During operation, proton-exchange-membrane fuel cells (PEMFCs) are subjected to mechanical and chemical stressors that contribute to membrane degradation, performance loss, and eventual failure. Together, synergistic effects between mechanical and chemical degradation mechanisms lead to accelerated degradation. A physics-based model is developed to understand the synergistic effects of chemical and mechanical degradation and the coupled nature of performance and durability in PEMFCs. The model includes pinhole existence and growth in the membrane, which increases crossover of reactant gases as well as subsequent formation of chemical-degradation agents that impact both transport and mechanical properties of the membrane.
The underlying performance model accounts for the multi-component gas diffusion, reaction kinetics, and transport across the membrane. The membrane mechanical model assumes that a circular pinhole is present in the membrane and calculates the swelling strains and the elastic or plastic stresses on the pinhole. Additionally, an empirical model for the chemical degradation of the membrane via hydrogen peroxide and subsequent hydrogen fluoride generation is used to modify the mechanical properties as a result of chemical degradation. The fuel-cell model is fully coupled with a mechanical model to determine the stresses on the membrane and subsequent growth of pinholes during transient operation. Simulation results show pinhole growth under humidity cycling conditions and an increase in gas-crossover fluxes and decrease in performance. Sensitivity studies show how the membrane mechanical properties impact both the performance and degradation behavior of the membrane.
Multiphase effects are incorporated into the model to account for the effects of flooding on membrane degradation. Liquid condensation in the fuel cell can cause defects such as pinholes to close. Modeling results analyze the conditions under which water condensation will occur in pinholes, which is determined by calculating the critical radius. As the surface of Nafion can change from hydrophobic to hydrophilic, a sensitivity analysis on the critical angle is carried out. In addition, liquid water also reduces the amount of catalyst surface area available and therefore slows down the formation of hydrogen peroxide that drives chemical degradation. The decrease in chemical degradation at high RH values is demonstrated.
Cerium ions are added to the membrane to extend its lifetime by scavenging radicals produced by crossover of reactant gases during PEMFC operation. The cerium ions also lead to a decrease in performance due to changes in the PEM transport properties and possible site blockage in the catalyst layers. The PEMFC performance and durability model is extended to include micro-kinetic framework that accounts for gas-crossover-induced degradation and concentrated-solution theory describes transport in the PEM. The transport model takes into account the coupled nature of the electrochemical driving forces that cause transport of cerium ions, protons, and water. The cell model predicts the migration of cerium out of the membrane and into the catalyst layers and its impact on performance. A comparison of dilute-solution-theory and concentrated-solution-theory approaches illustrates the interactions between water and cerium transport in the cell. Transient simulations show that low concentrations of cerium in the membrane (less than 1% of membrane sulfonic acid sites occupied by cerium) are required to optimize these design tradeoffs.
Combining the mechanical and chemical degradation models, the mitigation effects of cerium on the coupled degradation methods can be shown. The model results show how the presence of a pinhole in the membrane shifts the distribution of cerium in the cell from the cathode into the anode and membrane. As the presence of cerium slows down the chemical degradation rate of the membrane, the rate of change of the mechanical properties of the membrane decreases. The model also shows how cerium modifies the mechanical and chemical degradation rates of the membrane under humidity- and voltage-cycling conditions.
Finally, three approaches for modeling the electrochemical impedance response of a PEMFC are compared using two case studies: a porous electrode with linear kinetics and a fuel cell cathode with Tafel kinetics. These approaches may be applied to the development of a physics-based electrochemical impedance model for a full fuel cell model. The first approach uses a transient-model approach, which is much slower and more prone to errors. However, this approach requires no additional modification of the time domain equations describing the system. The second and third approaches transform the transient model into frequency space and linearizing around the steady-state conditions. This approach is quick and accurate, but is impractical for highly coupled, nonlinear systems of equations. This approach applied to the fuel cell cathode with Tafel kinetics allows for analysis of system properties that change over time as a result of membrane degradation.
