From the anomalous diffusion impedance to the closed-form, infinite-series and integral formulations of the voltammetric response of thin-film insertion materials under restricted diffusion conditions. A modelling contribution based on the anomalous mass transfer function

Abstract

Abstract The voltammetric response of one-step reversible electrochemical reactions (involving dissolved redox species) to a linear potential ramp can be modelled using the calculation method proposed in our previous work (J. Electroanal. Chem. 818 (2018) 84) provided that the mass transfer function for the species involved in the electrochemical reaction is known in closed form under one-dimensional mass transport conditions. The above approach applies in this short communication to the direct insertion reaction in thin-film planar materials under both anomalous and spatially restricted (confined) diffusion conditions. The Faradaic current is obtained first as an alternating infinite series well suited to formal analysis, and then as an integral formulation well suited to numerical computation. Finally, closed-form expressions of the voltammograms are derived at very low or very high values of the potential sweep rate, respectively. Two anomalous diffusion models taken from the electrochemical literature are investigated and compared, based on their voltammetric responses. The voltammetric peak coordinates obtained from the best model are thoroughly examined, and closed-form approximations are proposed for the voltammetric peak current and potential at very low or very high potential sweep rates. A zone diagram is plotted to illustrate the conditions for observation of those limiting situations. Finally, following a referee's request, an alternative modelling approach is proposed in Appendix, which does not require the use of scientific computation software. This approach involves both the Integral Equation method formalism and numerical inversion of Laplace transform.