(Invited) Transient Models for Porous Electrodes for Electrochemical Energy Conversion
Authors: Svensson Ann Mari , Sunde Svein 
Published: February 2020

Successful development of a number of electrochemical devices, like batteries, supercapacitors, fuel cells, and electrolysers, rely on the development of stable and efficient porous electrodes. Such electrodes are, however, complex structures composed of several phases, with a number of processes (transport, chemical and electrochemical reactions) occurring in each phase. Distinguishing the impacts of the various coupled phenomena on the overall performance is a challenging task. In combination with complex geometries, the various processes would generally cause highly non-uniform current distributions, both on the nano- and micro scale (i.e. catalyst particle as well as within the active layer), and on the macro scale (i.e along channels), which obscures the interpretation of experimental data further.

Transient electrochemical techniques, like cyclic voltammetry and impedance spectroscopy, are well-known techniques for characterization of relevant electrodes, and provides important information on the limiting processes. Impedance spectroscopy is a powerful tool which can resolve contributions from various processes, provided that the time constants differ sufficiently. Due to it’s non-destructive nature, impedance spectroscopy is very well suited as a diagnostic tool applied also during operation, in order to reveal valuable information related to problems with stability and degradation, which most of these systems suffer from. The interpretation of impedance spectra is however not straightforward, and mathematical models can provide useful tools for the interpretation of experimental data. Models of impedance spectra based on descriptions of the physical processes is in many cases a very viable route compared to the conventional fitting to equivalent circuits.

The highly porous, multi-phase structure cannot be modelled in geometric detail without causing inadequate model complexity. Mathematical modelling of the electrochemical response of porous electrodes has been performed along two main paths. One approach is transmission line models, where the structure of the electrode is idealized, for example by considering pores to be identical and cylindrical. This approach was first presented by de Levie [1]. An example of an extensive transmission line model for porous oxygen electrodes, with detailed considerations of geometry (the surface of the carbon electrode was modelled as a plane covered with hexagonally oriented conducting spheres), is provided in Ref. 2. The other approach is to apply porous electrode theory [3], where the actual geometry of the pores is neglected, and reaction rates are averaged over the interfacial area between solid phase and the pores. A comparison of these two approaches is included.

For porous oxygen electrodes, like fuel cell cathodes, where three phases are present, the so-called flooded agglomerate model has been frequently applied. Here, the oxygen reduction reaction is assumed to occur inside agglomerate particles flooded with liquid electrolyte, and the agglomerates are incorporated into porous electrode models. Stationary models for liquid and polymer fuel cell electrodes based on flooded agglomerate models are presented in Ref. 4. Impedance models of active layers of the PEM fuel cell cathode based on flooded agglomerate models have been developed by Jaouen and Lindbergh [5], and in Ref. 6 for alkaline cells. All of these models reveal highly nonuniform local current distributions inside agglomerates, as well as along the active layer. Porous intercalation electrodes applicable for Li-ion batteries have been presented in Refs. 7,8. Zavalis et al. [8] accounted for the complex transport in non-aqueous electrolytes.

This work will include examples of porous electrode models developed for binary electrolytes, applicable to alkaline fuel cell electrodes, and supercapacitor electrodes. Effects particularly related to transport in binary solutions will be addressed, as well as effects of limitations of the solid state conduction. Furthermore, results for impedance models developed for three phase electrodes typical of fuel cells, as well as impedance models of expanding intercalation electrodes are discussed.

References

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2. C.C.Waraksa, G. Chen, D.D. Macdonald, J. Electrochem. Soc. 150 (2003) E429

3. J. Newman, K.E. Thomas-Alyea, Electrochemical Systems, third ed., Wiley Inter-science, NJ (2004)

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5. F. Jaouen, G. Lindbergh, J. Electrochem. Soc., 150 (2003) A1699

6. A.M. Svensson, H. Weydahl, S. Sunde, Electrochim. Acta, 53 (2008) 7483-7490

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9. T G. Zavalis, M.H. Klett, M. Kjell, M. Behm, R.W Lindström, G. Lindbergh, Electrochim. Acta, 110 (2013) 335-348