Short communication

Determination of electrochemical kinetic parameters using the bond-henderson-oldham“global analysis”

Global Analysis is applied to simulated cyclic voltammograms obtained at electrodes with cylindrical geometry to calculate the characteristic transport, kinetic and thermodynamic parameters that describe the electron transfer process. The capacity to directly analyze for various electron transfer models is also demonstrated and the results indicate that the accuracy in obtaining the important transport, kinetic and thermodynamic parameters is excellent.

The electrochemical reduction of 3-cyanopyridine, 1, and 2,6-dicyanopyridine, 2, has been studied in N,N-dimethylformamide. Each compound undergoes a one-electron reduction to form the corresponding anion radical and the anion radicals dimerize to form σ-dimer dianions that are oxidized at potentials considerably less negative than the original reduction process. At 298 K the dimerization rate constants are 4.1 × 10⁴ and 6.45 × 10⁴ M⁻¹ s⁻¹ (3.7 × 10⁴ M⁻¹ s⁻¹ in drier solvent) for 1 and 2 respectively. For both 1 and 2, the dimerization is completely irreversible at 298 K but for 2 reversibility begins to appear at slow scan rates at higher temperatures as evidenced by the growth of an anodic peak due to oxidation of the anion radicals to the original neutral 2.

Global Analysis is applied to cyclic voltammograms obtained with the inlaid disk electrode geometry to calculate the characteristic transport, kinetic and thermodynamic parameters that describe the electron transfer process. The approximation that the concentration of the electroactive species at the electrode surface can be obtained by convolution of the current with a function appropriate under reversible conditions is tested. The results indicate that the approximation becomes less valid when the influence of combined slow electron transfer and mixed diffusion is apparent, which affects the accuracy of kinetic parameters but has only minor effect on the thermodynamic and transport parameters.

Convolutive modeling provides a valuable alternative to digital simulation as a means of predicting the outcome of a voltammetric experiment, for comparison with the laboratory version. Methods based on either of two conjugate functions are described, differing in the direction that the convolution takes. Other than the requirement of uniform accessibility of the electrode surface, convolutive modeling places few restrictions on the range of experiments that may be modeled. The electrode reaction may have any degree of reversibility and may, or may not, be coupled to a first-order chemical process. The diffusivities of the reactant and product may be equal or unequal. The current may be the controlled electrical variable, or the current may be monitored in an experiment in which the potential is controlled. A range of experimental techniques is addressed in this article, including current-reversal chronopotentiometry and cyclic voltammetry without and with a following chemical reaction. Algorithms are reported for each of the two convolution routes. Examples treated in detail include both planar and spherical diffusion fields. The heterogeneous rate constant was varied in all instances, reversible, quasi-reversible, and near-irreversible cases being considered. Differences between the predictions of the two routes was found to be insignificant, both of the theoretical voltammograms agreeing excellently with analytical formulas, where these are available for comparison. In the case of quasi-reversible cyclic voltammetry, the prediction of the convolutive model was evaluated by global analysis: the input parameters were recovered with only minor discrepancies.

Sensitivity analysis is a commonly accepted methodology of studying the effect of parameter variations on the behaviour of mathematical models in various branches of chemical kinetics. However, it has not yet found wider application in electrochemical kinetics. In this paper we perform an introductory investigation of the utility of formal methods of sensitivity analysis for the modelling of electrochemical transients. We calculate and analyse first-order parametric sensitivity coefficients for the cyclic voltammetric transient corresponding to a quasi-reversible charge-transfer reaction E_qrev, assuming potential-dependent charge-transfer coefficients, and for the chronopotentiometric transient corresponding to a C_revE reaction mechanism, taken as example problems. We show that this local sensitivity analysis provides straightforward quantitative answers to a number of fundamental questions about the dependencies of the transients on model parameters. Therefore, we recommend that sensitivity analysis be used in conjunction with traditional digital simulations, resulting in an added insight into the behaviour of kinetic models.

A procedure which utilizes a linearized version of the Oldham–Zoski current-potential equation has been developed for the evaluation of electrode kinetic parameters from near-steady state voltammograms obtained at microdisk electrodes. The inherent advantage of the method is its mathematical simplicity relative to the other procedures already available in the literature. The procedure is applied to synthetic data obtained under near-steady state conditions from the fast quasi-explicit finite difference simulation of quasi-reversible electron transfer at a microdisk electrode. A procedure using non-linear optimization based on the Marquardt algorithm is also applied to the simulated data. Near-steady state voltammograms showing the effect of a potential dependent charge transfer coefficient are presented and analyzed. The robustness of the analysis is tested with voltammograms containing a random noise component and the near-steady state terms inherently present in experimental data. Application of the Oldham–Zoski equation to the simulated voltammograms enables the fidelity of both methods to be established over a wide range of heterogeneous kinetic conditions.