Understanding of Water Transport through Membrane Electrode Assembly in PEFC
Authors: Kageyama Miho , Nakamichi Kimiyo , Tominaga Mikito , Kawase Motoaki 
Published: December 2024

Introduction
In PEFC, water generation, electroosmosis drag, and back diffusion alter the humidity, which affects transport properties such as proton conductivity and effective oxygen diffusion coefficient. Since the sorption and desorption of water in the membrane is slower than other processes, dynamic water behavior should be considered to estimate the cell performance precisely. Though water diffusion in Nafion™ membrane was extensively investigated [1, 2], the water transport through a membrane electrode assembly (MEA) has not been fully investigated. In this study, the water permeation flux through MEA was measured, and the effective water diffusion coefficients in a membrane and catalyst layer (CL) were formulated respectively and dynamic moisture content change in MEA was simulated.
Experimental
CLs made of Pt-loaded carbon (Pt 50 wt%) and Nafion ionomer (I/C = 1.0) with a thickness of 4, 9, and 13 μm on both sides of Nafion™ membrane (NR-212) were prepared as MEAs. They were installed separately in a JARI cell whose active area was 5.0 cm×5.0 cm. Fig. 1 shows the schematic of the measurement system. Nitrogen with different humidity was supplied to both sides of the cell at 300 cm3/min (20 °C, 1 atm). The water vapor at cell outlet was collected to calculate the water permeation flux through MEA at cell temperatures of 60, 70, and 80 °C and moisture content of 4−7.
Results and discussion
Water permeation flux through a membrane, N
A
(M), is expressed as follows:

N
A
(M)= c
(M)
ρ
(M)
D
eA
(M) dλ/dz (1)
where c
(M) is the ion-exchange capacity [mol/kg], ρ
(M) is the density of membrane [kg/m3], λ is the moisture content, and D
eA
(M) is the effective diffusion coefficient through a membrane [m2/s]. By considering the sorption equilibrium between the ionomer and vapor phases, the apparent effective diffusion coefficient through CL, D
eA
(E)
app, which includes the transport in the vapor phase and that in ionomer, can be defined as follows:

N
A
(E) = c
(M)
ρ
(M)
D
eA
(E)
appdλ/dz (2)
From eqs. (1) and (2), the water permeation resistance is expressed as follows:

c
(M)
ρ
(M)(λS

– λp
)/N
A
(M) = 2δ
(E)/D
eA
(E)
app + δ
(M)/D
eA
(M) (3)
where λs
and λp
respectively denote the moisture content of ionomer at the CL surface on the supply and permeate sides.
By measuring water permeation resistance through MEAs with different CL thicknesses, the CL and membrane resistances can be separated. Fig. 2 shows the relationship between the water permeation resistance and the CL thickness at λ = 6. λ was estimated from RH using the GAB equation [3]. D
eA
(E)
app and D
eA
(M) were obtained from the slope and the intercept of the trendline in Fig. 2, respectively. These properties were obtained at various moisture contents and temperatures as shown in Figs. 3 and 4. At each temperature, D
eA depends linearly on λ and is lower for higher λ. The temperature dependency was Arrhenius-type and the activation energy depended on λ. They were expressed as a function of temperature and λ as follows:

D
eA
(E)
app = (-1.55×10-10 + 1.21×10-9
λ) exp (-E
a
(E)/R (1/T - 1/T
ref)) m2/s (4)

D
eA
(M) = (-7.58×10-11 + 5.92×10-10
λ) exp (-E
a
(M)/R (1/T - 1/T
ref)) m2/s (5)

T
ref = 353.15 K, E
a
(E) = -3.81λ + 37.6 kJ/mol, E
a
(M) = -12.1λ + 122.5 kJ/mol
Reproduced D
eA
(E)
app and D
eA
(M) are shown in Figs. 3 and 4. D
eA
(E)
app is 1.8−5.3 times greater than D
eA
(M). It indicates that the contribution of vapor phase transport is higher than ionomer for water transport in CL.
The water balance of the membrane is expressed by the following equation:

c
(M)
ρ
(M)
∂λ/∂t = -∂N
A
(M)/∂z (6)
The unsteady moisture content distribution in MEA was calculated by solving eqs. (1), (2) and (6). By using obtained effective diffusion coefficients, the time-dependent water desorption in MEA (10 μm thick CLs on N115 membrane) was simulated when the moisture content was changed from 6 to 4 at 70 °C as shown in Fig. 5. Thus, it is possible to simulate the unsteady water sorption and desorption in MEA. The mass change during the sorption and desorption process can be simulated by integrating the moisture content distribution in MEA.
Conclusions
From the permeation experiments with MEA installed in a cell, the water transport properties in MEA were formulated as a function of temperature and moisture content. The ability to predict real-time moisture content in MEA makes it possible to know the cell performance where the loads changes from time to time.
References
[1] Schneider, N. S. et al., Polymer, 51 (3), 671−678 (2010).
[2] Mittelsteadt, C. K. et al., ECS Trans., 41 (1), 101−121 (2011).
[3] M. Kageyama et al., ECS Trans., 109 (9) 327−345 (2022).

Figure 1