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

Structure and conductivity of ionomer in PEM fuel cell catalyst layers: a model-based analysis

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.

Discerning the Difference Between Lumens and Scalariform Perforation Plates in Impeding Water Flow in Single Xylem Vessels and Vessel Networks in Cotton

The geometrical structure and spatial arrangement of lumens, bordered pits, and scalariform perforation plates in xylem vessels modulate water flow from roots to leaves. Understanding their respective hydraulic functions is essential to unveil how plants regulate their hydraulic networks to facilitate the ascent of sap under biotic and abiotic stresses but is challenging because of the opaque nature of the vessel networks and water flow within them. We made the first-ever effort to discern the difference between lumens and scalariform perforation plates in cotton in impeding water flow in single vessels and vessel networks using X-ray tomography and pore-scale numerical simulation. Three-dimensional structures of xylem vessels in the stem of two cotton cultivars were acquired non-invasively using X-ray computed tomography (CT) at high spatial resolution, and a lattice Boltzmann model was developed to simulate water flow through the xylem networks at micrometer scale. The detailed water velocity and pressure simulated using the model were used to calculate the hydraulic resistance caused by the lumens and the scalariform perforation plates in individual vessels and the vessel networks of the two cotton cultivars. The results showed that the hydraulic resistance spiked whenever water flowed across a perforation plate and that the overall hydraulic resistance caused by the perforation plates in an individual vessel accounted for approximately 54% of the total resistance of the vessel. We also calculated the hydraulic conductance of individual vessels and vessel networks using the simulated water velocity and pressure at micrometer scale and compared it with those estimated from the Hagen Poiseuille (HP) equation as commonly used in the literature by approximating the xylem vessels in the cotton as isolated tubes. While it was found that the HP equation overestimated the hydraulic conductance by more than 200%, the overestimate was largely due to the incapability of the HP equation to represent the perforation plates rather than its approximation of the irregular vessels by circular tubes.