The Difference in the Effects of IR-Drop from the Negative Capacitance of Fast Cyclic Voltammograms
Abstract
:1. Introduction
2. Materials and Methods
2.1. Chemicals
2.2. Voltammetry
3. Results
- (i)
- The flux of a univalent cationic redox species controlled both by diffusion and electric migration is expressed by the Nernst–Planck equation, j/F = −Ddc/dx − (DF/RT)c(dϕ/dx) [1], where c is its concentration, D is the diffusion coefficient, and ϕ is the potential in the solution at a distance from the electrode of x. It can be approximated to be j/F = −Dc*/δ − (DF/RT)c*(Δϕ/δ), on the basis of the concept of a diffusion layer [33]. Here, its thickness at the peak current, Ip, is given by δ = Dc*FA/Ip, where A is the electrode area. The ratio of the current component of the migration to that of the diffusion is (F/RT)Δϕ. When Δϕ was replaced by RsIp, the ratio became less than 0.5% under our experimental conditions. Therefore, migration had no contribution to the potential shift in our case.
- (ii)
- Electrode kinetics often cause potential shifts. Quantitatively accessible kinetics are represented by the Butler–Volmer equation. The theoretical peak currents and potentials for different scan rates can be obtained from the analytical equation at a given transfer coefficient α and a heterogeneous rate constant k0 [17]. Figure 3(c–e) shows the variation in Ip with Ep for several scan rates at α = 0.5 and some values of k0 via the use of our software for the kinetics, so that Ip vs. Ep were close to the experimental ones (a). However, the experimental plots (a) were different from the theoretical variations for any different values of k0. The inconsistency was also applied to other values of Rs (b). Since no potential shift was found in the 0.1 M KCl solution (b), it is not reasonable to explain the shift in terms of the heterogeneous kinetics. However, an explanation only due to kinetics has often been reported [2,3,4,5,6,7,8,9].
- (iii)
- A following chemical reaction causes a potential shift, as can be understood from the Nernst equation for reaction rates faster than the voltammetric rates. Ferrocenyl compounds, however, are not satisfied with the condition of the rates; hence, item (iii) is unsuitable for explaining the present potential shifts.
- (iv)
- The negative capacitance was brought about through the following steps according to Figure 4: a charge-transferred redox species (Fc) was coupled with a counterion (Cl−) for electric neutrality by responding to the externally applied field Eap to yield an electric dipole (Fc+-Cl−), where Cl− came from the supporting electrolyte because of the highest concentration of anions: the dipole with the dipole moment p was oriented in the direction for enhancing the external field by -pc/ε0 to yield the effective field Eef, which generated capacitance with a sign opposite to double-layer capacitance [16,34]. Negative capacitance has been obtained for ferrocenyl derivatives [18], ruthenium complex, iridium complex, and hemin [34] with ac-impedance. Since the voltammetric current from the negative capacitance was proportional to the scan rate, it depressed the diffusion tail to cause the potential shift [16]. The negative capacitance varied with electrode areas and scan rates, as the IR-drop did. The similarity in the properties stimulated us to distinguish their properties theoretically.
4. Theory of Effects of IR-Drop
5. Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Range of v | Advantages | Risks |
---|---|---|
(I) <0.2 V s−1 | Small background currents Easy extraction of diffusion currents Usage of low-cost potentiostats Possibility of theoretical analysis | Misleading kinetic reaction mechanisms Time consumption |
(II) <5 V s−1 | Possibility of subtraction of IR-drop Possibility of determining reaction mechanisms Evaluation of heterogeneous kinetics Comparison of the results with those by other rapid electrochemical methods Commercially available potentiostats | Discussion required for peak shifts Deformation of waveform Limited to microelectrodes in order to prevent large currents |
(III) <500 V s−1 | Detection of kinetics with milli-second orders such as neurotransmitters | Empirical search for detecting conditions A loss of theoretical support |
Variables | Ep | Ip0−Ip | ||
---|---|---|---|---|
IR | NC | IR | NC | |
c* | c* | 1 | c*3/2 | c* |
A(disk) | A1/2 | 1 | A5/4 | A |
v | v1/2 | v1/2 | v3/4 | v |
Rs | Rs | 1 | Rs1/2 | 1 |
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Liu, Y.; Aoki, K.J.; Chen, J. The Difference in the Effects of IR-Drop from the Negative Capacitance of Fast Cyclic Voltammograms. Electrochem 2023, 4, 460-472. https://doi.org/10.3390/electrochem4040030
Liu Y, Aoki KJ, Chen J. The Difference in the Effects of IR-Drop from the Negative Capacitance of Fast Cyclic Voltammograms. Electrochem. 2023; 4(4):460-472. https://doi.org/10.3390/electrochem4040030
Chicago/Turabian StyleLiu, Yuanyuan, Koichi Jeremiah Aoki, and Jingyuan Chen. 2023. "The Difference in the Effects of IR-Drop from the Negative Capacitance of Fast Cyclic Voltammograms" Electrochem 4, no. 4: 460-472. https://doi.org/10.3390/electrochem4040030
APA StyleLiu, Y., Aoki, K. J., & Chen, J. (2023). The Difference in the Effects of IR-Drop from the Negative Capacitance of Fast Cyclic Voltammograms. Electrochem, 4(4), 460-472. https://doi.org/10.3390/electrochem4040030