A Model for PEM Fuel Cell Impedance: Oxygen Flow in the Channel Triggers Spatial and Frequency Oscillations of the Local Impedance

2016

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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...

Section: Modelmentioning

confidence: 99%

“…9 differs from the Warburg impedance for the transport layer of a finite thickness, due to the presence of the frequency-dependent factor (1 + i /J ) in the denominator (see Ref. 8 …”

Section: Modelmentioning

confidence: 99%

mentioning

confidence: 99%

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

Reshetenko

2016

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“…[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.…”

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confidence: 99%

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

2017

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We report a physics-based analytical model for low-current PEM fuel cell impedance, which takes into account oxygen transport in the channel. The model is fast: fitting the model impedance to the experimental Nyquist spectrum takes about 2 minutes on a 2-GHz notebook. In addition to the transport and kinetic parameters of the catalyst layer, fitting returns the oxygen diffusion coefficient in the gas-diffusion layer and the resistivity due to oxygen transport in the channel. Maple worksheet with the fitting procedure is available for download.

“…2,[4][5][6]9,11,12,14,25,[30][31][32]35,36 It is worth noting that the numerical impedance models are slow for least-squares fitting of experimental spectra. Analytical models 7,16,[19][20][21] are fast enough for spectra fitting, but they are limited by the cell currents of about 100 mA cm −2 . One of the key cell parameters is the exchange current density i * of the oxygen reduction reaction (ORR) per unit volume of the electrode.…”

mentioning

confidence: 99%

PEM Fuel Cell Impedance at Open Circuit

2016

A physical model for PEM fuel cell impedance Z at open circuit potential (OCP) is developed and analytical expression for Z is derived. The OCP impedance is a sum of the cathode catalyst layer (CCL) and the gas-diffusion layer (GDL) impedances connected in series. The GDL impedance differs from the Warburg impedance, which is often used in modeling of fuel cell electrodes. A key parameter determining the OCP impedance spectrum is the Newman's dimensionless reaction penetration depth ε. In PEMFCs, ε is large, which makes the GDL impedance a small "invisible" additive to the CCL impedance. In a solid oxide fuel cell (SOFC) anode, ε is small, and the GDL impedance forms a well-resolved separate arc in the impedance spectrum at the OCP. In a real PEM fuel cell, a true OCP regime cannot be achieved due to hydrogen crossover through the membrane. Impedance measurements at zero current in the load yield an equivalent current density of hydrogen crossover through the membrane. Electrochemical impedance spectroscopy (EIS) provides a unique opportunity for in situ separation of contributions of transport and kinetic processes into a fuel cell potential. This powerful technique continuously attracts new researchers: the Scopus database shows that over the past decade, a number of publications on EIS in chemical engineering has been growing exponentially. At present, literature list on EIS in PEM fuel cells accounts several hundred items; the basic issues are discussed in books of Orazem and Tribollet 27 and Lasia.