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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: aecsanli@gmail.com (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.2

Amore 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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