Modeling of Relative Humidity-Dependent Impedance of Polymer Electrolyte Membrane Fuel Cells

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 X l 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]. R ion is the proton conduction resistance; R ct is the resistance of charge transfer in the ORR; T ct and P are parameters of the constant phase element. In this study, R ct was made a function of proton potential using Equation 2, where i 0 is the exchange current density of the cathode and n is the number of exchanged electrons. The potential X 0 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 10 6 to 0.1 Hz. Using the proposed model, a simulation was performed by varying R ion 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 R ct 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 cm 2 and the Pt loading was 0.4 mg pt 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 simul