Empirical Simulation of the I-E Curves of a H2/Air PEM Fuel Cell atAsymmetric Relative Humidity

Faisal Abdellatif Al-Odail,2 Mahmoud M. Saleh,*1,2 and Takeo Ohsaka*3

1Department of Chemistry, Faculty of Science, Cairo University, Cairo, Egypt

2Chemistry Department, College of Science, King Faisal University, Al-Hassa, Kingdom of Saudi Arabia

3Present Address: Research Institute for Engineering, Kanagawa University,3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama 221-8686

E-mail: mmsaleh@kfu.edu.sa, mahmoudsaleh90@yahoo.com, ohsaka1950@gmail.com

Received: July 26, 2016; Accepted: September 5, 2016; Web Released: November 24, 2016

M. SalehM. Saleh received his Ph.D. from University of South Carolina, US/Cairo University, Egypt in 1995. Heworked as a postdoctoral fellow with Prof. Juttner, Dechema, Germany (2004) and with Prof. Ohsaka, TIT,Japan (2005, 2008, 2009, 2012). His permanent position is a Prof. of Physical Chemistry at Cairo University.Currently, he focuses in the research in the field of electrocatalysis using nanoparticles directed to Fuel cellsand Biosensors, Modeling of electrochemical systems and Corrosion.

Takeo OhsakaTakeo Ohsaka was awarded Dr. of Eng. from Tokyo Institute of Technology (TIT) in 1981. He worked as apostdoctoral fellow with Professor Anson at California Institute of Technology in 1981–1982 and an assistantprofessor with Professor Oyama at Tokyo University of Agriculture and Technology in 1982–1990. He movedto TIT as an associate professor in 1990 and he was a professor in 1998–2016 and he is now a professoremeritus of TIT and a visiting professor at Kanagawa University. His main current research work focuses onthe design and development of new electrocatalysts for ORR, OER, HER, HOR, etc.

AbstractThe present work is dedicated to study the performance of

H2/Air proton exchange membrane (PEM) fuel cells (FC) byusing an empirical modeling and experimental results at sym-metric and asymmetric relative humidity. The empirical model-ing is presented by Kim’s equation which was used in simulat-ing the performance of the H2/Air PEM FC and in fitting theexperimental data at different operating conditions. The simula-tion of the cell performance helps to understand the impacts ofdifferent kinetics, ohmic and mass-transfer resistances on theI-E curves and hence on the performance of the FC. By fittingthe experimental data with the theoretical calculations, it ispossible to extract important kinetics, ohmic and mass-transferparameters at different temperatures and at different symmetricand asymmetric relative humidity. Although the exact physi-cal meanings of some fitting parameters are quite clear, othersare not.

1. Introduction

The current research in fuel cells (FC) aims to replace theordinary energy devices for essential reasons such as affording

renewable energy sources rather than the ordinary exhaustedpower sources such as oil and coal. Of these fuel cells, protonexchange membrane fuel cells (PEMFCs) represent an impor-tant category. Since PEMFCs are considered to be an eco-friendly energy source with reasonable power output, they havebeen explored extensively during the last decades.1­4 Whilescientists world-wide have been seeking to replace high costplatinum electrocatalysts in the anode and cathode,5­8 othersare looking for engineering design and transport problemswithin the fuel cell.2,9 Nevertheless, important achievementsshould be offered in order to sustain high performance, dura-bility and low cost of the PEM fuel cells. These offers maysmooth the way for real replacement of ordinary power sources.

Controlling the water levels within the PEMFC is one of themain issues that have been considered as a main design criteriafor operation of the PEMFC. Humidified gases (H2, Air (O2))are supplied to the anode and cathode compartments and alsowater is produced inside the cathode compartment due toreduction of O2 gas to water. Meanwhile the wetting of theNafion membrane should be controlled to maintain high con-ductivity of the membrane. Improper hydration of the mem-brane may cause low ionic conductance and hence may resultsin irreversible damage. PEM used in fuel cells such as H2/

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Air(O2)PEMFC should have optimum hydration to attain suita-ble high proton conductivity. Also, extra amounts of watercreates flooding and yet it should be removed to prevent suchflooding.10,11 Figure 1 shows a scheme of the water transportprocess in a typical H2/Air PEM fuel cell. Three phenomenahave been found to control the water transport inside thePEMFC. These are: electro-osmotic drag (H2O molecules aredragged by hydration of the produced H+ ions at the anodecompartment and its transfer to the cathode compartment), backdiffusion (H2O molecules move under the concentration differ-ence between the cathode and anode) and forced convectionunder the impact of pressure difference between the H2 and O2

gases. However, the convection effect is generally negligiblecompared to the effects of electro-osmotic drag and the backdiffusion, due to low membrane hydraulic permeability.12­14

Most PEMFC studies were performed at high relative humid-ity conditions (symmetric i.e., equal relative humidity at bothcathode and anode compartments). However, there are notmany research reports that consider the impacts of operating theH2/Air PEMFC at dry anode compartment conditions (H2 gasis dry).15­23 In the above studies, non-zero values of relativehumidity of the anode (RHA) and that of the cathode (RHC)were used. However, studying the cell performance at either(RHA = 0 and RHC º 0) and (RHA º 0 and RHC = 0) islimited. In this context, at different combinations of the abovevalues of RHA and RHC, we may be able to explore the impactsof the above mentioned phenomena of water transportation onwater rehydration of the Nafion membrane and its effects onthe current-potential (I-E) curves of the H2/Air PEMFC. Oneof the most important criteria to diagnose the performance ofFC is the potential-current (I-E) relation. From the I-E curvesone can test the performance of the FC power and the maximumcurrent loading. The simulation can help us in understandingthe behavior of the FC at different controlling parameters andoperating conditions and also help us in designing a better FC.The fitting of the experimental data (experimental I-E data) willhelp to extract important controlling parameters. Two modelingapproaches have been introduced for such simulation: Theoret-ical and empirical models. Theoretical modeling requires theknowledge of the fundamentals of the kinetics, ohmic, mass-and charge-transport processes to be directly included into the

model algorithm.24­26 Empirical modeling, on the other hand,aims to reproduce the experimental data (e.g., I-E curves) atdifferent conditions. Although empirical modeling is limited inits prediction ability and in the range of operational parameters,it is applied in many cases for analysis of H2/Air PEM fuel cellsince it is a fast and easy modeling processes.27­30 Empiricalmodeling for H2/Air PEM fuel cell aim to predict the current-potential curves (I-E) of the FC at different conditions. Mostof the empirical formulae were used to fit the I-E data at theconditions of symmetric relative humidity. In the present work,the fitting process will be at asymmetric conditions. Empiricalmodeling is going to be used to demonstrate the effects ofthe symmetric RH, and asymmetric RH (different values ofRHA and RHC) on the performance of the H2/Air PEM fuel cellat different temperatures. Polarization curves are collected atdifferent conditions and the influence of the electro-osmosis andback diffusion may be illustrated with the aid of an empiricalequation under some experimental conditions.

2. Experimental

The experimental details can be found elsewhere31 and arebriefly mentioned here. Nafion 212 membrane and 1.0mg cm¹2

Pt catalyst, 1.0mg cm¹2 Pt­Ru (0.766 Pt and 0.234 Ru) cata-lyst were used in all the experiments. The fuel cell of a JARIStandard type was purchased from NF Co., (Japan) and theMEA was of 25 cm2 area.

In a set of experiments, the RH of the H2 gas (anodecompartment), RHA was kept constant = 0 and the relativehumidity of air (O2) (cathode compartment), RHC was changedfrom 0 to 100%. The reverse was done for air, i.e., keepingair dry and changing the relative humidity of H2 (RHA) from0 to 100%. The above setup may be called asymmetric relativehumidity since the RH at the cathode and anode is different. Inboth cases the polarization curves of the cell were recorded.The gas flow rate was kept constant during the whole courseof measurements, i.e., at 300 cm3min¹1 and 1000 cm3min¹1 forH2 and air, respectively. The gas pressure was kept constantaccordingly at 1.5 and 25.3 kPa for H2 and air, respectively.

The polarization curves were measured by an NF®Fuel CellTest System (MTB-36714, Japan) coupled with a potentiostat.They were recorded using galvanodynamic technique with acurrent scan rate of 0.05Amin¹1. This scan rate was found tobe low enough to obtain stable constant values of potential. Thecurrent was scanned from lower currents (0A) to higher posi-tive values. The maximum current is taken where the cell volt-age goes below a minimum value. This minimum depends onthe operating conditions. The polarization curves were mea-sured with the air electrode as the working electrode and thehydrogen electrode as the reference and counter electrode. Fit-ting of the experimental data was performed using a Polymath5.1 fitting program. The fitting needed guessing values of thefitting parameters (E°, b, R, m and n) with a reasonable numberof iterations.

3. Results and Discussion

The following electrochemical reactions take place in ahydrogen/oxygen fuel;

H2 ! 2Hþ þ 2e ð1Þ

Figure 1. Schematic of the water transport within H2/airPEM fuel cell. 1: Electro-osmotic drag, 2: Back diffusionand 3: Water transport.

1456 | Bull. Chem. Soc. Jpn. 2016, 89, 1455–1461 | doi:10.1246/bcsj.20160259 © 2016 The Chemical Society of Japan

1=2O2 þ 2Hþ þ 2e ! H2O ð2ÞThe reversible (i.e., maximum) standard potential, E° for the

H2/O2 fuel cell reaction is 1.229 volts per mole of hydrogen(at 25 °C, unit activity for the species, liquid water product).Figure 2 shows a schematic representation of the differenttypes of cell potentials (including the reversible cell potential)and polarizations that take place within the cell. As can be seenin Figure 2, the cell potential deviates from the reversible(straight line) value as a result of the current flow. This current-potential curve for a FC is characteristic of specific geometry,catalyst/electrode characteristics, and electrolyte/membraneproperties and also specific operating conditions such as con-centration, flow rate, pressure, temperature, and relative humid-ity. Hence, the I-E curves depend on the kinetic, ohmic, andmass-transfer resistances. Figure 2 shows different types ofpolarizations as given for activation polarization at the cathode(curve 4) and at the anode (curve 6) and also ohmic polar-ization as given in curve 5.

3.1 Simulation of the I-E Curves. Many authors haveintroduced different empirical equations to reproduce the I-Ecurves under different experimental conditions.32­36 Of theseequations, Kim’ equation is going to be used in the presentstudy35 and it is given below:

Ecell ¼ E� � RcellI � B log I � m enI ð3ÞWhere Ecell is the cell potential in mV at any current densityI (mA cm¹2), E° is a fitting parameter corresponding to thereversible cell potential in mV, B is the Tafel slope, mVdec¹1,Rcell is the internal cell resistance (membrane resistance) inohmcm2, m and n are fitting parameters representing the mass-transfer limitations (m in mV and n in cm2/A). In the presentwork we used Kim’s empirical equation due to its simplic-ity. Moreover, it can cover the purpose of the present work.In this section, theoretical simulation of the I-E curves usingeq 3 at different values of the empirical parameters in eq 3.This will help us to understand the impacts of different param-eters on the performance and controlling processes of the cellperformance.

Figure 3 shows theoretical simulation of the I-E curve ofH2/air PEMFC at different values of the Tafel slope, B. Thecurves were calculated using eq 3 and using the followingvalues of the various parameters: E° = 1000mV, Rcell = 0.2ohm cm2, m = 0.004mV and n = 0.008 cm2/A. The B parame-ter is the Tafel slope of the oxygen reduction reaction. Highervalues of B (higher Tafel slopes) mean lower electrochemicalactivity of the catalyst. The figure demonstrates that as Bincreases the cell gives lower performance as indicated by thelower potential at the same current. Note that the role of thecatalyst is to increase the reaction kinetics at the cathodesurface. The activity of the catalyst is related to the electrodesurface composition, temperature, pressure, concentration ofthe reactant. The current (load) at which mass-transfer limita-tions take place is independent of the value of B. That is to saythe B value controls the kinetics of the cathodic electrocatalystand doesn’t have any effect on the mass-transfer limitation ofthe FC as indicated from the figure.

As it was mentioned above, the value of Rcell mainlyexpresses the cell membrane resistance. Figure 4 depictstheoretical I-E curves of the H2/Air PEM FC at differentvalues of Rcell. The curves were calculated using E° = 1000mV, B = 60mV, m = 0.004mV and n = 0.008 cm2/A. It canbe seen that increasing the value of Rcell of the FC gives lowerperformance, i.e., lower potentials at the same cell currents.The Rcell value represents the resistance of the membrane of theFC and an increase of the resistance of the fuel cell supportslower efficiency of the FC. When we throw light upon thethickness of the membrane, we found that there is a directrelation between the thickness and the resistance. An increasein the thickness of the membrane causes an increase in thedistance that the proton (see eq 1) would travel and yet itcauses slower proton transfer due to high membrane resis-tance. Thinner membrane, on the other hand, may cause fueltransport through the membrane (fuel cross-over) which lowersthe fuel efficiency. From the present simulation here, a chosenoptimum thickness of the membrane should be done where theresistance is not too high and in the same time is not permeableto fuel.

I / A cm-2

E cell /

V

1 Total loss

2 3

4

56

Figure 2. Schematic of Fuel Cell Polarization Curve.1: Activation (kinetic) polarization. 2: Ohmic polarization.3: Concentration polarization. 4: Cathode loss. 5: Mem-brane resistance. 6: Anode loss.

Icell / A cm-2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

B = 30 mV

60

90

120

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Ece

ll / V

Figure 3. Effects of the Tafel Slope, B on the I-E curves ofthe H2/air PEM fuel cell. The figure shows only theoreticalcalculations using E° = 1000mV, Rcell = 0.2 ohmcm2,m = 0.004mV and n = 0.008 cm2/mA.

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The parameters m and n are intended to describe the effectsof mass-transport limitations on the I-E curves. Figures 5 and 6show theoretical simulations of the effects of the parametersm and n on the I-E curves, respectively. The two parametersimplement the regions of the concentration polarization (mass-transport loss). As the value of m and/or n increase, the cellperformance supports lower values of cell potential at theregion of high current (mass-transfer-controlled region, seeFigure 2). It can be observed that the I-E curve is more sen-sitive to the value of n rather than the value of m. Hence, theparameter n has more pronounced effect than the parameterm in the mass-transport region. Mass-transfer limitation can becaused by either change in the porosity of the diffusion layer ofthe electrode or by the presence of water droplets or films in thediffusion layer. Using calculations, through the values of m andn parameters, it enabled us to choose the optimum conditions ofporosity, state of the diffusion layer and know whether therewere any water droplet or not (flooding conditions). As can beseen from Figure 5, the parameter m affects both the slope ofthe linear part of the I-E curve and the current at which the I-E

curve deviates from linearity. On the other hand, in Figure 6,the parameter n has major effects on the mass-transfer region,i.e., it determines how fast the current drops with the potential(after the linear region) and hence it determines the apparentlimiting current density. In general the parameter n has moresignificant impact on the region of high current density in theI-E curve than that of the parameter m. In this case it can besuggested that the parameter n is related to the mass-transferaffecting parameters like O2 pressure, temperature, humidity ofthe membrane and water levels in the channel and its transportmechanism. For instance higher values of n may suggest flood-ing conditions (water droplets), low pressure and/or low flowrates of the O2 gas.

3.2 Fitting of the Experimental Data. In this section, I-Ecurves were measured previously by the authors as given inRef. 31 at different RH and different temperatures. The RHwas changed in the symmetric relative humidity where relativehumidity at the cathode (RHC) and at the anode (RHA) hasequal value. Also, I-E curves were measured at the conditionsof asymmetric relative humidity where RHA is set to zero andRHC was changed or vice versa. In all cases, the experimentalI-E curves are fitted with the theoretical I-E curves calcu-lated from eq 3 using different parameters, i.e., E°, Rcell, B,m and n.

3.2.1 Symmetric RH: Figure 7 shows the effects of thesymmetric relative humidity, RH on the I-E curves at differentvalues of RH and at Tcell = 70 °C. Symmetric RH means thatRH is the same at both the cathode and anode compartments.The symbols show the experimental data and the solid linesshow the theoretical results at the same values of RH and Tcell.The theoretical curves were calculated using eq 3 and usingthe fitting parameters listed in Table 1. An RH of 20% cannotsupport any considerable performance of the H2/Air PEM FCat this cell temperature (Tcell = 70 °C). As RH increases to RHof 35%, fair performance is supported. On increasing RH to60%, the Ecell decreases sharply to lower values at I > 0.92A cm¹2. At further high RH (at RH 100%), the Ecell goes downto lower values at I > 0.65A cm¹2. At lower and moderate cellcurrents, however, the cell performance is controlled by kinetic

Icell / A cm-2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Rcell = 0.1 ohm cm2

0.2

0.3

0.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Ece

ll / V

Figure 4. Effects of the internal resistance, Rcell on the I-Ecurves of the H2/air PEM fuel cell. The figure shows onlytheoretical calculations using E° = 1000mV, B = 60mV,m = 0.004mV and n = 0.008 cm2/mA.

Icell / A cm-2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

0.2

0.4

0.6

0.8

1.0

1.2

m = 1x10-4 mV

1x10-2

10 0.3

E cel

l / V

Figure 5. Effects of the m parameter on the I-E curves ofthe H2/air PEM fuel cell. The figure shows only theoreti-cal calculations using: E° = 1000mV, Rcell = 0.2 ohmcm2,B = 60mV and n = 0.008 cm2/mA.

Icell / A cm-2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

n = 4x10-3 cm2 mA

9x10-3

7x10-3

8x10-3

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Ece

ll / V

Figure 6. Effects of the n parameter on the I-E curves ofthe H2/air PEM fuel cell. The figure shows only theoreti-cal calculations using: E° = 1000mV, Rcell = 0.2 ohmcm2,B = 60mV and m = 0.004mV.

1458 | Bull. Chem. Soc. Jpn. 2016, 89, 1455–1461 | doi:10.1246/bcsj.20160259 © 2016 The Chemical Society of Japan

and ohmic effects and hence at RH 60 and 100% support highercurrents than that at RH = 35%. It may be concluded that atlow RH (RH = 20%), the cell suffers from dry-out condi-tions where at high RH (60 and 100%), flooding of the cellcatalyst may cause mass-transfer resistance as seen from thecell current drop in the figure. Figure 8 demonstrates goodagreement between the experimental data and theoreticalresults. Hence, Kim’s equation can be used to predict the I-Ecurves at symmetric RH conditions under the present exper-imental conditions.

One can go through the physical meaning of the used fittingparameters at different RH values in Figure 8. The E° value(reversible cell potential) does not have significant effect onthe morphology of the I-E curves since the used E° values atdifferent RH are comparable. The Tafel slope, B has a highvalue at RH = 20% compared to that used in fitting the cases ofhigher values of RH (i.e., 35, 60 and 100%). This is consistentwith the facile kinetics charge transfer as evident from smallerslope at RH = 100%. For the Rcell fitting value, it is 1.1ohm cm2 at RH of 20%. This is consistent with the poorperformance (much lower Ecell) of the cell at this Rcell. Theother fitting values of Rcell in Table 1 are consistent with themorphology of the I-E curves at RH = 35, 60 and 100% asshown in Figure 7. For the m and n fitting values listed inTable 1, it can be seen that m at RH = 20% is much higher(m = 1.38) compared with the other values of m used at RH =35, 60 and 100%. Since the I-E is not so sensitive to smallchanges in the m value (see Figure 5), it can be concluded thatthe m values at RH = 35, 60 and 100% are almost the same.Hence, the n value will be controlling since small change in then value has more significant effect in the I-E curves as shownin Figures 5 and 6. At RH = 20%, the performance is notcontrolled by mass-transfer limitation but rather by the kineticand ohmic limitations. At RH = 35, 60 and 100%, however, asn increases from RH = 35 to 100%, the value of n increasespointing to more mass-transfer limitation. This is consistentwith the results in Figure 7.

Figure 8 shows the effects of the I-E curves at the samedifferent values of RH used in Figure 8 but at Tcell = 90 °C.The symbols show the experimental data and the solid linesshow the theoretical results using the fitting parameters listed inTable 2. At this higher temperature, it is observed that the cellneeds RH of 60% in order to have reasonable performance ofthe FC and the cell lost its performance at lower RH (20 and35%) compared to the results in Figure 8 at Tcell = 70 °C. Inthis case at RH 60%, the cell supports high Ecell even at highcell current (load) and it suffers from mass-transfer limitationsonly at RH = 100%. At high RH, one can note that high tem-perature (Tcell = 90 °C) supports high-charge-transfer kineticsand lower ohmic resistance as evident from the obtained higherEcell at low and moderate cell currents compared to Tcell =70 °C at the same RH. Also at this high cell temperature, thetheoretical data are consistent with the experimental findings. Ifwe consider the fitting parameters in Table 2 and its trend wemay conclude the following. The B values at RH = 20% areless than at Tcell = 70 °C (see Table 1) at the same RH. Theother values of B in Table 2 at RH = 35, 60 and 100% arecomparable with the corresponding values in Table 1. The Rcell

Icell / A cm-2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.2

0.4

0.6

0.8

1.0

1.2

RH 100% 60% 35%

20%

Ece

ll / V

Figure 7. I-E curves of the H2/air PEM fuel cell at differentRH at 70 °C. Symbols show the experimental data andsolid lines show the theoretical calculations. The fittingparameters are listed in Table 1.

Table 1. Fitting parameters used in the theoretical calcu-lations of I-E curves in Figure 7

RH/% 20 35 60 100

E°/mV 915 913 923 958B/mVdec¹1 90 54 41 45Rcell/ohmcm2 1.1 0.26 0.14 0.05m/mV 1.4 1.2 © 10¹4 9.0 © 10¹5 7.1 © 10¹5

n/cm2mA¹1 0.014 0.011 0.015 0.020R2 0.99 0.98 0.98 0.99

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Icell / A cm-2

RH =100%

60%

35%20%

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Ece

ll / V

Figure 8. I-E curves of the H2/air PEM fuel cell at differentRH at 90 °C. Symbols show the experimental data andsolid lines show the theoretical calculations. The fittingparameters are listed in Table 2.

Table 2. Fitting parameters used in the theoretical calcu-lations of I-E curves in Figure 8

RH/% 20 35 60 100

E°/mV 922 911 904 912B/mVdec¹1 74 57 47 42Rcell/ohm cm2 1.1 0.95 0.29 0.18m/mV 13 0.07 5.4 © 10¹5 5.7 © 10¹4

n/cm2mA¹1 0.1 2.3 © 10¹4 0.01 0.012R2 0.98 0.98 0.99 0.99

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value in Table 2 decreases as RH increases pointing to the wet-ting ability to the Nafion membrane at higher RH. However, thevalues of Rcell in Table 2 (T = 90 °C) are slightly higher thanthat on Table 1 (T = 70 °C) pointing to the trade-off betweenthe dry-out effects and higher membrane conductivity at hightemperature. The m and n values can be compared only atRH = 60 and 100% since the cell performance is mass-transfercontrolled. The m and n values at RH = 100% are higher thanat RH = 60% pointing to more mass-transfer resistance due tohigher humidity and flooding case.

3.2.2 Asymmetric RH: In this section, the effects of asym-metric relative humidity on the I-E curves are explored. Thiswas done by fixing the relative humidity at the anode at zerovalue (RHA = 0, dry conditions) and changing that of thecathode, RHC. Figure 9 depicts I-E relations at different RHCand RHA is set to zero at T = 70 °C. The symbols show theexperimental data and the solid lines show the theoreticalresults. The theoretical results were calculated using eq 3 andthe fitting parameters listed in Table At RHC = 20%, the celllost its performance completely and it is observed that theperformance is much worse than that at symmetric RH at thesame value (20%). The cell sustains its ordinary performance(as in case of symmetric RH) only at RHC of 35, 60 and 100%.At this high RHC and dry conditions of the anode (RHA = 0),the prevailing mechanism is the back diffusion of water mole-cules due to higher pressure and higher flow rate at the cathodecompared to that at the anode. This diffusion can supportreasonable wetting of the membrane and yet reasonable internalresistance and hence support high performance as that sup-ported at the same values of symmetric relative humidity (seeFigure 8). The theoretical curves in Figure 10 show an agree-ment with the experimental data.

Figure 10 shows the I-E curves at fixed RHC = 0 anddifferent RHA (asymmetric RH) at T = 70 °C. The experi-mental data are shown in symbols whereas the theoreticalcalculations are shown in solid lines. The cell performanceis lost if RHC is kept at 0% (dry cathode) and the anodecompartment is humidified at values of RHA between 20 and

100%. Only at RHA = 100%, the cell can sustain moderateperformance at this condition of dry cathode compartment. Themechanism of electro-osmotic drag of water from the anodeto the cathode is important only when the anode compartmenthumidity, RHA equals 100% at the present temperature. Thetheoretical curves show reasonable agreement with the exper-imental I-E curves.

Note that this is the first report on fitting the I-E curvesof H2/air PEM fuel cell with an empirical formula with thecell operating under asymmetric conditions. The impacts ofthe fitting parameters used in the different figures are givenhere. For instance, Table 3 lists the fitting parameters used infitting the I-E curves in Figure 9. The fitting parameters mayhave the following meanings. The B and Rcell values at RHC =20% are much higher compared to those at higher RHC(RHC = 35, 60 and 100%). This indicates that the kineticsand ohmic resistances at RHC = 20% are controlling factorsfor the cell behavior. The value of Rcell at RH = 35, 60 and100% are comparable. It seems that the back diffusion of waterto the anode site at much higher rates at high RHC (100%) maysupport reasonable wetting and hence conductivity to the cellmembrane. In Figure 10, Table 4 shows that Rcell decreaseswith the value of RH. This may indicate that only at RHA =100% that can support reasonable membrane resistance viaelectro-osmotic mechanism but at the lower RHA (20, 35 and60%) cannot support such wetting of the membrane. The values

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.2

0.4

0.6

0.8

1.0

1.2

RHC=100%

60%

35%

20%

Icell / A cm-2

E cel

l / V

Figure 9. I-E curves of the H2/air PEM fuel cell at differentRHC (asymmetric conditions) and RHA = 0 at 70 °C.Symbols show the experimental data and solid lines showthe theoretical calculations. The fitting parameters arelisted in Table 3.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Icell / A cm-2

RHA=100%

35%

20%60%

Ece

ll / V

Figure 10. I-E curves of the H2/air PEM fuel cell atdifferent RHA (asymmetric conditions) and RHC = 0 at70 °C. Symbols show the experimental data and solid linesshow the theoretical calculations. The fitting parametersare listed in Table 4.

Table 3. Fitting parameters used in the theoretical calcu-lations of I-E curves in Figure 9

RHC/% 20 35 60 100

E°/mV 916 914 918 968B/mVdec¹1 150 53 53 42Rcell/ohm cm2 8.2 0.50 0.98 0.16m/mV 1.1 1.3 © 10¹4 1.2 © 10¹4 3.3 © 10¹4

n/cm2mA¹1 0.15 0.011 0.014 0.018R2 0.99 0.95 0.99 0.99

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of m and n, on the other hand, are meaningless since the cell atthese values of RH is not mass-transfer controlled.

4. Conclusion

Empirical modeling has been used to simulate and reproduceexperimental I-E data of a H2/air PEM fuel cell operating atsymmetric and asymmetric conditions. The model has beentested theoretically for the significance of the fitting parametersthat represent kinetic, ohmic and mass-transfer resistance on thecell performance. Possible reasonable performance of the cellcan be achieved at symmetric relative humidity of >27% and athigher relative humidity at the cathode (RHC > 35%, RHA =0) can support rehydration of the anode side of the Nafionmembrane through back diffusion of water from the cathode tothe anode compartment. Fitting of the experimental I-E curveswith the empirical equation (Kim’s equation) shows goodagreement with using of the fitting parameters.

This work was financially supported by the Ministry ofEducation, Culture, Sports, Science and Technology, Japan andalso by New Energy and Industrial Technology DevelopmentOrganization (NEDO), Japan.

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Table 4. Fitting parameters used in the theoretical calcu-lations of I-E curves in Figure 10

RHA/% 20 35 60 100

E°/mV 911 914 907 902B/mVdec¹1 75 45 51 55Rcell/ohmcm2 18 2.0 1.6 0.014m/mV 1.6 5.2 © 10¹3 1.0 9.6 © 10¹8

n/cm2mA¹1 0.26 0.052 7.6 © 10¹6 0.016R2 0.99 0.99 0.95 0.94

Bull. Chem. Soc. Jpn. 2016, 89, 1455–1461 | doi:10.1246/bcsj.20160259 © 2016 The Chemical Society of Japan | 1461