Sci Rep. 2023 Aug 29;13(1):14127. doi: 10.1038/s41598-023-40637-0.
Efforts in design and optimization of catalyst layers for polymer electrolyte fuel cells hinge on mathematical models that link electrode composition and microstructure with effective physico-chemical properties. A pivotal property of these layers and the focus of this work is the proton conductivity, which is largely determined by the morphology of the ionomer. However, available relations between catalyst layer composition and proton conductivity are often adopted from general theories for random heterogeneous media and ignore specific features of the microstructure, e.g., agglomerates, film-like structures, or the hierarchical porous network. To establish a comprehensive understanding of the peculiar structure-property relations, we generated synthetic volumetric images of the catalyst layer microstructure. In a mesoscopic volume element, we modeled the electrolyte phase and calculated the proton conductivity using numerical tools. Varying the ionomer morphology in terms of ionomer film coverage and thickness revealed two limiting cases: the ionomer can either form a thin film with high coverage on the catalyst agglomerates; or the ionomer exists as voluminous chunks that connect across the inter-agglomerate space. Both cases were modeled analytically, adapting relations from percolation theory. Based on the simulated data, a novel relation is proposed, which links the catalyst layer microstructure to the proton conductivity over a wide range of morphologies. The presented analytical approach is a versatile tool for the interpretation of experimental trends and it provides valuable guidance for catalyst layer design. The proposed model was used to analyze the formation of the catalyst layer microstructure during the ink stage. A parameter study of the initial ionomer film thickness and the ionomer dispersion parameter revealed that the ionomer morphology should be tweaked towards well-defined films with high coverage of catalyst agglomerates. These implications match current efforts in the experimental literature and they may thus provide direction in electrode materials research for polymer electrolyte fuel cells.