High temperature polymer electrolyte fuel cells (HT-PEM) offer certain advantages over the low temperature polymer electrolyte membrane fuel cells (LT-PEM). Numerical modeling is a powerful tool to understand the thermo-chemical and physico-chemical processes that takes place within the gas diffusion layer (GDL) and the catalyst layer (CL) during the cell operation. The models reported in the literature varies from simple analytical expressions to 3D models. Most of these models are based on a general Butler-Volmer equation, without giving any importance to the underlying charge transfer mechanism, and therefore the exchange current densities are fitted to some arbitrary order with respect to hydrogen and oxygen concentrations. Furthermore, most of these models are validated by reproducing the IV curve often by a one dimensional model by resolving the electrode thickness. Whenever such as validation is done, the fuel and oxidant depletion along the cell length and hence the fuel utilization is not accounted for. To the best of our knowledge no attempt has been done to date to validate the experimentally measured axial current density profile. A predictive model should be capable of predicting the measured axial current density profile and the IV curves.

The objective of the current work is to develop an electrochemical model based on elementary step charge transfer that occur at the anode and cathode of the HT-PEM fuel cell. In order to develop the mechanistic steps, dissociative adsorption of H₂ and O₂ is considered. In addition, to account for performance drop in presence of CO, adsorption of CO is also considered in the elementary step reactions. Assuming the protonation reaction to be rate limiting at the anode three phase interface and OH formation to be rate limiting at the cathode three phase interface, Butler-Volmer expressions are derived for the charge transfer reactions at the respective electrodes.The exchange current density at the anode follows

i=i_oa [exp (β_afη_a) - exp (-β_cfη)],

and at the cathode follows

i=i_oc [exp (-β_cfηc) - exp ((1+β_a)fη_c)].

Here, the exchange current densities at the anode and cathode are respectively given by
i_0a =i*x [(K_H2p_H2)^1/4]/[1+(K_COp_CO)+(K_H2p_H2)^1/2)]
and
ioc = i*x [(p_H2/p⁰)^1/4 (K_O2p_O2)^3/8]/[1+(K_O2p_O2)^1/2+(p_H2/p⁰) exp (- ΔG*/RT)].

The equilibrium constants appearing the expression for the exchange current densities are evaluated from the adsorption desorption equilibrium of the reactant species (H₂, O₂, and CO). The adsorption rates are calculated from the sticking coefficients. The activation energy for the desorption reactions is calculated using Unity Bond Index Quadratic Exponential Potential method (UBI-QEP) and the frequency factor for the desorption reactions is calculated from transition state theory.

The electrochemical model is incorporated into a quasi-two dimensional numerical transport model of the cell.
The transport model accounts for the species transport in the flow channels and diffusive transport across the thickness of the electrode (GDL + CL). The diffusive transport in the porous electrode is modeled using Dusty Gas Model (DGM). The resulting governing equations for the species transport are solved using the ODE solver CVode. The electrochemical model, i.e., the Butler-Volmer equations and the cell voltage equation, forms a set of algebraic equations, which are solved using a damped Newton iteration for every call made by the CVode solver.
The whole model is implemented in C++. The model developed can predict the current density and species profiles along the cell length and the thickness of the catalyst layer required to achieve best cell performance. The current density profile predicted by the model along the length is validated by comparing against the experimental measurements reported in the literature. For demonstrating the capability of the model, a comparison between the simulated IV curves and the experimental measurements (Li et. al, 2003 ECS) is given in the Figure.