Determination of the τ/ε-Ratio for Gas Diffusion Substrates and Microporous Layers in an Operating Fuel Cell
Authors: Berger Anne , Gasteiger Hubert Andreas 
Published: July 2022

Proton-exchange-membrane fuel cells (PEMFCs) are expected to play a major role in the electrification of the transportation sector,[1] with recent focus shifting to the heavy-duty market. One essential aspect for increasing the power density of a PEMFC is optimizing the mass transport in the gas diffusion layer (GDL) on the cathode side of the cell. A careful choice of the commonly used carbon fiber based GDL is therefore necessary to optimize the performance at different relative humidity conditions. Among other important GDL properties such as the pore size distribution and the thermal conductivity, the porosity (ε) and the tortuosity (τ) are important descriptors. The τ/ε-ratio has been characterized for diffusion media using in-situ or ex-situ techniques.[2-3] This study is based on the theory developed by Baker et al.[2] In addition to their work, which solely considers molecular diffusion, we will present a method to include Knudsen diffusion occurring in smaller pores for the in-situ evaluation of the τ/ε-ratio. This adaptation makes it possible to evaluate GDL substrates to which carbon black (creating small pores) has been added to increase the electrical conductivity,[4] and also to extend the theory to the microporous layer (MPL).
In this study, we characterize the τ/ε-ratio for two GDL substrates (without the addition of an MPL), one from Toray and one from Freudenberg, using limiting current measurements in an operating fuel cell. The τ/ε-ratio describes the deviation of the effective diffusivity compared to ideal molecular diffusion. However, depending of the range of pore diameters in the gas diffusion medium, a mixture of molecular diffusion and Knudsen diffusion has to be taken into account. Fig. 1 shows the theoretical contribution ratio of Knudsen diffusion and molecular diffusion (left y-axis) versus the relevant range of pore diameters for different pressures. The graphic illustrates that Knudsen diffusion dominates at lower pore sizes, while molecular diffusion is mostly present at larger pore sizes. An increase in pressure shifts the regime of molecular diffusion to smaller pores. In addition to the theoretical contribution ratio, Fig. 1 depicts the pore size distribution of a Toray and a Freudenberg GDL substrate determined by mercury intrusion porosimetry (MIP). While the Toray paper has a narrow pore size distribution at pores of 30-50 µm, where only molecular diffusion occurs, the Freudenberg GDL contains a broader range of larger pores at 10-40 µm (molecular diffusion) together with the presence of small pores at ca. 70-80 nm that derive from the addition of carbon black and that present a medium where Knudsen and molecular diffusion occur.
After the validation of the principle, the method is transferred to determine the τ/ε-number of a microporous layer based on vapor-grown carbon-fibers (VGCF), whose transport properties in a PEMFC have been described previously.[5]

References

[1] O. Gröger, H. A. Gasteiger, J.-P. Suchsland, J. Electrochem.
Soc.
2015, 162, A2605-A2622.
[2] D. R. Baker, D. A. Caulk, K. C. Neyerlin, M. W. Murphy, J. Electrochem. Soc.
2009, 156, B991.
[3] D. Kramer, S. A. Freunberger, R. Flückiger, I. A. Schneider, A. Wokaun, F. N. Büchi, G. G. Scherer, Journal of Electroanalytical Chemistry
2008, 612, 63-77.
[4] K.-D. Wagner, A. Bock, K. Salama, A. Weller, Vol. US 2010/0219069 A1, Carl Freudenberg KG 2010.
[5] C. Simon, J. Endres, B. Nefzger-Loders, F. Wilhelm, H. A. Gasteiger, J. Electrochem. Soc.
2019, 166, F1022-F1035.

Acknowledgements

We gratefully acknowledge funding from the Swiss National Foundation under the funding scheme Sinergia (project grant number 180335). We also thank Michael Striednig and Christoph Simon for initial work on the topic.

Figure 1: Left y-axis: theoretical contribution ratio of Knudsen (green) and molecular diffusion (orange) versus pore diameter for different absolute pressures of 115 kPaabs (solid lines), 150 kPaabs (dashed lines), 200 kPaabs (dotted lines), and 300 kPaabs (dash-dotted lines). With smaller pores and lower pressures, more contributions from Knudsen diffusion can be expected. Right y-axis: log. differential intrusion measured by MIP analysis for the Toray (blue) and the Freudenberg (grey) GDL substrates, whereby the Freudenberg GDL shows pores at ~70-80 nm that are caused by the addition of carbon black.

Figure 1