(13f) Interpretation of Activation and Concentration Overpotentials in Electrochemical Systems

In electrochemical systems, the cell potential that has to be applied to reach a given current density is important as it defines the voltage efficiency. The cell potential can be described as the sum of an equilibrium potential that represents the minimum required potential based on the thermodynamics, and additional overpotentials that represent the additionally required potential due to different effects. These additional overpotentials are often quantified in Literature [1, 2]. Two key overpotentials are the activation overpotential η_act, representing the overpotential due to reaction kinetics, and the concentration overpotential η_conc, representing the overpotential due to mass transfer limitations. However, different approaches are used in literature for partitioning the total overpotential into η_act and η_conc. In most cases, the overpotential η_conc representing the contribution by mass transfer limitations is defined as the difference between the equilibrium potentials evaluated at the bulk concentrations and at the surface concentrations, and is often termed “diffusion overpotential” or “concentration overpotential”. As this η_conc is calculated based on the equilibrium potential, we refer to it as equilibrium-based concentration overpotential η_{conc(eq-based)}. Works in literature have already suggested that η_{conc(eq-based)} does not describe the effect of mass transfer limitations on the cell potential and therefore should not be used in the case of a significant surface activation overpotential η_act,surf (activation overpotential evaluated under surface conditions with respect to the equilibrium potential at the surface) [3, 4]. Nevertheless, it is often applied irrespectively of the present η_act,_surf. Alternatively, a differently defined η_conc can be used that is applicable to quantify the effects of mass transfer limitations on the cell potential at any η_act,surf [2]. As this η_conc is calculated based on the total activation overpotential (taking into account mass transfer limitations), we refer to it as activation-based concentration overpotential η_{conc(act-based)}. To our surprise, in literature this η_{conc(act-based)} does only seem to be applied together with the Tafel equation valid at high η_act,surf, but not together with the Butler-Volmer equation.

We provide a critical discussion of the two potential partitions resulting from the use of η_{conc(eq-based)} or η_{conc(act-based)}. We highlight how in each potential partition η_act and η_conc have different meanings. To show the differences between the possible alternatives to partition the total overpotential, we compare three approaches for potential partition: (a) the potential partition based on η_{conc(eq-based)} together with the Butler-Volmer equation, (b) the potential partition based on η_{conc(act-based)} together with the Butler-Volmer equation, and (c) the potential partition based on η_{conc(act-based)} together with the Tafel equation. For the comparison, we consider both a fictitious illustrative example and a practical example from water electrolysis. The results demonstrate that the most frequently used approach (a) can lead to misleading results concerning the effect of mass transfer limitations on the cell potential when it is applied at significant η_act,surf. We demonstrate the practical relevance of this in the context of supersaturation of product gases in water electrolysis, for which large values of η_{conc(eq-based)} are mentioned in literature [5,6]. Further, we show how approach (c) only results in reliable results when η_act,surf is high enough. In the intermediate range of η_act,surf, only approach (b) provides the desired results concerning the effect of mass transfer limitations on the cell potential. It surprises us that approach (b) does not seem to be usually applied in literature, as it is the only approach to reliably quantify the effect of mass transfer on the cell potential at any η_act,surf. The potential partitions also differ in terms of the definition of η_act that is used to quantify the effect of reaction kinetics on the cell potential. Therefore, the definition and meaning of each η_act and η_conc should be carefully considered so that misinterpretations can be prevented.

Acknowledgments

The authors gratefully acknowledge the financial support by the German Federal Ministry of Education and Research (BMBF) within the H2Giga project PrometH2eus (grant number 03HY105A).

References

[1] Haverkort, J. W., & Rajaei, H. (2021). Voltage losses in zero-gap alkaline water electrolysis. Journal of Power Sources, 497, 229864.

[2] Hammoudi, M., Henao, C., Agbossou, K., Dubé, Y., & Doumbia, M. L. (2012). New multi-physics approach for modelling and design of alkaline electrolyzers. International Journal of Hydrogen Energy, 37(19), 13895–13913.

[3] C. H. Hamann, A. Hamnett, W. Vielstich, Electrochemistry, 2., completely rev. and updated edition ed., Wiley-VCH, Weinheim, 2007

[4] M. Enyo, T. Yokoyama, Theory of concentration overpotential and applicability of the rotating disk electrode to the analysis of electrode kinetics, Electrochimica Acta 15 (1970) 183–191.

[5] Zhao, X., Ren, H., & Luo, L. (2019). Gas Bubbles in Electrochemical Gas Evolution Reactions. Langmuir, 35(16), 5392–5408.

[6] Leistra, J. A., & Sides, P. J. (1987). Voltage Components at Gas Evolving Electrodes. Journal of The Electrochemical Society, 134(10), 2442–2446.