Quantification Method of Mass Transfer Resistance in Cathode Catalyst Layer in PEFC
Authors: Ogawa Hikaru , Okada Yuji , Kageyama Miho , Gyoten Hisaaki , Murakami Shuka , Kawase Motoaki 
Published: February 2024

Introduction
To spread PEFCs, it is important to optimize the cathode catalyst layer (CCL) because the oxygen reduction reaction (ORR) in CCL is sluggish. Our previous study proposed that the mass transfer resistance in the through-plane direction in CCL can be quantified by measuring ORR rate dependency on oxygen partial pressure, effective oxygen diffusion coefficient, ORR rate constant, or CCL thickness[1]. In this study, dependency of the polarization curve on the oxygen partial pressure was measured with commercial supported-platinum catalysts at fixed RH and temperature. The objective of this study is to establish the quantification methods of mass transfer resistances in CCL.
Theory
In our previous study[2, 3], the current density, i is expressed as

i = 4F
δ
(C)
k
vcm

p
Oc

F
e [A/m2], (1)
where δ
(C) is the cathode catalyst layer (CCL) thickness, k
vc is the reaction rate constant per unit volume of CCL [mol/(Pa·m3·s)] which does not include through-plane mass transport resistance. p
O is the oxygen partial pressure [Pa]. The subscripts m and c denote PEM–CCL boundary and CCL–gas diffusion layer boundary, respectively. F
e is the effectiveness factor, a function of the following 4 dimensionless moduli, M
Om
, M
pm
, P
Om
, and y
Oc
. F
e is defined as the ratio of the observed reaction rate to the reaction rate which does not have the influence of through-plane mass transfer resistance. M
Om
denotes the ratio of O2 diffusion resistance to the reaction resistance. M
pm
denotes the ratio of proton transfer resistance to the reaction resistance. P
Om
is defined as the ratio of O2 diffusion resistance to the convection resistance. y
Oc
denotes the oxygen mole fraction. Definitions of the dimensionless four moduli are expressed as

M
Om
=δ
(C) (k
vcm

RT/D
eO)0.5, (2)

M
pm
= δ
(C) (4F
k
vcm

RT/(σ
ep
b
c))0.5, (3)

P
Om
= δ
(C)
N
gm
/(C
g
D
eO), (4)

y
Oc
= p
Oc
/P, (5)
where R, T, σ
ep, N
gm
and P denotes the gas constant [J/(mol K)], cell temperature [K], effective proton conductivity [S/m], total gas flux [mol/(m2 s)] and total pressure [Pa], respectively. When the cathode emf at the PEM–CCL boundary, E
cm
, T, and relative humidity (RH) are fixed, M
Om
is fixed. F
e and M
pm
are proportional to i/p
Oc
and p
Oc

0.5, respectively. The relationship between F
e and M
pm
shown in Fig. 1 corresponds to that between i/p
Oc
and p
Oc

0.5. Thus, F
e and M
pm
can be determined just by fitting experimental data of i/p
Oc
plotted against p
Oc
0.5 to the theoretical curves.
Results and Discussion
Polarization curves shown in Fig. 2 were measured at 80 °C and 0.77 of inlet RH at varied p
Oc
. As expected from Eq. (1), current densities at a fixed E
cm
increases when p
Oc
increases. The current densities at the fixed E
cm
are plotted against p
Oc
as shown in Fig. 3. The current density is sublinear against p
Oc
. This is because M
pm
expressed in Eq. (3) increased when p
Oc
is higher. The ORR rate is lower than the value expected from the Tafel equation when mass transfer resistance increases.
The dimensionless moduli were determined by fitting the theoretical relationship to the measured i/p
Oc
vs. p
Oc

0.5 graph. From the determined dimensionless moduli, the ORR rate and mass transport parameters, k
vc⊕, D
eO and σ
ep were also obtained and these values are shown in Table 1 with values in literature[4, 5].Effective proton conductivity, σ
ep is relatively low compared with values in literature. This resulted from an experimental error in the current density at p
Oc
of 16 kPa. Lowering the current density at high p
Oc
leads to decrease in σ
ep because M
pm
increases when p
Oc
is raised. By extensively measuring the polarization curves dependency on p
Oc
, the ORR rate parameters and mass transport parameters can be determined more accurately. Recalculated results using the obtained mass transport parameters are shown in Figs. 3 and 4. The recalculated results appropriately reproduced the ORR rate dependency on E
cm
and p
Oc
.
Conclusions
The through-plane mass transfer resistance in CCL was quantified by measuring the ORR rate dependency on the oxygen partial pressure. From the determined dimensionless moduli, mass transport parameters were obtained. Recalculated results appropriately reproduced the ORR rate dependency on cathode emf and oxygen partial pressure.
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 2020–2023) conducted by the New Energy and Industrial Technology Development Organization (NEDO), Japan.

Figure 1