Mathematical Model of Hydrogen Peroxide Production in Anode, Cathode, and Membrane of LT-PEMFC
Authors: Kregar Ambroz , Kravos Andraž , Katrašnik Tomaž 
Published: July 2022

Degradation of proton exchange membrane in low-temperature fuel cells represents one of the main limiting factors for wider adoption of this clean, carbon emission free energy device. In combination with mechanical degradation caused by membrane swelling and shrinkage during water content change, chemical degradation of the membrane is considered to be the main mechanism leading to loss of membrane conductivity, membrane thinning and eventual pinhole formation.
Chemical degradation is caused by the attack of reactive radical species on the perfluorinated polymer chains of the membrane, which are formed in Fenton reaction between hydrogen peroxide and ions of transition metals, which are inevitably present in the membrane in small traces. Since the metal ions are recycled in Fenton reactions, the rate of chemical degradation is mainly determined by the production of hydrogen peroxide, formed as a side product to water in reaction between oxygen and protons in the fuel cell. [1]
The source of hydrogen peroxide production in low-temperature fuel cells have long been debated in scientific literature. On one hand, the abundance of oxygen in the cathode suggest that the production takes place there, but high local electric potential strongly promotes 4-electron reaction, forming water, over 2-electron reaction required for production of hydrogen peroxide [2]. The conditions in the anode are reversed, low electric potential is well suited for peroxide production, but the concentration of oxygen, present in the anode due to diffusion through the membrane, is in general expected to be quite low, making it a rate limiting factor for the peroxide production in the anode. The last possible source of hydrogen peroxide is closely related to the degradation of platinum (Pt) catalyst in the cathode. When Pt catalyst nanoparticles dissolve due to high local electric potential on the cathode, part of the dissolved ions diffuses into the membrane, where it is reduced by counter-diffusing hydrogen from the anode. These Pt particles in the membrane, the so-called Pt band, serve as a catalyst for the reaction between diffusing oxygen from cathode and hydrogen in anode. Since these particles are not electrically connected to either anode or cathode, their electric potential is determined by the rates of oxygen reduction and hydrogen oxidation on their surface, which result in production of water and potentially also hydrogen peroxide.
The complex interplay between the processes determining the peroxide production, explained above, suggest that different sources of peroxide might be relevant in different fuel cell operation conditions and at different states of health of the fuel cell. To explore this question quantitatively, we propose a mathematical model of peroxide production which describes physical and electrochemical processes for hydrogen peroxide production in fuel cell catalysts and the membrane, relevant for hydrogen peroxide production: oxygen and hydrogen diffusion in the membrane, electrochemical oxygen reduction in the cathode, anode and on Pt band inside membrane, hydrogen oxidation on Pt band and electric charging of Pt particles in the band due to electrochemical reactions on their surface. To provide realistic internal states of the fuel cell during operation, the model is coupled with advanced spatially and temporally resolved model of the fuel cell operation. [3]
Preliminary results of the model indicate that main source of peroxide production depends on the fuel cell operating conditions. In fresh fuel cell, where Pt band in membrane is not yet formed, low current densities and high fuel cell voltages promote the peroxide formation mainly on the anode from the diffused oxygen, while at high current densities the electric potential on the cathode is low enough to allow for significant peroxide production there, outweighing the production on the anode. The formation of the Pt band shifts the production of peroxide from anode to the Pt particles in the band, since large amount of the oxygen is consumed there and therefore its diffusion to the anode is reduced.
The results indicate that the question of where the peroxide is formed cannot be resolved by a single answer and that the use of sufficiently complex models, coupling physical and electrochemical processes in different fuel cell components, are required to properly manage fuel cell operation in order to avoid or at least mitigate its detrimental effects of chemical membrane degradation.
[1] Frühwirt, P., Kregar, A., Törring, J. T., Katrašnik, T., Gescheidt, G. (2020). Physical Chemistry Chemical Physics, 22(10), 5647–5666.
[2] Sethuraman, V. A., Weidner, J. W., Haug, A. T., Motupally, S., Protsailo, L. V. (2008). Journal of The Electrochemical Society, 155(1), B50.
[3] Kregar, A., Tavčar, G., Kravos, A., Katrašnik, T. (2020). Applied Energy, 263(March), 114547.