Continuum Modeling of Gas and Ions Transport in a High-Surface-Area Carbon (HSC) Nanopore
Authors: Wang Shiyi , Shibata Masao Suzuki , Chowdhury Anamika , Weber Adam Z. 
Published: September 2023

PEM fuel cell (PEMFC) is one of the promising energy conversion devices for emission-free transportation applications. It is beneficial in faster charging and better scalability compared to battery-powered vehicles, making PEMFC a viable option for heavy-duty vehicles which require higher efficiency and longer lifetimes. To economically compete with the combustion engine and improve commercialization, the PEMFC cathode desires optimization in enhancing the utilization of the expensive Pt catalyst. Integration of high-surface-area carbon (HSC) has shown to increase accessible Pt surface by diminishing ionomer poisoning as Pt particles can be loaded inside the nanoscale micropores (<5 nm) that ionomer cannot penetrate due to size restriction. However, separating Pt catalysts from ionomers requires a water pathway to deliver the proton to the interior catalyst surface, leading to RH-dependent electrochemical surface area (ECSA). In this work, we develop a steady-state, isothermal continuum model to study the gas and ions transport within HSC nanopores. The pore is represented as a straight cylindrical channel filled with water with an ionomer domain at the pore mouth serving as a proton reservoir. The ionomer phase contains H+, OH-, and background stationary SO3
- while the water phase only includes H+ and OH-. The Poisson-Nernst-Plank equations describe the flux of ions, and O2 transport is described by Fick’s law. Non-ideal behaviors including nanoconfinement effects and dielectric saturation are considered in the pore water phase, reflected by corrections in ion chemical potentials, diffusion coefficients of transport species, and dielectric constant. The electrical double layer (EDL) at the water-electrode interface is depicted as discrete finite domains applying the Gouy-Chapman-Stern (GCS) theory, with the oxygen reduction reaction (ORR) occurring at a finite reaction plane at the outer Helmholtz plane (OHP) through both acidic and alkaline reaction pathways. Donnan potential drop is solved at the ionomer-pore water interface and governs potential distribution in the pore water phase, further determining ionic concentrations at the catalyst surface and thus the kinetic region of polarization curves. The strong-adsorbed water adlayers due to nanoconfinement effects create a transport barrier for O2 approaching the catalyst surface, leading to higher mass transport resistance. A comparison between a flooded pore scenario (only a water phase exists in the pore) and a wetted pore scenario (the pore wall is covered by a water film while a gas phase also exists in the pore) shows that mass transport is hindered in the flooding pore as O2 dissolves in the pore water through a limited pore-ionomer interfacial area, while pore gas phase in the wetted pore serves as an extra O2 resource. This suggests that the management of HSC water uptake needs to avoid pore flooding while ensuring enough wettability to allow proton transport. The model is expected to couple with HSC pore size distribution measured from experiments and upscale to a cell-level model in future work.