Determination Method of Dimensionless Moduli for Estimation of PEFC Performance
Authors: Kageyama Miho , Yamaguchi Kazuhiro , Heggo Dalia , Ma Yulei , Ogawa Hikaru , Kawase Motoaki 
Published: December 2020

Introduction
To predict PEFC performance without complicated simulation or a lot of experimental data is required for the optimum design of the cell, especially the cathode catalyst layer (CCL). In our previous study, the effectiveness factor of CCL was reported to be a function solely of 4 dimensionless moduli which were derived from the isothermal one-dimensional model of the cathode consisting of oxygen balance, oxygen transport, proton transport, reaction stoichiometry, and rate [1]. In this study, the dependency of the oxygen reduction reaction (ORR) rate on CCL thickness is analyzed and a method to determine dimensionless moduli is proposed.
Theory
The current density, i, is a product of the reaction rate without through-plane mass transfer resistances, k
vcm

p
Oc
, and the effectiveness factor, F
e.
k
vc is the reaction rate constant per unit volume of CCL [mol/(Pa·m3·s)] and p
O is the oxygen partial pressure [Pa], and the subscript m denotes PEM–CCL boundary and the subscript c denotes CCL–gas diffusion layer (GDL) boundary.

i = 4 F
δ
k
vcm

p
Oc

F
e [A/m2], (1)
where δ is the CCL thickness, and F is the Faraday constant. F
e is a function of 4 dimensionless moduli, M
Om
, M
pm
, P
Om
, and y
Oc
.

M
Om
: Ratio of oxygen diffusion resistance to reaction resistance (Thiele modulus),

M
pm
: Ratio of proton transport resistance to reaction resistance (our modulus),

P
Om
: Ratio of oxygen diffusion resistance to convection resistance (Peclet number), and

y
Oc
: Oxygen mole fraction.

M
Om
and M
pm
are defined as follows:

M
Om
= δ (k
vcm

RT / D
eO)1/2 = c
MO
δ, (2)

M
pm
= δ [4Fk
vcm

p
Oc
/ (σ
ep
b
c)]1/2 = c
Mp
δ, (3)
where D
eO is the effective oxygen diffusion coefficient [m2/s], and σ
ep is the effective proton conductivity [S/m].
Eqs. (1) and (2) indicate that the relationship between i and δ corresponds to the relationship between F
e
M
Om
and M
Om
when the other parameters are fixed. The former relationship is obtained from measurements and the latter is obtained from the theory.
Experimental
The membrane electrode assembly (MEA) was consisted of the catalyst layers made of TEC10E30E (Tanaka Kikinzoku Kogyo K.K.) catalyst with Nafion® ionomer and membrane (DuPont NR-212). Ionomer/carbon weight ratio was 1.0, and the CCL thickness was 10, 28.3, and 46.8 mm (Pt loading was 0.15, 0.43, and 0.71 mg/cm2). H2 and O2 were humidified in bubblers at 75 ˚C. H2 flow rate was 600 cm3/min, and O2 flow rate was 300 cm3/min. The cell was operated at 80 °C and the pressure at the cell outlet was 1 atm.
Results and Discussion
To determine the dimensionless moduli from experimental data, dependency of ORR rate on p
Oc
, D
eO, k
vcm
, and δ can be used for the analysis. Fig. 1 shows the effects of these variables on F
e at fixed P
Om
and y
Oc
. By fitting the theoretical curve with the experimental data, dimensionless moduli, M
Om
and M
pm
can be determined. As shown in the figures, a wide range of data is desirable to determine dimensionless moduli. Since total pressure range is limited, it is not realistic to determine the dimensionless moduli from the total pressure dependency.
The dependency of ORR rate on δ was measured as shown in Fig.2. Fig. 3 shows current density measured at E
cm
= 0.7 V using MEAs with different CCL thicknesses and dimensionless model analysis. F
e
M
Om
has a maximum point against M
Om
as expected [2]. As δ increases, the Pt amount increases proportionally but the transport resistance increases M
Om
and M
pm
and as a result, the effectiveness factor decreases. Consequently, the increase in the current density is limited. Tafel slope, b
c = 0.0346 V was obtained from the experiment using Pt-sputtering catalyst for the analysis [3]. At E
cm
= 0.7 V, M
Om
and M
pm
were determined to be 0.38 in the case of δ = 10 mm. D
eO = 7.27×10-8 m2/s and σ
ep = 18.3 S/m are determined from Eqs. (2) and (3).
Determination of M
Om
and M
pm
from the I-V measurements using MEAs with different δ's was demonstrated as an example. Measurements using a single MEA at different p
Oc
's, measurements using MEAs with different δ's or using MEAs with different Pt/C catalysts can be used for the determination of the dimensionless moduli.
When dimensionless moduli are determined, the optimum CCL structure such as CCL thickness and Pt/C ratio can be investigated. Direction for improving the performance can be suggested.
References
[1] M. Kawase et al., ECS Trans., 75(14), 147-156(2016).
[2] M. Kawase et al., AIChE J. 63(1), 249-256 (2017).
[3] K. Murase et al., 31st Int. Symp. Chem. Eng. (Chiang Mai, Dec. 2018).

Figure 1