(Invited) Modeling Current-Distribution Effects on the Impedance of Electrodes Covered with Films
Authors: Sunde Svein , Tjelta Morten 
Published: February 2020

Impedance analysis of films at electrodes, electroactive or porous, are frequently based on equivalent circuits or other simplified analysis techniques. While these simplified models often capture the essential features of the spectra, non-idealities and artefacts associated with the measurements will often have to be lumped into circuit elements or combination of such which are difficult to interpret, as in other areas of impedance spectroscopy. Analysis based directly on mathematical models may not only offer a deeper understanding of the data and their possible interpretation, but also in some cases shed light on artefacts encountered in experimental measurements. In addition, models may suggest novel experimental methods. Thus, Tribollet, Orazem and co-workers [1,2,3] showed in a series of papers how the high-frequency part of disk electrodes will be affected by the current distribution at the electrode, for example leading to apparent constant-phase element behavior in case of an ideally polarized electrode. Model results for the local impedance at the electrodes are useful for interpretation of the more recent local impedance methods were also provided.
Frequency dispersion may also occur in the direction normal to the electrode, which typically takes place in for example porous electrodes. In this work we present attempts at modeling the simultaneous effects of both the two-dimensional frequency dispersion associated with current distribution along the electrode and through the electroactive film normal to the electrode. The analysis was simplified by employing essentially one-dimensional impedance models for the local interfacial impedance as the boundary conditions of a model based on the Laplace equation for the global and other impedances of the electrode as a whole, thus including also the effects of the current distribution on the impedance.
In addition to subjecting a disk electrode to the modeling study indicated above, we also performed calculations for square electrodes. The effect of current distributions were quite different for the two electrodes. For example, the quantity dlog(-Z'')/d(log Ω), where Z'' represents the imaginary part of the impedance and Ω a dimensionless angular frequency, which for an ideally polarized electrode in the absence of current-distribution effects would be equal to -1, typically displayed a positive shift at high frequency for an ideally polarized disk electrode. However, for and ideally polarized square electrode the same quantity displayed negative shift at high frequency as shown in the figure. We interpret these results as being due to differences in the weight with which edge-like and center-like local impedances contribute to the global impedance in the two cases.

Aknowledgement

This work was funded by NTNU.

References

1. V. M.-W. Huang, V. Vivier, M. E. Orazem, N. Pebere, and B. Tribollet, J. Electrochem. Soc. 154 (2007) C81
2. V. M.-W. Huang, V. Vivier, I. Frateur, M. E. Orazem, and B. Tribollet, J. Electrochem. Soc. 154 (2007) C89
3. V. M.-W. Huang, V. Vivier, M. E. Orazem, N. Pebere, and B. Tribollet, J. Electrochem. Soc. 154 (2007) C99
4. M. Tjelta and S. Sunde, J. Electroanal. Chem. 737 (2015) 65

Figure 1