A Method To Evaluate Heterogeneous Electron-Transfer Kinetic Parameters Using Convolution Integral Techniques (chronoamperometry, Monte Carlo, Newton-Cotes, Non-Reversible)

A data-analysis method was developed to evaluate the heterogeneous kinetic parameters, k('0) and (alpha), of a non-reversible electron-transfer with or without a following first-order deactivation of the electron-transfer product. The method is based on a convolution integral equation, which describes the time-dependence of the faradaic current at any applied overpotential. A Newton-Cotes formula and current data obtained from potential step chronoamperometric experiments are used to numerically approximate the convolution integral, which permits evaluation of the heterogeneous rate constant of the electron-transfer. Linear regression analysis of rate constants evaluated at several applied overpotentials permits calculation of the standard parameters, k('0) and (alpha). Computer-generated data were used to test the accuracy of several Newton-Cotes formulae for two forms of the convolution integral equation. The ability of the method to accommodate determinate and indeterminate errors in the experimental parameters used in data analysis was also studied. The accuracy and precision of this method permits determination of k('0) and (alpha) for all values of the first-order deactivation rate constant. The method is computationally so simple that it can be performed on a hand-held calculator.