Electron Surface‐Confined Reduction of [PMo12O40]3− at Glassy Carbon and Boron‐Doped Diamond Electrodes

“…In recent work, the Oxford Computing and Monash University Electrochemistry Groups have been developing protocols that reliably and efficiently parameterize complex electrochemical processes (see for example). In summary, very large data sets containing current, potential, and time domain information are collected at high resolution using instrumentation having 18 bit DAC and ADC converters . Experiment‐theory comparisons are then undertaken at levels ranging from fully heuristic to highly automated data optimization multi‐parameter fitting exercises in attempts to define uniquely the thermodynamic, kinetic, capacitance and resistance and other parameters that are included in the model.…”

Integration of Heuristic and Automated Parametrization of Three Unresolved Two‐Electron Surface‐Confined Polyoxometalate Reduction Processes by AC Voltammetry

“…As an alternative to the fully heuristic method, multi‐parameter fitting aided by computationally efficient data optimization or more sophisticated approaches are now available to assist with solving the inverse problem in voltammetry ,. Data optimization methodology, underpinned by statistics and facilitated by high speed computing, has been developed to support many branches of science.…”

“…As an alternative to the fully heuristic method, multiparameter fitting aided by computationally efficient data optimization or more sophisticated approaches are now available to assist with solving the inverse problem in voltammetry. [8,[10][11][12][13][14][15][16][17][18] Data optimization methodology, underpinned by statistics and facilitated by high speed computing, has been developed to support many branches of science. Now, just as there are many voltammetric simulation packages available for modelling the forward problem, there is an extensive range of software packages available to support complex theory-experiment data optimization exercises.…”

Separating the Effects of Experimental Noise from Inherent System Variability in Voltammetry: The [Fe(CN)_6]^3−/4− Process

“…For comparison, the right column plots show the samples of θ i with no hierarchical model (and thus no hyper-parameter samples). This is identical to the analysis done in our previous paper 1. Histograms of hyper-parameter samples of µ (left) and Σ (right) obtained by applying the hierarchical MCMC algorithm 1 to the ten experimental ac voltammetric datasets for the reduction of aqueous 1 mM [Fe(CN) 6 ] 3− .…”