Reliability of the spherical agglomerate models for catalyst layer in polymer electrolyte membrane fuel cells

The spherical agglomerate model with a single diameter is a common approach to describe the average electrochemical reaction rate in the catalyst layer of PEM fuel cells. Real agglomerates are highly irregular, and approximating them by independent spheres could give rise to errors. In this paper, we investigated these errors using nanotomography and numerical simulations. Three-dimensional microstructure of a cathode catalyst layer was acquired using FIB/SEM nanotomography, and oxygen diffusion and the associated electrochemical reaction in the microstructure were simulated using pore-scale modelling. The simulated concentration and reaction rates at the pore scale were volumetrically averaged to obtain the average reaction rates. These simulated average reaction rates were then compared with the results predicted by the spherical agglomerate model using an average diameter estimated from the 3D microstructure. The comparisons revealed that the spherical agglomerate model substantially overestimated the reaction rates when the overpotential is high because of its incorrect description of the contact areas between the agglomerates and the macropores through which the oxygen diffuses. We also fitted the spherical agglomerate model to the simulated reaction rates by treating its diameter as a fitting parameter. The results showed that the value of the diameter needs to increase with the overpotential in order to match the simulated data. These findings implicate that the spherical agglomerate model needs to be used with care in catalyst layer design as its diameter is just a fitting parameter rather than a geometrical description of the agglomerates.