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peroxide fuel cell
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Advanced mathematical model for the passive direct borohydride/peroxide fuel cell Ays‚e Elif Sanli a,*, Mehmet Levent Aksu b, Bekir Zu¨htu¨ Uysal a a b
Gazi University, Faculty of Engineering, Department of Chemistry, Ankara, Turkey Gazi University, Faculty of Education, Department of Chemistry, Ankara, Turkey
article info
abstract
Article history:
In the literature a mathematical model has been developed for the direct borohydride fuel
Received 18 January 2011
cells by Verma et al. [1]. This model simply simulates the fuel cell system via kinetic
Received in revised form
mechanisms of the borohydride and oxygen. Their mathematical expression contains the
21 March 2011
activation losses caused by the oxidation of the borohydride and the concentration over-
Accepted 24 March 2011
potential increased by the reduction of oxygen. In this study a direct borohydride/peroxide
Available online 7 May 2011
fuel cell has been constructed using hydrogen peroxide (H2O2) as oxidant instead of the oxygen. Therefore we created an advanced model for peroxide fuel cells, including the
Keywords:
activation overpotential of the peroxide. The goal of our model is to provide the informa-
Fuel cell
tion about the peroxide reduction effect on the cell performance. Our comprehensive
Borohydride
mathematical model has been developed by taking Verma’s model into account. KH2 O2 used
Hydrogen peroxide
in the advanced model was calculated as 6.72 104 mol cm2 s1 by the cyclic voltam-
Mathematical model
mogram of Pt electrode in the acidic peroxide solution. Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Fuel cells promise to replace batteries for portable devices due to their potentially higher energy and nearly zero recharge time. The hydrogen proton exchange membrane fuel cells (PEMFC), and the liquid-feed types direct methanol fuel cells (DMFC) as well as the direct borohydride fuel cells (DBFC) are considered as three potential types of fuel cells for such applications. Compared to the hydrogen PEMFC, the liquidfeed type fuel cells has further advantages of easier fuel delivery and storage, no cooling or humidification need, and simpler design. The DBFC is a quite novel fuel cell that is based upon the borohydride oxidation on the anode and oxygen reduction on
the cathode [2,3]. The anode, cathode and cell reactions are as follow: Anode : BH 4 þ 8OH /BO2 þ 6H2 O þ 8e
E0anode ¼ 1:24 Vðvs SHEÞ
(1)
Cathode : 2O2 þ 4H2 O þ 8e /8OH E0cathode ¼ 0:40 Vðvs SHEÞ
(2)
Cell reaction : BH 4 þ 2O2 /BO2 þ 2H2 O
E0cell ¼ 1:64 Vðvs SHEÞ
* Corresponding author. Tel.: þ90 (555)9650121; fax: þ90 (312)2238693. E-mail address: [email protected] (A.E. Sanli). 0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.03.141
(3)
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Subscripts a anode act activation B bulk borohydride BH4 c cathode conc concentration hydrogen peroxide H2O2 ohm ohmic sodium hydroxide OH p peak r reversible S surface 1 cell.1 2 cell.2
Nomenclature a A C E Ecell F i i0 iL K n h Rohm R T
transfer coefficient electrode surface area, cm2 concentration, mol/l potential, V cell potential, V Faraday constant current density, mA cm2 exchange current density, mA cm2 limiting current density, mA cm2 reaction rate constant, mol cm2 s1 electron number transferred overpotential, V ohmic resistance, ohmcm2 ideal gas constant, J/molK temperature, K
It is an alkaline type of fuel cell because the borohydride ions are not chemically stable in the acidic media [4]. The DBFC, thermodynamically and energetically, can be compared to PEMFC and DMFC. The cell potential of the DBFC is higher than those of the PEMFC (1.23 V) and DMFC (1.21 V). The theoretical conversion efficiency of the DBFC (0.91) is similar to that of the DMFC (0.91) but it is higher than that of the PEMFC (0.83). Oxidation of the borohydride depends on the anode catalyst [5e7]. There are two types of direct borohydride fuel cells due to the oxidant used in cathode: i. Direct borohydride/air fuel cells [8e11] ii. Direct borohydride/peroxide fuel cells [12e21] The oxidant of the DBFC is generally oxygen. But the first advantage of the use of H2O2 is that the peroxide theoretically provides 30% higher specific energy for the fuel cell than the O2-based DBFC (1,1959 and 9295 Wh kg1, respectively). The other advantage is that the use of such a peroxide extends the operation of the fuel cell to locations with limited air convection. Hydrogen peroxide reduces into water in the acidic medium according to the following reaction: H2 O2 þ 2Hþ þ 2e /2H2 O E0cathode ¼ 0:87 Vðvs SHEÞ
(4)
The total cell reaction is: E0cell ¼ 2:1 Vðvs SHEÞ BH 4 þ 4H2 O2 /BO2 þ 6H2 O
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(5)
Besides these advantages, the use of peroxide solution as an oxidant instead of oxygen improves the cell potential from the view point of reaction activity and mass transportation. The comparison of H2O2 reduction reaction (PRR) and O2 reduction reaction (ORR) were examined in the H2/O2 fuel cell and the H2/H2O2 fuel cell [22]. The limiting reduction current due to the mass transport limitation for H2O2 was found higher than that for ORR by a factor of fourteen. In addition, the exchange current densities due to the activation losses were calculated as 1.0 103 A cm2 for PRR and 1.0 104 A cm2 for ORR. A higher reaction rate of H2/H2O2 fuel cell was found, which lead to a better performance for H2/H2O2 fuel cell. Consequently, the higher exchange current density and faster mass transport
provides a higher performance than that of the H2/O2 fuel cell at high current densities [22]. A mathematical model for DBFC (with air) was developed by Verma et al. based on the reaction mechanism available in the literature to predict the cell voltage at a given current density. The cathode reaction in the alkaline condition was investigated and reported that the oxygen reduction kinetics was more favorable at the cathode as compared to the oxidation of borohydride at anode [1,23]. Thus, it was assumed that the activation overpotential at the cathode was less significant compared to that at the anode. The electro-oxidation reaction mechanism of the borohydride was used to model the activation overpotential. In the modeling of ohmic overpotential it was assumed that the ohmic losses were proportional to the current density and resistance of the electrolyte which decreased with the increase in temperature. Similar to activation overpotential, it was reported that the effect of the concentration overpotential at the anode was reduced considerably. The expression of the concentration overpotential was simplified in terms of the oxygen concentration at the cathode catalyst layer [1]. On the other hand in the direct borohydride/peroxide fuel cell, the reduction mechanism of the hydrogen peroxide may affect the activation overpotential. In this study, we have developed a new expression that contains the influence of the peroxide. Our models developed here, employ the equations and approximations similar to those used in prior models based on reaction mechanism available in the literature to predict the cell voltage at a given current density [1]. Consequently KH2 O2 has been calculated experimentally and the activation overpotential of the cathode due to the reduction mechanism of hydrogen peroxide has been proposed similar to that at the anode side. In this study, three mathematical models were compared with the experimental data for two passive cells, Cell.1 and Cell.2.
2.
Experimental
Experiments were carried out by using two cells described below. The passive cell modeled in this paper was used in our previous performance studies as the test cell [24].
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2.1.
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Preparation of MEA
Ag needles (Alfa Aiser, 350 mesh) and Pt/C powders (Alfa Aiser) were used to prepare catalyst inks for the anode and cathode materials, respectively. Catalyst slurries were prepared by mixing Pt/C powder (10%) and Ag needles with isopropyl alcohol. 5 wt% Nafion solution (Alfa Aiser) was added to the mixture and ultrasonicated for 15 min. The inks were stirred with an ultrasonic bath and brushed onto the carbon cloths (Fuel Cell Store). The catalyst coated carbon layers was then dried at the room temperature. Nafion-117 (Fuel Cell Store) was used as the membrane. The membrane was boiled in 2 M H2O2 solution and 1.5 M H2SO4 solution for 1 h each, respectively. It was rinsed in de-ionized water for 1 h. Then Nafion-117 was activated by 1.5 M H2SO4 for 2 h. After it was dried, the membrane was hot-pressed between two carbon cloth electrodes at 150 C for 3 min under 1.2 bar.
2.2.
Construction of the cells
The experiments were carried out with two passive cells which have different catalyst loads. The cells were attached with containers for the fuel and the oxidant storage. The fuel was prepared by dissolving NaBH4 (1 M) in the NaOH solution (6 M). Acidic peroxide solution (2 M H2O2 þ 1.5 M H2SO4) was injected into the oxidant chamber. The configurations of the two different cells were as follows: Cell.1: The cell.1 had a surface area of 4 cm2 and a loaded catalysis of 37 mg cm2. The compartments of the fuel and the oxidant had a volume of 6 ml. Cell.2: The area of the electrodes of the Cell.2 was 16 cm2 with the catalyst loading of 62 mg cm2 on the carbon paper. The compartments of the fuel and the oxidant were 4 ml in volume.
2.3.
Cyclic voltammetric study
The cyclic voltammetry was carried out with a Pt (bulk, from BASS) working electrode in the acidic peroxide solution (2 M H2O2 þ 1.5 M H2SO4) of 20 ml in order to obtain the reaction rate constant of the peroxide. The experiment was performed between the potentials of 1.8 V and 0.8 V at the scan rate of 50 mV s1. A Pt wire (BASS) and Saturated Calomel Electrode (SCE, from BASS) were used as the counter and reference electrodes, respectively.
3.
Fig. 1 e The schematic illustration of the passive direct borohydride/peroxide fuel cell used in the experiments.
temperature of 25 C. The model was formulated based on the following general simplifications and assumptions: i. The fuel cell was assumed to operate under steady-state conditions. ii. The fuel and the oxidant concentrations remained constant during the operation (no concentration polarization). iii. The cell was operated at the room temperature; the change of temperature was small and not taken into consideration. Three models, Model.1, Model.2 and Model.3, were derived as being described as the following and compared with the experimental polarization curves. In the Fig. 2 the polarization and the power curves of Cell.1 and Cell.2 obtained experimentally are shown. From Fig. 2, it is therefore obvious that the catalyst loading would have a marked effect upon the performance. The more the catalyst is loaded the more the
Result and discussions
The passive direct borohydride/peroxide fuel cell (DBPFC) sketched in Fig. 1 consists of a fuel and an oxidant tank, an anode catalyst and a cathode catalyst, Nafion-117 membrane, the current collectors and the cell body. Fig. 2 shows the polarization curves when the passive fuel cell operates with the fuel of the basic borohydride solution and the oxidant of acidic peroxide solution. The polarization curves show the typical sharp decrease that DBFCs have similar behavior due to the ohmic resistance of the cell and the irreversibility of the cell reactions [15]. All experiments were carried out at a room
Fig. 2 e The polarization curves of Cell.1 and Cell.2 performed with 1 M NaBH4 D 6 M NaOH solution as the fuel and acidic H2SO4 solution (1.5 M H2SO4 D 2 M H2O2) as the oxidant.
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fuel and the oxidant react [25,26]. The cell power was raised up to 7 mW cm2 from 4.5 mW cm2, as the amount of the catalysis increased.
3.1.
The development of Model.1
As it is known, a polarization curve is the most important characteristic of the fuel cell and its performance. There are three types of potential losses in the fuel cell. The performance of the cell is generally reduced due to the electrical losses which is known as activation overpotential, and ohmic resistance of the electrolyte, electrolyte-electrode interface and the electrodes. Further, the loss occurs due to the mass transfer resistance experienced by the fuel and oxidant to reach the anode and cathode, which is known as the concentration overpotential. Thus the cell voltage, Ecell, is written as follows; Ecell ¼ E ðhact þ hohm þ hconc Þ
(6)
Ohmic losses can be expressed by Ohm’s law: hohm ¼ i Rohm
(7)
ButtlereVolmer equation gives the relation between the loss of potential and the current density as follows, it is called activation overpotential [27]: hact ¼
RT i ln aF i0
(8)
When the reactant is consumed faster than it can reach the surface, the current density is called the limiting current density. This relation is called the concentration losses and given by Nernst equation; hconc ¼
RT CB RT iL ¼ ln ln CS iL i nF nF
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polarization) and the exchange current density (i0). For our test cell these parameters were calculated from the polarization curves (Fig. 3 and Fig. 4). Fig. 3a and b are the Tafel plots of the experimental polarization curves of the Cell.1 and Cell.2. The exchange current densities observed are 2.99 103 mA cm2 and 5.15 103 mA cm2 (iL,1, iL,2) for Cell.1 and Cell.2, respectively. The passive Cell.1 has an open circuit potential (OCP) of 1.28 V (Er,1) measured from Fig. 3a and ohmic resistance Rohm,1 of 0.066 Ucm2 calculated from slope of the polarization curve in Fig. 4a. The values of OCP and Rohm,2 for Cell.2 were calculated as 1.1 V and 0.07 Ucm2 from Figs. 3b and 4b, respectively. The values for both cells are tabulated in Table 1. The exchange current densities are the observed values and were given as Er in the Table 1. The observed values of Er are different due to load of the catalysis that cause to generation of different electrical current. By replacing these data in the Eq. (11), the mathematical models for Cell.1 and Cell.2 can be obtained in terms of the cell voltages and currents as follows: i Ecell;1 ¼1:28 0:0856 ln 2:99 103 19:3 i 0:066 0:00428 ln 19:3 i i Ecell;2 ¼1:1 0:1284 ln 3 5; 15 10 14:3 0:00428 ln i 0:07 14:3 i
hact;a þ hact;c þ hohm þ hconc;a þ hconc;c
(9)
(10)
On the other hand, the relation between fuel cell potential and current density is proposed by Barbir for PEM fuel cells as the following (Eq. (11)) [27]. This model was developed by neglecting the losses of the potential caused by the anode (activation and concentration) comparing with the cathode losses. It is known that in a PEM fuel cell majority of the overpotential takes place on the cathode side because of the slow reduction kinetic of oxygen and low diffusion rate of oxygen through the electrode surface. This equation depending on the exchange current density and the limiting current density gives a good approximation with the polarization curves of PEM fuel cells obtained experimentally. In this study Eq. (11) was used as the first approximation in order to develop a model that describes the passive DBPFC [28,29]. Ecell ¼ Er
RT i RT iL i Rohm ln ln iL i aF i0 nF
(11)
The parameters used in the Model.1 are the limiting current density (iL), the slope in the linear region RU (the ohmic
ð13Þ
The Model.1 is validated against the experimental data of Cell.1 and Cell.2 in Fig. 5. The dash lines indicate the model
The potential losses composed of activation and concentration polarizations on both the anode and cathode and of ohmic losses can be rewritten as follows; Ecell ¼ Er
ð12Þ
Fig. 3 e Predicted Tafel plot of a) Cell.1 and b) Cell.2.
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Fig. 4 e Polarization curve of a) Cell.1 and b) Cell.2.
prediction and the solid lines are the experimental polarization curves of Portable DBPFC. It can be obviously seen in Fig. 5 that the Model.1 is not compatible with the experimental data as expected. The Eq. (11) offered by Barbir for PEMFCs is not suitable for our fuel cell system [27].
3.2.
Development of Model.2
A more realistic expression for DBFC was developed by Verma et al. Their mathematical model depended on the activation polarization of the anode side caused by oxidation kinetics of
Table 1 e The parametric values of the Cell.1 and Cell.2.
Er, V Rohm, U cm2 aBH4 a aH2 O2 b nBH4 c nH2 O2 d i0, mA cm2 iL, mA cm2 KBH4 , mol cm2 s1 R, J mol1K T, K CBH4 , mol cm3 COH, mol cm3 CH2 O2 , mol cm3 a b c d
From literature: [15]. Accepted. From literature: [19]. Calculated.
Cell.1
Cell.2
1.28 0.066 0.3 1b 6c 2d 2.99 103 19.3 0.001a 8.314 298 1 6 2
1.1 0.07 0.2 1b 6c 2d 5.15 103 14.3 0.001a 8.314 298 1 6 2
Fig. 5 e Comparisons of the experimental polarization curves with the curves obtained by the Model.1 a) for Cell.1 and b) for Cell.2.
borohydride. In their study the following electro-oxidation reaction mechanism was taken into account and the reduction reaction of the oxygen in the cathode side was ignored [1]. þ BH 4 þ 2OH 5HBO2ad þ 5H þ 8e OH 5OHad þ e HBO2ad þ OHad þ e /BO 2 þ H2 O
(14)
The relationship between the activation overpotential and the current density for the anode side depending on the rate expressions of the borohydride was given as the following, where KBH4 is a constant for sodium borohydride: hact;a ¼
! 0:5 i C1 RT BH4 COH ln KBH4 anF
(15)
In our study, Eq. (15) and the value of KBH4 calculated by Verma and given in Table 1 were used in order to develop the Model.2 for our passive DBPFC constructed by Ag anode and Pt/C cathode. The total voltage drop in the cell was modeled by the following Eq. (17) [1]. Ecell ¼ E hact;a þ hohm " Ecell ¼ Er
0:5 i C1 RT BH4 COH ln KBH4 aBH4 nBH4 F
(16) !#
!
i Rohm
(17)
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The values used in the Eq. (17) for the calculations of the cell voltage are listed in Table 1. The expressions of Model.2 for Cell.1 and Cell.2 may be written as follows: Ecell:1 ¼ 1:28 ½0:0143 lnði 408Þ ði 0:066Þ
(18)
Ecell:2 ¼ 1:1 ½0:0214 lnði 408Þ ði 0:07Þ
(19)
Fig. 6a and b are the IeV curves of the experimental data and the model created with Eq. (18) and Eq. (19), respectively. Fig. 6a and b show the effect of activation overpotential of the anode. It can be concluded that, besides there being a small difference between the two curves, the model and the experimental curves, Model.2 characterizes the DBPFC better than the Model.1. Unlike Model.1, the simulations of Model.2 indicated that the activation overpotential effects the polarization of the cell significantly. The oxidation mechanism of the NaBH4 upon the Ag surface is a slow reaction. Accordingly, this mechanism causes the activation overpotential in the anode that it is highly effective on the cell performances of the DBPFCs [30,25]. From Table 1, by comparing Cell.1 and Cell.2, it is seen that the open circuit potential (1.28 V) and the exchange current density of Cell.1 (2.99 103 mA cm2) are higher than that of Cell.2 (1.1 V, 5.15 103 mA cm2). The higher exchange current density is, the easier it is for the reaction to continue. Therefore the power density of Cell.1 increased up to 7 mW cm2 while Cell.2 had
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a power density of 4.5 mW cm2. The transfer coefficients are a measure of the symmetry of the activation energy barrier.
3.3.
The development of Model.3
Model.3 was developed by adding the expression of the cathodic activation overpotential based on the reduction of peroxide in the cathode of Model.2. In our system, Pt used as the cathode catalyst causes to the indirect reduction of the peroxide that the peroxide generates the oxygen rather than the water according to the following mechanism: H2 O2 /O2 ðgÞ þ 2Hþ þ 2e
(20)
The reaction rate constant of the hydrogen peroxide was obtained by using the cyclic voltammetric method (CV). For this purpose, the following equation (Eq. (21)) derived from the reduction mechanism of the hydrogen peroxide (Eq. (20)) was developed for the cathode side of DBPFC: ! i C2 RT H2 O2 ln KH2 O2 aH2 O2 nH2 O2 F
hact;c ¼
(21)
By placing Eq. (21) to Eq. (10), Model.2 (Eq. (15)) was expanded and the following equation (Eq. (22)) was obtained. Eq. (22) is the third expression (Model.3) that besides the anodic activation loss, involves the cathodic activation loss due to the peroxide. !# " 0:5 i C1 RT BH4 COH ln Ecell ¼Er KBH4 aBH4 nBH4 F !# ! " RT KH2 O2 i R ð22Þ ln ohm aH2 O2 nH2 O2 F i C2 H2 O2
3.3.1. The calculation of the reaction rate constant of the hydrogen peroxide in acidic media Cyclic voltammetry has become a very popular technique for the electrochemical systems and has proven to be very useful in obtaining information about electrode reactions. If the system shows the irreversible behavior based on the kinetics of interfacial electron transfer, then kinetic parameters can be obtained by CV [28]. Since the observed ieE response depends upon K, in addition to A (electrode surface area), C (the peroxide concentration) and n (the number of electron transferred) and a (transfer coefficient), the full representation of the CV behavior in terms of these parameters would involve a large number of plots. Accordingly, KH2 O2 can be determined from the following equation [28]: anH2 O2 F ip ¼ 0:227$n$F$A$C0 $KH2 O2 $exp Ep E0 RT
(23)
For an irreversible wave Er is the potential where the current is at the peak value (ip). In Fig. 7 the CV graph of the Pt electrode taken in 2 M acidic H2O2 solution is seen. The peak current and peak potential were calculated from Fig. 7 and given as follows: ip ¼ 1:02 102 A Fig. 6 e The curves of polarizations and simulations predicted by Model.2 a) for Cell.1 and b) for Cell.2.
Ep ¼ 1:681 Vðvs SHEÞ
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Fig. 7 e CV graph of Pt working electrode obtained in 2 M H2O2 D 1.5 M H2SO4 solution.
The reaction rate constant of the reduction mechanism of the peroxide was calculated as 6.72 104 by placing these values in the Eq. (23). The results are given in Table 2. Cell.1 and Cell.2 can be modeled with the following equation called Model.3. The values were taken from Table 1: 0:000121 Ecell:1 ¼1:28 0:0143 lnði 408Þ 0:0128 ln i ði 0:066Þ
ð24Þ
0:000121 Ecell:2 ¼1:1 0:0214 lnði 408Þ 0:0128 ln i ði 0:07Þ
ð25Þ
The simulation data calculated by Model.3 was fitted to the experimental data in Fig. 8. A Good congruence with the experimental data as shown in Fig. 8 suggests that Model.3 provides a good prediction of the polarization characteristics of DBPFC. The deviation between the Model.2 and Model.3 was obviated by adding the activation overpotential of the cathode. The results verified that the neglecting of the concentration overpotentials is an accurate approach. The values of the cell tests indicated that in the DBPFC the anode experienced greater polarization
Table 2 e The values for calculating the reaction rate constant of the hydrogen peroxide in the acidic solution. Parameter ip, A Ep, V (vs. SHE) n a F R, Jmol2 s1 T, K A, cm2 C0 a, mol/cm3 E0a, V (vs. SHE) KH2 O2 , mol cm2 s1 a Accepted.
1.02 102 1.681 2 0,2a 96500 8.314 298 0.1268 2 103 1.77 6.72 104
Fig. 8 e The comparison of the experimental curves and the simulation curves fitted with Model.3.
loss than the cathode and the activation overpotential of the peroxide has a significant effect on the cell performance and cannot be neglected [25,31e33].
4.
Conclusion
In our study, the direct fuel cell constructed for the use of borohydride as a fuel and peroxide as an oxidant has been tested and currentevoltage characteristic curves have been obtained for two cells. The mathematical models for prediction of voltage at a given current of the fuel cell have been developed by taking into account the losses due to ohmic overpotentials and activation overpotentials of the borohydride and peroxide. The concentration overpotentials have been ignored. The models are solved numerically against the experimental data. The Model.3 considered as the base model that reasonably predicts the experimental data on cell voltage and current. It must be underlined that besides the ohmic overpotential, both the activation overpotentials of the anode and the cathode have the profound effect on the performance of the DBPFC. Clearly, reduction reaction of peroxide is an important mechanism that cannot be neglected in the model. With the model, it is intended to provide a useful tool for the basic understanding of electrochemical phenomena in DBPFC.
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Acknowledgment This work has been supported by Republic of Turkey Ministry of Industry and Trade- Project No: 635.TGSD.2010.
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[17] Sanli E, C¸elikkan H, Aksu ML, Uysal BZ. The oxidation of NaBH4 on electrochemicaly treated silver electrodes. Int J Hydrogen Energy 2008;33:2097e104. [18] Sanli E, C¸elikkan H, Aksu M Levent, Uysal B Zu¨htu¨. Impedance analysis and electrochemical measurements of a direct borohydride fuel cell constructed with Ag anode. Electrochem Soc Trans 2007;5:137e45. [19] Sanli E, C¸elikkan H, Aksu M Levent, Uysal B Zu¨htu¨. Anodic behavior of Ag metal electrode in direct borohydride fuel cells. Int J Hydrogen Energy 2006;31:1920e4. [20] Wu Haijun, Wang Cheng, Liu Zhixiang, Zongqiang Mao. Influence of operation conditions on direct NaBH4/H2O2 fuel cell performance. Int J Hydrogen Energy 2010;35: 2648e51. [21] Fu Pei, Wang Ying, Wang Xianyou, He Peiying, Chen Quanqi, Wang Xingyan, et al. Performance of supported AueCo alloy as the anode catalyst of direct borohydride-hydrogen peroxide fuel cell. Int J Hydrogen Energy 2010;35:8136e42. [22] Bussayajarn Narissara, Harrington David A, Therdthianwong Supaporn, Therdthianwong Apichai, Djilali Ned. The cathodic polarization prediction of H2/H2O2 fuel cells by using eis spectra, 30th congress on science & Technology of Thailand, vol. 30; 2004. [23] Byrd Ethan D, Miley George H. Simulation studies of the membrane exchange assembly of an all-liquid, proton exchange membrane fuel cell. J Power Sources 2008;176: 222e8. [24] Sanli AE, Aytac¸ Aylin. Response to disselkamp: direct peroxide/peroxide fuel cell as a novel type fuel cell. Int J Hydrogen Energy 2011;36:869e75. [25] Selvarani G, Prashant SK, Sahu AK, Sridhar P, Pitchumani S, Shukla AK. A direct borohydride fuel cell employing Prussian Blue as mediated electron-transfer hydrogen peroxide reduction catalyst. J Power Sources 2008;178:86e91. [26] Celik Cenk, Boyaci San Fatma Gul, Sarac Halil Ibrahim. Effects of operation conditions on direct borohydride fuel cell performance. J Power Sources 2008;185:197e201. [27] Barbir F. PEM fuel cells: theory and practice, 33e61. Elsevier Inc.; 2005. 249e257. [28] Bard AJ, Faulkner LR. Electrochemical methods, fundamentals and applications. 2nd ed. John Wiley & Sons; 2001. 11e24, 156e161, 226e246, 366e377. [29] Jo Jang-Ho, Yi Sung-Chul. A computational simulation of an alkaline fuel cell. J Power Sources 1999;84:87e106. [30] Chatenet Marian, Micoud Fabrice, Roche Ivan, Chainet Eric. Kinetics of sodium borohydride direct oxidation and oxygen reduction in sodium hydroxide electrolyte Part I. BH 4 electro-oxidation on Au and Ag catalysts. Electrochim Acta 2006;5:5459e67. [31] Sanli A. Elif, Uysal B. Zu¨htu¨, C¸elikkan Hu¨seyin, Aksu M. Levent. The performance study of portable direct borohydride/ peroxide fule cell. 2rd Proceedings of 3rd National Boron Workshop, Ankara, Turkey, 17e18 April 2008. [32] Sanli A. Elif. Direct use of The sodium borohydride by the electrochemical oxidation in fuel cells, Ph.D. Thesis, Gazi University, 2008. [33] Sanli Ays‚e Elif, Aytac¸ Aylin, Uysal B Zu¨htu¨, Aksu M Levent. Recovery of NaBH4 from BH3OH hydrolyzed intermediate on the AgI surface treated with different electrochemical methods. Catal Today, 2011. doi:10.1016/j.cattod.2010.12.024.
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Advanced mathematical model for the passive direct borohydride/peroxide fuel cell Ays‚e Elif Sanli a,*, Mehmet Levent Aksu b, Bekir Zu¨htu¨ Uysal a a b
Gazi University, Faculty of Engineering, Department of Chemistry, Ankara, Turkey Gazi University, Faculty of Education, Department of Chemistry, Ankara, Turkey
article info
abstract
Article history:
In the literature a mathematical model has been developed for the direct borohydride fuel
Received 18 January 2011
cells by Verma et al. [1]. This model simply simulates the fuel cell system via kinetic
Received in revised form
mechanisms of the borohydride and oxygen. Their mathematical expression contains the
21 March 2011
activation losses caused by the oxidation of the borohydride and the concentration over-
Accepted 24 March 2011
potential increased by the reduction of oxygen. In this study a direct borohydride/peroxide
Available online 7 May 2011
fuel cell has been constructed using hydrogen peroxide (H2O2) as oxidant instead of the oxygen. Therefore we created an advanced model for peroxide fuel cells, including the
Keywords:
activation overpotential of the peroxide. The goal of our model is to provide the informa-
Fuel cell
tion about the peroxide reduction effect on the cell performance. Our comprehensive
Borohydride
mathematical model has been developed by taking Verma’s model into account. KH2 O2 used
Hydrogen peroxide
in the advanced model was calculated as 6.72 104 mol cm2 s1 by the cyclic voltam-
Mathematical model
mogram of Pt electrode in the acidic peroxide solution. Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Fuel cells promise to replace batteries for portable devices due to their potentially higher energy and nearly zero recharge time. The hydrogen proton exchange membrane fuel cells (PEMFC), and the liquid-feed types direct methanol fuel cells (DMFC) as well as the direct borohydride fuel cells (DBFC) are considered as three potential types of fuel cells for such applications. Compared to the hydrogen PEMFC, the liquidfeed type fuel cells has further advantages of easier fuel delivery and storage, no cooling or humidification need, and simpler design. The DBFC is a quite novel fuel cell that is based upon the borohydride oxidation on the anode and oxygen reduction on
the cathode [2,3]. The anode, cathode and cell reactions are as follow: Anode : BH 4 þ 8OH /BO2 þ 6H2 O þ 8e
E0anode ¼ 1:24 Vðvs SHEÞ
(1)
Cathode : 2O2 þ 4H2 O þ 8e /8OH E0cathode ¼ 0:40 Vðvs SHEÞ
(2)
Cell reaction : BH 4 þ 2O2 /BO2 þ 2H2 O
E0cell ¼ 1:64 Vðvs SHEÞ
* Corresponding author. Tel.: þ90 (555)9650121; fax: þ90 (312)2238693. E-mail address: [email protected] (A.E. Sanli). 0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.03.141
(3)
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Subscripts a anode act activation B bulk borohydride BH4 c cathode conc concentration hydrogen peroxide H2O2 ohm ohmic sodium hydroxide OH p peak r reversible S surface 1 cell.1 2 cell.2
Nomenclature a A C E Ecell F i i0 iL K n h Rohm R T
transfer coefficient electrode surface area, cm2 concentration, mol/l potential, V cell potential, V Faraday constant current density, mA cm2 exchange current density, mA cm2 limiting current density, mA cm2 reaction rate constant, mol cm2 s1 electron number transferred overpotential, V ohmic resistance, ohmcm2 ideal gas constant, J/molK temperature, K
It is an alkaline type of fuel cell because the borohydride ions are not chemically stable in the acidic media [4]. The DBFC, thermodynamically and energetically, can be compared to PEMFC and DMFC. The cell potential of the DBFC is higher than those of the PEMFC (1.23 V) and DMFC (1.21 V). The theoretical conversion efficiency of the DBFC (0.91) is similar to that of the DMFC (0.91) but it is higher than that of the PEMFC (0.83). Oxidation of the borohydride depends on the anode catalyst [5e7]. There are two types of direct borohydride fuel cells due to the oxidant used in cathode: i. Direct borohydride/air fuel cells [8e11] ii. Direct borohydride/peroxide fuel cells [12e21] The oxidant of the DBFC is generally oxygen. But the first advantage of the use of H2O2 is that the peroxide theoretically provides 30% higher specific energy for the fuel cell than the O2-based DBFC (1,1959 and 9295 Wh kg1, respectively). The other advantage is that the use of such a peroxide extends the operation of the fuel cell to locations with limited air convection. Hydrogen peroxide reduces into water in the acidic medium according to the following reaction: H2 O2 þ 2Hþ þ 2e /2H2 O E0cathode ¼ 0:87 Vðvs SHEÞ
(4)
The total cell reaction is: E0cell ¼ 2:1 Vðvs SHEÞ BH 4 þ 4H2 O2 /BO2 þ 6H2 O
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(5)
Besides these advantages, the use of peroxide solution as an oxidant instead of oxygen improves the cell potential from the view point of reaction activity and mass transportation. The comparison of H2O2 reduction reaction (PRR) and O2 reduction reaction (ORR) were examined in the H2/O2 fuel cell and the H2/H2O2 fuel cell [22]. The limiting reduction current due to the mass transport limitation for H2O2 was found higher than that for ORR by a factor of fourteen. In addition, the exchange current densities due to the activation losses were calculated as 1.0 103 A cm2 for PRR and 1.0 104 A cm2 for ORR. A higher reaction rate of H2/H2O2 fuel cell was found, which lead to a better performance for H2/H2O2 fuel cell. Consequently, the higher exchange current density and faster mass transport
provides a higher performance than that of the H2/O2 fuel cell at high current densities [22]. A mathematical model for DBFC (with air) was developed by Verma et al. based on the reaction mechanism available in the literature to predict the cell voltage at a given current density. The cathode reaction in the alkaline condition was investigated and reported that the oxygen reduction kinetics was more favorable at the cathode as compared to the oxidation of borohydride at anode [1,23]. Thus, it was assumed that the activation overpotential at the cathode was less significant compared to that at the anode. The electro-oxidation reaction mechanism of the borohydride was used to model the activation overpotential. In the modeling of ohmic overpotential it was assumed that the ohmic losses were proportional to the current density and resistance of the electrolyte which decreased with the increase in temperature. Similar to activation overpotential, it was reported that the effect of the concentration overpotential at the anode was reduced considerably. The expression of the concentration overpotential was simplified in terms of the oxygen concentration at the cathode catalyst layer [1]. On the other hand in the direct borohydride/peroxide fuel cell, the reduction mechanism of the hydrogen peroxide may affect the activation overpotential. In this study, we have developed a new expression that contains the influence of the peroxide. Our models developed here, employ the equations and approximations similar to those used in prior models based on reaction mechanism available in the literature to predict the cell voltage at a given current density [1]. Consequently KH2 O2 has been calculated experimentally and the activation overpotential of the cathode due to the reduction mechanism of hydrogen peroxide has been proposed similar to that at the anode side. In this study, three mathematical models were compared with the experimental data for two passive cells, Cell.1 and Cell.2.
2.
Experimental
Experiments were carried out by using two cells described below. The passive cell modeled in this paper was used in our previous performance studies as the test cell [24].
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2.1.
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Preparation of MEA
Ag needles (Alfa Aiser, 350 mesh) and Pt/C powders (Alfa Aiser) were used to prepare catalyst inks for the anode and cathode materials, respectively. Catalyst slurries were prepared by mixing Pt/C powder (10%) and Ag needles with isopropyl alcohol. 5 wt% Nafion solution (Alfa Aiser) was added to the mixture and ultrasonicated for 15 min. The inks were stirred with an ultrasonic bath and brushed onto the carbon cloths (Fuel Cell Store). The catalyst coated carbon layers was then dried at the room temperature. Nafion-117 (Fuel Cell Store) was used as the membrane. The membrane was boiled in 2 M H2O2 solution and 1.5 M H2SO4 solution for 1 h each, respectively. It was rinsed in de-ionized water for 1 h. Then Nafion-117 was activated by 1.5 M H2SO4 for 2 h. After it was dried, the membrane was hot-pressed between two carbon cloth electrodes at 150 C for 3 min under 1.2 bar.
2.2.
Construction of the cells
The experiments were carried out with two passive cells which have different catalyst loads. The cells were attached with containers for the fuel and the oxidant storage. The fuel was prepared by dissolving NaBH4 (1 M) in the NaOH solution (6 M). Acidic peroxide solution (2 M H2O2 þ 1.5 M H2SO4) was injected into the oxidant chamber. The configurations of the two different cells were as follows: Cell.1: The cell.1 had a surface area of 4 cm2 and a loaded catalysis of 37 mg cm2. The compartments of the fuel and the oxidant had a volume of 6 ml. Cell.2: The area of the electrodes of the Cell.2 was 16 cm2 with the catalyst loading of 62 mg cm2 on the carbon paper. The compartments of the fuel and the oxidant were 4 ml in volume.
2.3.
Cyclic voltammetric study
The cyclic voltammetry was carried out with a Pt (bulk, from BASS) working electrode in the acidic peroxide solution (2 M H2O2 þ 1.5 M H2SO4) of 20 ml in order to obtain the reaction rate constant of the peroxide. The experiment was performed between the potentials of 1.8 V and 0.8 V at the scan rate of 50 mV s1. A Pt wire (BASS) and Saturated Calomel Electrode (SCE, from BASS) were used as the counter and reference electrodes, respectively.
3.
Fig. 1 e The schematic illustration of the passive direct borohydride/peroxide fuel cell used in the experiments.
temperature of 25 C. The model was formulated based on the following general simplifications and assumptions: i. The fuel cell was assumed to operate under steady-state conditions. ii. The fuel and the oxidant concentrations remained constant during the operation (no concentration polarization). iii. The cell was operated at the room temperature; the change of temperature was small and not taken into consideration. Three models, Model.1, Model.2 and Model.3, were derived as being described as the following and compared with the experimental polarization curves. In the Fig. 2 the polarization and the power curves of Cell.1 and Cell.2 obtained experimentally are shown. From Fig. 2, it is therefore obvious that the catalyst loading would have a marked effect upon the performance. The more the catalyst is loaded the more the
Result and discussions
The passive direct borohydride/peroxide fuel cell (DBPFC) sketched in Fig. 1 consists of a fuel and an oxidant tank, an anode catalyst and a cathode catalyst, Nafion-117 membrane, the current collectors and the cell body. Fig. 2 shows the polarization curves when the passive fuel cell operates with the fuel of the basic borohydride solution and the oxidant of acidic peroxide solution. The polarization curves show the typical sharp decrease that DBFCs have similar behavior due to the ohmic resistance of the cell and the irreversibility of the cell reactions [15]. All experiments were carried out at a room
Fig. 2 e The polarization curves of Cell.1 and Cell.2 performed with 1 M NaBH4 D 6 M NaOH solution as the fuel and acidic H2SO4 solution (1.5 M H2SO4 D 2 M H2O2) as the oxidant.
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fuel and the oxidant react [25,26]. The cell power was raised up to 7 mW cm2 from 4.5 mW cm2, as the amount of the catalysis increased.
3.1.
The development of Model.1
As it is known, a polarization curve is the most important characteristic of the fuel cell and its performance. There are three types of potential losses in the fuel cell. The performance of the cell is generally reduced due to the electrical losses which is known as activation overpotential, and ohmic resistance of the electrolyte, electrolyte-electrode interface and the electrodes. Further, the loss occurs due to the mass transfer resistance experienced by the fuel and oxidant to reach the anode and cathode, which is known as the concentration overpotential. Thus the cell voltage, Ecell, is written as follows; Ecell ¼ E ðhact þ hohm þ hconc Þ
(6)
Ohmic losses can be expressed by Ohm’s law: hohm ¼ i Rohm
(7)
ButtlereVolmer equation gives the relation between the loss of potential and the current density as follows, it is called activation overpotential [27]: hact ¼
RT i ln aF i0
(8)
When the reactant is consumed faster than it can reach the surface, the current density is called the limiting current density. This relation is called the concentration losses and given by Nernst equation; hconc ¼
RT CB RT iL ¼ ln ln CS iL i nF nF
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polarization) and the exchange current density (i0). For our test cell these parameters were calculated from the polarization curves (Fig. 3 and Fig. 4). Fig. 3a and b are the Tafel plots of the experimental polarization curves of the Cell.1 and Cell.2. The exchange current densities observed are 2.99 103 mA cm2 and 5.15 103 mA cm2 (iL,1, iL,2) for Cell.1 and Cell.2, respectively. The passive Cell.1 has an open circuit potential (OCP) of 1.28 V (Er,1) measured from Fig. 3a and ohmic resistance Rohm,1 of 0.066 Ucm2 calculated from slope of the polarization curve in Fig. 4a. The values of OCP and Rohm,2 for Cell.2 were calculated as 1.1 V and 0.07 Ucm2 from Figs. 3b and 4b, respectively. The values for both cells are tabulated in Table 1. The exchange current densities are the observed values and were given as Er in the Table 1. The observed values of Er are different due to load of the catalysis that cause to generation of different electrical current. By replacing these data in the Eq. (11), the mathematical models for Cell.1 and Cell.2 can be obtained in terms of the cell voltages and currents as follows: i Ecell;1 ¼1:28 0:0856 ln 2:99 103 19:3 i 0:066 0:00428 ln 19:3 i i Ecell;2 ¼1:1 0:1284 ln 3 5; 15 10 14:3 0:00428 ln i 0:07 14:3 i
hact;a þ hact;c þ hohm þ hconc;a þ hconc;c
(9)
(10)
On the other hand, the relation between fuel cell potential and current density is proposed by Barbir for PEM fuel cells as the following (Eq. (11)) [27]. This model was developed by neglecting the losses of the potential caused by the anode (activation and concentration) comparing with the cathode losses. It is known that in a PEM fuel cell majority of the overpotential takes place on the cathode side because of the slow reduction kinetic of oxygen and low diffusion rate of oxygen through the electrode surface. This equation depending on the exchange current density and the limiting current density gives a good approximation with the polarization curves of PEM fuel cells obtained experimentally. In this study Eq. (11) was used as the first approximation in order to develop a model that describes the passive DBPFC [28,29]. Ecell ¼ Er
RT i RT iL i Rohm ln ln iL i aF i0 nF
(11)
The parameters used in the Model.1 are the limiting current density (iL), the slope in the linear region RU (the ohmic
ð13Þ
The Model.1 is validated against the experimental data of Cell.1 and Cell.2 in Fig. 5. The dash lines indicate the model
The potential losses composed of activation and concentration polarizations on both the anode and cathode and of ohmic losses can be rewritten as follows; Ecell ¼ Er
ð12Þ
Fig. 3 e Predicted Tafel plot of a) Cell.1 and b) Cell.2.
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Fig. 4 e Polarization curve of a) Cell.1 and b) Cell.2.
prediction and the solid lines are the experimental polarization curves of Portable DBPFC. It can be obviously seen in Fig. 5 that the Model.1 is not compatible with the experimental data as expected. The Eq. (11) offered by Barbir for PEMFCs is not suitable for our fuel cell system [27].
3.2.
Development of Model.2
A more realistic expression for DBFC was developed by Verma et al. Their mathematical model depended on the activation polarization of the anode side caused by oxidation kinetics of
Table 1 e The parametric values of the Cell.1 and Cell.2.
Er, V Rohm, U cm2 aBH4 a aH2 O2 b nBH4 c nH2 O2 d i0, mA cm2 iL, mA cm2 KBH4 , mol cm2 s1 R, J mol1K T, K CBH4 , mol cm3 COH, mol cm3 CH2 O2 , mol cm3 a b c d
From literature: [15]. Accepted. From literature: [19]. Calculated.
Cell.1
Cell.2
1.28 0.066 0.3 1b 6c 2d 2.99 103 19.3 0.001a 8.314 298 1 6 2
1.1 0.07 0.2 1b 6c 2d 5.15 103 14.3 0.001a 8.314 298 1 6 2
Fig. 5 e Comparisons of the experimental polarization curves with the curves obtained by the Model.1 a) for Cell.1 and b) for Cell.2.
borohydride. In their study the following electro-oxidation reaction mechanism was taken into account and the reduction reaction of the oxygen in the cathode side was ignored [1]. þ BH 4 þ 2OH 5HBO2ad þ 5H þ 8e OH 5OHad þ e HBO2ad þ OHad þ e /BO 2 þ H2 O
(14)
The relationship between the activation overpotential and the current density for the anode side depending on the rate expressions of the borohydride was given as the following, where KBH4 is a constant for sodium borohydride: hact;a ¼
! 0:5 i C1 RT BH4 COH ln KBH4 anF
(15)
In our study, Eq. (15) and the value of KBH4 calculated by Verma and given in Table 1 were used in order to develop the Model.2 for our passive DBPFC constructed by Ag anode and Pt/C cathode. The total voltage drop in the cell was modeled by the following Eq. (17) [1]. Ecell ¼ E hact;a þ hohm " Ecell ¼ Er
0:5 i C1 RT BH4 COH ln KBH4 aBH4 nBH4 F
(16) !#
!
i Rohm
(17)
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The values used in the Eq. (17) for the calculations of the cell voltage are listed in Table 1. The expressions of Model.2 for Cell.1 and Cell.2 may be written as follows: Ecell:1 ¼ 1:28 ½0:0143 lnði 408Þ ði 0:066Þ
(18)
Ecell:2 ¼ 1:1 ½0:0214 lnði 408Þ ði 0:07Þ
(19)
Fig. 6a and b are the IeV curves of the experimental data and the model created with Eq. (18) and Eq. (19), respectively. Fig. 6a and b show the effect of activation overpotential of the anode. It can be concluded that, besides there being a small difference between the two curves, the model and the experimental curves, Model.2 characterizes the DBPFC better than the Model.1. Unlike Model.1, the simulations of Model.2 indicated that the activation overpotential effects the polarization of the cell significantly. The oxidation mechanism of the NaBH4 upon the Ag surface is a slow reaction. Accordingly, this mechanism causes the activation overpotential in the anode that it is highly effective on the cell performances of the DBPFCs [30,25]. From Table 1, by comparing Cell.1 and Cell.2, it is seen that the open circuit potential (1.28 V) and the exchange current density of Cell.1 (2.99 103 mA cm2) are higher than that of Cell.2 (1.1 V, 5.15 103 mA cm2). The higher exchange current density is, the easier it is for the reaction to continue. Therefore the power density of Cell.1 increased up to 7 mW cm2 while Cell.2 had
8547
a power density of 4.5 mW cm2. The transfer coefficients are a measure of the symmetry of the activation energy barrier.
3.3.
The development of Model.3
Model.3 was developed by adding the expression of the cathodic activation overpotential based on the reduction of peroxide in the cathode of Model.2. In our system, Pt used as the cathode catalyst causes to the indirect reduction of the peroxide that the peroxide generates the oxygen rather than the water according to the following mechanism: H2 O2 /O2 ðgÞ þ 2Hþ þ 2e
(20)
The reaction rate constant of the hydrogen peroxide was obtained by using the cyclic voltammetric method (CV). For this purpose, the following equation (Eq. (21)) derived from the reduction mechanism of the hydrogen peroxide (Eq. (20)) was developed for the cathode side of DBPFC: ! i C2 RT H2 O2 ln KH2 O2 aH2 O2 nH2 O2 F
hact;c ¼
(21)
By placing Eq. (21) to Eq. (10), Model.2 (Eq. (15)) was expanded and the following equation (Eq. (22)) was obtained. Eq. (22) is the third expression (Model.3) that besides the anodic activation loss, involves the cathodic activation loss due to the peroxide. !# " 0:5 i C1 RT BH4 COH ln Ecell ¼Er KBH4 aBH4 nBH4 F !# ! " RT KH2 O2 i R ð22Þ ln ohm aH2 O2 nH2 O2 F i C2 H2 O2
3.3.1. The calculation of the reaction rate constant of the hydrogen peroxide in acidic media Cyclic voltammetry has become a very popular technique for the electrochemical systems and has proven to be very useful in obtaining information about electrode reactions. If the system shows the irreversible behavior based on the kinetics of interfacial electron transfer, then kinetic parameters can be obtained by CV [28]. Since the observed ieE response depends upon K, in addition to A (electrode surface area), C (the peroxide concentration) and n (the number of electron transferred) and a (transfer coefficient), the full representation of the CV behavior in terms of these parameters would involve a large number of plots. Accordingly, KH2 O2 can be determined from the following equation [28]: anH2 O2 F ip ¼ 0:227$n$F$A$C0 $KH2 O2 $exp Ep E0 RT
(23)
For an irreversible wave Er is the potential where the current is at the peak value (ip). In Fig. 7 the CV graph of the Pt electrode taken in 2 M acidic H2O2 solution is seen. The peak current and peak potential were calculated from Fig. 7 and given as follows: ip ¼ 1:02 102 A Fig. 6 e The curves of polarizations and simulations predicted by Model.2 a) for Cell.1 and b) for Cell.2.
Ep ¼ 1:681 Vðvs SHEÞ
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Fig. 7 e CV graph of Pt working electrode obtained in 2 M H2O2 D 1.5 M H2SO4 solution.
The reaction rate constant of the reduction mechanism of the peroxide was calculated as 6.72 104 by placing these values in the Eq. (23). The results are given in Table 2. Cell.1 and Cell.2 can be modeled with the following equation called Model.3. The values were taken from Table 1: 0:000121 Ecell:1 ¼1:28 0:0143 lnði 408Þ 0:0128 ln i ði 0:066Þ
ð24Þ
0:000121 Ecell:2 ¼1:1 0:0214 lnði 408Þ 0:0128 ln i ði 0:07Þ
ð25Þ
The simulation data calculated by Model.3 was fitted to the experimental data in Fig. 8. A Good congruence with the experimental data as shown in Fig. 8 suggests that Model.3 provides a good prediction of the polarization characteristics of DBPFC. The deviation between the Model.2 and Model.3 was obviated by adding the activation overpotential of the cathode. The results verified that the neglecting of the concentration overpotentials is an accurate approach. The values of the cell tests indicated that in the DBPFC the anode experienced greater polarization
Table 2 e The values for calculating the reaction rate constant of the hydrogen peroxide in the acidic solution. Parameter ip, A Ep, V (vs. SHE) n a F R, Jmol2 s1 T, K A, cm2 C0 a, mol/cm3 E0a, V (vs. SHE) KH2 O2 , mol cm2 s1 a Accepted.
1.02 102 1.681 2 0,2a 96500 8.314 298 0.1268 2 103 1.77 6.72 104
Fig. 8 e The comparison of the experimental curves and the simulation curves fitted with Model.3.
loss than the cathode and the activation overpotential of the peroxide has a significant effect on the cell performance and cannot be neglected [25,31e33].
4.
Conclusion
In our study, the direct fuel cell constructed for the use of borohydride as a fuel and peroxide as an oxidant has been tested and currentevoltage characteristic curves have been obtained for two cells. The mathematical models for prediction of voltage at a given current of the fuel cell have been developed by taking into account the losses due to ohmic overpotentials and activation overpotentials of the borohydride and peroxide. The concentration overpotentials have been ignored. The models are solved numerically against the experimental data. The Model.3 considered as the base model that reasonably predicts the experimental data on cell voltage and current. It must be underlined that besides the ohmic overpotential, both the activation overpotentials of the anode and the cathode have the profound effect on the performance of the DBPFC. Clearly, reduction reaction of peroxide is an important mechanism that cannot be neglected in the model. With the model, it is intended to provide a useful tool for the basic understanding of electrochemical phenomena in DBPFC.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 8 5 4 2 e8 5 4 9
Acknowledgment This work has been supported by Republic of Turkey Ministry of Industry and Trade- Project No: 635.TGSD.2010.
references
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