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

Abstract

In acidic media, three well-defined surface confined overall two electron transfer reactions derived from closely spaced oneelectron steps are observed in the DC and AC voltammetry of ½PMo 12 O 40 � 3À . In this study, parameterization of these processes by sinusoidal AC voltammetry at glassy carbon (GC) and boron doped diamond (BDD) electrodes has been undertaken in 1 M HClO 4 . The experiment-simulation comparison of even a simplified reaction scheme required estimation of 21 parameters, which is an exceptionally large number in voltammetry. The six reversible potentials were robustly recovered from data obtained at low (9.02 Hz) and higher (60.05 Hz) frequencies at both GC and BDD electrodes. Examination of the harmonic content by the Fourier transformed version of AC voltammetry enabled imperfections in the model associated with faradaic and non-faradaic aspects of the voltammetry to be readily detected. After consideration of these imperfections, all processes were considered to be reversible within experimental uncertainty. Subtle differences in reversible potentials observed at both electrodes account for electrode dependence in shapes of the overall two electron steps. Fits of experimental data were superior using BDD at both frequencies and for the higher frequency GC case. Non-compliance with an assumed potential independent model of the double layer capacitance was considered to be a significant contributor to discrepancies found with the GC electrode.[a] Dr.

A Voltammetric Perspective of Multi-Electron and Proton Transfer in Protein Redox Chemistry: Insights From Computational Analysis of Escherichia coli HypD Fourier Transformed Alternating Current Voltammetry

“…The acid dependence and simulation details for this and related polyoxometalates have been reviewed ( Bond, 2002 ). A fully analogous situation to the present study ( Robinson et al, 2018 ; Robinson et al, 2019 ) has been demonstrated to apply for surface confined reduction of [PMo 12 O 40 ] 3- ; in highly acid media it is shown to be well modelled by treatment as two closely spaced one-electron reduction steps rather than a simultaneous two-electron reduction processes. Conversely, more exotic electron-proton transfer schemes like the elegant “wedge” scenario are necessary for describing electron and proton transfer via an intermediate H-bond complex in some organic molecules ( Clare et al, 2019 ).…”

“…Other researchers have published work on the experimental measurement and theoretical modelling of solution phase voltammetry of such electrochemical-electrochemical stepwise multiple electron transfer processes ( Evans, 2008 ; Lopez-Tenes et al, 2014 ). We, and others, have published a number of analogous studies on surface confined species such as the H2ase-MFHypD system we describe here ( Finklea, 2001 ; Lee et al, 2011 ; Stevenson et al, 2012 ; Robinson et al, 2018 ; Robinson et al, 2019 ).…”

A Comparison of Bayesian Inference Strategies for Parameterisation of Large Amplitude AC Voltammetry Derived from Total Current and Fourier Transformed Versions

“…Data optimisation based on total current and harmonic percentage has been successfully employed in previous studies. [15,16,[44][45][46] Thus, as expected, the TCDS objective function provides an excellent fit to the synthetic data and excellent recovery for all parameters. On the other hand, the MLE-TCDS objective function slightly overestimates the faradaic component parameters and underestimates the non-faradaic capacitance ones as shown in Figures 3a, 3c, 3d, even for this simplest possible scenario where the double layer capacitance is simulated and fitted as a potential independent constant (c 0 ).…”

“…PINTS has been used previously to fit synthetic and experimental total current AC voltammetric data. [15,16,[44][45][46] However, a major advantage of large amplitude AC voltammetry, not available in the total current method, is access to resolved harmonics at integer multiples of the frequency of the applied sine wave. These harmonics provide variable levels of sensitivity to some of the parameters of interest in this study.…”

A perceived paucity of quantitative studies in the modern era of voltammetry: prospects for parameterisation of complex reactions in Bayesian and machine learning frameworks

“…The optimisation approach gives, at least for well-posed problems with close to perfect models, the globally optimal solution for the parameters of interest, but generally gives only point estimates of the parameter values. Parameterisation of over 20 variables from a single data set has been achieved using this approach [30].…”