The Influence of Homogeneous Reactions on the Impedance Response of a Rotating Disk Electrode
Authors: Harding Morgan , Tribollet Bernard , Orazem Mark E. 
Published: February 2020

For a number of systems, the impedance response at an electrode surface may be influenced by homogeneous reactions in the electrolyte. Hauser and Newman have discussed the influence of homogenous consumption of cuprous ion on the impedance response associated with dissolution of a copper rotating disk electrode [1]. Remita et al. have shown that, for a deaerated aqueous electrolyte containing dissolved carbon dioxide, the hydrogen evolution is enhanced by the homogeneous dissociation of CO2 [2]. Similarly, homogeneous dissociation of acetic acid enhances cathodic reduction of hydronium ions [3]. Coupled electrochemical and homogeneous reactions are also involved in sensors used to monitor glucose concentrations for management of diabetes [4].

A mathematical model has been developed for the impedance response associated with the coupling of homogeneous and heterogeneous electrochemical reactions. The model accounts for a homogeneous reaction in the electrolyte where species AB reacts reversibly to form A- and B+. The B+ species then reacts electrochemically on a rotating disk electrode to produce B. An analytic expression for velocity was employed that combined a three-term velocity expansion near the electrode surface to a three-term expansion that applied far from the electrode. The nonlinear expression for the homogeneous reaction was employed in which the concentrations of both A- and B+ were assumed to be dependent on position.

The model development required two steps. The nonlinear coupled differential equations governing this system were solved under the assumption of a steady state. The concentrations resulting from the steady-state simulation were used in the solution of the linearized set of differential equations describing the sinusoidal steady state. The diffusion impedance showed two capacitive loops. The low-frequency loop has a characteristic dimensionless frequency K=2.5, which is in agreement with the characteristic frequency associated with diffusion in the absence of homogeneous reactions. The characteristic frequency of the high-frequency loop could be expressed in terms of a reaction layer thickness that was a function of the rate of the homogeneous reaction [5]. The diffusion impedance accounting for a homogeneous reaction was smaller in magnitude than the diffusion impedance in the absence of a homogeneous reaction.

Reference

K. Hauser and J. Newman, “Singular Perturbation Analysis of the Faradaic Impedance of Copper Dissolution Accounting for the Effects of Finite Rates of a Homogeneous Reaction," Journal of The Electrochemical Society, 136 (1989) 2820-2831.

E. Remita, B. Tribollet, E. Sutter, V. Vivier, F. Ropital, and J. Kittel, “Hydrogen Evolution in Aqueous Solutions Containing Dissolved CO2: Quantitative Contribution of the Buffering Effect," Corros. Sci., 50 (2008) 1433-1440.

T. Thu, B. Brown, S. Nešić, and B. Tribollet, “Investigation of the Electrochemical Mechanisms for Acetic Acid Corrosion of Mild Steel,” Corrosion, 70 (2014) 223–229.

A. Heller and B. Feldman, “Electrochemical Glucose Sensors and Their Applications in Diabetes Management,” Chemical Reviews, 108 (2008) 2482–2505.

V. G. Levich, Physicochemical Hydrodynamics, Prentice Hall, Englewood Cliffs, NJ, 1962.

T. von Kármán, “Über Laminaire und Turbulente Reibung,” Zeitschrift für angewandte Mathematik und Mechanik, 1 (1921) 233–252.