Comparison of Two Physical Models for Fitting PEM Fuel Cell Impedance Spectra Measured at a Low Air Flow Stoichiometry

Abstract

Local impedance spectra of a segmented PEM fuel cell operated at an air flow stoichiometry of λ = 2 are measured. The local spectra are fitted with the recent 1D and quasi-2D (q2D) physical models for PEMFC impedance. The q2D model takes into account oxygen transport in the gas channel, while the 1D model ignores this transport assuming infinite stoichiometry of the air flow. Analysis of the q2D expression for the GDL impedance Z ∞ gdl at λ → ∞ shows that the contribution of Z ∞ gdl to the total cell impedance rapidly decays with the frequency growth. We derive an equation for the boundary frequency f lim , above which this contribution is small. We show that the 1D model can be fitted to the high-frequency part ( f > f lim ) of a spectrum acquired at λ 2, ignoring the low-frequency arc due to the oxygen transport in the channel. Comparison of fitting parameters resulted from the 1D and q2D models confirms this idea. Polymer electrolyte membrane fuel cells (PEMFCs) generate electricity due to splitting the hydrogen-oxygen combustion reaction into two half-reactions producing and consuming charged particles. Understanding transport and kinetic potential losses in these cells is crucial for cell design. Electrochemical impedance spectroscopy (EIS) provides a unique opportunity to separate contributions of different processes into the total potential loss in a cell.1,2 Deciphering experimental impedance spectra requires modeling though.The simplest and fastest way to rationalize the spectra is the transmission line modeling (TLM). This approach aims at construction of equivalent electric circuit, which has a spectrum close to the measured one. The circuit is usually assembled out of R, C and L-elements, and out of a number of elements representing classic impedances of electrochemical systems. Two well-known examples are the Warburg element, 3 which describes impedance of a transport layer attached to a planar electrode, and Gerischer element 4 representing impedance of a transport layer with the distributed chemical reaction. The TLM has been widely used in fuel cell studies (see e.g. Refs. 5 and 6); however, validity of this approach cannot be rigorously proved. First, there is no guarantee, that the selected equivalent circuit is unique. Second, the classic solutions for impedance of a system with the planar electrode 3,4 are, in general, not applicable to a porous catalyst layer with the distributed electrochemical reaction. 7,8 In addition, determination of the cell physical transport and kinetic parameters from the equivalent circuit elements is usually beyond the scope of the TLM.This explains growing interest in physical modeling of PEMFC impedance.9-22 Generally, a physical impedance model can be obtained from any transient performance model of a cell by making a standard procedure of linearization and Fourier-transform (see e.g. Ref. 23 for mathematical details). The resulting system of linear equations for the perturbation amplitudes is, in general, a complex-valued boundary-value problem (BVP), which ca...

A Fast Low-Current Model for Impedance of a PEM Fuel Cell Cathode at Low Air Stoichiometry

“…This leads to somewhat higherσ p and C dl , as compared to Ref. 21. The oxygen diffusion coefficients in the CCL and GDL by the order of magnitude agree with those reported, 21 taking into account that D ox increases with the cell current density.…”

“…31,32 The double layer capacitance is 50% higher, than the value reported for this MEA in Ref. 21. Here, however, we used a more accurate equation for the impedance Z ct+ p , which takes into account a rapid decay of the proton conductivity through the CCL depth, while in Ref.…”

“…Note that in Ref. 21, the spectra have been measured from individual segments and from the whole cell; here we use the data for the whole cell. The LF arc in Figure 1 represents the combined oxygen transport in the GDL and cathode channel.…”

“…Here, however, we used a more accurate equation for the impedance Z ct+ p , which takes into account a rapid decay of the proton conductivity through the CCL depth, while in Ref. 21 this parameter was assumed to be independent of the distance from membrane. This leads to somewhat higherσ p and C dl , as compared to Ref.…”

“…[3][4][5][6][7][8][9][10][11][12][13][14] Most of these models are numerical and they are slow to be used in algorithms for spectra fitting. A "faster" alternative is analytical modeling of impedance; [15][16][17][18][19][20][21][22][23] however, fast analytical models have been developed for the case of infinite stoichiometry of the air (oxygen) flow in the cathode channel.…”