Approved for public release; distribution unlimited. 
The findings in this report are not to be construed as an 

official Department of the Army position unless so 

designated by other authorized documents. 

Citation of manufacturer’s or trade names does not 

constitute an official endorsement or approval of the use 

thereof. 

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

return it to the originator. 
Army Research Laboratory 

Adelphi, MD 20783-1197 

ARL-TR-2237 August 2000 

Origin of Potential Drops of 

Bipolar Polymer Electrolyte 

Membrane Fuel Cells in 

Constant Current Discharge 

Rongzhong Jiang, Charles Walker, and Deryn Chu 

Sensors and Electron Devices Directorate 

Sponsored by 

U.S. Army Materiel Command 

5001 Eisenhower Avenue 

Alexandria, VA 22333-0001 

Approved for public release; distribution unlimited. 
Abstract 

Empirical equations were developed to describe the potential-time 

behaviors of polymer electrolyte membrane fuel cell (PEMFC) stacks 

at constant current discharge. When either ambient temperature or 

discharge current is too high, the experimental potential-time curves 

are inclined or have fallen rapidly within a short discharge time. 

Various experimental potential-time curves are fitted well with the 

empirical equations at different discharge current and ambient 

temperatures. The effect of parameters of the empirical equations on 

the shape of the potential-time curve is also analyzed. Mass transfer 

is likely a reason for the rapid falling of the potential, and polymer 

electrolyte dehydration is responsible for the inclination of the 

potential-time curves. Empirical equations are helpful for forecasting 

and explaining the long-term discharge performance of the PEMFC 

stacks. 

ii 
Contents 

1. 

2. 

3. 

4. 

5. 

6. 

Introduction ....................................................................................................................................... 1 

Experimental Setup .......................................................................................................................... 2 

Development of Empirical Equations .......................................................................................... 3 

Calculated Results ............................................................................................................................ 6 

4.1 Effect of Tb - T, .......................................................................................................................... 6 

4.2 Effect of S .................................................................................................................................. 6 

4.3 Effect of T,,L Value ..................................................................................................................... 6 

4.4 Effect of Parameter A .............................................................................................................. 6 

4.5 Effect of Parameter B ............................................................................................................... 7 

Experimental Results ........................................................................................................................ 9 

5.1 Temperature-Time Curve ....................................................................................................... 9 

5.2 Potential-Time Curves ............................................................................................................. 9 

Conclusions ..................................................................................................................................... 13 

Acknowledgment ................................................................................................................................... 14 

References ................................................................................................................................................ 15 

Distribution ............................................................................................................................................. 17 

Report Documentation Page ................................................................................................................. 19 

Figures 

1. Constant current discharge performance of a PEMFC stack at an ambient temperature of 

20 “C and at different discharge currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 

2. Constant current discharge performance of a PEMFC stack at different ambient 

temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................ 4 

3. Calculated curves of stack temperature versus time for a PEMFC stack at a constant current 

discharge with use of an empirical equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 

4. Calculated curves of stack voltage versus time for a PEMFC stack at a constant current 

discharge with use of an empirical equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 

5. Variation of stack temperature versus time for a PEMFC stack at a constant current 

discharge and an ambient temperature of 20 “C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 

6. Constant current discharge performance of a PEMFC stack at an ambient temperature 

of 20 “C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................ 10 

7. Constant current discharge performance of a PEMFC stack at different ambient 

temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............... 11 

8. Stack voltage dropping with time when either discharge current or ambient temperature 

was too high for a PEMFC stack at a constant current discharge condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 

. . . 

111 
Tables 

1. Parameters used for calculations of potential-time curves for a 50-W bipolar PEMFC 

stack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................. 10 

iv 
1. Introduction 

For cleaner air and less emitted pollution, fuel cells have been considered 

one of the most promising innovative energies for electric vehicles and for 

portable power sources. Among many kinds of fuel cells, polymer electrolyte membrane fuel cells (PEMFCs) have received much attention in the 

last two decades [l-14] because of their light weight, compactness, high 

power, and low cost. To understand and improve the performance of 

PEMFCs, researchers have developed several models [8-131 to explain the 

behavior of potential variation with the discharge current for single cells 

and for fuel cell stacks. Kim et al [8] have modeled the potential-current 

curves for a single fuel cell using an empirical equation, including processes 

of activation, ohmic, and mass transfer. Amphlett et al [9-lo] have tried to 

describe the relationship of the potential and current of the Ballard Mark IV 

fuel cell using mechanistic and empirical methods. Chu and Jiang [ll-131 

have described the potential-current behaviors of PEMFC stacks in the presence of all electrode processes and mass transfer. However, modeling or 

description of the potential-current behaviors of PEMFCs alone is not enough 

to know or evaluate the overall performance of fuel cells or fuel cell stacks, 

because practical fuel cells have to be working for a long time at different 

ambient temperatures. 

During long-term operation of fuel cells, the temperature of a fuel cell stack 

may change with time. How to assess the effect of temperature and time 

changes on the performance of fuel cell stacks is a primary consideration 

when all electrode processes and mass transfer are present. This research is 

to study the long-term performance of PEMFC stacks at constant current 

discharge, instead of describing the potential-current behaviors only. 
2. Experimental Setup 

We used a bipolar PEMFC stack that could provide about 50 W of output 

power in optimum condition. The open-circuit potential was about 42 V 

The active electrode area was about 18 cm2, and the volume of the stack was 

about 250 cm3. The stack was humidified with water steam and ini.tially run 

at 0.5 A for several hours to reach a stable performance before we used it to 

generate data. 

We also used a high purity of hydrogen (99.99%) as fuel and compressed air 

as oxidant. The ambient temperature was controlled with a Tenney Environment Chamber (model BTRC), which was programmed through a computer with Linktenn II software. An Arbin battery tester (model BT-2043) 

was used to program and control constant current discharge. A HewlettPackard electronic load (model 6050A) and a Hewlett-Packard multimeter 

were used to measure current and voltage when the stack voltage was greater 

than 35 V. A Matheson digital flowmeter (LFE 1000H) was used to measure 

the hydrogen flow. A hydrogen purger was used and set to a 10-s length per 

5-min period for all measurements. We adjusted the inlet hydrogen and air 

pressures to 3 and 5 psi, respectively An electric fan (about 10 W) was placed 

toward the stack during stack evaluation for heat dissipation, and a thermocouple was used to measure stack temperature. 

2 
3. Development of Empirical Equations 

The potential-time curves of PEMFC stacks are not always flat-they sometimes incline slowly or decline rapidly For example, when the discharge 

current is too high, the stack potential falls rapidly within a short discharge 

term. Figure 1 shows the potential-time curves of a 50-W bipolar fuel cell 

stack at an ambient temperature of 20 “C and at different discharge currents. When the current is 1.0 or 1.5 A, the potential-time curve is only slightly 

inclined. However, when the current is equal to or higher than 2.0 A, the 

stack potential falls rapidly within about 35 min of constant current discharge. Figure 2 shows the potential-time curves of a 50-W bipolar fuel cell 

stack at constant current (1.0 A) discharge and at different ambient temperatures. When the temperature is equal to or higher than 30 “C, the 

potential-time curve is inclined slowly and then falls rapidly within about 

40 mm. The origin of the inclined or declined potential-time curves will be 

explored in this report. Apparently, the discharge potential-time behavior 

of the PEMFC stack is affected by the variations of stack temperature and 

discharge time. All the previous models [8-131 were unable to explain or 

describe this phenomenon. We developed the following equations to solve 

the problem. 

For a fuel cell stack, the stack potential can be described as [ll-131 

E = E. - Eact - Eohmic - Emass I 

E=E,-blog(i)-(R+AR)i-E,,,,. 

Figure 1. Constant 45 

current discharge 

performance of a 40 

PEMFC stack at an 

ambient temperature of 35 

20 “C and at different 

discharge currents. z 30 

2i-l 

2 25 

9 

‘5 20 

s 

cn 

15 

(1) 

(2) 

40 60 80 100 120 140 

Time (min) 

3 
Figure 2. Constant 

current discharge 

(1.0 A) performance of 

a PEMFC stack at 

different ambient 

temperatures. 

5 

$j 15 

10 

5 

0 

0 

0 

f 

i 

i 30 “C 

/ , / / / 1 

0 20 40 60 80 100 120 140 

Time (min) 

Here, E, (V) is the open-circuit potential of the stack. Eohmic (V) is the ohmic 

over potential of the stack, which is equal to the sum of the ohmic over 

potentials of all single cells linked in a series. E,m,,, (V) is the over potential 

of the stack caused by mass transfer. The z1 value is the sum of Tafel slopes 

of all single cells linked by series, and R is the sum of ohmic resistances of 

all single cells linked by series. The AR is the incremental value of R because 

of temperature and relative humidity changes. 

At constant current discharge, the sum of E, and activation over potential 

can be considered a constant if we neglect their variations with temperature. However, the value of R may change appreciably with time, because 

the effects of stack temperature and polymer electrolyte membrane 

dehydration on stack ohmic resistance are significant. In addition, the stack 

temperature may increase with time at constant current discharge until 

reaching a steady state with the ambient. When stack temperature is too 

high, the fuel and air transfers may be blocked, interrupted, or unbalanced, 

causing an appearance of mass transfer over potential. For simplification, 

equation (2) is rewritten as 

E=E,-ARi-E,,,,. (3) 

Here, E, (V) is the apparent potential of the stack at a specific current value, 

which is equal to the potential at the initial time of constant current discharge. By analyzing a large number of potential-time curves of PEMFC 

stacks at constant current discharge and at different ambient temperatures 

and relative humidity, we found that the E,,,, can be described as 

E mass = i A exp[l/(T,,, - T)] . (4) 

4 
Here, A (Q) is a parameter that affects the rate of stack impedance jump at 

high temperatures because of mass transfer. T,,, (“C) is the stack temperature that is high enough to initiate mass-transfer over-potential appearance, 

and T (“C) is the stack temperature at any time. 

AR can be described as 

AR = i B exp[N (T- 7’,)/(Tb - TO)] . (5) 

Here, B (Q) is a parameter that affects the rate of ohmic resistance change 

with stack temperature, N is a function parameter that determines a curvature of selective functions with a different value for each kind of polymer 

electrolyte stack, Tb (“C) is the stack temperature at a steady condition with 

ambient, and TO (“C) is the ambient temperature. 

Therefore, equation (3) can be rewritten as 

E = E, - i A exp[l/(TwL - T)] + i B exp[N (T- T,)/(T, - TO)] . (6) 

In equation (6), if an increase of stack temperature causes stack resistance to 

increase, such as polymer electrolyte dehydration at high temperature, the 

operator on the rightmost side should be minus and vice versa. Moreover, 

the stack temperature (T) is a function of time. To obtain the potential-time 

function of the stack, we need to find the stack temperature by experiments. 

Sometimes, we only know a few points of stack temperature from experiments in a long term of constant current discharge, which is not enough to 

describe the whole range of stack temperature. Therefore, we need to find a 

temperature-time function to calculate the other unknown points for the 

stack. 

Unfortunately, stack temperature variation is dependent on many factors, 

such as stack power, stack size, stack shape, stack-cooling styles, the value 

of discharge current, and heat dissipation coefficient. It is difficult to obtain 

an analytical solution. However, an empirical equation to describe the stack 

temperature-time behavior is obtained for PEMFC stack: 

T = To + (Tb - To) f/(f + S) , (S > 0) . (7) 

Here, TO, Tb, and 7’ are described in equation (6), f (min) is discharge time, 

and S (min) is a time parameter that affects the rate of stack temperature 

change. At the beginning of discharge, the stack temperature change is the 

fastest. As time increases, the stack temperature change gradually becomes 

slower. 

With equations (6) and (7), we can calculate the potential-time curves of 

PEMFC stacks for all electrode processes and mass transfer. 
4. Calculated Results 

To understand the physical meanings of the parameters described in equations (6) and (7) more clearly, we have performed a series of calculations by 

varying one parameter only and keeping other parameters constant. These 

calculated results are summarized in the following sections. 

4.1 Effect of Tb - TO 

Figure 3(a) shows the calculated data of stack temperature versus time 

with the use of equation (7), which explain the effect of 7’[, - T, on the 

temperature-time curve at constant current discharge. The stack temperature grows quickly at the beginning of the discharge, especially in the first 

20 min. Then the growth slows and the temperature-time curve gradually 

becomes flat. Through the increase of the value of I’[, - To, the plateau of 

the temperature-time curve becomes higher. 

4.2 Effect of S 

Figure 3(b) also shows the calculated data of stack temperature versus 

time with the use of equation (7), which explain the effect of S on the 

temperature-time curve at constant current discharge. Through the increase 

of the value of S, the rate of stack temperature growth decreases, but the 

plateau of the temperature-time curve changes only a little. 

4.3 Effect of TII Value 

Figure 4(a) shows the calculated data of stack voltage versus time, which 

explain the effect of T,,, value on potential-time behavior. With increasing 

time, the stack temperature gradually reaches the value of T,,, and the stack 

potential begins to decline because of mass-transfer over-potential occurrence. If stack temperature is smaller than the value of T,,l, there is no masstransfer occurrence and no potential falling phenomenon. Because the maximum stack temperature is 43 “C in figure 4(a) (see the top x curve), the 

potential-time curve is falling only when the T,,, value is equal to or smaller 

than 43 “C. 

4.4 Effect of Parameter A 

Figure 4(b) also shows the calculated data of stack voltage versus time, which 

explain the effect of parameter A on potential-time behavior. With the increase of the value of parameter A, the rate of stack potential declination 

becomes more significant. 

6 
Figure 3. Calculated 

curves of stack 

temperature versus 

time for a PEMFC 

stack at a constant 

current discharge 

with use of an 

empirical equation. 

Parameters used: 

(a) T, = 20 “C, 

S = 4.0 min, and 

different Tb - T, 

values and 

(b) T, = 20 “C, 

T,-T0=25’C,and 

different S values. 

(4 90 

80 

70 

3 

e 60 

i?! 

z$ 50 

5 

p 40 

: 

3 

30 

cn 20 

10 

0 I I 1 / I 

20 40 60 8b 100 120 140 

Time (min) 

0 

(b) 50 

T us=20 

-+S=lO 

4.5 Effect of Parameter B 

0 20 40 60 80 100 120 140 

Time (min) 

Figure 4(c) also shows the calculated data of stack voltage versus time, which 

explain the effect of parameter B on the potential-time behavior. Here, the 

symbol of the term on the rightmost side in equation (6) is considered minus. By increasing the value of parameter B, no apparent effect is shown on 

the rate of the potential falling. However, the plateau of the potential-time 

curve becomes more inclined. 
Figure 4. Calculated 

curves of stack voltage 

versus time (solid lines) 

for a PEMFC stack at a 

constant current 

discharge with use of 

an empirical equation. 

Parameters used: (a) E, 

= 33 V, A = 0.2 R, B = 0, 

i= LOA, T[]-T = 

14.1 “C, s = 4.o’klin, 

T, = 30 “C, and varying 

T,?, values; (b) EN = 33 V, 

T],, = 43 “C, B = 0, 

i = 1.0 A, 

- 25 

0 i 20 

T,, - To = 14.1 “C, 

S = 4.0 min, T, = 30 “C, 

and varying A values; 

and (c) E,( = 33 V, 

T,,, = 43 “C, A = 0.2 R, 

i = 1.0 A, 

T,, - T” = 14.1 “C, 

S = 4.0 min, T, = 30 “C, 

N = 11, and varying B 

values. Top line is 

curve of stack 

0 20 40 

Time (min) 

60 80 

(b) 40 I 45 

(a 

+A = 0.40 

U-A = 0.20 

+A=O.lO 

U A = 0.02 

temperature versus 

time. 

0 20 40 60 80 

Time (min) 

T 

40 

Time (min) 

40 

G 

e 

20 

50 

40 

o^ 

e 

30 2 

iii 

ii 

20 J-2 

Y 

2 

cn 

IO 

0 

60 80 

8 
5. Experimental Results 

5.1 Temperature-Time Curve 

By using equation (7), we compare the stack temperatures experimentally 

recorded with the calculated data. Figure 5 shows the temperature-time 

curve obtained from a 50-W PEMFC stack at constant current discharge 

(1.5 A) and at a 20 “C ambient temperature. The points were experimental 

data, and we calculated the line using equation (7) (T, = 20 “C, Tb- T, = 19.5 “C, 

and S = 4.0 min). As shown in the figure, the calculated curve fits well with 

the experimental points. In the following calculations for stack potentialtime curves, we keep the term S constant (4.0 min) and use different T, and 

Tb - T, values. 

5.2 Potential-Time Curves 

Eficf of Discharge Current: Figure 6 shows a series of potential-time curves 

at constant current discharge with different current values for a 50-W PEMFC 

stack. The points and lines were obtained from experiments and caiculations, respectively As shown in the figure, all calculations fit with the experimental points quite well. All the parameters used for the calculations 

are shown in table 1. With the discharge current increasing, the difference 

in stack temperature at steady state (Tb) and ambient temperature (T,) increases, and the stack apparent potential (E,) decreases. However, the stack 

temperature that causes mass-transfer over-potential occurrence (T,) remains unchanged when ambient temperature is kept constant at 20 “C. 

Figure 5. Variation of 50 

stack temperature 

versus time for a 

PEMFC stack at a 40 

constant current 9 

discharge (1.5 A) and G 

an ambient temperature of 20 “C. Points 

$ 30 

5 

and line were 

obtained from experi- e 

mental and calculated Z 20 ‘: 

data, respectively. B 

Calculation paracn 

meters: T, = 20 “C, 10 

q&=19.5 "C, 

and S = 4.0 min. 

0 

0 60 80 

Time (min) 

9 
Figure 6. Constant 

current discharge 

performance of a 

PEMFC stack at an 

ambient temperature of 30 

20 “C. Points and lines 

were obtained from 

experimental and = 

calculated data, 

respectively. 

10 - 

5- 

0 I I 

0 20 40 60 80 100 120 140 

Time (min) 

Table 1. Parameters 

used for calculations of ?b (“C) l(A) 6, (V) A W B k-Q T,,, (“C) Tl,- To (“C) S bin) 

potential-time curves 

for a 50-W bipolar 

PEMFC stack. 

20 1.0 33.0 0.6 0.0 44.0 14.0 4.0 

20 1.5 31.0 0.7 0.0 44.0 20.0 4.0 

20 2.0 30.0 0.4 0.0 44.0 26.4 4.0 

30* 1.0 33.0 0.2 0.2 43.0 14.1 4.0 

-5 3.0 24.5 0.1 0.0 38.0 53.6 4.0 

*For this calculation, the parameter N equals 11. 

Furthermore, at a low value (1.0 A) of constant current discharge, the 

potential-time curve is relatively flat. Increasing the discharge current value 

(1.5 A) causes the potential-time curve to become inclined. If the discharge 

current is too high (2.0 A), the potential-time curve is declined and falls 

rapidly until reaching zero voltage. 

Effect ofAn~bient Telqerattlre: Figure 7 shows the effect of different ambient 

temperatures on the potential-time behavior for a 50-W PEMFC stack. The 

points and lines were obtained from experiments and calculations, respectively. The parameters used for calculations are shown in table 1. With the 

increase of the ambient temperature from 20 to 30 “C, the values of E,, Till, 

and Tl,- T, do not seem to change significantly. However, the stack Ti, value 

at an ambient temperature of 30 “C is about 10 “C higher than that at an 

ambient temperature of 20 “C when each has the same value of discharge 

current (1.0 A). Therefore, at a higher ambient temperature, the stack temperature reaches its T,,, value (43 “C) faster. As expected, at T, = 20 “C, the 

potential-time curve is relatively flat, but at T, = 30 “C, it becomes inclined 

and falls rapidly to zero voltage within about 40 min. The plateau of 

potential-time curve is inclined slowly if the parameter B is not zero. Therefore, the parameter B indicates whether the polymer electrolyte membrane 

is dehydrated. 

10 
Figure 7. Constant 

current discharge 

(1.0 A) performance of 

a PEMFC stack at 

different ambient 

temperatures. Points 

and lines were 

obtained from 

experimental and 

calculated data, 

respectively. 

40 

0 20 40 60 80 100 120 140 

Time (min) 

Origin ofPotential Declining: Figure 8 shows a series of potential-time curves 

at constant current discharge for a 50-W PEMFC stack. All these potentialtime curves are declined and their potentials ‘fall to zero rapidly within 

different times. The points and lines in the figure were obtained from experiments and calculations, respectively. As shown in the figure, all calculations fit with the experimental points quite well. All the parameters used 

for the calculations are shown in table 1. At -5 “C (ambient) and 3.0 A, the 

discharge current is too high (3.0 A), causing its potential to decline rapidly. 

At 30 “C (ambient) and 1.0 A, the ambient temperature is too high, causing 

its potential to fall in a short time. At 20 “C (ambient) and 2.0 A, the potentialtime curve is also declined, because of a too-high internal stack temperature caused by a long-term constant current discharge. Therefore, when either ambient temperature or discharge current is too high, which will cause 

stack internal temperature to increase rapidly, the fuel and air flows may be 

blocked, interrupted, or unbalanced. Also, a mass-transfer problem may 

occur and cause a correspondent declination of the potential-time curve in 

a short time. Besides, when stack internal temperature is too high, the polymer electrolyte membrane may dehydrate, causing an inclination to the plateau of the potential-time curve. 

11 
Figure 8. Stack voltage 35 

dropping with time 

when either discharge 

current or ambient 30 

temperature was too 

high for a PEMFC stack z 25 

at a constant current 

discharge condition. $ 20 

Points and lines were 5 

obtained from > 

experimental and “0 15 

m 

calculated data, tz 

respectively. 10 

5 

2 

3O"C,l 

-0.5 “C, 3.0 A 

.O A 

20 30 

Time (min) 

50 

12 
6. Conclusions 

Several empirical equations are developed to describe the experimental stack 

temperature-time and the stack potential-time curves for PEMFC stacks at 

constant current discharge. The experimental stack temperature-time curve 

fits quite well with equation (7), which contains the parameters of ambient 

temperature (TO), stack temperature at a steady state (TJ, and time factor 

(S). The experimental potential-time curves at different discharge current 

and ambient temperatures are simulated with equation (6), which contains 

the parameters of stack internal temperature (T), stack mass-transfer temperature (T,), and potential decreasing rate factor (A). All these experimental potential-time curves fit quite well with the empirical equations. When 

stack temperature reaches the value of T,,, a mass-transfer problem occurs, 

and the potential-time curve is declined rapidly. If either ambient temperature or discharge current is too high, the stack temperature will reach the 

T,, value and cause a mass-transfer problem. In addition, when the stack 

internal temperature is too high, the polymer electrolyte membrane will 

dehydrate, causing an inclination of the potential-time curve. 

The empirical equations (6) and (7) are helpful for stack design, because 

they are likely used for forecasting the stack’s long-term performance. We 

may conduct calculations by setting different parameters for the empirical 

equations. For example, we may calculate a series of stack temperaturetime curves to determine how fast the stack temperature will increase when 

obtaining a maximum stack power. Also, we may calculate a.series of the 

stack discharge potential-time curves to decide what the stack performance 

will be, given a specific ambient temperature or discharge current. 

13 
Acknowledgment 

We wish to thank the U.S. Department of the Army and the Army Materiel 

Command for their financial support of this project. 

14 
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“Performance modeling of the Ballard Mark IV solid polymer electrolyte 

fuel cell, II. Empirical model development,“J.‘Electrockem. Sot. 142 (1995), 9. 

11. D. Chu and R. Jiang, “Comparative studies of polymer electrolyte membrane fuel cell (PEMFC) stacks and single cells,” 1. Power Sources, 80 (1999), 

226. 

12. D. Chu and R. Jiang, “Performance of polymer electrolyte membrane fuel 

cell (PEMFC) stacks, Part I. Evaluation and simulation of an air-breathing 

PEMFC stack,” J. Power Sources, 83 (1999), 128. 

15 
13. D. Chu, R. Jiang, and C. Walker, “Analysis of PEM fuel cell stacks using an 

empirical current-voltage equation,” 1. Apy. Electrochem. 30 (2OOQ), 365. 

14. D. Chu and R. Jiang, “Performance of polymer electrolyte membrane fuel 

cell stack,” Proc. J. Electuochenz. Sot. 27 (1998), 470. 

16 
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REPORT DOCUMENTATION PAGE Form Approved 

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AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED 

August 2000 Progress, Ott 1998 to Sept 1999 

.TITLEANDSUETITLE Origin of Potential Drops of Bipolar Polymer 

Electrolyte Membrane Fuel Cells in Constant Current Discharge 

5. FUNDING NUMBERS 

DA PR: N/A 

PE: 62120A 

.AUTHOR(S) Rongzhong Jiang, Charles Walker, and Deryn Chu 

. PERFORMING ORGANIZATION NAME(S) AND ADDRESS 

U.S. Army Research Laboratory 

Attn: AMSRL- SE-DC email: dchu@arl.mil 

2800 Powder Mill Road 

Adelphi, MD 20783-1197 

9. PERFORMING ORGANIZATION 

REPORT NUMBER 

ARL-TR-2237 

. SPONSORlNGlMDNlTORlNG AGENCY NAME(S) AND ADDRESS 

U.S. Army Materiel Command 

5001 Eisenhower Avenue 

Alexandria, VA 22333-0001 

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AMS code: 622120.H16 

~za. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; 

distribution unlimited. 

12b. DISTRIBUTION CODE 

13. ABSTRACT (Maximum 200 words) 

Empirical equations were developed to describe the potential-time- behaviors of polymer 

electrolyte membrane fuel cell (PEMFC) stacks at constant current discharge. When either 

ambient temperature or discharge current is too high, the experimental potential-time curves are 

inclined or have fallen rapidly within a short discharge time. Various experimental potential-time 

curves are fitted well with the empirical equations at different discharge current and ambient 

temperatures. The effect of parameters of the empirical equations on the shape of the 

potential-time curve is also analyzed. Mass transfer is likely a reason for the rapid falling of the 

potential, and polymer electrolyte dehydration is responsible for the inclination of the 

potential-time curves. Empirical equations are helpful for forecasting and explaining the 

long-term discharge performance of the PEMFC stacks. 

14.SUBJECTTERMS Fuel cell stack, discharge performance, PEMFC, fuel cell 

modeling 

15. NUMBER OF PAGES 

25 

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Unclassified 

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19