Modeling of Oxygen Diffusion Resistance in PEFCs in the Intermediate Potential Region
Authors: Suzuki Takahisa , Yamada Haruhiko , Morimoto Yu 
Published: February 2020

The current-voltage performance of polymer electrolyte fuel cells (PEFCs) in the intermediate voltage region has received attention from the standpoint of increasing the maximum power of the cell. The performance-limiting factors in this kinetic-mass transport mixed control region were first considered as a protonic resistance in the polymer electrolyte, an oxygen diffusion resistance in the pores of the catalyst layer (CL) and gas diffusion layer (GDL), and a diffusion resistance of the dissolved oxygen in the polymer electrolyte that covers the catalyst. These three factors were taken into consideration in mathematical models that predict the performance, which resulted in the predictions much better than experimental results. To bridge the gap, the diffusion resistance in the catalyst agglomerates, which are composed of carbon-supported catalysts and an ionomer, was proposed. However, huge agglomerates that the models assumed were not observed in the scanning electron micrographs of the cross sections of the catalyst layers. In the meanwhile, Kudo and Morimoto measured the oxygen diffusion resistance using Nafion thin films and concluded that the interfacial resistance at the Nafion-Pt or Nafion-gas interface gave rise to the diffusion resistance [1]. The existence of the resistance at the Nafion-Pt interface was supported by molecular dynamics simulations [2]. In this work, the interfacial resistance estimated from the measurement of limiting current densities was incorporated into the performance model and the model predictions were compared with experimental results. The discrepancy between them was assumed to stem from a dependence of diffusion resistance on the electrode potential and then the dependency was analyzed.
In the experiments, the cell was operated at 65 °C with a large excess flow rate of hydrogen and 1% oxygen balanced with nitrogen, both humidified to 80% relative humidity, under atmospheric pressure. The condition was selected to reduce the overpotential variation in the through-plane direction caused by the protonic resistance and to avoid the effect of the produced water and generated heat, and thus to emphasize the effect of oxygen diffusion. Following the seminal studies of Mashio et al. [3], we decomposed the diffusion resistance into two resistances in series, namely, the one caused by molecular diffusion (Rmolec) and the remainder (Rother). Rmolec was estimated with the aid of limiting-current density measurements using 1% oxygen balanced with helium instead of 1% O2-N2. Rother was calculated by subtracting Rmolec from the overall diffusion resistance. We well call Rother determined by this procedure as Rother
ref.
The main features of the model to analyze the experimental results are as follows: (1) One-dimensional through-plane distribution is considered; (2) The anode CL and GDL are neglected; (3) Overpotential distribution and hence the reaction rate distribution is taken into account; (4) The oxygen reduction reaction rate is expressed by Tafel equation and is proportional to the oxygen concentration at the catalyst surface; (5) Oxygen concentration at the catalyst surface is calculated using the diffusion resistance and reaction rate.
In Figure 1a, an experimental result (dotted line) and a model prediction (solid line) of the performance of a cell are compared. In the model, constants in Tafel equation are selected so that the prediction fits to the experiment in the activation-controlled region; the membrane and CL resistances were the values measured by impedance spectroscopy; Rmolec and Rother
ref were used as the diffusion resistances. The model prediction gives larger current density than the experiment in the intermediate cathode potential region. We assumed that the discrepancy stemmed from the constant Rother (= Rother
ref), and therefore hypothesized that Rother is a function of electrode potential. We therefore increased Rother from Rother
ref at each potential to find the value that the current density from model prediction matched the experimental value. The resulting Rother is shown in Fig. 1b as a function of cathode potential (Rother
ref is shown as a dashed line). Rother increased with potential except for high potential region, where the effect of diffusion resistance on the performance is less significant and hence the accuracy of the fitting is deteriorated. The effect of catalyst loading will be discussed and a mathematical formulation of Rother will be presented.
[1] K. Kudo, Y. Morimoto, ECS Trans., 50, 1487 (2012)
[2] R. Jinnouchi, K. Kudo, N. Kitano, Y. Morimoto, Electrochim. Acta, 188, 767 (2016)
[3] T. Mashio, A. Ohma, S. Yamamoto, K. Shinohara, ECS Trans., 11, 529 (2007)

Figure 1