Dynamic Water Transport through the Perfluorinated Sulfonic-Acid Membrane
Authors: Kageyama Miho , Lu Kai , Nakamichi Kimiyo , Kawase Motoaki 
Published: November 2022

Introduction
The proton exchange membrane (PEM) is indispensable material for proton transport in PEFC. Since RH affects the effective proton conductivity and the effective oxygen diffusivity through the catalyst layer as well as the proton conductivity, the electroosmotic drag coefficient, the effective diffusivity of water, and the gas permeances of PEM, water behavior which determines relative humidity is most important.
To estimate the PEFC performance over time, the dynamic change in transport properties of PEM should be reproduced over full range of operating temperature and moisture content. Though water diffusion in Nafion™ membrane was extensively investigated [1, 2], the transport properties have not been formulated as the function of both temperature and moisture content. In this study, the effective water diffusivity and the skin layer water transfer coefficient were formulated from the experimental results measured by the permeation method and the sorption/desorption method.
Experimental
–Permeation experiments
A Nafion™ membrane, NR-212, N115 or N117 with different thickness (at relative humidity, RH of 50 %), 51 μm, 127 μm, and 183 μm, respectively, was set in a Japan Automobile Research Institute (JARI) standard cell whose active area was reduced to 2.0 cm×2.0 cm. The cell was placed in the constant temperature and humidity oven (ESPEC, LHL-113). Nitrogen was supplied to both sides of the cell at 300 cm3/min (20 °C, 1 atm). The relative humidity of the supplied gas was controlled by the bubbler temperature. The water vapor flowing out of the cell was collected with an ice-cooled trap to estimate the water permeation flux of the membrane.
–Sorption/desorption experiments
The membrane was placed in a desiccator in which RH was controlled by saturated salt solution method at room temperature (22 °C). The weight of the membrane was recorded constantly. After reaching equilibrium, the membrane was placed in another RH condition and weighed.
Results and discussion
The moisture content of the membrane, λ was calculated by a GAB sorption equation in which paraments were fit using reported water equilibrium experimental data [3, 4, 5, 6] as shown in Fig. 1. Schematic diagram of permeation mechanism is shown in Fig. 2. Water permeation flux through the membrane, N
A
(M) is expressed as follows:

N
A
(M)=c
(M)
ρ
(M) (λ
-m
-λm
)/(1/k
A++1/k
A-+δ
(M)/D
eA
(M)) (1)
where c
(M) is the ion-exchange capacity [mol/kg], ρ
(M) is the density of dry membrane [kg/m3], λ is the moisture content, k
A is the skin layer mass transfer coefficient [m/s], δ
(M) is the membrane thickness [m] and D
eA
(M) is the effective diffusivity [m2/s]. The subscript A means absorbed water, m is the surface of the membrane, - is the supply side and + is the permeate side. Total resistances calculated by eq. (1) were plotted against the membrane thickness. D
eA
(M) and k
A calculated from the trendlines are shown in Figs. 3 and 4, and Arrhenius plots of D
eA
(M) are shown in Fig. 5.
Skin layer mass transfer coefficient, k
A can be obtained directly from the sorption/desorption experiments at low temperature. k
A obtained from the permeation and sorption/desorption experiments are summarized in Fig. 6 and they are located on an identical line. The transport properties at λ= 5 are expressed as follows as an example:

D
eA
(M) = 3.35×10–5 m2 s–1 exp(–3760 K/T)

k
A = 1.27×105 ms–1 exp(–8330 K/T)
Since these transport properties depend on the moisture content, the desorption is faster than sorption and vice versa even at completely same range of moisture content. This is because the moisture content in the skin layer is always different during sorption and desorption even with the same moisture content variation range.
Conclusions
From the permeation experiments and the sorption/desorption experiments, the transport properties over wide range of temperature and moisture content of the perfluorinated sulfonic-acid membrane were formulated. Considering the change in k
A and D
eA depending on the moisture content, the sorption and desorption rate are unequal even in identical RH range.
Acknowledgement
This work was supported by the FC Platform Program: Development of design-for-purpose numerical simulators for attaining long life and high-performance project (FY 2020–FY 2022) conducted by the New Energy and Industrial Technology Development Organization (NEDO), Japan.
References
[1] Zawodzinski, T. A. et. al., J. Phys. Chem.,
95 (15), 6040-6044 (1991).
[2] Mittelsteadt, C. K. et. al., ECS Trans., 41 (1), 101−121 (2011).
[3] T. E. Springer, et. al., J. Electrochem. Soc., 138(8), 2334–2342 (1991).
[4] J.T. Hinatsu, et. al., J. Electrochem. Soc., 141(6), 1493–1498 (1994)
[5] K. D. Kreuer, et. al., Solid State Ionics, 35-36(2018)
[6] A.Z. Weber et. al., J. Electrochem. Soc., 151(2), A311–A325(2004).

Figure 1