CNT nanostructured cathode catalyst layer for PEM fuel cells

CNT nanostructured cathode catalyst layer for PEM fuel cells

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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 7 ( 2 0 1 2 ) 8 4 3 9 e8 4 5 0

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Experimental verification for simulation study of Pt/CNT nanostructured cathode catalyst layer for PEM fuel cells A. Abedini a,b,*, B. Dabir a,b, M. Kalbasi a a

Department of Chemical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran 15875-4413, Iran b Energy Research Center, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

article info

abstract

Article history:

In this study, parametric study on the cathode catalyst layer in a Proton Exchange

Received 10 December 2011

Membrane (PEM) fuel cell was conducted. Steady-state, two dimensional (2D) and non-

Received in revised form

isothermal conditions were proposed as critical hypotheses of work in essence. Multi-

12 February 2012

component mass diffusion along with convection mechanism in a single cell, conduction

Accepted 16 February 2012

changes of proton and electron with experimental data and Knudsen diffusion which has

Available online 17 March 2012

a crucial impact on the simulation task in nanoscale, were considered in our study. Moreover, carbon nanotube (CNT), platinum (Pt) and Nafion loading effects as well as the

Keywords:

porosity characteristics in a single-phase flow at different catalyst layer (CL) thicknesses

PEM fuel cell

were thoroughly investigated. The results presented herein, revealed that the amount of Pt

Nonisothermal modeling

and CNT has more profound effect than catalyst porosity. Based on the results derived, the

Nanostructured catalyst layer

model presented could be a promising mean to develop and construct a nanostructured

Carbon nanotube

catalyst layer. Meanwhile, our modified agglomerate model predicts the performance of fuel cell systems in different experimental conditions. Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

Low operation temperature, rapid start-up and high power density have made Polymer Electrolyte Membrane Fuel Cells (PEMFCs) a potential and viable device for power generation. However, some challenges remain against commercialization of this emerging device and numerous efforts have been devoted to obviate these drawbacks. Recently, PEMFCs have been profoundly studied in order to understand the performance and predict the behavior of them by modeling their electrochemical processes. One of the most widely investigated processes to be studied is Cathode site, especially support type and catalyst used in, because it acts as a site for

oxygen reduction reactions and serves as a rate determining step in the performance of the electrochemical device. There are various techniques to model the electrochemical behavior of PEMFCs based on the structure of catalyst layer and reactions take place at special sites of reactivity. Primary models are based on the simple hypotheses of catalyst layer which is considered as a boundary between Gas Diffusion Layers (GDLs) and membrane layer [1]. Low computational complexity is the main privilege of these models and Lum and McGuirk evaluated the effects of structural parameters and diffusibility on cell performance using these simple models [2]. Tiedemann and Newman presented second type of models in which the catalyst layer is considered as a fully or semi

* Corresponding author. Department of Chemical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran 15875-4413, Iran. Tel.: þ98 21 6454 3172; fax: þ98 21 6454 2611. E-mail addresses: [email protected], [email protected] (A. Abedini). 0360-3199/$ e see front matter Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2012.02.093

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flooded with liquid water [3]. In this state, oxygen should pass through the liquid layer to reach the reaction sites. In the third type of models, the catalyst layer is thoroughly simulated. The conformation of this model, is that the PEMFCs are hypothesized as a reactor domain filled with catalyst particles like a reactor in petrochemical processes. This model known as agglomerate model which has been proposed by Iczkowski and Cutlip [4]. These agglomerated particles which are located between the Gas Diffusion Layers and membrane layer are considered in different shapes such as spherical, cylindrical and slab particles [16e18]. Recently, more interesting cylindrical nanostructured agglomerate model has developed that reaction happens only on a smooth surface of CNTs [13,19]. In this type of catalyst layer, platinum uniformly deposited on the CNTs like a surrounding shell and both of them are covered with a thin layer of Nafion. The advantages of these new types of catalyst have been experimentally proved and the modeling trials should be conducted to elucidate the role of structural parameters on the cell performance and optimize the cell efficiency [7,20]. Du et al. proposed a 1D model in which the reaction components should pass through the membrane layer and arrive at the Pt surface [12,14]. Then, Daiguji and Xing introduced a more detailed 2D model which considered the Knudsen and multi-component (MaxwelleStefan) diffusion [13,19]. Moreover, this 2D model has not investigated the effects of proton conduction and temperature. Hussain et al. have implemented a 3D model in which they evaluated the impact of proton conduction in an isothermal condition and did not take the humidification of reactant into account [21]. It is worth of mentioning that a complete cell with a support catalyst of nanotube has not been simulated. The recent model, has validated its model accuracy without considering the convection at the inlet and outlet of the cell and moreover has not investigated the effect of the Gas Diffusion Layers on the distribution of reactants. In present study, in addition to considering the above parameters, a complete cell consists of a spherical model for anode and ordered catalyst layer model for cathode by taking the variation of temperature along the cell into account and the effect of this temperature changes on the humidity variation of reactants and electrolyte conduction in the interdigitate current has been thoroughly simulated. Meanwhile, more complicated structural parameters which are considered in the production of cells have been compared with the experimental data [7].

2.

Modeling framework

2.1.

Processes considered in the model

As can be seen in Fig. 2, humidified hydrogen and air are fed at process temperature into anode and cathode in counter current mode. Multi-component reactants diffuse through GDL and reach the reaction sites at CL. In this modeling study, spherical agglomerate is considered as catalyst for Hydrogen reaction (H2 / 2Hþ þ 2e) at anode and carbon nanotube based   1 catalysts for oxygen reaction O2 þ 2Hþ þ 2e /H2 O þ Heat 2

at cathode. Fig. 1 illustrates this mechanism. The Hþ produced at anode is transmitted through the covering electrolyte of the spherical catalysts to the membrane layer of electrolyte separating two electrodes and reach the cathode. These protons at the cathode boundary reach the Pt surface through the cylindrical electrolytes covering the CNTs for Oxygen Reduction Reaction (ORR). As a result, the electrons transmitted from Carbon Black (CB) to the anode GDL and from anode GDL to the cathode GDL through the external current. Then, the electrons are conducted along the CNTs to reach the Pt surface. Moreover, humidified air provides the oxygen needed for reduction reaction. Surface of the CNTs which is uniformly covered with Pt particles has been coated with a thin layer of Nafion. Hence, oxygen is easily diffused through the gaps between CNTs and reaches the reaction site after dissolving in the Nafion layer. The cathode reaction occurs at the interface between the catalyst (Pt) and the Nafion ionomer, whereas, the anode reaction is took place by diffusing of reactants into the spherical particles due to the agglomerated catalysts. As the interdigitate current is considered in both of the electrodes, the convection term and consequently the effect of viscosity variation on the reactant distribution should be applied in the modeling scheme.

2.2.

Governing equations

According to the conditions mentioned in the previous section, the variables of each domain and the governing equations of those variables are presented in Fig. 2 and Table 2. The reaction components in the GDL and CL domain are defined on the basis of the diffusion and convection equation of MaxwelleStefan that are listed for anode and cathode in Table 2 in which the term Si corresponds to sink/source term which are separately described in Table 3. With regards to the nonisothermal process of the cell and nanoporosity structures between the CNTs for transmitting the reactants, we should consider these conditions in the governing equations in order to simulate the cell behavior in more accurate way. In this matter, diffusivity coefficient in the MaxwelleStefan equation is defined as follow: 1=2  T1:75 1 1 þ Dij ¼ 3:16  108  2 $ Mi Mj P ci1=3 þ cj1=3

(1)

where T, P and M are temperature, pressure, molecular weight respectively and ci and cj are molar diffusion volume of

Fig. 1 e Schematic of a single cell with anode and cathode appropriate catalyst layer and flow channels.

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8 6 0:66 > > mH2 ¼ 0:21  10 T   < mH O ¼ 0:00584  106 T1:29 2 2 mi N s m ¼ m ¼ 0:237  106 T0:76 > > : N2 mO2 ¼ 0:246  106 T0:78

8441

(6)

Reactant oxygen and hydrogen gases should pass through the covering membrane to reach the reaction sites. In order to attain the reactant’s concentration at the reaction site as a function of relative pressure of the gases at the anode and cathode Henry’s law is formulated as follow: Ci ¼

Pi Hi

(7)

where Hi is the Henry’s law constant and Pi is partial pressure.

2.2.1.

Fig. 2 e Schematic view of modeled single cell with size depiction (rescaled) and the variables.

2

DO2 ;m

species in m3/mol, which are expressed for each reactants as follow: cH2 ¼ 7:07  106 ; cH2 O ¼ 12:7  106 ; cO2 ¼ 16:6  106 ; cN2 ¼ 17:9  106 In Eq. (1), in order to consider the diffusion in the nanoscale, the Knudsen diffusion coefficient should be defined as follow [6]: DKi ¼

1=2  2 8RT rp 3 pMi

(2)

And by considering the correction using Bruggeman relation, the diffusion coefficient for binary components of gas is given by [6]: Dij ¼ Dij 3 k3=2

(3)

This relation is applied for all computational domains except cathode CL [19]. Because of variation of viscosity in the course of reaction, the viscosity of gas mixture by considering the temperature changes is considered in the simulation as follow [6,22]: n¼

n m 1X xi mi P ¼ r r i¼1 nj¼1 xj fij

(4)

DO2 ;m

r ¼ rb ;

C ¼ CO2

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3 m þ 3 s Þ ra rb ¼ 3s

(8)

(9)

(10)

(11)

where 3 m is volume fraction of electrolyte and 3 s is volume fraction of solid in the catalyst layer and is presented as follow: 

3v

mi is the viscosity of each component which is given according to temperature [6]:

¼0

where CO2 , ac, hc, Vp/Sp, a, CO2 are oxygen concentration in gas phase, cathode charge transfer coefficient, cathode activation overpotential, volume to surface ratio of the catalyst, the effective surface area of catalyst, dissolved oxygen concentration between gas and electrolyte phase, respectively and rb is defined by the following relation [14]:

 1=2 " 1 Mi 1þ fij ¼ pffiffiffi 1 þ Mj 8

(5)

!

    dCO2 ;m CO2 ac Fhc Vp exp  ¼ iref 0;c a dr CO2 ;ref RT Sp

r ¼ ra ;

3s

!1=2   #2 Mj 1=4 Mi

d CO2 ;m 1 dCO2 ;m þ dr2 r dr

where DO2 ;m and CO2 ;m are oxygen diffusion coefficient in membrane and oxygen concentration in membrane phase, respectively. We considered the oxygen variation along the CNTs, in addition to radial changes by taking the thickness of catalyst into account. As the reaction is occurred at the interface of electrolyte and CNTs, the boundary condition for Eq. (8) is defined as follow:

where r, xi and fij are density, species mole fraction and a dimensionless coefficient respectively which is defined by the following relation: mi mj

Oxygen reaction at cathode

The oxygen solved in the electrolyte should diffuse along the radius of the nanotubes cylindrically to reach the Pt surface. The electrolyte covered the nanotubes is essential for proton transmittance, however could be a barrier against the oxygen to reach the catalyst. Therefore, the oxygen gradient along the radius of nanotubes is expressed as follow [12]:

¼

 1 1  ðPt=CÞ mPt þ rPt ðPt=CÞrc LCL

(12)

Then, porosity can be achieved by this relation. ¼ 1  3m  3s

(13)

As the rate of ORR is the function of oxygen concentration in the electrolyte, so the local overpotential is expressed on the basis of ButlereVolmer theory. Because of the effect of the current density on the performance of the PEMFC, the forward

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current density is applied in the ButlereVolmer [19]. By solving Eq. (8), the following equation is obtained (for detail see Ref. [12]):   ac Fhc airef 0;c exp  PO2 RT    V$ic ¼ rb CO2 ;ref 1 þ K ln HO2 ra

Dagg ¼ DH2 ;m ðð1  3 mac Þð3 mic ÞÞ1:5 (14)

ra and rb are the inner and outer radius of the cylindrical electrolyte which is shown in Fig. 1 and K is the dimensionless parameter.



airef 0;c

2.2.2.

  Vp ac Fhc exp  Sp RT ra CO2 ;ref DO2 ;m 4F

(15)

Hydrogen reaction at anode

The oxidation reaction of hydrogen at anode is occurred by diffusing the hydrogen through the electrolyte covering the spherical lumps of CB. The governing equation of this reaction was firstly proposed by Broka as follow [23]: 0

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i0;a aR2agg

FDagg @ 1 R2agg 2FCH2 ;ref Dagg 0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi11    i0;a aR2agg AA CH  CH ;ref exp 2Fha (16)  [email protected] 2 2 2FCH2 ;ref Dagg RT

V$ia ¼  6ð1  3 mac Þ

which is different from diffusion of H2 in the CL and is expressed as follow and other constants are mentioned in Table 1 as base case parameters (for detail see Ref. [23]):

2.3.

(17)

Parameters of the modeling

In this study, we used the experimental parameters of previous reliable articles. Proton conduction in the polysulfonic acid membrane (Nafion 117) is one of the crucial parameters, which depends on the temperature and the amount of water inside the membrane. Springer et al. proposed a formula for proton conduction and its relation with temperature and water content [24]:    1 1  sm ¼ s0m exp 1268 303 T

(18)

s0m ¼ 0:5139  l  0:326

(19)

where l is membrane water content. Relations (18) and (19) are based on the hypothesis that there is no liquid water content in the catalyst layer, so the amount of equilibrium water in the electrolyte is based on the humidity content in the reactants at 30  C [24] and 80  C [15]. leq ðaw ; TÞ ¼

where CH2 and Dagg are hydrogen concentration in gas phase and the diffusivity coefficient in the spherical aggregates

0:043 þ 17:81aw  39:85a2w þ 36a3w at T ¼ 30  C 0:3 þ 10:8aw  16a2w þ 14:1a3w at T ¼ 80  C (20)

Table 1 e Base case condition for proposed model. Parameters The GDL conductivity [S/m] Universal gas constant [J/(mol K)] Operating temperature (for isothermal condition) [K] Operating pressure [atm] Faraday’s constant [C/mol] Permeability of GDL [m2] Reference pressure [kPa] Anodic exchange current density [A/m2] Radius of agglomerate [mm] Micro porosity of anode CL Macro porosity of anode CL Henry’s constant of H2 [(Pa m3)/mol] Electric conductivity of CL [S/m] Inner radius of electrolyte at cathode CL [nm] Relative humidity Permeability of the CL [m2] Mass loading of platinum per unit aria of CL [mg/cm2] Platinum density [kg/m3] Carbon density [kg/m3] Platinum mass fraction [%wt] Volume fraction of electrolyte in cathode CL [%vol] Membrane density [kg/m3] Membrane equivalent weight [kg/mol] Membrane adsorption/desorption constant [1/s] Entropy associated with ORR [J/(mol K)] Thermal conductivity of CL [W/(m K)] Thermal conductivity of membrane [W/(m K)] Thermal conductivity of GDL [W/(m K)]

Notation (symbols)

Value

Source

sGDL s

1400 8.314 333 1.34 96,485.3 8.7  1012 134 104 0.1 0.2 0.4 6.69  104 72,700 25 1 1013 0.3 0.2 21,450 1800 15% 0.2 2000 1.1 10,000 163.7 0.67 0.67 1.67

[5] [6] [7] [7] [6] [8]

R T P F KGDL Pref i0,a Ragg 3 mic 3 mac

HH 2 sCL s ra RH KCL mPta mPtc rPt rC Pt/C 3m

rm EWm kad DSc kc km kG

[9] [5] [10] [11] [12] [7] [8] [7] [13] [11] [7] [14] [2] [15] [8] [8] [8] [8]

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 7 ( 2 0 1 2 ) 8 4 3 9 e8 4 5 0

where aw is the activity coefficient of water which is defined as follow:

Table 2 e Adopted equations for calculation domains. Layer

aw ¼

xH2 O P Psat

(21)

where Psat is the water saturation pressure and is in the form of:

GDL

GDLa

Psat ¼  2:1794 þ 0:02953ðT  273:15Þ  9:1837  105 ðT  273:15Þ

(22)

For Tafel-slope cathode charge transfer coefficient, which is dependent on temperature is expressed as follow [25]: ac ¼ 0:495 þ 2:3  103 ðT  300Þ

  4001 ¼ 3:507  log10 iref 0;c T

GDLc

CL

(24) CLa

Variation of oxygen diffusion by temperature in the electrolyte is reported in Ref. [25]. We used following relation in our modeling [26].   25; 000 (25) DO2 ;m ¼ 0:0438exp RT Moreover, the temperature dependant diffusion of hydrogen in the electrolyte which is presented by Yeo and McBreen is defined as follow [27,28]:   2602 DH2 ;m ¼ 4:1  103 exp  T

(26)

It should be noted that the temperature is expressed in Kelvin. For applying effect of temperature on the Henry’s law, we used the following equation [28]:   666 HO2 ¼ exp  þ 14:1 T

V$ rwH2 u  rwH2

1   VP A D þ ðx  w Þ Vx ¼0 j j j j¼1 ij P

Pn

1:5 sGDL Vfs Þ ¼ 0 V$ð3 GDL s

(23)

The reference exchange current density of ORR was obtained by interpolating the experimental data presented in Ref. [25] and is expressed as follow:

Equations    KGDL VP ¼0 V$ r  m V$ðkG VTÞ ¼ ST

2

þ 1:4454  107 ðT  273:15Þ3

8443

1   VP A D þ ðx  w Þ Vx ¼0 ij j j j j¼1 P 1   P VP A V$ pwH2 O u  rwH2 O nj¼1 Dij Vxj þ ðxj  wj Þ ¼0 P

V$ pwO2 u  rwO2

Pn

1:5 sGDL Vfs Þ ¼ 0 V$ð3 GDL s    KCL V$ r  VP ¼ SP m V$ðkc VTÞ ¼ ST

1   VP A Vx D þ ðx  w Þ ¼ SH2 j j j j¼1 ij P

1:5 r 3 sm V$  3 1:5 Dw m VðlÞ  nd Vfm ¼ Sl EWm F V$ rwH2 u  rwH2

Pn

1:5 CL V$ð3 CL ss Vfs Þ ¼ Sfs 1:5 V$ð3 CL sm Vfm Þ ¼ Sfm

1   VP A Dij Vxj þ ðxj  wj Þ ¼ SO 2 P 1   P VP A V$ pwH2 O u  rwH2 O nj¼1 Dij Vxj þ ðxj  wj Þ ¼ SH 2 O P

r 3 sm Vfm ¼ Sl V$  3 Dw m VðlÞ  nd EWm F V$ð3 CL sCL Vf Þ ¼ S fs s s V$ð3 CL sm Vfm Þ ¼ Sfm

r sm Membrane V$  Dw m VðlÞ  nd Vfm ¼ 0 EWm F CLc

(27)

V$ pwO2 u  rwO2

Pn

j¼1

V$ðsm Vfm Þ ¼ 0 V$ðkm VTÞ ¼ ST

And for water diffusion coefficient, following relations are used [24]:    1 1 Dw ¼ Dw;30  1010 exp 2416  (28) 303 T APt ¼ 2:2779  105 ðPt=CÞ3 1:5857  105 ðPt=CÞ2 Dw;30 ¼ 2:563  0:33l þ 0:0264l2  6:71  104 l3

and nd is the electro-osmotic drag coefficient of water which has been mentioned in Table 2 and expressed as follow: nd ¼

2:5 l 22

(30)

Effective surface area of reaction is another parameter, which is of prime importance in the modeling of catalyst layer and depends on the content of Pt loading (mPt) and thickness of catalyst layer (LCL) [26]. As we face some difficulties in the loading of Pt in low thicknesses of catalyst. a¼

APt mPt LCL

 2:0153  105 ðPt=CÞ þ 1:5950  105

(29)

(31)

In above equation, APt is theoretical loading platinum and a function of Pt/C or CNT mass fraction which is written as follow [29]:

(32)

By applying the parameters mentioned above in our modeling framework, we can precisely investigate the nanocatalyst in the experimental environment which developed by Van Bruinessen.

3.

Boundary conditions and solution scheme

All the boundaries and computational domains applied in our modeling are illustrated in Fig. 2. Because of interdigitated current at anode and cathode, the inlet and outlet pressures are set to 135 kPa and reference pressure, respectively. As the electrolyte is nonconductive for electrons, so at the interface of membrane and CL, the following relation is considered for electrons.

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1.2

Layer

Si

3

1

2.5

GDL

ST ¼ ss(Vfs)

CLa

MH2 V$ia r  MH2 O Kad m ðleq  lÞ 2F EWm MH V$ia SH2 ¼  2 2F r Sl ¼ Kad m ðleq  lÞ EWm Sfs ¼ V$ia Sfm ¼ V$ia ST ¼ hV$ia þ ss ðVfs Þ2 þ sm ðVfm Þ2   MO2 V$ic V$ic r  MH2 O þ Kad m ðleq  lÞ SP ¼ 4F 2F EWm MO2 V$ic SO2 ¼ 4F   V$ic r þ Kad m ðleq  lÞ SH2 O ¼ MH2 O 2F EWm r Sl ¼ Kad m ðleq  lÞ EWm Sfs ¼ V$ic Sfm ¼ V$ic DSc T ST ¼ V$ic þ hV$ic þ ss ðVfs Þ2 þ sm ðVfm Þ2 4F SP ¼ 

Membrane

ST ¼ sm ðVfm Þ2

n$ðss Vfs Þ ¼ 0

(33)

where n is normal vector and ss and fs are electron conductivity and electronic phase potential. Moreover, as the GDL is nonconductive for protons the following equation is expressed at the interface of CL and GDL. n$ðsm Vfm Þ ¼ 0

n$ðVCi Þ ¼ 0

(35)

For other interfaces, the normal flux for reactants is set to zero (symmetry condition). Meanwhile, terms related to the base condition, are presented in Table 1. We used a finite element scheme for solution of the 2D simulation task in a CFD package.

4.

Results and discussion

4.1.

Model validation

We compared the modeling results with the experimental data reported by Van Bruinessen using base parameters presented in Table 1. These validation results are shown in a polarization plot and Power density and there can be seen a nice agreement between the modeling results and experimental ones as showed in Fig. 3. In Figs. 3 and 4 the dot plot

2

0.6

1.5

0.4

1

Experimental Data Isothermal Model

0.5

Nonisothermal Model 0 0

200

400

600

800

1000

1200

0 1400

Current Density (mA/cm2)

Fig. 3 e Polarization curve and power density curve of experimental data [7] and our model to comparison. Pt/ CNT mass fraction becomes 15% (wt.%) using the base case value of LCL [ 15 mm, CO2 ;ref [1:32 mol=m3 , CH2 ;ref [1:71 mol=m3 and mPt [ 0.2 mg/cm2 as mentioned inRef. [7] to validate presented model in comparison with experimental data.

represents the experimental data, dash and continuous plots denote our modeling results for isothermal and nonisothermal conditions, respectively. This agreement is high in the low current densities in both Figs. 3 and 4. However, in the

(34)

where sm and fm are proton conductivity and protonic phase potential. In this modeling, the current collector of the anode is considered as base electrode and cathode as a cell voltage. As we hypothesized that the membrane layer is the perfect separating of electrodes, so no reactants can diffuse along the membrane and the boundary condition for both of the electrodes is as follow:

0.8

0.2

1.2 Experimental Data 1

Isothermal Model Nonisothermal Model

Cell Voltage (V)

CLc

Cell Voltage (V)

2

Power Density (W/mgPt)

Table 3 e Source/sink terms for appropriate domains.

0.8

0.6

0.4

0.2

0

0

500

1000

1500

Current Density

2000

2500

(mA/cm2)

Fig. 4 e Polarization curve of experimental data [20] and our model for further comparison. The base case value of LCL [ 15 mm, CO2 ;ref [1:84 mol=m3 , CH2 ;ref [2:53 mol=m3 , T [ 343 K, P [ 2 atm and mPt [ 0.2 mg/cm2 as mentioned inRef. [7] to validate another model in comparison with experimental data.

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334.6

high current densities, due to some phenomena including producing liquid water or condensation of water vapor, the agreement decreases. As can be observed in Fig. 3, in the low cell voltage, because of more consumption oxygen in the reaction site, the modeling results are above the experimental plots. More oxygen consumption at cathode causes low mole fraction as shown in Fig. 5 in spite of high oxygen diffusion at high temperature condition in nonisothermal modeling in comparison with isothermal modeling at T ¼ 333 K. By comparing the results of isothermal and nonisothermal modeling in Fig. 3, we came to the conclusion that both of them show similar results in the low current density, however, by increasing the current density, the cell temperature increased (Fig. 6) and causes an increase in the diffusion of reactants and rate of reaction which resulted in the increment of cell voltage. These results are shown in Fig. 7 for oxygen diffusion coefficient at three different cell voltages. In our proposed model, for anode and cathode site overpotential these formulation are applied [11]: ha ¼ fs  fm

(36)

hc ¼ fs  fm  Eth

(37)

where Eth is the theoretical voltage has been formulated as follow [28]: Eth ¼ 1:229  0:8456  103 ðT  298:15Þ þ 4:31  105 T ln PH2 þ 0:5ln PO2 (38) where PH2 and PO2 are hydrogen and oxygen partial pressure, respectively.

4.2.

Effect of catalyst thickness and porosity

It is clear from Fig. 8 (left side) that the thick catalyst layer lowers the activation overpotential. In this condition, thickness of catalyst layer is regulated in accordance with related parameters. In Fig. 8 (left), the porosity has been constant to investigate the effect of the catalyst layer thickness on the cell performance. For each thickness, the amount of the loading

Temperature (K)

334.4

334 V=0.35v 333.8 333.6

333.2

V=0.7v

0

5

10

Fig. 6 e Temperature distribution along cathode site at three different cell voltages.

has been chosen proportional with the porosity to fix the porosity by changing the thickness. In fact, by increasing the Pt loading on the thick catalyst layer, there would be more reaction site for the reactants and this is clear from Fig. 8. On the other hand, it can be seen in Fig. 8 (right side) increasing the Pt loading, due to the increased thickness of catalyst, the distance which should be passed by reactants to reach the reaction sites increases and results in an increase in the diffusion resistance, so the interior parts of the catalyst remain intact. Meanwhile, thick catalyst layer increases the resistance against the electron and proton conduction. However, due to the wide sites of reaction, the resistance against diffusion and conduction is compensated. As can be seen in Fig. 8 (right), although the porosity was lower in graph (LCL ¼ 7.5 mm, mPt ¼ 0.1, 3 v ¼ 0.4) than graph (LCL ¼ 15 mm, mPt ¼ 0.1, 3 v ¼ 0.6), however, the activation

0.1785 0.178 V=0.7v

0.1775

xO2

V=0.35v

0.176

0.1755

0.1755

0.175

0.175

10

CLc length(µm)

15

V=0.35v

0.1765

0.176

5

V=0.5v

0.177

0.1765

0

V=0.7v

0.1775

V=0.5v

0.177

15

CLc length(µm)

0.178

0.1745

V=0.5v

333.4

0.1785

xO2

334.2

0.1745

0

5

10

15

CLc length(µm)

Fig. 5 e Oxygen mole fraction at cathode site for nonisothermal (left) and for isothermal (right) conditions.

8446

2.34E-05

2.32E-05

2.33E-05

2.32E-05

Oxygen Diffusion (m2/s)

Oxygen Diffusion (m2/s)

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 7 ( 2 0 1 2 ) 8 4 3 9 e8 4 5 0

2.32E-05 2.31E-05 V=0.35v

2.30E-05

V=0.5v 2.29E-05

V=0.7v

2.28E-05 2.27E-05

2.31E-05 2.31E-05 2.30E-05 V=0.35v

2.30E-05

V=0.5v

2.29E-05

V=0.7v 2.29E-05 2.28E-05

0

5

10

2.28E-05

15

0

5

CLc length(µm)

10

15

CLc length(µm)

Fig. 7 e Oxygen diffusion coefficient variation along cathode catalyst layer in nonisothermal (left) and isothermal (right) conditions.

overpotential has been reduced. Whereas, the graph indicating the higher porosity shows the higher activation overpotential than previously mentioned graph and this higher overpotential has lowered the cell performance. By decreasing the conductive resistance of the reactants in the lower thicknesses at constant mPt, the cell performance has been improved in spite of decreasing the porosity. For more investigations, the results have been repeated for graphs (LCL ¼ 30 mm, mPt ¼ 0.2, 3 v ¼ 0.6) and (LCL ¼ 15 mm, mPt ¼ 0.2, 3 v ¼ 0.4). Comparison of two graphs (LCL ¼ 7.5 mm, mPt ¼ 0.1, 3 v ¼ 0.4) and (LCL ¼ 30 mm, mPt ¼ 0.2, 3 v ¼ 0.6) revealed that the graph with higher porosity than the other, indicates better cell performance, however as can be seen, the amount of Pt loading is different for both of them. To investigate whether this behavior was affected by porosity or Pt loading, we have evaluated the effect of Pt loading by changing the porosity in constant thickness.

4.3.

Effect of mPt loading

As can be observed in Figs. 9 and 10, by reducing the mPt loading, the activation overpotential has been increased which is an undesirable condition, whereas the porosity of layer for oxygen diffusion has been increased. In contrast, an increase in the mPt loading caused a decrease in the activation overpotential which resulted in the improvement of cell performance. More succinctly, in all of the catalyst thicknesses, increasing the mPt loading decreased both of the activation overpotential and porosity which can be seen in Figs. 9 and 10 for catalyst thicknesses of 30, 15 and 7.5 mm. Meanwhile our results suggested that the porosity has less impact on the cell performance. It is worth mentioning that thick catalyst layers need more amount of Pt for loading and this should be put into account in the commercialization procedures. It is clear in Figs. 9 and 10, that by decreasing the porosity and increasing the Pt loading in all of the thicknesses the

1.2

1.2

LCL=15µm, mPt=0.1, LCL=7.5µm, mPt=0.1, LCL=30µm, mPt=0.2, LCL=15µm, mPt=0.2,

LCL=7.5µm, mPt=0.1, v=0.4 1

LCL=15µm, mPt=0.2, v=0.4 LCL=30µm, mPt=0.4, v=0.4

0.8

Overpotential (V)

Overpotential (V)

1

0.6 0.4 0.2 0

v=0.6 v=0.4 v=0.6 v=0.4

0.8 0.6 0.4 0.2

0

100

200

300

Current Density

400

(mA/cm2)

500

0

0

100

200

300

400

Current Density (mA/cm2)

Fig. 8 e Effect of catalyst layer thickness on activation overpotential. Appropriate mPt loading considered for different thickness (left) and increasing transport resistance with increasing CL thickness depleted cell performance (right).

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1.2 LCL=30µm, mPt=0.2, v=0.6

Overpotential (V)

1

LCL=30µm, mPt=0.4, v=0.4 LCL=30µm, mPt=0.7, v=0.1

0.8 0.6 0.4 0.2 0

0

200

400

Current Density

600

800

(mA/cm2)

Fig. 9 e mPt loading effect on overpotential for 30 mm catalyst layer.

activation overpotential has been reduced indicating that the amount of the Pt loading has more effect on the activation overpotential than the porosity, therefore, it is clear in Fig. 8 (right) that improvement of the cell performance was more affected by Pt loading than porosity.

4.4.

Effect of mass ratio of Pt/CNT

Ratio of Pt/CNT is of immense importance in the construction of nanocatalyst layers and has two impacts on the cell performance: (i) amount of Pt loading and (ii) amount of CNT loading. In the constant loading of Pt, by increasing the ratio of Pt/CNT, relative loading of carbon decreases (according to the relation: Pt/CNT ¼ mPt/(mPt þ mCNT)) which resulted in diminishing the surface area of reaction sites and increment

in the porosity which makes it easier for oxygen to diffuse through the pores. Fig. 11 (left) shows that by increasing the Pt/CNT, limiting current density gradually decreases because the effect of decreasing the surface area of reaction sites was more pivotal than the effect of increasing the porosity. In the constant loading of mCNT, mPt loading increased as the ratio of mPt/CNT increased which had various impacts on the cell performance. Increasing the Pt/CNT decreased the surface area of the reaction according to Eq. (32), however, increasing the mPt has more impact on the increasing of a according to Eq. (31). Moreover, increasing the mPt and Pt/CNT has two different influences on the porosity of CL. It is clear in Fig. 11 (right) that the Pt content has been increased as the Pt/CNT increases and as a result, the cell performance has been discernibly enhanced and limiting current density has been shifted to higher values demonstrating the dominant role of mPt in the cell performance. It is observed in Fig. 11, that increasing the mPt and mCNT in the constant amount of mPt/ CNT has increased the limiting current density. This can be attributed to the increasing of the catalyst surface at the cathode needed for oxygen reaction has been increased due to the increment of Pt content. It should be noted that in both of the conditions (i) and (ii), the porosity of catalyst layer has been changed with variations of mPt and mCNT and the variation range of these parameters has been regulated according to the possibility of porous layer in CL thickness of 15 mm.

4.5.

Effect of Nafion loading

The amount of Nafion loading has dramatically influenced the layer porosity, proton conductivity and oxygen diffusion. As we mentioned in previous section, the layer porosity had no impact on the cell performance. As the covering layer of the catalyst increased by increasing the Nafion thickness, oxygen diffusion to reach the reaction sites encountered with problems. This resulted in a decrease in the limiting current density which is obvious in Fig. 12 (left). In the low values of current density, the proton conductivity was enhanced due to more presence of electrolyte in spite of low oxygen diffusion

1.2

1.2 LCL=15µm, mPt=0.1, v=0.6 CL=15um,mPt0.1 LCL=15µm, mPt=0.2, v=0.4 CL=15um,mPt0.2 LCL=15µm, mPt=0.35, =0. CL=15um,mPt0.35

0.8

Overpotential (V)

Overpotential (V)

1

1

0.6 0.4 0.2 0

0.8

LCL=7.5µm, mPt=0.05, CL=7.5um,mPt0.05

v=0.6

LCL=7.5µm, mPt=0.1, CL=7.5um,mPt0.1

=0.4

LCL=7.5µm, mPt=0.15, CL=7.5um,mPt0.15

v=0.2

0.6 0.4 0.2

0

100

200

300

Current Density (mA/cm2)

400

0

0

50

100

150

200

Current Density (mA/cm2)

Fig. 10 e mPt loading effect on overpotential for 15 mm catalyst layer thickness (left) and for 7.5 mm catalyst layer thickness (right).

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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 7 ( 2 0 1 2 ) 8 4 3 9 e8 4 5 0

3000

3000 2500

Limiting Current Density (mA/cm2)

Limiting Current Density (mA/cm2)

mPt=0.4 mPt=0.3 mPt=0.2 2000

mPt=0.1

1500 1000 500

2500

2000

1500

1000 mCNT=0.02 500

mCNT=0.015 mCNT=0.01

0

0

0.1

0.2

0.3

0

0.4

Pt/CNT

0

0.1

0.2

0.3

0.4

Pt/CNT

Fig. 11 e Different Pt/CNT ratio effect on limiting current density with constant mPt (left) and constant mCNT (right).

1.2

1.2 rb=28nm rb=28nm 1

rb=30nm rb=30nm

rb=35nm rb=35nm rb=37nm rb=37nm

0.6 0.4 0.2 0

eps_mem0.4 m=0.4

rb=33nm rb=33nm

0.8

Cell Voltage (V)

Cell Voltage (V)

1

m=0.5 eps_mem0.5

eps_mem0.3 m=0.3

0.8

eps_mem0.2 m=0.2 =0.1 eps_mem0.1

0.6 0.4 0.2

0

500

1000

1500

2000

Current Density (mA/cm2)

0

0

500

1000

1500

2000

Current Density (mA/cm2)

Fig. 12 e Effect of Nafion loading with variation of surrounded ionomer around the CNT deposited Pt on polarization curve (left) and effect of Nafion volume faction at constant ionomer thickness (rb [ 30 nm) around CNT deposited Pt on polarization curve (right).

in thick-coated electrolyte as can be seen in Fig. 12 (left) the cell performance has been improved. However, by increasing the current density of cell due to the high need for oxygen in the reaction sites and enhanced diffusion resistance which was attributable to the increased amount of volumetric fraction of electrolyte, the cell performance has been decreased. To prove this statement, we neglected the increasing of the covering layer of nanotubes. In this condition, increasing the Nafion loading caused an increase in the current density because of enhancing the proton conductivity without a change in the oxygen diffusion and this is illustrated in Fig. 12 (right).

5.

Conclusion

In this work, a 2D CFD-based model for PEM fuel cell considering the catalyst layer parameters which are of critical

importance in the cell performance is proposed. Emphases are placed on the effect of the anodic and cathodic reactions to compare the experimental data with modeling calculations. We just investigated the reduction reaction at the cathode because the cathodic reaction is more crucial than anodic one. It was indicated that thick catalyst layer should be loaded with large content of mPt to reduce the diffusion resistance and electron and proton conduction. It was cleared that, in a constant thickness of catalyst layer activation overpotential decreases and consequently the cell performance increases as the amount of mPt increases. Moreover, at constant amount of mPt, increasing the Pt/CNT ratio resulted in a decrease in the limiting current density. It is because of decreasing mCNT and losses activation area available for reaction. Additionally, at a certain limiting current density, specially between 1500 and 2000 mA/cm2, we can gain this current by adjusting the practical manufacturing suggesting that the amount of Pt should be optimum to reduce the costs. It was shown that,

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 7 ( 2 0 1 2 ) 8 4 3 9 e8 4 5 0

large amount of Nafion led to an increase in the thickness of surrounding layer of Pt-loaded nanotubes which resulted in an increment in the diffusion resistance and decrease in the limiting current density. If this effect is neglected, increasing the Nafion loading would lead to the increasing of proton conduction which cause the enhancement of limiting current density and cell performance in spite of decreasing of catalyst porosity.

Acknowledgements The authors seriously appreciate Ms. Forough Ameli and Mr. Payam Khoshkenar’s generous offers and theirs constructive comments. Also, we sincerely express our gratitude to the “Energy Research Center” at Amirkabir University of Technology and their co-operation without which this report could not have come to light.

Appendix A. Nomenclature

a APt C D Eth EWm F H i i0 k K LCL M mCNT mPt nd P Pt/C r R RH S T w x

effective surface area, m1 theoretical platinum loading, m2 kg1 concentration, mol m3 diffusivity, m2 s1 theoretical cathode potential, V membrane equivalent weight, kg mol1 Faraday’s constant, C mol1 Henry’s constant, atm cm3 mol1 current density, A m2 exchange current density, A m2 thermal conductivity, W m1 K1 permeability, m2 catalyst layer length, m molecular weight, kg mol1 carbon nanotube loading, kg m2 platinum loading, mg cm2 electro-osmotic drag coefficient pressure, Pa platinum to carbon (CB or CNT) ratio radius, nm universal gas constant, J mol1 K1 relative humidity source/sink temperature, K mass fraction mol fraction

Greek letters a charge transfer coefficient s conductivity, S m1 3 volume fraction f electrode potential, V h overpotential, V l water content m viscosity, Pa s carbon density, kg m3 rc rPt platinum density, kg m3

c

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molar diffusion volume, m3 mol1

Subscripts and superscripts a anode ad adsorbtion agg agglomerate c cathode CL catalyst layer eq equivalent eff effective GDL gas diffusion layer i,j species index k Knudsen diffusion m membrane ref reference s solid sat saturation v void fraction w water vapor

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