Modeling of Relative Humidity-Dependent Impedance of Polymer Electrolyte Membrane Fuel Cells
Authors: Tanaka Akihisa , Nagato Keisuke , Tomizawa Morio , Inoue Gen , Nakao Masayuki 
Published: November 2022

1. Introduction
Polymer electrolyte membrane fuel cells (PEMFCs) are highly efficient devices that utilize hydrogen energy. The large overpotential of PEMFCs, particularly under low relative humidity (R.H.) conditions [1], is a challenge. Equivalent circuit modeling is an effective technique for impedance analysis, in which circuit elements are used to simulate electrode reactions [2]. The transmission line model (TLM) is often used for porous electrodes including PEMFCs [3]. In this study, a TLM was constructed considering the resistance distribution in the cathode catalyst layer (CCL), and the dependence of the impedance on R.H. was investigated.
2. Modeling
Figure 1 shows a TLM. The proton potential Xl
was set as a parameter for each triple phase boundary (TPB), where an oxygen reduction reaction (ORR) occurs. At a certain TPB, Equation 1 holds based on Kirchhoff's current law [4]. Rion
is the proton conduction resistance; Rct
is the resistance of charge transfer in the ORR; Tct
and P are parameters of the constant phase element. In this study, Rct
was made a function of proton potential using Equation 2, where i0
is the exchange current density of the cathode and n is the number of exchanged electrons. The potential X0 of the TPB on a Nafion membrane was specified as the boundary condition. Subsequently, the model impedance was calculated by varying the frequency f from 106 to 0.1 Hz.
Using the proposed model, a simulation was performed by varying Rion
to be similar to the measured impedance spectra in the next section. For comparison, a simulation was performed under the same conditions using a conventional TLM in which Rct
is a constant value.
3. Experimental
A membrane electrode assembly (MEA) was prepared by spraying a catalyst ink with an ionomer/carbon weight ratio of 0.92 onto a Nafion membrane. For both the cathode and anode, the electrode area was 1 cm2 and the Pt loading was 0.4 mgpt cm-2. Power generation tests were conducted at a cell temperature of 80 °C. Gases flowing at 200 sccm were supplied to the cathode at an oxygen partial pressure of 0.2 atm and to the anode at a hydrogen partial pressure of 0.4 atm. The impedance spectra of the MEA were measured under various R.H. conditions by electrochemical impedance spectroscopy [5] in the potentiostatic mode at 0.7 V. The distribution of relaxation times (DRT) analysis [6] was conducted on the impedance spectra.
4. Results and discussion
Figure 2 shows the experimental and simulation results. The left and right columns show the impedance spectra and the DRT analysis results, respectively.
Based on the analysis of DRT peaks by Heinzmann et al. [7], the peak in the mid-frequency range, PM, is associated with the resistance of charge transfer in the ORR, whereas the peak group in the high-frequency range, PH, is associated with the resistance of proton conduction. The PH of the DRT of the measured impedance increases as R.H. decreases. This indicates that a decrease in R.H. promotes a decrease in proton conductivity. The increase in Rion
in the simulation represents a decrease in proton conductivity, which increases the PH as shown in both simulation results. As the proton conductivity decreases, the PM of the DRTs of the measured impedance and the calculated impedance using the proposed model increases. However, the PM of the DRT of the calculated impedance using the conventional model does not change. This indicates that the proposed model can accurately simulate the actual phenomena in the CCL. The reason for the increase in PM caused by the decrease in proton conductivity could be that the local charge transfer resistance increases by a decrease in the proton potential at each TPB.
5. Conclusions
A TLM was constructed to predict the dependence of impedance on R.H. Experimental results showed that an unsatisfactory proton conductivity resulted in an increase in the charge transfer resistance. The results of the simulation with varying proton conduction resistances using the proposed model are consistent with the experimental trend. In future studies, circuit parameters should be appropriately determined by fitting the model to the measured impedance spectra.
References
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[4] J. H. Teng, Int. J. Electr. Power Energy Syst.
27, 327–333 (2005).
[5] X. Yuan et al., Int. J. Hydrogen Energy.
32, 4365–4380 (2007).
[6] S. Dierickx et al., Electrochim. Acta.
355, 136764 (2020).
[7] M. Heinzmann et al., J. Power Sources.
402, 24–33 (2018).

Figure 1