ECS Transactions, 35 (1) 1007-1014 (2011)
10.1149/1.3570081 © The Electrochemical Society
Exchange Current Density of Solid Oxide Fuel Cell Electrodes
T. Yonekuraa㧘Y. Tachikawab㧘T. Yoshizumia㧘Y. Shiratoria,c㧘K. Itoa,b,c, and K. Sasakia,b,c
a
Department of Mechanical Engineering Science, Faculty of Engineering
b
International Research Center for Hydrogen Energy
c
International Institute for Carbon-Neutral Energy Research (WPI)
Kyushu University, Motooka 744, Nishi-ku, Fukuoka 819-0395, Japan
It is desired to develop computational procedures to simulate
internal current density, anode/cathode gas concentrations, and
temperature distribution in solid oxide fuel cell (SOFC) systems. In
this study, the influences of various operational conditions on the
exchange current density, the essential parameter to simulate SOFC
performance, are revealed and discussed. The anodic exchange
current density depended strongly on the humidity of H2-based fuel
gas, and it exhibited the highest value at around 40% H2O. The
cathodic exchange current density was strongly affected by the
operational temperature. Parameters necessary to describe
dependencies of exchange current density on various operational
parameters were determined by fitting measured exchange current
density values with empirical equations.
Introduction
In recent years, solid oxide fuel cells (SOFCs) have attracted a lot of attention due to e.g.,
their high energy conversion efficiency. Furthermore, SOFC, all solid state fuel cell, has
flexibility in system design. However, this flexibility leads to a wide variety of existing
system designs of planar and tubular types. Therefore, it is strongly desired to develop a
computational procedure to predict SOFC performance and distributions of current
density, gas composition, and temperature, which is indispensable to optimize cell and
stack designs.
The relation between electrode overvoltage Ș and current density i is generally given
by the Butler-Volmer equation
­ § Į n FȘ ·
ª (1 − Į ) n FȘ º ½
i = i0 ®exp¨
¸ − exp «−
»¼ ¾
RT
¬
¯ © RT ¹
¿,
[1]
where i0 is the exchange current density affected by microstructure and operational
conditions (e.g., operating temperature and gas composition, etc.), Į_ is transfer coefficient,
_㨋
_ _is
n is number of electrons transferred by the corresponding electrode reaction, F
Faraday constant, R
_ _is universal gas constant, and _T㨋is absolute temperature. In this study,
we aim to acquire the dependence of exchange current density on the operational
conditions that must be known for simulating electrode performance of SOFCs, which is
essential to develop a simulation technique for SOFC systems.
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ECS Transactions, 35 (1) 1007-1014 (2011)
Experimental
Fabrication of Electrolyte-Supported Single Cells
A schematic drawing of the SOFC used in this study is given in Figure 1. In this study,
typical electrolyte-supported cells with scandia-stabilized zirconia (ScSZ: 10 mol%
Sc2O3 – 1 mol% CeO2 – 89 mol% ZrO2) were used to investigate the influence of the
operating conditions on exchange current density. NiO-ScSZ cermet was used for anodes,
and LSM-ScSZ (LSM: (La0.8Sr0.2)0.98MnO3) composite material was used for cathodes.
Anode layers were screen-printed on ScSZ electrolyte plates (thickness: 200 ȝm,
diameter: 20 mm), followed by sintering in air at 1300oC for 3 hours. Cathode layers
were then screen-printed on another side of the electrolyte plates, followed by sintering in
air at 1200oC for 5 hours. Both geometric areas of the electrode layers were ca. 8 mm x 8
mm (0.64 cm2). Concerning reference electrodes, Pt paste with a geometric area of ca.
0.04 cm2 was painted adjacent to the cathode. Pt meshes were attached to the electrode
surfaces as current collectors.
Pt paste: Reference electrode in air
30 㱘m
30 㱘m
Cathode
200 㱘m
Electrolyte
ScSZ: 10Sc1CeSZ
Anode
56% NiO - 44% ScSZ
60 㱘m
30 㱘m
LSM: (La0.8Sr0.2)0.98MnO3
50% LSM - 50% ScSZ
80% NiO - 20% ScSZ
S = 0.64 cm2
Figure 1. Schematic drawing of the SOFC used in this study.
Overvoltage Measurement and Calculation of Exchange Current Density
After reduction treatment for 1 hour at 1000oC under H2 flow (3 vol% H2O),
electrochemical characteristics of SOFC single cells were measured under the conditions
shown in Table I. For the measurement of electrochemical properties of the cathode, 3%
wet H2 was supplied to the anode side with a flow rate of 100 mL min-1, and the mixture
of O2 and N2 was supplied to the cathode side with a flow rate of 150 mL min-1. Cathodic
overvoltage was measured by means of current interruption method at 250, 300, 350, 400
mA cm-2 for various oxygen partial pressures in cathode compartment. On the other hand,
humidified H2 was supplied to the anode side and dry air was supplied to the cathode side
for the measurement of anode properties. Anodic overvoltage was measured for various
H2/H2O ratios. Furthermore, temperature dependences of cathodic and anodic
overvoltages were measured, for which 3% wet H2 and dry air were fed to the anode and
the cathode, respectively. From the measured overvoltage values, cathodic and anodic
exchange current densities were obtained using the Butler-Volmer equation (Equation
[1]).
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ECS Transactions, 35 (1) 1007-1014 (2011)
TABLE I. Experimental Conditions
Objective
Anode gas
(100 ml min-1)
Cathode gas
(150 ml min-1)
Operating temperature
/ oC
Cathodic exchange current density
vs. O2 concentration
3% wet H2
N2 + O2
800, 850, 950
Anodic exchange current density
vs. humidity
Wet H2
Dry air
800, 850, 950
Cathodic and anodic exchange
current density
vs. operating temperature
3% wet H2
Dry air
800, 850, 900, 950, 1000
Empirical Equations Describing Exchange Current Density
Several empirical equations to express exchange current density i0 have been reported
(1-10). In this study, we adopted Equations [2] and [3] for the exchange current densities
of cathode and anode reactions, respectively,
§ pO 2
i0,c = Ȗ c ¨
¨ pO , ref
© 2
i0,a
§ pH 2
= Ȗa ¨
¨ pH ,ref
© 2
·
¸
¸
¹
A
C
·
− Eact,c ·
¸ exp§¨
¨ RT ¸¸
¸
©
¹
¹
§ pH 2 O
¨
¨ pH O,ref
© 2
B
·
− Eact,a
¸ exp§¨
¨ RT
¸
©
¹
[2]
·
¸¸
¹
[3]
i0,a are exchange current densities, Ȗ_c and Ȗ_a are pre-exponential factors, E___
where __
i0,c and __
act,c
and E___
are
activation
energies for cathode and anode reactions, respectively. Indices _A,
act,a
p x and p___
_, and C_ stand for partial pressure dependence, and __
B
x, ref are partial pressure and
reference partial pressure of species x (x = H2, H2O, and O2). In Equation [3], the
pH and __
pH O on __
i0,a obtained by
i0,a can be treated independently. First, i__
influences of __
0,c and __
the overvoltage measurements were plotted in 3D diagrams as functions of gas
Ȗ
Ȗ
Eact,c E
_, B
_, C
_, ___,
___,
composition and temperature. Then, A
act,a _c and _a were determined so that
the measured results could be fitted with Equations [2] and [3].
2
2
Results
Cathodic Exchange Current Density vs. Operating Conditions
i0,c is summarized in Figure 2(a). The 3D
The influence of the operating conditions on __
plot shows the fitting result by Equation [2]. Dependences on O2 concentration and
temperature are emphasized in Figure 2(b) and 2(c), respectively._i_0,c slightly decreased
pO _. On the other hand,
with decreasing O2 concentration, indicating weak dependence on __
strong dependence on operating temperature was clearly observed. These results suggest
that higher electrochemical activity of cathode materials becomes essential with
decreasing operating temperature.
2
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ECS Transactions, 35 (1) 1007-1014 (2011)
(c)
(a)
Experimental data
Fitted results
1.8
Fitted results: 5 %
Fitted results: 21 %
-2
i0,c / A cm
0.9
1050
1000
950
900
850
800
750
0.9
0.6
o
0.6
1.2
C
-2
i 0,c / A cm
1.2
ur
e
/
0.3
(b)
pe
10
5
entra
tion /
%
Te
m
20
15
O2 co
nc
ra
t
0.0
0
0.3
0.0
750
800
850
900
950
1000
1050
o
Temperature / C
Temperature: 800 oC
o
Temperature: 850 C
Temperature: 950 oC
Fitted results: 800 oC
o
Fitted results: 850 C
Fitted results: 950 oC
1.8
1.5
-2
O2 concentration: 21 %
1.5
1.5
i0,c / A cm
O2 concentration: 5 %
1.8
1.2
0.9
0.6
0.3
0.0
0
5
10
15
20
25
O2 concentration / %
Figure 2. Dependences of cathodic exchange current density on O2 concentration in
cathode gas and operational temperature: (a) 3D representation, (b) dependence on O2
concentration, (c) dependence on temperature. Fuel: 3% wet H2 (100 ml min-1), oxidant:
mixture of O2 and N2 (150 ml min-1).
Following empirical equation related to the cathode reaction was obtained by the
fitting procedure:
i0,c
§ pO 2
= 3.3 ×10 ¨
¨ pO ,ref
© 2
5
·
¸
¸
¹
0.30
[
§ − 1.3 × 105 J mol −1
exp¨¨
RT
©
]·¸ [A cm ]
¸
−2
¹
[4]
.
Anodic Exchange Current Density vs. Operating Conditions
i0,a is summarized in Figure 3(a).
The influence of the operating conditions on __
Dependences on humidity and temperature are separately shown in Figures 3(b) and 3(c),
respectively. In these diagrams, fitting results are also plotted. Although the experimental
data are relatively scattered, i__
0,a increased with increasing humidity and took the
maximum value at around 40% RH, indicating that there is an optimum humidification
level for anode reactions. On the other hand, whereas the dependence on operating
temperature was unclear for 3% RH, it became obvious at 40% RH. Control of fuel
humidity is critical for getting maximum performance of the anode.
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ECS Transactions, 35 (1) 1007-1014 (2011)
(a)
(c)
Experimental data
Fitted results
4.0
3.5
3.0
3.0
-2
i0,a / A cm
2.0
1.5
60
40
Humid
20
ity / %
0
3.5
3.0
-2
800
850
900
950
1000
1050
o
Temperature / C
Temperature: 800 oC
Temperature: 850 oC
Temperature: 950 oC
Fitted results: 800 oC
Fitted results: 850 oC
Fitted results: 950 oC
4.0
i0,a / A cm
1.5
0.0
750
Te
m
80
2.0
0.5
pe
ra
tu
re
0.0
2.5
1.0
/
0.5
(b)
1050
1000
950
900
850
800
750
o
1.0
C
i0,a / A cm
-2
2.5
Humidity: 3 %
Humidity: 40 %
Fitted results: 3 %
Fitted results: 40 %
2.5
2.0
1.5
1.0
0.5
0.0
0
20
40
60
80
100
Humidity / %
Figure 3. Dependences of anodic exchange current density on humidity of cathode gas
and operational temperature, (a) 3D representation, (b) dependence on humidity, (c)
dependence on temperature. Fuel: wet H2 (100 ml min-1), oxidant: dry Air (150 ml min-1).
Empirical equation for i__
0,a (Equation [5]) was obtained by fitting data in Figure 3,
while only a poor fitting to the experimental data could be made at lower operating
temperatures:
i0,a
§ pH 2
= 3.5 × 10 ¨
¨ pH ,ref
© 2
2
·
¸
¸
¹
0.41
§ pH 2 O
¨
¨ pH O,ref
© 2
·
¸
¸
¹
0.40
[
§ − 6.2 ×10 4 J mol −1
exp¨¨
RT
©
]·¸ [A cm ]
¸
.
−2
[5]
¹
Discussion
Mechanism of Cathode Reactions
Eact,c have been reported in the
C and ___
Concerning the cathode reactions, the values of __
Eact,c obtained in this study was
literature (1-5). These values are summarized in Table II. ___
close to that reported by Nagata et al. and Costamagna et al. This may support the
validity of the present approach.
On the other hand, as for the index C
_ showing partial pressure dependence, the value
experimentally determined in this study, 0.30±0.04, was close to 0.25 as reported by
Okamoto et al (1). They discussed the reason for C_ = 0.25 and concluded that ionization
of dissociatively-adsorbed Oad on electrode surface and subsequent diffusion of ionized
Oad to three phase boundaries (TPB) were the rate-determining process.
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ECS Transactions, 35 (1) 1007-1014 (2011)
TABLE II. Cathodic Exchange Current Densities Reported in the Literature
Author
C
Eact,c / J mol-1
Mechanism
Cathode /
Electrolyte
H. Okamoto
(1983) (1)
0.25
---
Ionization of Oad on the Pt surface
and diffusion of ionized one to TPB.
Pt / YSZ
J. Mizusaki
(1987) (2)
0.5
---
Dissociative adsorption of O2(g)
on the Pt surface.
Pt / YSZ
S. Nagata
(2001) (3)
0.5
1.3×105
---
LSM / YSZ
K. Yasumoto
(2002) (4)
0.5
---
Surface diffusion of Oad.
LSM / YSZ
P. Costamagna
(2004) (5)
0.25
1.2×105
---
---
This study
0.30
1.3×105
LSM / ScSZ
Mechanism of Anode Reactions
TABLE III. Anodic Exchange Current Densities Reported in the Literature
Eact,c
Author
A
B
Mechanism
/ J mol-1
1
1
---
M. Mogensen
(1993) (6)
J. Mizusaki
(1994) (7)
2
1
---
-0.25
~
0.25
0.25
~
0.5
---
0
1
---
J. Mizusaki
(1994) (8)
low pH
2
high pH
2
p H 2O
>> pH
2
p H 2O
Preparation of H2O on
the YSZ surface.
H+ad,Ni
Behavior of
as
a kind of catalyst.
Anode /
Electrolyte
Ni-YSZ
/ YSZ
OH exchange at the
TPB between the Pt
and the YSZ surface.
Pt
/ YSZ
Nondissociative
adsorption of H2O(g)
or reaction of
H2(g) and Oad.
Ni-YSZ
/ YSZ
0.5
0
---
T. Yamamura
(1995) (9)
1
-0.5
6.81×104
---
Pt
/ YSZ
S. P. Jiang
(1999) (10)
0.1
0.5
7.0×104
---
Ni-YSZ
/ YSZ
S. Nagata
(2001) (3)
0.266
-0.266
1.2×105
---
Ni-YSZ
/ YSZ
P. Costamagna
(2004) (5)
1
1
1.0×105
---
---
This study
0.41
0.40
6.2×104
<< pH
2
Ni-ScSZ
/ ScSZ
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ECS Transactions, 35 (1) 1007-1014 (2011)
Eact,a have been reported in
A , _B_, and ___
Concerning the anode reactions, the values of__
the literature (3,5-10). These values are summarized in Table III. Reaction mechanism is
more complex compared to the cathode reaction because both H2 and H2O are involved in
the anode reaction. In fact, a wide variety of A
_ and B
_ have been reported as listed in Table
III. E___
obtained
in
this
study
was
close
to
that
reported
by Yamamura et al. and Jiang et
act,a
al.
pH and p___,
i0,a on __
Indices A
_ and B
_ represent the partial pressure dependence of __
H O
respectively. One can evaluate the anode reaction as the surface reactions related to H2
and H2O are independent. Concerning adsorption of H2O, Mizusaki et al. (8) have
performed thermodynamic considerations on the anode reaction taking (i) adsorption of
H2O, (ii) dissociation of adsorbed H2O, (iii) dissociation of OHad, and (iv) ionizing of Oad
and subsequent diffusion to TPB, into account. Finally, they found that the coverage of
0 .5
pH O Besides, concerning dissociative adsorption of H2, they also found
Had depends on _____.
0.5
pH
that the coverage of Had depends on ____.
Therefore, anodic exchange current density
0.5
0.5
pH O if the coverage of Had dominates the anode reaction. The
pH
may depend on ____㨯____
experimental values A
_ = 0.41±0.17 and B
_ = 0.40±0.09 in this study close to 0.5 imply that
anode reaction in this study may also be dominated by Had coverage.
2
2
2
2
2
2
Summary and Outlook
The influences of the operating conditions on anodic and cathodic exchange current
densities of SOFCs were experimentally clarified, and empirical equations for the
exchange current densities have been determined. By using these equations, simulation of
SOFC performance will become more accurate although further considerations are
required with respect to the dependences on partial pressures. Prediction of power
generation characteristics of SOFCs based on the deduced equations will be compared
with experimental results under various operating conditions.
Acknowledgments
This study was partially supported by the project “Development System and
Elemental Technology on Solid Oxide Fuel Cell (SOFC)” of New Energy and Industrial
Technology Development Organization (NEDO), Japan.
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61 (2004).
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terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).
ECS Transactions, 35 (1) 1007-1014 (2011)
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