A simple and accurate fitting equation for half of the faradaic impedance arc of a PEM fuel cell

• We consider a physical equation for the low-current catalyst layer impedance.
• Asymptotic expansion of this equation is performed.
• The result is an impedance of the parallel RC-circuit connected in series with the proton resistivity Rp.
• This result is valid for sufficiently small frequencies.
• Fitting this equation to literature spectra validates the model.

An asymptotic solution to the physical model for the impedance Z of the cathode catalyst layer (CCL) in a PEM fuel cell at a small current density is derived. The solution shows that for sufficiently low frequencies, Z is equivalent to the impedance of a parallel RC circuit connected in series with the CCL proton resistance. This leads to a simple explicit relation between the imaginary and real parts of Z  ; with the typical fuel cell parameters, this relation is valid up to the frequency f≃100f≃100 Hz. Fitting this equation to the low-frequency part of the faradaic impedance arc yields the Tafel slope of the oxygen reduction reaction and the CCL proton conductivity. The method is illustrated with the experimental impedance spectra taken from literature.