ARTICLE pubs.acs.org/ac
Implementation of a Statistically Supported Heuristic Approach to Alternating Current Voltammetric Harmonic Component Analysis: Re-evaluation of the Macrodisk Glassy Carbon Electrode Kinetics for Oxidation of Ferrocene in Acetonitrile Elena Mashkina and Alan M. Bond* School of Chemistry, Monash University, Clayton, 3800, Victoria, Australia
bS Supporting Information ABSTRACT: Sinusoidal large amplitude ac voltammetric techniques generate very large data sets. When analyzed in the frequency domain, using a Fourier transform (FT)-band filtering- inverse FT sequence, the data may be resolved into the aperiodic dc, fundamental, second, and higher order ac harmonics. Each of these components exhibit a different level of sensitivity to electrode kinetics, uncompensated resistance and capacitance. Detailed simulations illustrate how the heuristic approach for evaluation of each data subset may be implemented and exploited in the assessment of the electrode kinetics for the fast Fc h Fcþ þ e (Fc = ferrocene) oxidation process at a glassy carbon macrodisk electrode. The simulations presented in this study are based on the Butler-Volmer model and incorporate consideration of the uncompensated resistance (Ru), double-layer capacitance (Cdl), rate constant (k0), and charge transfer coefficient (R). Error analysis of the heuristically evaluated simulation-experiment comparison is used to assist in establishing the best fit of data for each harmonic. The result of the heuristic pattern recognition type approach for analysis of the oxidation of ferrocene (0.499, 0.999, and 5.00 mM) at a glassy carbon macrodisk electrode in acetonitrile (0.1 M Bu4NPF6) implies that k0 g 0.25 cm s-1 on the basis of analysis of the first 4 harmonics and plausibly lies in the range of 0.25-0.5 cm s-1 with R = 0.25-0.75 when analysis of the next four harmonics is undertaken. The k0 value is significantly faster then indicated in most literature reports based on use of dc cyclic voltammetry under transient conditions at glassy carbon macrodisk electrode. The data analysis with a sinusoidal amplitude of 80 mV is conducted at very low frequency experiments of 9 Hz to minimize contribution from electrode heterogeneity, frequency dispersion, and adsorption, all of which can complicate the response for the oxidation of Fc in acetonitrile at a glassy carbon electrode.
he ferrocene (Fc)-ferrocenium (Fcþ) redox couple (Fc0/þ) has been of wide interest for over 50 years.1 Under many circumstances, such as those encountered under dynamic voltammetric conditions at a macrodisk electrode, the one-electron oxidation process (eq 1) is close to reversible2
T
Fc h Fcþ þ e
ð1Þ
The Fc0/þ redox couple is highly significant in the voltammetric literature because it has been recommended by IUPAC for reference potential calibration purposes1 on the basis that the process is commonly found to be close to reversible and because the solvent dependence of the reversible formal potential (E0) is theoretically small. While the process is often assumed to be fast, the exact value of the heterogeneous electron charge transfer rate constant (k0) for this process has been of considerable debate. Initially, the majority of studies used to estimate k0 employed cyclic voltammetry at a macrodisk electrode under transient conditions and assumed that the Butler-Volmer model for electron transfer with mass transport by linear diffusion is applicable. Typically, rate constants for the Fc0/þ process were reported to be
