Analytical Model for the Hydrogen Transport Impedance at a PEMFC Anode
Authors: Chaparro Antonio M , Duque Luis , Folgado M. Antonia 
Published: November 2022

Impedance techniques are most useful for the characterization of kinetic processes in fuel cell electrodes. For 'proton exchange membrane fuel cells' (PEMFC) electrochemical impedance reflects cathode kinetics, where larger overvoltage occurs due to slower oxygen reduction reaction [1]. The anode kinetics is considered fast enough and therefore without a signal in the impedance. However this may not be the case under certain conditions, like high current densities, anodic flooding events, side hydrogen kinetics, ultra-low catalyst loading, among others.
In order to study anode limitations and kinetics, independent from cathode kinetics, we have recently developed an impedance technique called ‘current modulation hydrogen flow-rate spectroscopy’ (CH2S), that relates the hydrogen inlet flux with fuel cell current. A general description of the technique and results are given in another communication of this congress (#I01A-1406). To help understanding the information provided by CH2S and the analysis of results, a theoretical analysis is desirable based on fundamental transport equations in the PEMFC anode.
In this communication we have calculated the transfer function of CH2S for two cases of anode kinetics (Fig. 1a): Case 1 with pure hydrogen diffusive behavior in the gas diffusion layer (GDL), and Case 2 that includes the possibility of a hydrogen reversible chemical reaction in the GDL. Case 2 can be assimilated to a situation where hydrogen is stored in the electrode by the reversible formation of a hydrogen adsorbed species (X-H2). This possibility is of high interest for small portable PEMFC running without external hydrogen storage.
Hence, the transfer function of CH2S is:
H (jω)=nF
QH2

/
I
= nFADH2 (dc
H2

/dx)x=LGDL /
I
(Eq.1)
Where
I
is the current perturbation, and
Qi

and
cH2

are the perturbed flow rate and concentration, respectively. The electrode is considered as a continuous porous medium characterized by an effective diffusion coefficient for H2 (DH2
) in the GDL, where transport is governed by the second Ficks´law. Hydrogen kinetics in the GDL is first order, with k1, k-1 rate constants for desorption and adsorption, respectively (Fig. 1a). Before the GDL, H2 transport is considered fast enough, without an impact on the transfer function.
Transport equations for Cases 1 and 2 have been solved analytically by conventional methods using the appropriate boundary conditions. From the solutions, the CH2S transfer functions (Eq. 1) have been calculated and plotted in Fig. 1b) as Nyquist plot. For the simple diffusion, a skewed semicircle is obtained with high frequency cut at H' = 0 and low frequency at H' = 1. The null high frequency cut is due to limited hydrogen transport rate and experimental set-up response rate; the unit low frequency cut reflects the stoichiometric hydrogen consumption. The maximum of the semicircle is related with the diffusion constant and GDL thickness (ωmax=2DH2/LGDL
2). . For Case 2, the low frequency cut extends beyond unit (H'>1) , and a new signal can be distinguished due to hydrogen kinetics in the GDL.
It is shown that the CH2S impedance technique can be used to study hydrogen transport and kinetics in the anode of a PEMFC.
Acknowledgement: The work is partially financed by the ELHYPORT project (PID2019−110896RB-I00), Spanish Ministry of Science and Innovation.
[1] A. Lasia, in 'Electrochemical Impedance Spectroscopy and its Applications', Springer Science+Business Media New York 2014

Figure 1