Advantage of Fractional Calculus Based Hybrid-Theoretical-Computational-Experimental Approach for Alternating Current Voltammetry

The dynamic electrochemical behavior of electroactive species is believed to be represented better by the fractional calculus, because it can consider the history of mass-transfers of that species near the electrode surface. The elucidation of mathematical fundamentals of fractional calculus has been recently introduced for batteries, supercapacitors and a few voltammetry studies. The working equations for faradaic fundamental and second-harmonic (SHac) components of alternating current (ac) for ac voltammetry of an electrochemically reversible redox reaction on an electrode of macroscopic diameter have been derived here by using generalized formulae of the fractional calculus. A computation code is written in Python language with a matrix based algorithm developed based on latest, accurate, efficient and stable Grunwald-Letnikov-Improved fractional-order differentiation equation. That computational code is used to find the concealed faradaic fundamental, SHac components of the total current and other double-layer parameters of experimentally recorded voltammograms of ruthenium(III/II) redox reaction on gold-disc electrode by a common electrochemical workstation without having inbuilt Fourier transformation features. The amplitude of the computed faradaic current concealed in the experimental data gets enhanced through this hybrid theoretical-computational-experimental approach and thus it keeps scope of application and further improvement in electroanalysis.