A platinum degradation reaction model for the high-speed computation in the integrated fuel cell system simulator and its validation by the accelerated stress test data of the commercial fuel cells
Authors: Hasegawa Shigeki , Kim Sanghong , Kageyama Miho , Kawase Motoaki 
Published: December 2024

Abstract

The modeling and numerical methods to estimate the Pt degradation rate were developed for a year-long and system-scale durability simulation in an acceptable accuracy and computational time. The model could reproduce the published voltage cycle results of the MEA of 2nd-generation MIRAI in the relative error of 0.38 % and 180 times faster computational speed than the actual time with a standard laptop. It was confirmed from the voltage cycle simulation that even the small number of the coarse particles considerably accelerated the Pt degradation.

Modeling and numerical methods:

The reaction rate equations of the reaction rates among Pt, PtO, and Pt2+ in the literature [1][2] were employed and the mass transport equations among the particle sizes discretized at 0.1 nm were added. The reaction rate constant of Pt → Pt2+ + 2e- [1] was optimized to reproduce the experimental results and the other parameters were unchanged from those in the literature [1][2]. The particle size distribution (PSD) of Pt in the cathode catalyst layer measured with the MEA of 2nd generation MIRAI by nano X-ray CT [3] is shown in Fig. 1. The coarse particles with the diameters of 8.7, 13.2, 20.6, 44.1, and 85.1 nm were observed in the PSD. The PSD data were pre-processed to create the initial particle density distribution (PDD) data by the following process: Removal of the particles smaller than 1 nm; cubic interpolation of the PSD data by the 0.1 nm discretized diameter from the 0.5 nm bin width; removal of the particles with less than 1 count; scaling particle numbers at each diameter to derive the PDDs with the ECSA of 90 m2-Pt/m2 [3] and the loading of 0.17 mg-Pt/cm2 [4] in the cathode catalyst layer of 2nd-generation MIRAI. The derived PDDs are shown in Figs. 2(a)–2(f). The PDDs calculated from the ECSA and loading agreed when the particles of 85.1 and 44.1 nm were removed as shown in Fig.2(c). They were adopted as the initial PDD in this study. For high-speed computation in the integrated fuel cell system simulator the current authors had presented [5], the non-iterative solver by the explicit Euler method with the low-pass filter by the discrete first order lag [6] was developed (solver 1). Fig. 3 shows the solutions obtained by the developed solver, the 4th-order Runge Kutta solver (solver 2), and the iterative solver with the implicit Euler method and relaxation method [6] (solver 3). The numerical oscillation was observed in the solution by solver 2. The solution by solver 1 was similar to the converged solution by solver 3. The model was implemented on MATLAB/Simulink environment as the open-loop simulator as shown in Fig. 4. The published voltage cycle conditions of 0.95–0.6 V, 80 °C, 100 % relative humidity [4] were input to the simulator. The impact of the coarse particle was also investigated by setting the PDD in Fig. 2(f), where all of the coarse particles were removed, as the initial value and compared with the case in Fig. 2(c).

Results and discussion:

Fig. 5 shows the experimental and simulation results of the ECSA fractional retention during the 30,000 voltage cycles. The calculation results by the solvers 1 and 3 agreed in the maximum relative error of 1.3×10-4 %. The maximum relative error between the experimental and calculated ECSA at 500, 1000, 3000, 10000, and 30000 cycles was 0.38 % and the acceptable accuracy was confirmed. The computational time using solver 1 for 180,000 s of the actual experimental time was 1002 s with a standard laptop (Toshiba dynabook G83/HS; Intel Core i7-1165G7 @ 2.80 GHz / 2.80 GHz CPU; 16 GB RAM). In case of the initial PDD of Fig. 2(f), the ECSA fractional retention at 30,000 voltage cycles was improved from 44.7 to 69.4 %. Even the small number of the coarse particles considerably accelerated the Pt degradation.

References

[1] R. M. Darling and J. P. Meyers, J. Electrochem. Soc., 150(11), A1523–A1527 (2003).

[2] W. Bi and T. F. Fuller, J. Electrochem. Soc., 155(2), B215–B221(2008).

[3] K. Amemiya et al., PEFC&E 22 in 242nd. ECS Meeting (Atlanta, GA, US, Oct. 9–13, 2022), I01Z-1692.

[4] T. Takahashi et al., J. Electrochem. Soc., 169, 044523 (2022)

[5] S. Hasegawa et al., ECS Trans., 109(15), 15–70 (2022).

[6] W. H. Press et al., “Numerical recipes in C: the art of scientific computing, 2nd Edition” (Cambridge University Press, New York, US, 2010).

Figure 1