Dual-Frequency Alternating Current Designer Waveform for Reliable Voltammetric Determination of Electrode Kinetics Approaching the Reversible Limit

Alternating current (ac) voltammetry provides access to faster electrode kinetics than direct current (dc) methods. However, difficulties in ac and other methods arise when the heterogeneous electron-transfer rate constant (<i>k</i>⁰) approaches the reversible limit, because the voltammetric characteristics become insensitive to electrode kinetics. Thus, in this near-reversible regime, even small uncertainties associated with bulk concentration (<i>C</i>), diffusion coefficient (<i>D</i>), electrode area (<i>A</i>), and uncompensated resistance (<i>R</i>_u) can lead to significant systematic error in the determination of <i>k</i>⁰. In this study, we have introduced a kinetically sensitive dual-frequency designer waveform into the Fourier-transformed large-amplitude alternating current (FTAC) voltammetric method that is made up of two sine waves having the same amplitude but with different frequencies (e.g., 37 and 615 Hz) superimposed onto a dc ramp to quantify the close-to-reversible Fc^0/+ process (Fc = ferrocene) in two nonhaloaluminate ionic liquids. The concept is that from a single experiment the lower-frequency data set, collected on a time scale where the target process is reversible, can be used as an internal reference to calibrate <i>A</i>, <i>D</i>, <i>C</i>, and <i>R</i>_u. These calibrated values are then used to calculate <i>k</i>⁰ from analysis of the harmonics of the higher-frequency data set, where the target process is quasi-reversible. With this approach, <i>k</i>⁰ values of 0.28 and 0.11 cm·s^–1 have been obtained at a 50 μm diameter platinum microdisk electrode for the close-to-diffusion-controlled Fc^0/+ process in two ionic liquids, 1-ethyl-3-methylimidazolium bis­(trifluoromethanesulfonyl)­imide and 1-butyl-3-methylimidazolium bis­(trifluoromethanesulfonyl)­imide, respectively

Mass-Transport and Heterogeneous Electron-Transfer Kinetics Associated with the Ferrocene/Ferrocenium Process in Ionic Liquids

The ferrocene/ferrocenium (Fc^0/+) redox couple is regarded as a kinetically facile process under voltammetric conditions. It also possesses a nearly “solvent independent” formal potential, and for this reason is commonly used as a “reference” redox system for electrochemical studies in nonaqueous electrolyte media. Fc^0/+ has also been adopted as a “model system” in ionic liquid (IL) media, although conflicting reports on the mass-transport and kinetics have brought its “ideality” into question. In this study, the mass-transport and heterogeneous electron-transfer kinetics associated with the Fc^0/+ process at a platinum electrode are reported in 14 ILs with dynamic viscosities (η) ranging from 20 to 620 cP. The diffusivity of Fc (<i>D</i>_Fc) was calculated in each of the ILs using convolution voltammetry and was found to be inversely proportional to the viscosity of the medium, as per the Stokes–Einstein relation (i.e., <i>D</i> ∝ 1/η). The heterogeneous electron-transfer rate constant (<i>k</i>⁰) associated with the Fc^0/+ process was measured in each of the ILs using large-amplitude Fourier transformed alternating current (FTAC) voltammetry, and a plot of ln­(<i>k</i>⁰) versus ln­(η) was found to be linear, with a slope of −1.0, as predicted by the Marcus theory of electron transfer for an adiabatic process that involves predominantly solvent reorganization rather than inner-shell vibrations. Analysis of the ln­(<i>k</i>⁰) versus ln­(η) data suggests a slight dependence of <i>k</i>⁰ on the constituent anion of the IL, which is thought to arise due to electrostatic interactions between the anion and positively charged Fc⁺. Finally, extrapolating the <i>D</i> versus 1/η and ln­(<i>k</i>⁰) versus ln­(η) plots to η values typically encountered in acetonitrile-based electrolyte media (i.e., 0.5 cP) predicts <i>D</i> and <i>k</i>⁰ values of approximately 2 × 10^–5 cm² s^–1 and 10 cm s^–1, in excellent agreement with literature reports. Overall, the results presented in this study strongly suggest that the Fc^0/+ redox couple displays the characteristics of an “ideal” outer-sphere electron transfer process in IL media

Direct Detection of Electron Transfer Reactions Underpinning the Tin-Catalyzed Electrochemical Reduction of CO₂ using Fourier-Transformed ac Voltammetry

Two underlying electron transfer processes that directly underpin the catalytic reduction of carbon dioxide (CO₂) to HCOO^– and CO at Sn electrodes have been detected using the higher order harmonic components available in Fourier-transformed large-amplitude ac voltammetry. Both closely spaced electron transfer processes are undetectable by dc voltammetry and are associated with the direct reduction of CO₂ species and have reversible potentials of approximately −1.27 and −1.40 V vs Ag/AgCl (1 M KCl). A mechanism involving a reversible inner-sphere one-electron reduction of CO₂ followed by a rate-determining CO₂^•– protonation step is proposed. Molecular CO₂ has been identified as the dominant electroactive species that undergoes a series of coupling electron transfer and chemical reactions to form the final products. The substantial difference in the catalytic responses of Sn­(SnO_<i>x</i>)-modified glassy carbon and Sn foil electrodes are attributed to their strongly preferred Sn (200) orientation and polycrystalline states, respectively. The Fourier-transformed ac technique should be generally applicable for predicting the performance of Sn catalysts