A model for water transport in the membrane and an impedance spectroscopy study of the effect of relative humidity on PEM fuel cell parameters

TL;DR

This work addresses water management and impedance interpretation in PEM fuel cells by linking a one-dimensional membrane impedance model for liquid water transport with a two-phase, through-plane cathode impedance model and fitting to impedance spectra across anode/cathode RHs of 32/32%, 50/50%, and 100/100% for current densities from 100 to 1000 $\mathrm{mA\,cm^{-2}}$. It introduces a nonlinear membrane diffusivity $D_w(\lambda)$ and a sorption isotherm $\Lambda(RH)$ within a dimensionless perturbation framework, solved efficiently using SciPy solvers and parallel computation. The results reveal that mean CCL liquid saturation $\bar{s}$ decreases with current due to a liquid-pressure gradient, while CCL oxygen diffusivity $D_{ox}$ increases as larger pores participate in current conversion; the ORR Tafel slope grows with current, and the double-layer capacitance increases with RH, indicating larger electrochemically active surface area. High-frequency resistance also decreases with RH, highlighting improved anode-side humidification at higher RH. Overall, the coupled model provides mechanistic insight into RH effects on transport and impedance and offers a practical tool for diagnosing and optimizing water management in PEMFCs.

Abstract

Effective water management is essential for the optimal performance of PEM fuel cells. We have developed an impedance model for liquid water transport through the membrane and coupled it with the two-phase model for cathode side impedance. The complete model was fitted to experimental spectra measured at anode/cathode relative humidities (RH) of 32/32\%, 50/50\% and 100/100\% within a current density range of 100 to 1000 mA cm$^{-2}$ and an air flow stoichiometry of 2. Cathode catalyst layer (CCL) saturation decreases with current density due to a growing liquid pressure gradient. For all RH values, the CCL oxygen diffusivity increases dramatically with cell current due to progressive involvement of larger pores into the proton current conversion. Higher RH leads to higher double layer capacitance, which indicates that liquid water increases the electrochemically active surface area.

Figures (10)

• Figure 1: Schematic of the cell layers and the $x$--coordinate.
• Figure 2: Points -- the diffusion coefficient $D_w$ of water in membrane measured by van Bussel et al. Bussel_98. Solid line -- the analytical fit, Eq.\ref{['eq:Dmfit']}.
• Figure 3: Points -- the membrane water sorption isotherm measured by Hinatsu, Mizuhata and Takenaka Hinatsu_94, solid line -- Eq.\ref{['eq:Lam']}. The points were digitized from the best-fit curve provided in Ref.Hinatsu_94
• Figure 4: The experimental (points) and interpolated (lines) IR-corrected polarization curves of the cell operated at the indicated relative humidities. The points are interpolated using cubic spline just as an eye guide.
• Figure 5: The experimental spectra (points) and fitted model Eq.\ref{['eq:Zcell']} (open circles) for the indicated current densities (mA cm$^{-2}$). To improve readability, half of the points (10 per decade) are shown. The regime of cell operation is indicated in Table \ref{['tab:oper']}, RH 32/32%.