Determination of Surface Area and Reaction Rate Constant from Cyclic Voltammetry Considering Voltage-Dependence of the CPE Parameters

Abstract

Due to its advantages such as sensitive response to a reaction and easy implementation, cyclic voltammetry has been used as an electrochemical method for analyzing complex mechanics in electrochemistry. Analytical relationships between peak potentials or peak current magnitudes with scan rates have been developed for different situations [1–3]. However, under most circumstances, the current responses of cyclic voltammetry consist not only the faradaic current generated by the reaction of interest, but also the non-faradaic current from an electrical double layer. Using the analytical relationships without considering ohmic drop and the non-faradaic current leads to incorrect kinetic and thermodynamic information obtained from the cyclic voltammogram interpretation [4]. Therefore, it is important to model the entire voltammogram to characterize the complex mechanism [5]. To model the ohmic drop effect and the non-faradaic current, commercial softwares such as DigiSim© and DigiElch© apply a concept of an electrical circuit with cyclic voltammetry simulation. They use a pure capacitor connecting in parallel to the faradaic impedance to act as the double layer capacitor and a resistance connecting in series to those elements to represent the ohmic resistance. Although it is rarely used in simulating voltammetric responses, a constant phase element (CPE) is widely accepted and used to model the electrical double layer capacitor (EDLC) in electrochemical impedance spectroscopy (EIS) analysis. A model for simulating the cyclic voltammetry responses which combines the effects of ohmic resistance, CPE, mass transfer, and faradaic processes was proposed [6]. The set of equations conventionally used to simulate voltammetric responses such as Fick’s second law and Butler-Volmer equation were used to solve for the faradaic current, while the time-domain response of a CPE was used to describe the non-faradaic current. The total current can be obtained by applying a concept of an electrical circuit. In that study, the CPE parameters were assumed to be constant throughout the potential window and it was proved to be reasonable. However, in some systems, it is known that such an assumption does not hold true [7]. In this study, commercial EDLCs were investigated. The CPE parameters were evaluated using cyclic voltammetry and EIS at several voltages. The cyclic voltammetry experiments were conducted under a narrow voltage window since it was observed that the responses under such a narrow voltage window can be described by the constant CPE parameters. This is understandable since the EIS approach also performed under a narrow voltage window. In cyclic voltammetry approach, the CPE parameters were determined by fitting the obtained currents with analytical solutions, while they were obtained by fitting the R-CPE circuit with the EIS spectra in EIS approach. It was found that the CPE parameters were different at each potential, as shown in Fig. 1a and both methods showed good agreement when compared with each other. These voltage-dependent parameters and the ohmic resistance were applied to the approximate solution proposed in [6] to simulate the entire voltammogram of the selected commercial EDLCs. Fig. 1b clearly shows a reasonable agreement between the numerical results and the experimental data in a case of the voltage-dependent CPE parameters and it is clear that the constant CPE parameters failed to predict the voltammetric responses. This result suggested that it is important to consider voltage-dependence of the CPE parameters in modeling the non-faradaic current and the difference between the response during forward and backward scans of an EDLC can be attributed to this dependency. Since it is essential to correctly predict the entire voltammogram to obtain kinetic and thermodynamic information in a system involving faradaic reaction, using our proposed approach to simulate the non-faradaic current would lead to more accurate prediction of such important information. Acknowledgment The authors would also like to express their gratitude to the Ministry of Education, Culture, Sports, Science and Technology, Japan, for providing financial support under the scholarship program for foreign students.