Comparison of measured current density distributions at PEFC withcalculated distributions by using measured membrane properties
Kazuo ONDA, Hironori KOORI, Takuya TANIUCHI and Takuto ARAKI
Department of Electrical and Electronics Engineering
Toyohashi University of Technology, Toyohashi 441-8580
JAPAN
E-mail: onda@eee.tut.ac.jp
Abstract
The water management factors such as transmissivity and electro-osmotic coefficient of water
vapor through the membrane and power loss factors such as activative and resistive overpotentials were measured. The numerical distributions of current density under various operating conditions agreed well with the measured distributions by segmented electrodes.
Keywords: Polymer Electrolyte Fuel Cell, Current density distribution, Membrane properties
measurement
1. Introduction
Since membrane physical properties have significant impacts on the performance of Polymer
Electrolyte Fuel Cell(PEFC), it is necessary to know the water management factors such astransmissivity and electro-osmotic coefficient of water vapor through the membraneelectrode assembly (MEA), and power loss factors such as activation and resistive overpotentials. Nevertheless, the effects by these factors on PEFC are not cleared sufficiently. The
objective of the present investigation is set to obtain basic information of the membrane
properties and to establish a numerical code, which can describe well the performance ofPEFC.
2. Measurements of Membrane Properties and Overpotentials
2.1 Experimental Apparatus
An overview of the experimental apparatus is illustrated in Fig.1. Air and modified reformed
Mass flow controller Heating water

Humidifier
Reformed
gas
H280％

Anode

PEFC

Mass flow controller

Segmented electrode
Shunt resistance12mΩ
Gas sampling port

Humidifier
CathodAir
O221％,N278％etc

MEA
Electrode area
：10cm2＃1＃8
Acryl frame
Diffusion
electrode(Carbon Cloth)

GrooveExhaust gas

Separato

Electronicload

Exchaust gas

Gas sampling port

Separator

AC impedance meter Separator

Figure1. Experimental apparatus
1

Figure 2. Configuration of cell and segmented electrodesfuel from gas cylinders are regulated by mass flow controllers, and led to fuel cell(FC). The
humidifiers placed before FC control the dew-point temperatures of air and fuel. Electronic
resistive load (PLZ-152WA, Kikusui Elec. Co.) is connected to FC instead of actual loading,and measuring the current and voltage of FC. Figure 2 shows the FC assembly, where the
MEA (Gore Select, Japan Gore-Tex Inc.) of 20µm thickness is set between the two electrodes.
Carbon cloths are inserted between the MEA and separators as diffusion electrodes. One sideof which consist of segmented electrodes with grooves for air or fuel supply and the segmented electrodes are mold in an electrically insulating plate as shown in Figure 2, formeasuring current density distributions. Additionally, several holes are drilled in the grooves
to measure concentration changes of hydrogen and oxigen to get another current density
distribution.
2.2 Water Vapor Diffusivity through Diffusion Electrodes, and Transmissivity andElectro-osmotic coefficient through MEA
To obtain the diffusive properties, the cell outlet humidities at both anode and cathode were
measured with supplying different humidities to both FC inlets. The measurement procedure
was essentially the same as those described previously(1). Measured water vapor diffusivity
for diffusion electrode Ddiff at cell temperature Tmem=50˚C and 60˚C are plotted in Fig. 3. The
diffusivity did not change against relative humidity. This result is consistent with a simple
following equation,
Ddiff = f ⋅ D Air − H O(1)

2

where DAir-H2O is water vapor diffusivity in air, and f is effective porosity of diffusion
electrodes. In the case of out carbon cloth, f is calculated to be about 0.25.
Transmissivity through MEA Tr is also shown in Fig. 3. Our measured Tr was about 7 times
higher than the ones by Nguyen et. al.(2) and lower than ones by Yamada et.al.(3). However,
the tendency of Tr, which rose as relative humidity increase, was consistent with those by
Nguyen et.al. So we approximate Tr as to 7 times greater than those of Nguyen et.al.
Electro-osmotic coefficients nd are determined similarly with the diffusion coefficient exceptthat the electric current was made flow to transport water electro-osmotically. Figure 4 shows
the nd as a function of relative humidity. The electro-osmotic coefficient nd became large
when the humidity increases. nd at MEA temperature of 50˚C agreed with that by Nguyenet.al.(2). nd by Yamada who performed similar experiment with us was almost same as ours
especially in a case of using carbon cloth, however, the tendency of nd against humidity was
inverse.

Dair-H2O
Ddif for Carbon Cloth (Tdif=60℃)-5

10(Tdif=50℃)-6

10

Tr for Nafion112(Yamada et al,Tmem=80℃)
Tr for MEA(Tmem=50℃)(Tmem=60℃)

Tr for Nafion117(Nguyen et al,Tmem=60℃)
0.4

0.5

0.6

GORE SELECT(Tmem=60℃)

0.8

GORE SELECT(Tmem=50℃)
0.6

0.4

0.2

Nafion112(Yamada et al,Tmem=80℃,Carbon Pape
Nafion112(Yamada et al,Tmem=80℃,Carbon Cloth)

0.0(Tmem=50℃)-7

10

Nafion117(Nguyen et al)

1.0

Electro-osmotic coeff. nd

Diffusion coeff. Ddif and transmissivity Tr
of water vapor [m2･s-1]

1.2

0.3
0.7

0.4

0.5

0.6

0.7

0.8

Relative humidity

Relative humidity

Figure 3. Change of Tr and Ddiff of water vapor
by relative humidity

Figure 4. Change of electro-osmotic
coefficient by relative humidity20.9

2.3 Ionic Resistivity and Activation Overpotential of MEA
Resistive and activative overpotentials are important factors of PEFC power generation
performance. The ionic resistance was measured by AC impedance meter (SOLARTRON
SI1280B), supplying air with the same humidity to both anode and cathode to avoid the
movement of water through MEA. The parameters for MEA resistance are the membrane
temperature Tmem and the flow relative humidity a. The measured MEA resistivity is plottedagainst relative humidity a in Fig. 5. The resistivity did not depend on the membrane
temperature, but depended only on relative humidity a. Therefore the following experimental
ionic resistivity ρ, a function of only relative humidity a, was employed in the following
numerical analysis.
 a − 0.089 
 a − 0.089 
ρ = 57.3 + 383. exp − + 244 exp −0.
049
0.268 [Ω·cm](2)

For measuring activation overpotential η act , the relatively high flow rates of 600cc/min were
provided to hold the low utilization rate of H2 and O2 in order to prevent variation of η act
along the flow by the distributed current density. η act was derived by subtracting the cellvoltage Vcell and the resistive overpotential ir from the Nernst potential VNernst as follows.

η act = VNernst − Vcell − ir

[V]

(3)

Here, the spatially averaged partial pressures of active materials were used to determine
VNernst considering water vapor pressures. The experimental conditions for ηact measurement
were as follows; FC temperature : 60˚C, cathode O2 partial pressure PO : 0.05, 0.2, 1.0;
anode H2 partial pressure PH : 1.0. Figure 6 shows the change of activation overpotential byoxygen concentration and current density. The activation overpotential increased almost
linearly except for the region of very low current density where is not so important forpractical application. Therefore we employed the following empirical formula in the following numerical analysis.
22η act =

0.065
i + 0.455
PO02.81

[V]

(4)

0.6
600

Tmem=50℃
Tmem=60℃
Tmem=70℃
Tmem=80℃

500
400

0.5

Overpotential ηact [V]Membrane resistivity ρ [Ω･cm]

700

300

50℃

200
100

80℃
Nguyen et al

0
0.0

0.1

0.2

0.4

Cell pressure=1atm
Measured (CO2=100%)
Approximeted eqn.(CO2=100%)
Measured(Oxygen20%)
Approximeted eqn.(Oxygen20%)
Measured(Oxygen5%)
Approximeted eqn.(Oxygen5%)

0.3

0.2

0.1
0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0

Relative humidity a

0.0

0.2

0.4

0.6

0.8

1.0

Current density [Acm-2]

Figure 6 Change of membrane resistance byrelative humidity

Figure 5. Change of membrane resistance byrelative humidity32.4 Measurement of Current Distribution
Current distributions were measured by two different methods to confirm the reliability ofmeasurement. First method adopted the segmented electrodes cell to measure the current
distribution by shunt resistances. Another method adopted gas chromatography to measuregas composition changes to be converted to the current distribution through the decreased
flow rate of H2 or O2. N2 mixture fuel and air were employed in this measurement to keep theconstant flow rate of N2 as reference. H2 gas mixed with 20% N2 (not CO2) was used as fuel,because CO2 is easy to be solved in water and not giving the correct reference.
Figure 7 and 8 show the measured current densities for two average current density of
0.3A/cm2 and 0.4A/cm2, respectively. The current density estimated by gas chromatography
fluctuated to some extent, but are compatible with that by the segmented electrodes cell. Thus
we could confirm the measurement reliability of current density distribution by two methods.
3. Numerical Analysis of Power Generating Performance
3.1 Computational Procedure
Following assumptions were adapted to our numerical analysis(4).
1.
2.

Parallel flow type fuel cell is targeted.
There are 8 parallel grooves for each side of fuel and air separator, and all of thegrooves have the same flow rate and performance.
The gas flow along the groove is assumed to be plug flow.
Owing to the constant temperature water, which is circulated through separator, thecell temperature is assumed to be kept constant.
Effect of flooding due to generated water at cathode is ignored.

3.
4.
5.

Control volume method was used to solve the simultaneous equations for mass and charge,energy conservation equations with an equivalent electric circuit for FC. The energy conservation equation for MEA is shown in appendix as a representative equations for equation forevery conservation. The Nernst potential is given by
0.5
RTmem PH PO
V Nernst = E +ln
2FPH O ,c
o

2

(8)

2

2

The resistance overpotential is given by the following integration of membrane resistivity
through its thickness tmem.
0.6

0.7
0.6

Current density [A/cm2]

Current density [A/cm2]

0.5

0.4

0.3

0.2

Gas chromatograph(Anode)
Gas chromatograph(Cathode)Segmented electrode cell

0.1

0.5
0.4
0.3

Gas chromatograph(Anode)
Gas chromatograph(Cathode)Segmented electrode cell

0.2
0.1
0.0

0.0
1

2

3

4

5

6

7

1

8

Electrode number

2

3

4

5

6

7

8

Electrode number

Figure 7. Comparison of measured current
distributions i mean I=0.3A/cm2

Figure 8. Comparison of measured current
distributions i mean I=0.4A/cm2
4

 1

a
η ohm = ρda t mem i∫a aa − ac

a

(9)

c

3.2 Results of Current Distribution Numerical Analysis
The current density distributions calculated by the numerical simulation are shown in Fig. 9,
10 and 11. The conditions used in the analysis are summarized in Table 1. The agreement
between the numerical and measured results was good on the whole. The measured showed
higher current density at inlet, and lower current density at outlet than the calculated. This
discrepancy might be due to the effect of generated water at a downstream cathode, hindering
the site for electrochemical reaction. Especially in a situation with higher oxygen utilization
ratio of 80%. The current density tends to increase at inlet when the current density decreases
near outlet probably by the flooding. Revised empirical formula for the activation overpotential may lead the calculated results closer to the measured, but we are now trying to include
the generated water in our simulation to avoid the performance degradation by water flooding.

Table 1 Experimental conditions
used in analysis
Current density [A/cm2]

0.6

Fig.9

Fig.10
Fig.11
60
48
91
136
182
60
Not humidified

Cell temperature[℃]
Anode flow rate[cc/min]Cathode flow rate[cc/min]
Anode dew temperature[℃]
Cathode dew temperatuer[℃]Measured (I=0.4A/cm2)
Numerical (I=0.4A/cm2)
Measured (I=0.3A/cm2)
Numerical (I=0.3A/cm2)
Measured (I=0.2A/cm2)
Numerical (I=0.2A/cm2)

0.7

Fuel and oxygen utilization ratio(i m =0.2) 0.4-0.4

0.4-0.26

0.4-0.2

Fuel and oxygen utilization ratio(i m =0.3) 0.6-0.6

0.6-0.4

0.6-0.3

Fuel and oxygen utilization ratio(i m =0.4) 0.6-0.6

0.8-0.53

0.8-0.4

0.5
0.4
0.3
0.2
0.1
0.0
0

5

10

15

20

25

Channel length [cm]Figure 9 Comparison between the measured
and the numerical(Air flow 90cc/min)
Measured (I=0.4A/cm2)
Numerical (I=0.4A/cm2)
Measured (I=0.3A/cm2)
Numerical (I=0.3A/cm2)
Measured (I=0.2A/cm2)
Numerical (I=0.2A/cm2)

0.7

0.5

0.7
0.6

Current density [A/cm2]

Current density [A/cm2]

0.6

Measured (I=0.4A/cm2)
Numerical (I=0.4A/cm2)
Measured (I=0.3A/cm2)
Numerical (I=0.3A/cm2)
Measured (I=0.2A/cm2)
Numerical (I=0.2A/cm2)

0.4
0.3
0.2
0.1

0.5
0.4
0.3
0.2
0.1

0.0

0.0
0

5

10

15

20

25

0

5

10

15

20

25

Channel Length [cm]Channel length/cm

Figure 10. Comparison between the measured
and the numerical(Air flow rate of 135cc/min)Figure 11. Comparison between the measured
and the numerical(Air flow 180cc/min)
5

4. Conclusion
The water management factors such as transmissivity and electro-osmotic coefficient ofwater vapor through the membrane electrode assembly, and power loss factors such asactivative and resistive overpotentials have been measured. These factors were adopted toanalyze our experimental results of PEFC power generation tests by our two-dimensional
simulation code. The code considers simultaneously the mass, charge and energy conservation equations with the equivalent electric-circuit for PEFC to give numerical distribution ofhydrogen/oxygen concentrations, current density, and gas/cell-component temperatures alonggas flow. The calculated distributions of current density under various operating conditions
have agreed well with the measured distributions at segmented-electrodes cell. Hydrogen/Oxygen concentration changes measured by gas chromatography along the gas flows havealso given the experimental current distributions, which coincides almost with that by thesegmented-electrodes. Degradation factors for cell performance were also discussed from thenumerical results by the simulation code. Also further improvements for out experiment andanalysis have been pointed out.
Appendix
Energy conservation equation for MEA as as represent ative one for other elements.
t mem wcell

dT 
d 
 k mem mem 
dy 
dy 

= wcell k dif , a − memTmem − Tdif , a∆x diff , a − mem− wcell {N H , a H H −T22

dif , a+ wcell k dif ,c − mem22− N vap ,c H vap −T+ N liq , a H liq −T− N liq ,c H liq −T }dif , a∆x dif ,c − mem− N O , c H O −T

+ N vap , a H vap −T

dif , aTmem − Tdif ,c(10)

dif , cdif , cdif , c− wcell {N H ∆H LHV − i ( y )(V Nernst − η ohm − η act )}2

References[1] T.Kyakuno, K.Hattori, K.Ito and K. Onda, Proc. 15th IEEJ Conf., 2003. (in Japanese)[2] T.V.Nguyen and R.E.White: A Water and Heat Management Model for Proton-ExchangeMembrane Fuel Cells. J. Electrochem. Soc., Vol.140, No8, 1993.
[3] H.Yamada and Y.Morimoto, Electro-osmotic Drag and Diffusion Coefficient of Water in Polymer
Electrolyte Membrane. Proc. 70th anniversary Jpn. Electrochem. Soc. 2003. (in Japanese)[4] T. Aoki, N. Miyauchi, K. Ito, Y. Inui and K. Onda: Numerical Analysis of Polymer Electrolyte
Fuel Cell Using Empirical Equations for Overpotentials. Trans. IEE Japan, Vol. 122-B, No. 12,
2002 (in Japanese)6