i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 8 5 4 2e8 5 4 9
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Advanced mathematical model for the passive directborohydride/peroxide fuel cell
Ays‚e Elif Sanli a,*, Mehmet Levent Aksu b, Bekir Zuhtu Uysal a
aGazi University, Faculty of Engineering, Department of Chemistry, Ankara, TurkeybGazi University, Faculty of Education, Department of Chemistry, Ankara, Turkey
a r t i c l e i n f o
Article history:
Received 18 January 2011
Received in revised form
21 March 2011
Accepted 24 March 2011
Available online 7 May 2011
Keywords:
Fuel cell
Borohydride
Hydrogen peroxide
Mathematical model
* Corresponding author. Tel.: þ90 (555)965012E-mail address: [email protected] (A.E
0360-3199/$ e see front matter Copyright ªdoi:10.1016/j.ijhydene.2011.03.141
a b s t r a c t
In the literature a mathematical model has been developed for the direct borohydride fuel
cells by Verma et al. [1]. This model simply simulates the fuel cell system via kinetic
mechanisms of the borohydride and oxygen. Their mathematical expression contains the
activation losses caused by the oxidation of the borohydride and the concentration over-
potential increased by the reduction of oxygen. In this study a direct borohydride/peroxide
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
activation overpotential of the peroxide. The goal of our model is to provide the informa-
tion about the peroxide reduction effect on the cell performance. Our comprehensive
mathematical model has been developed by taking Verma’s model into account. KH2O2 used
in the advanced model was calculated as 6.72 � 10�4 mol cm�2 s�1 by the cyclic voltam-
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 the cathode [2,3]. The anode, cathode and cell reactions are as
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 liquid-
feed 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
1; fax: þ90 (312)2238693.. Sanli).2011, Hydrogen Energy P
follow:
Anode : BH�4 þ 8OH�/BO�
2 þ 6H2Oþ 8e�
E0anode ¼ �1:24 Vðvs SHEÞ (1)
Cathode : 2O2 þ 4H2Oþ 8e�/8OH�
E0cathode ¼ 0:40 Vðvs SHEÞ (2)
Cell reaction : BH�4 þ 2O2/BO�
2 þ 2H2O
E0cell ¼ 1:64 Vðvs SHEÞ (3)
ublications, LLC. Published by Elsevier Ltd. All rights reserved.
Nomenclature
a transfer coefficient
A electrode surface area, cm2
C concentration, mol/l
E potential, V
Ecell cell potential, V
F Faraday constant
i current density, mA cm�2
i0 exchange current density, mA cm�2
iL limiting current density, mA cm�2
K reaction rate constant, mol cm�2 s�1
n electron number transferred
h overpotential, V
Rohm ohmic resistance, ohmcm�2
R ideal gas constant, J/molK
T temperature, K
Subscripts
a anode
act activation
B bulk
BH4 borohydride
c cathode
conc concentration
H2O2 hydrogen peroxide
ohm ohmic
OH� sodium hydroxide
p peak
r reversible
S surface
1 cell.1
2 cell.2
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 en e r g y 3 6 ( 2 0 1 1 ) 8 5 4 2e8 5 4 9 8543
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 andDMFC. 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). Oxi-
dation 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 kg�1, 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:
H2O2 þ 2Hþ þ 2e�/2H2O E0cathode ¼ 0:87 Vðvs SHEÞ (4)
The total cell reaction is:
BH�4 þ 4H2O2/BO�
2 þ 6H2O E0cell ¼ 2:1 Vðvs SHEÞ (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
forORRbya factorof fourteen. Inaddition, theexchangecurrent
densities due to the activation losses were calculated as
1.0� 10�3Acm�2 for PRRand1.0� 10�4Acm�2 forORR.Ahigher
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 theH2/O2 fuel cell at
high current densities [22].
Amathematicalmodel 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 thealkaline conditionwas investigated
and reported that the oxygen reduction kinetics was more
favorable at the cathode as compared to the oxidation of boro-
hydride at anode [1,23]. Thus, it was assumed that the activa-
tion overpotential at the cathodewas less significant compared
to that at the anode. The electro-oxidation reactionmechanism
of the borohydride was used to model the activation over-
potential. In the modeling of ohmic overpotential it was
assumed that theohmic losseswereproportional to the current
density and resistance of the electrolyte which decreased with
the increase in temperature. Similar toactivationoverpotential,
it was reported that the effect of the concentration over-
potential at the anode was reduced considerably. The expres-
sion 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]. Conse-
quently KH2O2 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].
Fig. 1 e The schematic illustration of the passive direct
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 8 5 4 2e8 5 4 98544
2.1. 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-ionizedwater 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.
borohydride/peroxide fuel cell used in the experiments.
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 37mg cm�2. 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 cm�2 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 s�1. A Pt wire (BASS) and Saturated Calomel Electrode
(SCE, from BASS) were used as the counter and reference
electrodes, respectively.
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.
3. 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
temperature of 25 �C. Themodel 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 experi-
mentally 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
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 en e r g y 3 6 ( 2 0 1 1 ) 8 5 4 2e8 5 4 9 8545
fuel and the oxidant react [25,26]. The cell powerwas raised up
to 7 mW cm�2 from 4.5 mW cm�2, as the amount of the
catalysis increased.
Fig. 3 e Predicted Tafel plot of a) Cell.1 and b) Cell.2.
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 perfor-
mance 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 hconcÞ (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 ¼RTaF
� ln
�ii0
�(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 ¼RTnF
� ln
�CB
CS
�¼ RT
nF� ln
�iL
iL � i
�(9)
The potential losses composed of activation and concen-
tration polarizations on both the anode and cathode and of
ohmic losses can be rewritten as follows;
Ecell ¼ Er ���hact;a þ hact;c
�þ hohm þ �hconc;a þ hconc;c
��(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 polari-
zation 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 ��RTaF
� ln
�ii0
���RTnF
� ln
�iL
iL � i
���i�Rohm
�(11)
The parameters used in the Model.1 are the limiting current
density (iL), the slope in the linear region RU (the ohmic
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 � 10�3 mA cm�2
and 5.15 � 10�3 mA cm�2 (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 resis-
tance 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 andwere 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:
Ecell;1 ¼1:28��0:0856� ln
�i
2:99� 10�3
�
��0:00428� ln
�19:3
19:3� i
���i� 0:066
�ð12Þ
Ecell;2 ¼1:1��0:1284� ln
�i
5; 15� 10�3
�
��0:00428� ln
�14:3
14:3� i
���i� 0:07
�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
Fig. 5 e Comparisons of the experimental polarization
Fig. 4 e Polarization curve of a) Cell.1 and b) Cell.2.
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 8 5 4 2e8 5 4 98546
prediction and the solid lines are the experimental polariza-
tion 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].
curves with the curves obtained by the Model.1 a) for
Cell.1 and b) for Cell.2.
3.2. Development of Model.2Amore 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.
Cell.1 Cell.2
Er, V 1.28 1.1
Rohm, U cm2 0.066 0.07
aBH4
a 0.3 0.2
aH2O2
b 1b 1b
nBH4
c 6c 6c
nH2O2
d 2d 2d
i0, mA cm�2 2.99 � 10�3 5.15 � 10�3
iL, mA cm�2 19.3 14.3
KBH4 , mol cm�2 s�1 0.001a 0.001a
R, J mol�1K 8.314 8.314
T, K 298 298
CBH4 , mol cm�3 1 1
COH, mol cm�3 6 6
CH2O2 , mol cm�3 2 2
a From literature: [15].
b Accepted.
c From literature: [19].
d Calculated.
borohydride. In their study the following electro-oxidation
reaction mechanism was taken into account and the reduc-
tion reaction of the oxygen in the cathode sidewas ignored [1].
BH�4 þ 2OH�5HBO2ad þ 5Hþ þ 8e�
OH�5OHad þ e�
HBO2ad þOHad þ e�/BO�2 þH2O
(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 KBH4is a constant for sodium borohydride:
hact;a ¼�RTanF
�� ln
i� C�1
BH4� C�0:5
OH
KBH4
!(15)
In our study, Eq. (15) and the value of KBH4calculated 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 wasmodeled by
the following Eq. (17) [1].
Ecell ¼ E� �hact;a þ hohm
�(16)
Ecell ¼ Er �"
RTaBH4
nBH4F� ln
i� C�1
BH4C�0:5OH
KBH4
!#� i� Rohm
!(17)
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 en e r g y 3 6 ( 2 0 1 1 ) 8 5 4 2e8 5 4 9 8547
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
themodel createdwith 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�10�3mAcm�2) arehigher thanthatofCell.2 (�1.1V,
5.15 � 10�3 mA cm�2). 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 cm�2 while Cell.2 had
Fig. 6 e The curves of polarizations and simulations
predicted by Model.2 a) for Cell.1 and b) for Cell.2.
a power density of 4.5 mW cm�2. 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:
H2O2/O2ðgÞ 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:
hact;c ¼�
RTaH2O2
nH2O2F
�� ln
i� C�2
H2O2
KH2O2
!(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.
Ecell ¼Er�"
RTaBH4nBH4F
� ln
i�C�1
BH4�C�0:5
OH
KBH4
!#
�"
RTaH2O2
nH2O2F� ln
KH2O2
i�C�2H2O2
!#� i�Rohm
!ð22Þ
3.3.1. The calculation of the reaction rate constant of thehydrogen peroxide in acidic mediaCyclic 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 addi-
tion to A (electrode surface area), C (the peroxide concentra-
tion) 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, KH2O2 can be determined from the following
equation [28]:
ip ¼ 0:227$n$F$A$C0$KH2O2$exp
���anH2O2
FRT
��Ep � E0
��(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� 10�2A
Ep ¼ 1:681 Vðvs SHEÞ
Fig. 7 e CV graph of Pt working electrode obtained in 2 M
H2O2 D 1.5 M H2SO4 solution.
Fig. 8 e The comparison of the experimental curves and
the simulation curves fitted with Model.3.
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 8 5 4 2e8 5 4 98548
The reaction rate constant of the reduction mechanism of
the peroxide was calculated as 6.72 � 10�4 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 equa-
tion called Model.3. The values were taken from Table 1:
Ecell:1 ¼1:28��0:0143� lnði� 408Þ
��0:0128� ln
�0:000121
i
�� ði� 0:066Þ ð24Þ
Ecell:2 ¼1:1��0:0214� lnði� 408Þ
��0:0128� ln
�0:000121
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 exper-
imental data as shown in Fig. 8 suggests that Model.3 provides
a good prediction of the polarization characteristics of DBPFC.
Thedeviationbetween theModel.2 andModel.3wasobviatedby
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 rateconstant of the hydrogen peroxide in the acidic solution.
Parameter
ip, A 1.02 � 10�2
Ep, V (vs. SHE) 1.681
n 2
a 0,2a
F 96500
R, Jmol�2 s�1 8.314
T, K 298
A, cm2 0.1268
C0a, mol/cm3 2 � 10�3
E0a, V (vs. SHE) 1.77
KH2O2 , mol cm�2 s�1 6.72 � 10�4
a Accepted.
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 predic-
tion 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 borohy-
dride 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 en e r g y 3 6 ( 2 0 1 1 ) 8 5 4 2e8 5 4 9 8549
Acknowledgment
This work has been supported by Republic of Turkey Ministry
of Industry and Trade- Project No: 635.TGSD.2010.
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