I i 

1 -. 

Strip Cell Stack Design and 

Mass Transfer Phenomena in a 

Polymer Electrolyte Membrane 

Fuel Cell .Stack 

Rongzhong Jiang and Deryn Chu 

ARL-TR-2063 

Approved for public release; distribution unlimited. 

February 2000 

20000327 03 
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thereof. 

Destroy this report when it is no longer needed. Do not 

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I . 
Abstract 

A type of air-breathing polymer electrolyte membrane fuel cell 

(PEMFC) stack with a strip design structure was investigated. 

Potential-current curves for this PEMFC show typical mass transfer 

behavior. An empirical equation was developed to describe the 

kinetic processes of the stack, as opposed to only a single cell. A 

series of experimental potential-current and power-current curves 

including different humidities, temperatures, and stack lengths was 

extremely well fitted with the equation. A concept of mass transfer 

impedance is defined in this report. This empirical equation can be 

used to calculate the mass-transfer impedance quantitatively 

beyond the experimental points, for example, with decreasing 

humidity, where the mass-transfer impedance increases 

considerably. 

ii 

1. Introduction 

With the prominent features of light weight, low cost, high energy efficiency, high power density, nonemission, and operation at low temperature, polymer electrolyte membrane fuel cells (PEMFCs) have received 

much attention during the last 10 years [l-lo]. Most publications concentrate on a single cell of the PEMFC or one of its components, but recently 

PEMFC stacks of various types and functions were developed [U-14]. 

The performance of a PEMFC stack is different than that of a single 

PEMFC cell. In this report, we explore the differences of the electrode 

kinetic processes between PEMFC stacks and single cells, and promote 

PEMFC stacks in military and civilian applications as portable power 

sources. An air-breathing strip PEMFC stack, one of the newest types of 

PEMFC stack, has two desirable aspects: First, it produces a relatively 

high voltage in a compact volume. Second, it uses air directly as a cathode 

reactant, resulting in a great decrease in weight. In the strip design, the 

weight per active area is about 40 percent less than that of bipolar plate 

stacks [15]. The air-breathing strip PEMFC stack is a two-dimensional 

fuel-cell stack, with individual cells in the same plane [ll]. This design 

allows all the cells to access the same reservoir of hydrogen, and allows 

the opposite face to be openly exposed to the air. However, in the investigation of the strip PEMFC stack, mass-transfer phenomena were observed 

when the stack was operating at high current density. This is probably 

because of the low oxygen concentration in air [6], low humidity, or poor 

heat dissipation. Because it is sometimes necessary to operate at high 

current density, such as in an electric vehicle, understanding the electrode 

kinetic processes is important. Since the early 196Os, several modeling 

studies have been conducted that elucidate cell potential versus current 

density behavior [5]. However, analytic expressions for the currentpotential behavior have been developed only in special cases, such as 

when electrode reactions are either activation and ohmic or activation 

and mass-transfer controlled. When all forms of over-potentials (activation, ohmic, and mass transfer) are present, as at high current density, 

there are no analytical solutions for the second-order differential equations. Kim et al [5] have reported mass transfer phenomena in single 

PEMFC cells and modeled the potential-current behaviors with an empirical equation. Our research investigates the mass-transfer behavior in 

the strip air-breathing PEMFC stack and analyzes the electrode kinetic 

processes with an empirical equation. 
2. Experiment 

The air-breathing PEMFC stack was composed of either 10 cells or 5 cells 

connected in series. The active area of each electrode is approximately 

19 cm2. The open circuit voltage was approximately 9.4 V for the lo-cell 

stack and 4.8 V for the 5-cell stack. The air supply to the cathode was by 

convection from environmental air. The H, fuel was supplied through a 

sealed compartment at the anode side, and the stack was cooled naturally 

The electrolyte for the single cells was prepared with Nafion membrane 

(from DuPont Chemical Company). The cathode and anode both consisted of a commercially available catalyst (20% platinum on Vulcan 

XC-72 carbon from E-Tek) and aqueous Nafion solution. The Nafion 

membrane was located between the laminated cathode and anode layers, 

to form the membrane electrolyte assembly (MEA). The MEA was processed by hot pressing at 120 “C. The catalyst loading was 0.4 mg Pt/cm2 

for both electrodes. The MEAs, metal foams, carbon cloths, and metal 

meshes were held tightly to form single cells, which were linked in series 

to form a stack. A Matheson TF601 multimeter was used to measure the 

hydrogen (99.99%) flow rate. The temperature and humidity were controlled with a Tenney environmental chamber (model BTRC) and a 

heatless dryer (model HF 200A). A Hewlett-Packard electronic load 

(model 6050A) and multimeter were used to measure stack’s current and 

voltage, respectively. The Tenney environmental chamber was controlled 

through a computer with Linktenn II software. In order to get reproducible results, all electrochemical measurements were taken after equilibration of temperature and humidity for 2 hr. 
3. Results and Discussion 

3.1 Typical Electrochemical Behavior of Mass Transfer and 

Its Modeling 

Figure 1 shows a typical potential-current curve of a lo-cell strip airbreathing PEMFC stack. As current increases, voltage decreases, approaching 0 V. It is well known that the electrode polarization can be 

attributed to activation, ohmic, and mass-transfer processes. Activation 

occurs mainly at the beginning of the potential-current curve, the ohmic 

at the middle, and the mass transfer under high current conditions. Kim 

et al [5] and Rho et al [6] used an empirical equation to describe the 

potential-current behavior for a single cell. Here, we use the same equation for a PEMFC stack, but define each term differently At low and 

median currents, the stack potential-current curve can be described with 

the following equation: 

Ei=E,-Blog(lOOOi)-Ri . (1) 

Here, Ei (V) and i (A) are the experimentally measured stack potential and 

current, respectively, and E, (V) is the open circuit potential of the stack, 

which is equal to the sum of open circuit potential of all single cells connected in series. B (mV de&) is the sum of the Tafel slope for the oxygen 

reduction from all single cells connected in series, R (!2) represents the 

sum of the resistance of all the single cells connected in series, such as 

resistances in the electrolyte membrane, which causes a linear variation 

of potential with current. The top curve in figure 1 is the computercalculated result from equation (l), which deviates from the experimental 

points at higher currents. 

Figure 1. Typical 10.0 

potential-current 

behavior of strip 

PEMFC stacks (10 cells) 8.0 

with mass-transfer 

limitation. Points are 

obtained from experi- 9 

ment. Lines are ; 6.0 

computer-fitted curves = B 

with equations (1) and 24 

(2), respectively. 8 4.0 

0.0 

( 0.5 1 :o 1:5 2:o ‘. 2:5 

Stack current (A) 
3,2 

The entire current range of the potential-current curve can be described as 

Ei = E, - B 10g(1000 i) - Ri - i, m exp (ni,) , (2) 

&l =i-id (wheni>&), (3) 

i, = 0 (when i I id) . (4) 

Here, id (A) is the smallest value of current that causes the voltage deviation from the linearity in figure 1. The id value can be obtained from the 

experimental curve or from the calculated curve with equation (1). The 

m (Q) and YI (A-l) are the mass-transfer parameters, which can be obtained by fitting the potential-current curve with computer simulation. 

Equation (2) gives an excellent fit with the potential-current curves over 

the entire range of current. For instance, the bottom line shown in figure 1 

is the computer-fitted curve with equation (2), which accurately fits the 

experimental points. The two lines calculated in figure 1 both give the 

same values of E,, B, and R. We use equation (2) to analyze the following 

experimental data. 

Effect of Humidity 

Figure 2 shows the potential-current curves and power-current curves for 

the strip PEMFC stack operating at various humidity levels. The lines are 

fitted to the experimental points with equation (2). The voltage and 

power decreased with the percentage of relative humidity (RH), which 

implies that mass-transfer-controlled processes become more pronounced 

at low humidity. The power-current curves show a peak as current is 

increased. For RH at 90% and 70%, the maximum powers are 8.3 and 

6.5 W, respectively. The kinetic parameters, obtained from computer 

fitting, are listed in table 1. As humidity increases, the R and R values 

both decrease, but the id value increases. The n value was kept constant 

during each calculation. Here we define another parameter, mass-transfer 

impedance (R,), to analyze the electrode processes: 

R, = AE/i = [i, m exp(ni, )]/i . (5) 

In this study, we use only the m and n parameters to obtain the best fit 

with the experimental points, and we use equation (5) to calculate the 

mass transfer impedance beyond the range of experimental data. Figure 3 

shows the calculated mass transfer impedance at 70% and 90% RH. At 

lower humidity, much larger mass-transfer impedance occurred. The 

mass-transfer impedance starts from zero and increases very quickly with 

current for both humidity conditions. 

4 
Figure 2. Humidity 

effect on polarization behavior of 

strip PEMFC stacks 

(10 cells) at constant 

temperature of 30 “C. 

Points and lines are 

experimental data 

and computer-fitted 

curves, respectively. 

Table 1. Electrodekinetic and masstransfer parameters 

for strip PEMFC stack 

at different humidity 

levels. Temperature 

constant at 30 “C. 

Figure 3. Mass 

transfer impedance 

versus stack current at 

different humidity 

levels. Environmental 

temperature is 30 “C. 

10.0 

8.0 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 

Current (A) 

RH (9) (mVBde&) (i) 

id 

W> (lf, (Al’) (A) 

70 9.2 680 1.1 0.36 1.5 0.65 

90 9.2 600 1.08 1.0 1.5 1.34 

Max.* 10.0 670 1.25 0.20 1.5 1.83 

*Max. = maximized stack performance. 

0.6 

8.0 

F 6.0 - 

t 

2 

4.0 ,” 

s 

ul 

1.0 1.5 

Stack current (A) 

5 
3.3 Performance Maximization 

The performance of the strip PEMFC was maximized under the best 

humidity conditions: the hydrogen gas was introduced into the stack 

through a gas bubbler bottle, and the stack body was covered with a wet 

paper towel to keep humidity at saturation. This resulted in the best 

performance. Figure 4 shows the potential-current and power-current 

curves obtained from experimental data (points) and from computer 

calculations (solid lines). Compared with the condition of 90% RH, the 

maximized curves show better performance. The peak power for the 

maximized condition has reached -11 W, which is about 3 W more than at 

the 90% RH condition. The plot of mass transfer impedance versus stack 

current, with and without maximization, is shown in figure 5. The maximized curve has much smaller R, values than that of the 90% RH condition. Initially, mass transfer impedance differs little for the two curves 

(only -0.4 A current difference), but quickly becomes significant (-1.5 A 

current difference). The electrode kinetic parameters for the maximized 

condition are also shown in table 1. 

3.4 Effect of Temperature 

Figure 6 shows the potential-current and power-current curves for a 

series of environmental temperatures. At 10 “C, the potential-current 

curve is fitted well with equation (1), which implies that the electrode 

process at 10 “C is mainly controlled by activation and ohmic processes. 

Figure 4. 12.0. 

Performance of strip 

PEMFC stack (10 

cells), with and 10.0 

without maximization. Points and 

lines are experimen- Z 8’o 

tal data and al 

computer-fitted 

Z 

z 6.0 

curves, respectively. s 

5 

cn 

4.0 

2.0 2.5 

Current (A) 

10.0 

8.0 

z 

z 

6.0 5 cl 

?I 

s 

4.0 
Figure 5. Mass 2.5 

transfer impedance 

versus stack current, 

with and without 2.0 

maximizing stack 

performance. g 

p! 

Figure 6. Effect of 

environmental temperature on strip PEMFC 

stack performance. 

Humidity 70% RH. 

Lines from top to 

8.0 

bottom correspond to 

50,30, and 10 “C, 

z s o 

8 respectively. Points g 

and solid lines are 8 

experimental data 2 4.0 

and computer-fitted UJ 

curves, respectively. 

2.0 

2.0 3.0 

Stack current (A) 

.:p I WV, 10 “C A v, 30 “C 

1’ 

IQ I q w,1o~c A W30”C 0 w, 50 “C 

0.5 1.0 1.5 

Stack current (A) 

8.0 

At 30 and 50 “C, equation (2) must be used to obtain the best fit with the 

experimental points. It is not surprising that the mass transfer impedance 

seems to increase with temperature. At the beginning and middle current 

ranges, the higher temperature provides the highest voltage and power; 

but at the high current range, the lower temperature delivers the highest 

7 
voltage and power. The electrode kinetic parameters obtained at different 

temperatures are shown in table 2. The parameters at 30 and 50 “C are 

only slightly different. The plot of mass transfer impedance versus stack 

current at temperatures 30 and 50 “C is shown in figure 7; the two curves 

show only slight separation (-0.1 A current difference). When the environmental temperature increases, the temperature of the internal stack 

will be even higher. If heat dissipation in the stack is not fast enough, the 

polymer electrolyte membrane and other electrode components may 

dehydrate, decreasing the rate of mass transfer. 

3.5 Heat Transport in Strip PEMFC Stack 

We inserted a thermocouple into the stack to measure its internal temperature. Figure 8 shows the internal temperature variation with time 

under constant current operation (1.04 A). Even when the environmental 

temperature is held at 30 “C, the internal temperature increases with time. 

Table 2. Electrodekinetic and massT E0 id 

“C 

transfer parameters 

(V) (mVBdec”) (& (E) (A”) (A) 

for strip PEMFC 10 9.0 700 1.35 - - - 

- stack at different tem- 30 9.2 680 1.1 0.36 1.5 0.65 

peratures. Humidity 5o 9*3 680 0.75 0.36 1.5 0.55 

constant at 70% RH. 

Figure 7. Mass trans- 0.8 

fer impedance versus 

stack current at 

different environmental temperatures. 

Humidity constant at 0.6 

70% RH. 

g 

0.0 

1.0 

Stack current (A) 

8 
3.6 

Figure 8. Internal 

temperature variation 

with time for strip 

PEMFC stack at 

constant current 

operation (I = 1.04 A). 

Environmental temperature constant at 

30 oc. 

Figure 9. Comparison 

of strip PEMFC stack 

performance between 

short (5-cell) and long 

(lo-cell) stacks. Performance for both 

stacks is maximized. 

Points and lines are 

experimental data and 

computer-fitted data, 

respectively. 

At lower humidity, the internal temperature increases faster and equilibrates slower, because of higher resistance and mass transfer impedance, 

which produces more heat. The slow heat transport may also limit mass 

transfer phenomena. -, 

Effect of Stack Length 

In order to design a high-efficiency strip PEMFC stack, we must understand the kinetic processes of different stack lengths. Figure 9 shows the 

45.0 

40.0 

0 

e 

!z 

z 

c 

35.0 

$ 

E 

F 

30.0 

25.0 

( 

10.0 

8.0 

9 

2 0 40.0 6( I 80.0 100.0 120.0 

70% RH 

I M 90% RH 

Time (min) 

n E (V), 1 O-cell stack 

UP(W), 10-tell stat 

0.0 1.0 2.0 3.0 4.0 5.0 6.0 

Current (A) 

8.0 

z 

0.6 

g 

g 

Y 

$j . 

4.0 
potential-current and power-current curves for 5- and lo-cell stacks. The 

points in the figure were obtained from experimental data, and the lines 

were calculated with equation (2). The 5-cell stack data show much less 

curvature than do those of the lo-cell stack. However, the lo-cell stack has 

a peak power of -11 W, while the 5-cell stack has only -5 W. Table 3 

shows the kinetic parameters obtained from the calculations. It is interesting that the parameters of E,, B, R, and m for the 5-cell stack are about half 

that of the lo-cell stack, but the id value is about two times larger for the 

5-cell stack than for the lo-cell stack. Figure 10 shows a plot of mass 

transfer impedance versus stack current for the 5- and lo-cell stacks. The 

two curves are separated by a large gap (from 1.2 to 2 A). Although the 

5-cell stack has a much smaller impedance, the lo-cell stack is more 

efficient, because it produces a larger power density (more than double 

that of the 5-cell stack). 

Table 3. Electrodekinetic and massLength E, 

of stack (V) (mVBdec_‘) (& (z) (An_l) (A) 

id 

transfer parameters 

for different lengths 10 cells 10.0 670 1.25 0.20 1.5 1.83 

of strip PEMFC stacks 5 cells 4.95 315 0.715 0.08 1.5 3.05 

at maximized 

stack performance. 

Figure 10. Masstransfer impedance 

versus stack current 

for different lengths 

of stacks. Stack performance for both 

stacks is maximized. 

0.E 

0.5 

E 

al 0.4 

: 

$ 

B 

.- E 0.3 

ii 

c” 

I! 

;;; 0.2 

2 

r 

0.1 

0.0 

1 .o 2.0 3.0 4.0 5.0 6 

Stack current (A) 

10 
3.7 Stability Test 

Figure 11. Stability of 

strip PEMFC stack 

after maximization of 

stack performance. 

The strip PEMFC stack was tested under constant current operation. 

Figure 11 shows the voltage variation with time. No voltage decrease was 

observed for constant current operation at 1.54 A. However, when current 

is increased to 2.05 A, the voltage is not stable, decreasing quickly with 

time-probably because of poor heat dissipation and membrane 

dehydration. 

7.0 I 

~.O--‘I’--IC - mu I I 

W Eforl=lS4A 

1.0 

i 

+ E for I = 2.05 A 

0.0 0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 

Time (min) 
4. Conclusion 

An empirical equation was developed to describe the electrode processes 

of a PEMFC stack over the entire current range, including activation, 

ohmic, and mass-transfer processes. The potential-current and powercurrent curves of the strip PEMFC stack were fitted with the empirical 

equation under a variety of experimental conditions, such as humidity, 

temperature, and stack length, and a concept of mass-transfer impedance 

was defined. This empirical equation can be used to calculate the mass 

transfer impedance beyond the experimental points. For the strip PEMFC 

stack, the mass-transfer impedance occurs only at high current range. 

With a decrease in humidity, the mass-transfer impedance increases 

considerably. With temperature changes from 30 to 50 “C, the masstransfer impedance increases only slightly For the strip PEMFC stack at 

low-temperature operation, less mass-transfer impedance was observed, 

which is attributed to a heat-transfer problem at higher environmental 

temperature. Increasing the total number of cells in the PEMFC strip 

increases the mass-transfer impedance proportionally However, the 

overall power density for longer lengths of strip is larger. 

Acknowledgement 

The authors wish to thank the U.S. Army Materiel Command for its 

financial support of this project. 

12 
References 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

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12. 

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14. 

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(1988), 175. 

I. D. Raistrick, U.S. Patent 4,876,115 (1990). 

M. S. Wilson and S. Gottesfeld, I. A@. Electrochem. 22 (1992), l-7. 

J. Kim, S. M. Lee, S. Srinivasan, and C. E. Chamberlin, 1. Electrochem. Sot. 

142 (1995), 2670. 

Y. W. Rho, 0. A. Velev, S. Srinivasan, and Y. T. Kho, 1. Electrochem. Sot. 141 

(1994), 2084. 

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143 (1996), 3838. 

M. Uchida, Y. Aoyama, N. Eda, and A. qhta, J. Electrochem. Sot. 142 (1995), 

4143. 

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(1995), 3044. 

M. Uchida, Y. Aoyama, N. Eda, and A. Ohta, 1. Electrochem. Sot. 142 (1995), 

463. 

J. B. Lakeman and J. Cruickshank, Proc. 38th Power Sources Conference, 

Cherry Hill, NJ (June 1998), p 420. 

A. C. Oliver and E. Clarke, Proc. 38th Power Sources Conference, Cherry 

Hill, NJ (June 1998), p 424. 

L. l? Jarvice and D. Chu, Proc. 38th Power Sources Conference, Cherry Hill, 

NJ (June 1998), p 428. 

0. Polevaya and D. Bloomfield, Proc. 38th Power Sources Conference, 

Cherry Hill, NJ (June 1998), p 416. 

C. E. Chamberlin, I? A. Lehman, R. M. Reid and T. G. Herron, in Hydrogen 

Energy Process X, D. Block and T. N. Veziroglu, eds., Proc. 10th World 

Hydrogen Energy Conference 3, International Association for Hydrogen 

Energy, Cocoa Beach, FL (20-24 June 1994), pp 1659-1663. 

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I. TULLE AND SUBTLE Strip Cell Stack Design and Mass Transfer Phenomena 5. FUNDING NUMBERS 

in a Polymer Electrolyte Membrane Fuel Cell Stack DA PR: - 

PE: 62120A 

EAUTHOR(S) Rongzhong Jiang and Deryn Chu 

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13. ABSTRACT (Maximum 200 worn’s) 

A type of air-breathing polymer electrolyte membrane fuel cell (PEMFC) stack with a strip desig 

structure was investigated. Potential-current curves for this PEMFC show typical mass transfer 

behavior. An empirical equation was developed to describe the kinetic processes of the stack, as 

opposed to only a single cell. A series of experimental potential-current and power-current 

curves including different humidities, temperatures, and stack lengths was extremely well fitted 

with the equation. A concept of mass transfer impedance is defined in this report. This empirical 

equation can be used to calculate the mass-transfer impedance quantitatively beyond the 

experimental points, for example, with decreasing humidity, where the mass-transfer impedance 

increases considerably. 

14. SUBJECTTERMS 

Strip cell, fuel cell 

15. NUMBER OF PAGES 

22 

16. PRICE CODE 

87. SECURWY CLASSIFICATION 

OF REPORT 

Unclassified 

16. SECURITY CLASSIFICATION 

OFTHIS PAGE 

Unclassified 

19. SECURITY CLASSlflCATlON 

OF ABSTRACT 

Unclassified 

26. UMKATtON OF ABSTRACT 

UL 

Standard Form 296 (Rev. 2-69) 

Presc”bed by ANSl std. 239-18 

298-102 

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