Degradation of proton exchange membrane fuel cells due to CO and CO(2) poisoning

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Contents lists available atScienceDirect

Journal of Power Sources

j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / j p o w s o u r

Degradation of proton exchange membrane fuel cells due to CO and CO

2

poisoning

Wei-Mon Yan

a,∗

_{, Hsin-Sen Chu}

b

_{, Meng-Xi Lu}

b

_{, Fang-Bor Weng}

c

_{, Guo-Bin Jung}

c

_{, Chi-Yuan Lee}

c

a_{Department of Mechatronic Engineering, Huafan University, Taipei 223, Taiwan}

b_{Department of Mechanical Engineering, National Chiao Tung University, Hsin-Chu 300, Taiwan} c_{Department of Mechanical Engineering, Fuel Cell Center, Yuan Ze University, NeiLi, Taoyuan 320, Taiwan}

a r t i c l e i n f o

Article history:

Received 22 October 2008 Received in revised form 24 November 2008 Accepted 24 November 2008 Available online 6 December 2008

Keywords:

PEM fuel cell CO poisoning CO2poisoning

Degradation of cell performance

a b s t r a c t

The CO and CO2 poisoning effects on the degradation of cell performance of proton exchange

mem-brane fuel cell (PEMFC) under transient stage were investigated. The mechanism of CO poisoning lies in the preferential adsorbing of CO to the platinum surface and the blocking of active sites of hydrogen. These phenomena were described with adsorption, desorption, and electro-oxidation processes of CO and hydrogen in the present work. In addition, it is well known that the reverse water gas shift reaction (RWGS) is the main effect of the CO2poisoning, through which a large part of the catalytic surface area

becomes inactive due to the hydrogen dissociation. The predicted results showed that, by contaminating the fuel with 10 ppm CO at the condition of PH= 0.8 atm and PCO2= 0.2 atm, the current density of the PEM fuel cell was lowered 28% with rate constant of RWGS krsfrom zero to 0.02. With 50 ppm CO, the

performance drop was only 18%. For the reformed gas, CO2poisoning became much more signiﬁcantly

when the CO content in the reactant gas was small.

1. Introduction

Nowadays, hydrogen production from fossil fuel is one of present common ways, and is usually realized through such methods as steam reforming, partial oxidation and autothermal reform-ing. However, gas produced from reformer contains about 70–75% hydrogen, 20–25% carbon dioxide and also 10–100 ppm carbon monoxide. Fuel cell performance would be attenuated if the carbon monoxide concentration reaches to 5–10 ppm [1,2]. The mecha-nism of CO poisoning lies in the preferential adsorbing of CO to the platinum surface and the blocking of active sites of hydrogen [3]. Platinum is still the best catalyst layer for PEM fuel cell, however the operating temperature is about 60–100◦C in which the carbon monoxide absorption on the platinum catalyst layer would cause attenuation of the fuel cell performance. To improve CO tolerance of fuel cells, alloys are ordinary catalytic medium while Pt–Ru alloys are the most common catalytic medium for PEMFC as commercial fuel cells since Pt–Ru has better CO tolerance.

Gastiger et al.[4]concluded that the best mixing ratio of the Pt–Ru alloys is 1:1. Yu et al.[5]experimentally studied the struc-ture of the Pt–Ru alloys. They used the inner and outer catalyst layers to make a complete catalyst layer. The experimental results showed that this composite structure provides a higher CO toler-ance than traditional catalyst layer of the Pt–Ru alloys. Santiago et

∗ Corresponding author. Tel.: +886 2 2663 2102; fax: +886 2 2663 1119.

E-mail address:[email protected](W.-M. Yan).

al.[6]dispersed Ru onto the diffusion layer and having CO oxidized to CO2 before reaching catalyst layer. However the application of noble metal resulted in the increase in the cost. Therefore, part of researchers focused on how to resume the fuel cell performance after being poisoned by CO. Commonly aimed at CO oxidation, there are three methods as follows: oxidant-bleeding[7–11], self-oxidation[1,12]and current-pulsing[12–14].

Springer et al. [15] developed a CO poisoning model and described the effects of catalyst layer adsorption, desorption and electrochemical reaction when anode feed stream consisted of H2 and CO. The surface area of the catalyst layer differed with time due to the cover of H2and CO, consequently influenced the cell perfor-mance. In 2003, Chan et al.[16]proposed a mathematical model of polymer electrolyte fuel cell with different CO concentration, gas concentration cover ratio in steady state. Bhatia and Wang[17] extended Springer’s model[15]and investigated influence of CO on fuel cell performance. In their model, Bhatia and Wang neglected the current density produced by CO as well as the thickness effect of catalyst layer. Liu and Zhou[18]employed CFD software to inves-tigate the influence of CO poisoning on the cell performance of the PEM fuel. Chu and his co-workers[19]developed both single and two-phase flow model to analyze the transient CO poisoning pro-cess of the PEM fuel cell. Wang et al.[20]further investigated the CO poisoning effect on the high temperature PBI membrane fuel cell.

Bruijn et al.[21]further discussed the inﬂuence of CO2poisoning on cell performance and the results showed that the Pt–Ru alloys as catalyst layer had a better CO2tolerance when the temperature

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Nomenclature

a surface area per unit catalyst layer volume

(cm2_cm−3₎

Bi Tafel slope of species i (V)

bi,ads desorption rate constant of species i (atm) Ci concentration of species i (mol cm−3) Di diffusion coefﬁcient of species i (cm2s−1) EH activation energy of hydrogen (J mol−1)

F Faraday constant (C mol−1)

GCO Gibbs free energy of carbon monoxide (J mol−1)

i current density (A cm−2)

I operating current density (A cm−2)

ki,ads adsorption rate constant of species i (A cm−2atm−1) ki,ox electrochemistry reaction rate constant of species i

(A cm−2)

krs rate constant of reverse water gas shift reaction (A cm−2atm−1)

ni electron number of species i

P pressure (atm)

R universal gas constant (J mol−1K−1)

r interaction parameter of carbon monoxide (J mol−1) si stoichiometric number of species i

T temperature (K)

t time (s)

V0 open loop voltage (V)

V voltage (V)

X mole fraction

z axial coordinate (␮m)

Greek letters

˛ transport coefﬁcient

ˇ symmetry factor of CO adsorption

ε porosity

product of the catalyst layer surface density and Faraday constant (C cm−2)

inﬂuence area per unit CO

i fraction of the catalytic surface area covered by species i

voltage (V)

overvoltage (V)

proton transport coefﬁcient (m cm−1) electron transport coefﬁcient (m cm−1) Superscripts

0 initial value

c catalyst layer

in catalyst layer inlet Subscripts 0 initial value a anode c cathode i H2or CO ss steady state

was increased. Since then, Janssen[22]added CO2poisoning model into the CO poisoning model and assumed that the reverse water gas shift reaction (RWGS) is the reason of the CO2poisoning effects. The results showed that CO2poisoning would have the signiﬁcant effect when the CO content is small and at relatively low operating current density. At high operating current density, CO would be the dominating poisoning gas. Dhar et al.[23]developed a series of empirical correlations to determine the CO coverage in fuel cell

Fig. 1. Schematic diagram of the physical model.

and mainly investigated the inﬂuence of CO poisoning on phosphate fuel cell performance at various temperature as well as various CO concentrations. They found that CO coverage would have a liner relationship with ln[CO]/[H2] at various temperature. Batisa et al. [24]applied water gas shift reactor and methanation reactor to slow down CO poisoning and both these two reactors had a signiﬁcant relationship with CO2.

According to previous research, although there are studies on CO or CO2poisoning of fuel cell, still lack of investigation on combined CO and CO2poisoning on the degradation of cell performance of PEM fuel cell at transient time. This motivates the present study. In this work, both CO and CO2poisoning were combined to examine the transient degradation of cell performance and the signiﬁcance of CO2poisoning.

2. Analysis

The physical model of this work is shown schematically inFig. 1. The purpose of this study is to investigate the unsteady behaviors of hydrogen concentration, carbon monoxide concentration, plat-inum surface coverage and the current density distributions after anode catalyst layer of PEM fuel cell being poisoned by CO and CO2. Due to the main inﬂuence area of CO poisoning being on the anode catalyst layer, therefore, the examined domain is ﬁxed on anode cat-alyst layer. Origin is set on the interface between anode gas diffusion layer and anode catalyst layer (z = 0). Since catalyst layer thickness is far less than the catalyst layer length (width), so it could be con-sidered as one-dimensional system. To simplify the analysis, the following assumptions are made:

1. The system is one-dimensional Cartesian coordinate system. 2. The species are ideal gas.

3. The catalyst layer is porous medium with uniform porosity. 4. Only diffusion transport is considered in the catalyst layer. 5. Anode overvoltage is assumed to be constant.

With the above assumptions, the governing equations are described as follows: H2: εc∂ CH2 ∂t = εcDH2 ∂2_C H2 ∂z2 − diH2 dz

sH2 nH2F

(1)

(3)

CO : εc∂ CCO ∂t = εcDCO ∂2_C CO ∂z2 − diCO dz

_s CO nCOF

(2) where the ﬁrst term in both Eq.(1)or Eq.(2)stands for the con-centration variation with time in control volume, while the second term means the concentration variation rate due to diffusion and the third term is concentration consumption rate caused by elec-trochemical reaction.

If hydrogen, carbon monoxide and carbon dioxide exist on anode catalyst layer at the same time, adsorption, desorption and elec-trochemical reaction would happen between H2/CO and platinum surface of catalyst layer which consequently affect the coverage of H2/CO on platinum surface. Meanwhile, CO2 would start reverse water gas shift reaction and cause the adsorbed H2desorbed from the platinum catalyst layer. All these electrochemical reaction rates depend on each reaction rate constant and the coverage governing equations are as follows:

dH dt = kH,adsXH2P

1− H− CO

− bH,adskH,adsH −krsXCO2P 2 H− 2kH,oxHsinh

a BH2

(3) dCO dt = kCO,adsXCOP

1− H− CO

exp

−ˇrCO RT

−bCO,adskCO,adsCO exp

−

1− ˇ

rCO RT

+krsXCO2P 2 H− 2kCO,oxCO sinh

a BCO

(4) The term of the left side in Eq.(3)or Eq.(4)stands for rate of cov-erage, for the right side, the ﬁrst term means for the increased rate of absorbed H2/CO, the second term is decreased rate of desorbed H2/CO, the third term means the rate of desorbed H2caused by RWGS, and the fourth term means consumption rate caused by elec-trochemical reaction. The correction made by Li and Baschuk[10] was adopted for the ﬁrst and second terms of right side in Eq.(4).

In addition, Springer et al.[15]found that H2 adsorption rate constant and CO desorption rate constant had a relationship with the CO coverage on catalyst surface, the relationship are given by [15]:

kH,ads= kH0,ads exp

−ı (EH) RT

1− exp

CO CO− 1

(5)

bCO,ads= bCO0,ads exp

ı (GCO)

RT CO

(6) Due to the CO poisoning effect, H2and CO molecules exist on the catalyst layer surface, therefore, the generated current density caused by electrochemical reaction are mainly produced by H2and CO. Therefore, the standard Bulter–Volmer equation must be cor-rected on platinum surface coverage, and the modiﬁed equation is given as di dz = diH2 dz + diCO

dz = 2akH,oxH sinh

nH2a BH2

+4akCO,oxCO sinh

_n

COa BCO

(7) where the parameter, a, stands for the surface area per unit catalyst layer, while the ﬁrst term in right side stands for the generated cur-rent density from H2-electrochemical oxidation, the second term is the generated current density from CO-electrochemical oxidation.

Table 1

Values of the basic parameters used in this work.

Parameter Value T, temperature (K) 353 P, pressure (atm) 3 ˛, transfer coefficient 0.5 DH2, diffusion coefficient of H2(cm 2_s−1₎ _{2.59× 10}−6 DCO, diffusion coefficient of CO (cm2s−1) 5.4× 10−7

BH2, Tafel slope of H2electro-oxidation reaction (V) 0.032[13] BCO, Tafel slope of CO electro-oxidation reaction (V) 0.06[13]

ˇ, symmetry factor of CO adsorption 0.1[8]

r, interaction parameter of CO (J mol−1) 39.7[8]

kH2O,ads, adsorption rate constant of H2(A cm−2atm−1) 100

bH2,ads, desorption rate constant of H2(atm) 0.5[15]

kH2,ox, electrochemistry reaction rate constant of H2(A cm−2) 4[15] kCO,ads, adsorption rate constant of CO (A cm−2atm−1) 10[15] bCO0,ads, desorption rate constant of CO (atm) 1.51× 10−9 kCO,ox, electrochemistry reaction rate constant of CO (A cm−2) 1× 10−8[13] krs, rate constant for reverse water gas shift reaction (A cm−2atm−1) 0.02[18]

In this work, to simplify the analysis, the PEM fuel cell was assumed to initially keep in a non-operating state. This means that when t = 0, there is no reactant gas in the fuel cell and when t > 0, the reactant gas starts to ﬂow into the fuel cell. Therefore, the initial conditions are given by

CH2(z, 0) = C 0 H2(z, 0) (8) CCO(z, 0) = CCO0 (z, 0) (9) H(z, 0) = H0 (10) CO(z, 0) = H0 (11)

For the concentration boundary conditions, ﬁxed values of species at z = 0 were assumed:

z = 0 : CH2= CHin2, CCO= C

in

CO (12)

while at the interface between catalyst layer and membrane (z = Lc), due to the gas blocking effect of membrane, concentration ﬂuxes of species were set to be zero:

z = Lc: DH2 ∂CH2

∂z = 0, DCO ∂CCO

∂z = 0 (13)

For the condition of current density, the current density at z = 0 is assumed to be zero:

z = 0 : i = 0 (14)

3. Solution method

According to the assumptions, the governing equations, bound-ary conditions and initial conditions discussed in the previous sections, coupling with the parameters in Table 1, are non-linear and are difﬁcult to get the analytical solution. In this work, the control volume ﬁnite difference method is adopted to solve the non-linear, coupled ordinary differential equations. The detailed solution scheme is available in Ref.[25]. In addition, the Crank–Nicolson and Runge–Kutta methods are employed to solve for the concentration equations and the coverage equation of the catalyst layer, respectively.

To check the grid independence, solutions on various grid sys-tems are examined. It is found in the separate numerical runs that there is not any difference among the solutions with three grid arrangements: 500, 1000 and 2000 points. In order to save the calculating time, 500 grids are adopted for the present problem. Additionally, it is important to compare the predicted results with existing experimental data. It is apparent that the present predic-tions agree well with those of Oetjen et al.[26]. Through these

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Fig. 2. The transient evolution of H2distribution across the catalyst layer with

100 ppm CO.

Fig. 3. The transient evolution of CO distribution across the catalyst layer with 100 ppm CO.

preliminary tests, it is found that the numerical method is suitable for the present study.

4. Results and discussion

When the PEM fuel cell starts up, the cell performance would decay if the reactant gas contains a certain amount of CO. With the concentration of 100 ppm CO in the hydrogen of anode fuel, the coverage of the platinum will be changed. This is because the CO is easier to combine with the platinum to form a steady bond, which is difﬁcult to electrolyze to generate the current. The surface of platinum would be covered by the accumulating CO, leading to the decreasing of current density generated by the hydrogen. As indicated inFigs. 2 and 3, CO would struggle for the catalyst by com-peting with hydrogen as soon as it contacts with the catalyst layer. The quantity of CO adhering on the platinum surface lies on the diffusion velocity and the concentration when it goes through the catalyst layer. In addition, the consuming rate of hydrogen would be slowed with the decreasing reaction area between hydrogen and catalyst layer. The excessive hydrogen would diffuse to the bound-ary between the catalyst layer and the membrane, looking for a reactivity region. By contraries, CO is absorbed by the platinum sur-face and does not participate. Therefore, the consuming rate of CO

Fig. 4. The transient evolution of current density distribution across the catalyst layer induced by H2with 100 ppm CO.

Fig. 5. The transient evolution of current density distribution across the catalyst layer induced by CO with 100 ppm CO.

is very limited, leading to the accumulation of CO on the catalyst layer, as shown inFig. 3.

Figs. 4 and 5present the transient evolution of current den-sity distributions across the catalyst layer induced by H2and CO with 100 ppm CO, respectively. A close examination ofFigs. 4 and 5 reveals that the generated current density from CO-electrochemical oxidation could be neglected as compared to that from H-electrochemical oxidation. Therefore, the fuel cell current density was mainly produced from H2 electrochemical reaction and cur-rent density generated from CO-electrochemical reaction would be neglected in later discussion. In other words, once H2/Pt reaction surface area decreased, the fuel cell current density would decrease. Coverage is an important parameter for investigating the effect of CO poisoning on cell performance of PEM fuel cell. It is clearly seen inFig. 4that when PEM fuel cell is being poisoned by 100 ppm CO, the consequent current density dropped from 1.497 A cm−2to 0.393 A cm−2, dropping about 73.76%. In addition, time required for reaching steady state was prolonged from 1 s to 529 s for compet-ing platinum surface. In the CO poisoncompet-ing process, time required for reaching steady state would be affected by the change of cover-age which mainly depends on CO concentration and diffusion rate on catalyst surface. Since the diffusion rate of CO is relatively slow, much more time would be needed to reach catalyst layer surface. However, once contacted onto catalyst layer, CO would have a

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sta-Fig. 6. The steady-state current density distribution across the catalyst layer induced by H2with various CO2concentrations.

ble connection with platinum and then gradually accumulated on the platinum surface.

Above investigation just focused on the effect of CO poison-ing on cell performance, further discussion will examine the effect of CO2 poisoning on the characteristics of PEM fuel cell through reverse water gas shift reaction. For various CO2concentrations, Fig. 6shows steady-state current density distributions after PEM fuel cell being poisoned by CO2 for the condition of 0 ppm CO concentration. With increasing CO2concentration, poisoning effect was getting serious. When CO2concentration was 10% or 40%, the current density would drop 24.69% or 54.6%.

Fig. 7 presents the steady-state current density distributions across the catalyst layer induced by H2with various gas combina-tions of reactant gases. When CO concentration is 0 ppm and rate constant of reverse water gas shift reaction krsis zero (krs= 0), the existence of CO2only has a dilution effect on fuel gas. However, for the case of krs= 0.02, besides the dilution effect, the CO2also has poisoning effect which made the cell performance dropped from 1.21 A cm−2to 0.835 A cm−2, about 31% decrease. Therefore, the CO2 poisoning will be affected by the rate constant of reverse water gas shift reaction krs.

Fig. 8 shows that the transient evolutions of the H2 cover-age, CO coverage and current density in catalyst layer when the CO concentration and krs were 20 ppm and 0.02, respectively. A

Fig. 7. The steady-state current density distribution across the catalyst layer induced by H2with various gas combinations of reacting gases.

Fig. 8. Transient evolutions of (a) H2coverage proﬁle, (b) CO coverage proﬁle, and

(c) current density distribution induced by H2under the conditions of PH= 0.75 atm,

PCO2= 0.25 atm, and 20 ppm CO.

close examination ofFig. 8discloses that at the initial transient (t < 1 s), the current density was not affected by poisoning and the maximum H2 coverage was 0.8. As poisoning time elapsed, the accumulated CO coverage was getting more and more. The CO2 poi-soning effect caused H2coverage decreased with time and it spends about 494 s to reach the steady state. Meanwhile, H2coverage was

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Fig. 9. Steady-state distributions of (a) H2coverage proﬁle, (b) CO coverage proﬁle,

and (c) current density distribution induced by H2at PH= 0.8 atm and PCO2= 0.2 atm

with various CO concentrations.

only 0.12 and the current density had lowered from 1.217 A cm−2to 0.537 A cm−2, about 55.88% decrease. As shown inFig. 8(b), when PEM fuel cell reached the steady state, the CO coverage got max-imum value on catalyst layer surface (z = 0) and decreased with increasing position z.

The CO2poisoning effect on the PEM fuel cell depends on the rate constant of RWGS reaction krs. When krsis zero, the CO2poisoning effect can be neglected, otherwise the CO2poisoning effect should be considered.Fig. 9presents the inﬂuence of rate constant of RWGS reaction krson the steady-state distributions of the H2coverage, the CO coverage and the current density caused by H2in catalyst layer for various CO concentrations. An overall inspection inFig. 9reveals that for the conditions of the low CO concentration (10 ppm) with

Fig. 10. Comparison of predicted current density loss with experimental data[26]

under various CO concentrations.

CO2poisoning effects, the H2coverage decreased from 0.81 to 0.33 and the current density dropped from 1.262 A cm−2to 0.908 A cm−2. Nevertheless, for high CO concentration conditions, CO2poisoning has a little effect on H2coverage and current density of fuel cell. This is due to the fact that the platinum catalyst layer surface would be occupied by CO for high CO concentration condition, therefore, there are not enough Pt–H for CO2 to conduct reverse water gas shift reaction.

Fig. 10 shows the comparisons between present simulated results and the experimental data[26]. In this plot, only CO poi-soning was considered. The comparison shows a good agreement under various CO concentrations. At 50 ppm CO, the current density drops almost 58%. While CO concentration increases up to 100 ppm, more than 73% of performance loss is found from both prediction and experiment.

5. Conclusion

The present work mainly focuses on degradation of cell per-formance of PEM fuel cell at transient time due to CO and CO2 poisoning. According to the predicted results, the following con-clusions can be made:

1. The results showed that the higher CO concentration, the greater drop of cell performance.

2. When CO concentration is 0 ppm and CO2 pressure is 10% and 40%, the cell performance decreases 24.69% and 54.6%, respec-tively.

3. The CO2poisoning became much more signiﬁcantly when the CO content in the reactant gas was small.

4. At low current density conditions, CO2poisoning becomes much more signiﬁcant. The effect of RWGS reaction reduces as current density increases.

Acknowledgement

The authors would like to acknowledge the ﬁnancial support of this work by the National Science Council, R.O.C. through the contract NSC97-2212-E-211-001.

References

[1] J. Zhang, R. Datta, J. Electrochem. Soc. 149 (2002) A1423–A1431.

[2] J. Divisek, H.F. Oetjen, V. Peinecke, V. Schmidt, U. Stimming, Electrochim. Acta 43 (1998) 3811–3815.

(7)

[4] H.A. Gastiger, N. Markovic, P.N. Ross, E.J. Cairns, J. Phys. Chem. 98 (1994) 617–625.

[5] H.M. Yu, Z.J. Hou, B.L. Yi, Z.Y. Lin, J. Power Sources 105 (2002) 52–57. [6] E.I. Santiago, V.A. Paganin, M.D. Carmo, E.R. Gonzalez, E.A. Ticianelli, J.

Elec-troanal. Chem. 575 (2005) 53–60.

[7] R.J. Bellows, E. Marucchi-Soos, R.P. Reynolds, Electrochem. Solid-State Lett. 1 (1998) 69–70.

[8] V.M. Schmidt, J.L. Rodriguez, E. Pastor, J. Electrochem. Soc. 148 (2001) A293–A298.

[9] G. Lorenz, G.G. Scherer, A. Wokaun, Phys. Chem. 3 (2001) 325–329. [10] X. Li, J.J. Baschuk, Int. J. Energy Res. 27 (2003) 1095–1116.

[11] P.A. Adcock, S.V. Pacheco, K.M. Norman, F.A. Uribe, J. Electrochem. Soc. 152 (2005) A459–A466.

[12] A.H. Thomason, T.R. Lalk, A.J. Appleby, J. Power Sources 135 (2004) 204–211. [13] L.P.L. Carrete, K.A. Friedrich, M. Hubel, U. Stimming, Phys. Chem. 3 (2001)

320–324.

[14] W.A. Adams, J. Blair, K.R. Bullock, C.L. Gardner, J. Power Sources 145 (2005) 55–61.

[15] T.E. Springer, T. Rockward, T.A. Zawodzinski, S. Gottesfeld, J. Electrochem. Soc. 148 (2001) A11–A23.

[16] S.H. Chan, S.K. Goh, S.P. Jiang, Electrochim. Acta 48 (2003) 1905–1919. [17] K.K. Bhatia, C.Y. Wang, Electrochim. Acta 49 (2004) 2333–2341. [18] H.T. Liu, T. Zhou, J. Power Sources 138 (2004) 101–110. [19] C.P. Wang, H.S. Chu, J. Power Sources 159 (2006) 1025–1033.

[20] C.P. Wang, H.S. Chu, Y.Y. Yan, K.L. Hsueh, J. Power Sources 170 (2007) 235– 241.

[21] F.A. Bruijn, D.C. Papageorgopoulos, E.F. Sitters, G.J.M. Janssen, J. Power Sources 110 (2002) 117–124.

[22] G.J.M. Janssen, J. Power Sources 136 (2004) 45–54.

[23] H. Dhar, L. Christner, A. Kush, J. Electrochem. Soc. 134 (1987) 3021–3026. [24] M.S. Batista, E.I. Santiago, E.M. Assaf, E.A. Ticianelli, J. Power Sources 145 (2005)

50–54.

[25] S.L. Lee, Int. J. Heat Mass Transfer 32 (1989) 2065–2073.

[26] H.F. Oetjen, V.M. Schmit, U. Stimming, F. Trila, J. Electrochem. Soc. 143 (1996) 3838–3842.