Abstract
AbstractThe thermodynamic and electrode kinetic parameters that describe each of the three unresolved proton‐coupled two‐electron transfer processes of surface‐confined Keggin‐type phosphomolybdate, [PMo12O40]3− adsorbed onto glassy carbon electrode in 1.0 M H2SO4 have been elucidated by comparison of experimental and simulated AC voltammmetric data. Modelling of this problem requires the introduction of over 30 parameters, although this may be reduced to about half this number when intelligent forms of data analysis are introduced. Heuristic (i. e., an experimenter based trial and error method) and automated data optimization approaches are integrated in this very extensive parameter estimation exercise. However, obtaining a unique solution remains challenging for reasons that are outlined. In the final analysis and using the automated strategy, estimates of six reversible potentials, lower limits of the six electron transfer rate constants, the double layer capacitance, uncompensated resistance and surface coverage are reported, with others (such as the charge transfer co‐efficient) present in the model being unobtainable for reasons that are provided. The fit to experimental data using parameters obtained by automated data optimisation is excellent and slightly superior to that obtained by heuristic analysis. The parameters obtained by either method account for differences in shapes and current magnitudes of each of the overall two electron processes.
Highlights
Background currentModelling undertaken assumes that a simple RuCdl time constant applies at each potential and thatCdl is independent of potential
To mimic the 3 surface confined processes summarized in Eq 2–4, a series of well-known relationships were employed in combination to give a total model as follows: 1. Electron transfer model: the Butler-Volmer relationship was used for each of the six electron transfer steps which requires the introduction of six E0, six k0 and six α parameters
The mathematically more sophisticated Marcus-Hush relationship could have been used to model the electron transfer steps and thermodynamic and kinetic dispersion could have been included to reflect any heterogeneity in electron transfer associated with nonuniformly surface confined POM
Summary
Background currentModelling undertaken assumes that a simple RuCdl time constant applies at each potential and thatCdl is independent of potential. Modelling undertaken assumes that a simple RuCdl time constant applies at each potential and that. Cdl depends on potential, in the DC component (Figure 1b), with a lower dependence being evident in the total current (Figure 1c) or fundamental harmonic (see discussion below) when the DC term is removed. Close to ideal behaviour is evident in the second, third and fourth AC harmonic components, which as predicted theoretically are entirely devoid of background current (see discussion below). The background current is not fully capacitive, on the DC time scale (pseudo-capacitive behaviour). The background current at a POM sub-monolayer covered GC electrode is derived from GC containing functional groups such as quinones etc and POM species whose comparison depends on potential. The POM modified electrode is highly heterogeneous and difficult to fully model
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