Performance analysis of a PEM fuel cell cathode with multiple catalyst layers

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Performance analysis of a PEM fuel cell cathode with multiple catalyst layers M. Srinivasarao a, D. Bhattacharyya b, R. Rengaswamy c,*, S. Narasimhan a a

Department of Chemical Engineering, IIT Madras, India Department of Chemical Engineering, West Virginia University, Morgantown, USA c Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79423, USA b

article info

abstract

Article history:

The cathode catalyst layer (CL) of a PEM fuel cell (PEMFC) plays an important role in the

Received 22 December 2009

performance of the cell because of the rate limiting mechanisms that take place in it. For

Received in revised form

enhancing the performance of a PEMFC, the use of multiple, ultra thin CLs instead of

28 February 2010

a single CL is considered in the present work. Since the concentration of oxygen decreases

Accepted 19 March 2010

in a CL from the diffusion medium-CL interface towards the polymer membrane, the CL

Available online 28 April 2010

adjacent to the diffusion medium should be of higher porosity than the other CLs. Similarly, the CL adjacent to the polymer membrane should contain more ionomer than the

Keywords:

other CLs. Furthermore, liquid water should be removed without causing significant mass

Performance analysis

transport and/or ohmic losses. Therefore, the design parameters of a CL can be varied

Multiple catalyst layers

spatially to minimize losses in a PEMFC. However, such a continuously graded CL is diffi-

Steady state model

cult to manufacture due to lack of commercially available techniques and associated costs.

PEMFC

As an alternative, a combination of layers can be synthesized where each layer is manu-

Optimum platinum loading

factured with different design parameters. This approach provides the opportunity to

Graded catalyst layer

optimize the design parameters of each layer. With this objective in mind, a detailed steady state model of a PEMFC cathode with multiple layers is developed. The model considers liquid water in all the layers. The catalyst layer microstructure is modeled as a network of spherical agglomerates. For improved water management, a thin micro-porous layer is considered between the gas diffusion layer (GDL) and the first catalyst layer. The performance curves for various combinations of the design parameters are shown and the results are analyzed. The results show that there exists an optimum combination of design parameters for each catalyst layer that can significantly improve the performance of a PEMFC. ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

In a polymer electrolyte membrane fuel cell (PEMFC), the catalyst layer (CL) is a critical component of the membrane electrode assembly (MEA). Though the layer is thin (10 to 20 mm) in comparison to other porous layers, it plays a vital role in the cell performance as many rate limiting

mechanisms such as sluggish oxygen reduction reaction (ORR) take place in this thin layer. For increasing the extent of reaction, the reaction sites should be accessible to reactant gases, protons, and electrons. In other words, the triple phase boundary (TPB) line length should be increased for improving the cell performance. The three phase contact in a PEMFC is formed by carbon supported platinum particles (for electron

* Corresponding author. Tel.: þ1 806 742 1765. E-mail address: [email protected] (R. Rengaswamy). 0360-3199/$ e see front matter ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2010.03.092

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transfer), ionomer (for ionic transfer), and voids (for transfer of reactants and products in liquid and gaseous form) [1]. Four major problems in the CL are: i) under-utilization of the electro-catalyst ii) mass transfer losses due to transport of the gaseous species iii) ionic and ohmic losses, and iv) removal of liquid water from the reaction sites. To counter these problems, use of multiple layers of catalyst is investigated in this paper. Various experimental attempts have been made to enhance the performance of a cell by modifying the composition and structure of the CL. The studies are focused on different manufacturing/fabrication techniques for reduction of thickness and platinum loading of the CL, better distribution of platinum, reduction of ionomer loadings, and the usage of bi-catalyst layers. Parthasarathy et al. [2,3] studied the effects of temperature and pressure on the ORR kinetics and mass transport using experimentally obtained kinetic parameters of the electrodes. Wilson and Gottesfeld [4] fabricated CL and gas diffusion backings separately. The CLs were cast from solution as thin films that utilized the ionomer as a binder. These thin films were then hot pressed directly onto the ionomer membranes. In another study, Wilson and Gottesfeld [5] catalyzed the polymer membranes by direct applications of thin film CLs. This type of fabrication enhances the interfacial continuity of ionomer between the membrane and the CL. Wilson et al. [6] made electrodes with low platinum loading using thermoplastic ionomers. They have shown reasonably high performance with a platinum loading of 0.12 mg cm2 on the cathode CL. Cha and Lee [7] prepared thin CLs of thickness 3 to 6 mm by plasma sputtering technique by depositing platinum directly on the surface of Nafion. Multiple sputterings were used to increase the utilization of catalyst. By using the multiple sputters at a platinum loading of 0.043 mg cm2, the authors were able to get a performance similar to the conventional CL with a platinum loading of 0.4 mg cm2. Fischer et al. [8] used additional porosity in thin film electrodes and observed performance improvement in air operated cells. Gasteiger et al. [9] have studied the dependence of performance on platinum loading. They concluded that platinum loading on cathode side can be reduced to 0.2 mg cm2with a voltage loss of 10 mV at 1 Acm2. Rajalakshmi and Dhathathreyan [10] prepared nanostructured platinum catalyst layer by pulsed electrodeposition method. Compared to conventional method, this method used less platinum without causing any performance loss. Abaoud et al. [11] demonstrated a hybrid technique for making MEA by combining spraying and screen printing techniques. Spraying technique is used to make the GDL while screen printing is used to make the CL. The authors reported a current density of 2.1 Acm2 at 0.5 V with a platinum loading of 0.15 mg cm2. Yang et al. [12] fabricated thin catalyst layers using different organic solvents. Experimentally they found that the electrode supported by ethylene glycol gave better performance compared to other solvents. Numerous studies have also been done on improving platinum and ionomer distributions in the CL. Cheng et al. [13] investigated utilization of platinum and morphology of the CL. They have reported that by impregnation of catalyst with Nafion, platinum utilization can be increased significantly. Roshandel and Farhanieh [14] analyzed the effects of non-

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uniform catalyst loading on cell performance. More platinum was loaded under the channels compared to that under the shoulders. This variable loading resulted in a better performance due to reduction in the non uniformity of the reactant concentration at GDL/CL interface. Song et al. [15] have obtained optimal distributions of platinum and Nafion in the CL. From the results, they have concluded that the optimal distribution of Nafion content is a linearly increasing function and that of platinum is a convex increasing function across the thickness of the CL. Sun et al. [16] and Kamarajugadda and Mazumder [17] studied the effect of CL structure and composition on cell performance numerically with a single phase model. Lai et al. [18] investigated the effect of Nafion loading on the cell performance and the activity of the catalyst by electrochemical methods. Ionomer loadings in the range of 0e2 mg cm2were used in making the CL. From the results, it was concluded that the CL with a Nafion loading of 1 mg cm2performed significantly better than the other loadings due to a lower interfacial and reaction resistances. Yoon et al. [19] studied the effect of pore structure of a CL on the cell performance by experimentally making three CLs namely fine, normal, and coarse structures. The literature review shows that a number of researchers have considered both experimental and theoretical approaches to study the effect of change in composition and structure on the cell performance. However, all these studies are done considering a single CL. Recently, Mukherjee and Wang [20] studied bi-layer cathode CL by direct numerical solution (DNS). Different electrolyte and void fractions were used in the CLs and it was concluded that high void fraction near the GDL and higher ionomer content near the polymer membrane gave better performance at various operating conditions. Kim et al. [21] considered a dual catalyst layer not only on the cathode side but also on the anode side. The authors demonstrated the effect of gradient in Nafion content on the cell performance. The dual CL coated MEA showed higher performance than a single CL coated MEA especially at high current densities. Though these are first attempts at studying multi layer reaction medium, the effect of liquid water is not considered in these studies. As the transport of liquid water plays a very important role in the performance of a PEMFC particularly at high current density, ignoring its effect can generate considerable inaccuracies in the results. Furthermore, use of more than two layers of CL provides more flexibility in manipulating the design parameters and their gradients. In the current study, four layers of CL, each of thickness 5 mm, are modeled considering effect of liquid water in all the layers. The primary objective of this study is to explore whether a multiple CL PEMFC performs better than a single CL PEMFC of the same thickness. The current state of the art for manufacturing is capable of making ultrathin CLs of thickness around 5 mm. The usual thickness of the conventional single CL is in the range of 10 to 30 mm. Therefore, four layers of CL are considered in this study to provide flexibility in the design. If the study indicates that the performance of a multilayer PEMFC is superior to that of a single-layer PEMFC, the model developed here can be utilized for optimizing not only the design parameters of individual layers, but also the thickness and the number of layers.

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The catalyst layer is characterized as a network of spherical agglomerates. Steady-state validation results of Rao et al. [1] showed that agglomerate characterization is quite accurate in predicting the fuel cell performance. Harvey et al. [22] also compared different modeling approaches and concluded that spherical agglomerate characterization predicts perceptible mass transport losses even at low voltages. Sun et al. [16] have also used spherical agglomerate characterization while Lin et al. [23,24] have used cylindrical agglomerate characterization. From the literature review presented before, it is found that techniques such as sputter deposition, direct decomposition, hybrid method, etc. can be used to make such ultra thin layers in addition to many conventional methods. Even though an increase in the thickness of a CL increases mass transfer resistance and platinum loading, it also increases the number of reaction sites. By optimizing the design parameters of each CL, it is possible to reduce the detrimental effects of a higher thickness. Since the ultimate goal of the multiple CL model development is to carry an optimization study, a detailed

analysis is performed in this paper to investigate whether such an optimum combination exists.

2.

Model development

A schematic of the PEMFC cathode with multiple catalyst layers considered in this work is shown in Fig. 1. The schematic shows the straight flow channels, diffusion layer (TGP 090), four layers of reaction medium, and the polymer membrane. The experimental design parameters and operating conditions are taken from Wang et al. [25] and Pasaogullari et al. [26]. A two-dimensional two-phase steady state model is developed with four layers of reaction medium. Though 2-D models may overpredict the performance at high current densities under certain conditions [27], a 2-D 2-phase model with detailed CL characterization can predict reasonably well. A number of researchers [28e30] have validated their 2-D models with experimental data. To reduce the model

Excess reactants and water droplets out

Y Diffusion due to conc. gradient

X

Electro osmotic drag

Flow field

GDL

M C C C C P L L L L L 1 2 3 4

MEM

Reactants gases in O2, N2, Water

Liquid water

Spherical agglomerates

GDL – Gas Diffusion Layer MPL–Micro-Porous Layer CL – Catalyst Layer MEM - Membrane Fig. 1 e Schematic of PEMFC cathode with multi reaction medium.

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complexity and computational load, the changes in the Z-direction are neglected in this paper. Since the main focus of the modeling study is on catalyst layer design, the effect of water accumulation under the land is also not considered in this model. As air flows through these channels, it moves through the GDL to reach the reaction medium. All the CLs in the reaction medium are modeled using a spherical agglomerate (Fig. 2) characterization. This characterization assumes that the CL consists of small spherical agglomerates and each one is assumed to be covered by a thin film of ionomer. It is also assumed that the water produced at the reaction sites diffuses through the ionomer film and reaches the agglomerate surface. There it forms an ultra thin layer before participating in condensation/evaporation process. Hence, the diffused oxygen first dissolves and then diffuses through this thin water film before it reaches ionomer/agglomerate surface. The Henry’s constants for air-water interfaces and aireionomer interfaces are given in Table 1. The complete mechanism along with the mathematical correlations is given elsewhere [1]. Condensation/Vaporization is considered in terms of interfacial transfer of water between liquid and vapor phase. The corresponding expressions are provided in Table 1. Details of the agglomerate characterization and the derivation of the corresponding equations can be found in Rao et al. [1]. In developing the model, the following major assumptions have been made: 1. Isothermal, steady state operation. 2. Water generated due to the ORR is in liquid form. 3. The modes of water transport through the membrane are electro-osmotic drag and back diffusion.

Fig. 2 e Schematic of a spherical agglomerate.

4. Electric conductivity and permeability of all the layers are isotropic. 5. Contact resistance between the cathode layers is negligible.

2.1.

Governing equations

Transport of the gaseous species in the GDL and the CLs is governed by diffusion due to concentration gradients. Since the pressure drop is significantly low in parallel flow geometry, convection effects are not considered. Liquid

Table 1 e Source terms. Component

Layer

Sf

Constitutive Relations

O2, N2

Flow channel

0

RO2 ¼ xkrxn CO2 jns

H2O (v)

Flow channel

Iw

H2O (l)

Flow channel

Iw

x ¼ j32 ðjcothðjÞ  1Þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi krxn j ¼ ragg Deff O2 ;mem

O2

GDL, MPL

0

O2

CL (1 to 4)

RO2

N2

GDL, MPL, CLs

0

H2O (v)

GDL, MPL, CLs

Iw

Di;eff ¼ 3k ð1  sÞ3=2 Dim

H2O (l)

GDL, MPL

Iw

Dim ¼ ð1  yi Þð

H2O (l)

CL (1 to 4)

2RO2 þ Iw

Nw ¼ 

fs

GDL, MPL

0

rw Kw krl dpc ð ds ÞVs Mw mw qffiffiffiffiffi krl ¼ s3 ; pc ¼ scosqc K3w JðsÞ

fs

CL (1 to 4)

nFRO2

HO2 ;mem ¼ 1:33expð666=TCell Þ

fr fr

CL (1 to 4) Membrane

nFRO2 0

HO2 ;W ¼ 5:08expð498=TCell Þ

RTcell =HO2 ;mem CO2 ;r         dmem =DO2 ;mem 1=a1 zkrxn þ dw =DO2 ;w HO2 ;w =HO2 ;mem 1=a1 zkrxn ) (  sÞ2 þ 1:263ð1  sÞ3 for qc < 90 JðsÞ ¼ 1:417ð1  sÞ  2:120ð1 1:417s  2:120s2 þ 1:263s3 for qc > 90 CO2 jns ¼



1þ

3 ð1  sÞ I w ¼ kc k yw ðpw  psat w Þqþ RTcell 3k srw sat kv ðpw  pw Þð1  qÞ Mw sat 1 þ ðjpw  psat w jÞ=ðpw  pw Þ q¼ 2 3=2

PN

yj 1 j¼1;isj Dij Þ

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water transport in gas channels is modeled using mist flow model. The gas and liquid transport in the gas channels modeled as plug flow with simultaneous exchange of species at the boundary between the gas channel and GDL. The diffusivities are calculated using Fick’s law. The effective diffusivities are found using Bruggeman relation considering the effect of liquid water. Effective electric and ionic conductivities are also evaluated using Bruggeman correlation. The liquid water transport is modeled using unsaturated flow theory (UFT) in the porous layers. The assumption of constant gas pressure results in a capillary pressure gradient that is equal to negative of the liquid pressure gradient. Darcy’s law is used to describe the flow of liquid water in the GDL, MPL and the CLs. The governing equations are given below. In these equations, Sf represents the source terms. The source terms and the required constitutive relationships are given in Table 1. Cathode flow channels

2.2.

v Gaseous species :  ðCi uÞ  VJi þ Sf ¼ 0 vy r v ðsuÞ  VNW;d þ Sf ¼ 0 Liquid water :  W MW vy

3.

Results and discussion

3.1.

Model validation

In the current study, the multi domain approach is used to solve the governing equations. In order to solve the equations, two boundary conditions are required at each interface for all the species. Typical boundary conditions for the gaseous species are continuity of the concentration and the flux. At CL4/membrane interface, zero flux conditions are considered for all the gaseous species. For liquid water, continuity of capillary pressure is considered along with continuity of flux. Capillary pressure is calculated using the Leverette’s equation. Zero flux condition is assumed for all the components at the entrance and exit points in the in-plane direction. A comprehensive review of various boundary conditions used in the existing literature that considers liquid water can be found in Rao et al. [1]. The boundary conditions used in this paper are given in Table 2.

(1) (2)

The developed model with a single CL is validated with the experimental data of Wang et al. [25]. The experimental cell consists of parallel channel geometry. The flow field consists of seven straight channels each of 1 mm width and 100 mm length. The total active area of the test cell is 14 cm2. Toray carbon paper (TGPH 090 with 20 wt% PTFE) is used as the GDL. A thin layer of MPL is coated on the GDL. Platinum loading of 0.4 mg cm2 is used on both the electrodes. The model parameters used in this study are shown in Table 3. The model is validated at an operating temperature of 70  C with 100% RH. Cathode exchange current density is used as a tuning parameter in validating

Cathode porous layers and membrane   Gaseous species : V  Deff i;k VCi;k þ Sf ¼ 0

(3)

Liquid water : VNw;k þ Sf ¼ 0

(4)

2 Electrons : keff;k ele V fs;k þ Sf ¼ 0

(5)

2 Protons : keff;l ion V 4r;l þ Sf ¼ 0

(6)

  ia mem ¼0 nd  Dmem Water through membrane : V VC w w F

Boundary conditions

(7)

Table 2 e Boundary conditions in X direction (C [ concentration, J [ Gas flux, N [ Liquid flux). Variables

CO2

CN2

CH2 O

s

Entrance

CO2 ¼ CO2 ;o

CN2 ¼ CN2 ;o

CH2 O ¼ CH2 O;o

GC/DL

DL CGC O2 ¼ CO2

DL CGC N2 ¼ CN2

DL CGC H2 O ¼ CH2 O

sGC ¼ sDL

DL/MPL

MPL CDL O2 ¼ CO2

MPL CDL N2 ¼ CN2

MPL CDL H2 O ¼ CH2 O

MPL pDL c ¼ pc

MPL JDL O2 ¼ JO2

MPL JDL N2 ¼ JN2

MPL JDL H2 O ¼ JH2 O

MPL NDL W ¼ NW

MPL/CL1

CL1/CL2

CMPL O2 JMPL O2 CCL1 O2

¼

CCL1 O2

¼

JCL1 O2

JMPL N2

¼

CCL2 O2

CCL1 N2

CL2 JCL1 O2 ¼ JO2

CL2/CL3

CCL2 O2 JCL2 O2

CL3/CL4

CL4/MEM

CCL3 O2

CMPL N2

¼ ¼

CCL3 O2

JCL3 O2

¼

CCL4 O2

¼

CCL1 N2

¼

JCL1 N2

JMPL H2 O

¼

CCL2 N2

CCL1 H2 O

CL2 JCL1 N2 ¼ JN2

CCL2 N2 JCL2 N2 CCL3 N2

CMPL H2 O

¼ ¼

CCL3 N2

JCL3 N2

¼

CCL4 N2

¼ ¼

CCL1 H2 O

JCL1 H2 O

¼

CCL2 H2 O

CL2 JCL1 H2 O ¼ JH2 O

CCL2 H2 O JCL2 H2 O CCL3 H2 O

¼ ¼

CCL3 H2 O

JCL3 H2 O

¼

CCL4 H2 O

pMPL c

¼

pCL1 c

NMPL W

¼

NCL1 W

pCL1 c

CL2 NCL1 W ¼ NW

eff;CL1 keff;m VfsjCL1 ele VfsjMPL ¼ kele

Vfr ¼ 0

fMPL ¼ fCL1 s s frjCL1 ¼ frjCL2

keff;CL1 VfsjCL1 ¼ keff;CL2 VfsjCL2 ele ele

keff;CL1 VfrjCL1 ¼ keff;CL2 VfrjCL2

fCL1 ¼ fCL2 s s

frjCL2 ¼ frjCL3

keff;CL2 VfsjCL2 ¼ keff;CL3 VfsjCL3 ele ele

¼

k

pCL3 c

¼

pCL4 c

frjCL3 ¼ frjCL4

keff;CL3 VfsjCL3 ¼ keff;CL4 VfsjCL4 ele ele

keff;CL3 VfrjCL3 ¼ keff;CL4 VfrjCL4

fCL3 ¼ fCL4 s s

frjCL4 ¼ frjMEM

VfCL4 ¼0 s

CL4 NCL3 W ¼ NW

VCCL4 H2 O

CMEM W

e

MPL fDL s ¼ fs

NCL3 W

CL4 JCL3 H2 O ¼ JH2 O

e

e

¼

VCCL4 N2

e

eff;m keff;d ele VfsjDL ¼ kele VfsjMPL

NCL2 W

CL4 JCL3 N2 ¼ JN2

¼0

fDL s ¼ Vcell

pCL3 c

VCCL4 O2

¼0

e

e

pCL2 c

NCL4 W MEM/ANODECL

¼

pCL2 c

fs

e

0

CL4 JCL3 O2 ¼ JO2

¼0

fr

¼ ¼

CCL4;EQ ðaÞ W

NMEM W

CMEM ¼ CCL;EQ ðaanode Þ W W

k

eff;CL2

eff;CL4

fr ¼ 0

VfrjCL2 ¼ k

VfrjCL4 ¼ k

eff;CL3

VfrjCL3

eff;mem

VfrjMEM

fCL2 ¼ fCL3 s s

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Table 3 e Model parameters. A m2 Pt1 J mol1 J mol1 A m2 Pt1 A m2 Pt1

ragg Kwo;GDL Kwo;MPL Kwo;CL kc kv

E 1 1 þþ iref (aþþ ¼ Tuning parameter) 0 expðRðTCell  Tref ÞÞa If Vcell > 0.79, 76,500 Else, 27,700 If Vcell > 0.79 , 3.85  104 Else, 1.50  102 If Vcell > 0.79, 1 Else, 0.495 þ 0.0023(Tcell  300) 0.1 8.7  1012 1  1014 3  1015 100 100

MPL kGDL ele , kele

1250

S m1

kCL ele

1000

S m1

rc rPt rw s qc (GDL, MPL, CLs)

1800 21,450 977.3 0.0625 110 , 120 , 100

kg m3 kg m3 kg m3 Nm1

io E iref o b

the model. The simulated data match very well with the experimental data. The validation results are presented in Fig. 3.

[16] mm m2 m2 m2 s1 atm1s1

[1] [26] [23] [1] [1]

[1] [1] [1] [26]

mPt 1  fPt fPt fionomer  þ þ

tCL fPt rC rPt 1  fionomer rionomer

(8)

mPt fionomer fPt 1  fionomer

(9)

Construction of a four layer reaction medium

It has been mentioned before that a model is developed with four thin CLs each of 5 mm thickness. In view of the physics of the processes that take place in a PEMFC, the design parameters for each CL are selected such that the CL near the diffusion medium (called CL1 in this work) has more voidage than any other CL and the CL near the membrane (called CL4 in this work) contains higher ionomer fraction than any other CL. So, the void fraction is gradually reduced from CL1 to CL4. In the same way, the ionomer fraction is gradually reduced from CL4 to CL1. In each CL, the following equations are used

[16]

to calculate the volume fractions of voids, ionomer, and solids. 3r ¼ 1 

3.2.

[16] [16]

3ionomer ¼

1 tCL rionomer

3s ¼ 1  3r  3ionomer

(10)

where, fPt , fionomer are weight fractions of platinum and ionomer respectively and are defined as fPt ¼

wPt wPt þ wC

fionomer ¼

wionomer wPt þ wC þ wionomer

(11) (12)

In the following sections, we show the effects of ionomer distribution and weight fraction of platinum on carbon at constant platinum loading.

3.3. Effects of various CL design parameters on the cell performance 3.3.1.

Fig. 3 e Comparison of polarization curves between experimental and simulation (Operating conditions: Tcell [ 70  C, P [ 2 atm, Air flow rate [ 0.505 LPM, 100%RH).

Graded weight fraction of ionomer

An increase in weight fraction of ionomer improves the conduction of protons in the CL. On the other hand, increase in weight fraction of ionomer decreases the voidage resulting in more mass transfer resistance. Since mass transfer losses are significant at high current densities, increase of ionomer fraction results in larger concentration overpotential. High loading of ionomer near the membrane can also cause flooding. The ionomer content has no effect on the solid fraction and hence the electric losses remain same. Fig. 4 shows performance curves of three PEMFCs. One PEMFC contains a single CL with an ionomer content of 22 wt%. The other

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Fig. 4 e Polarization curves for single and multiple CLs with graded wt% of Ionomer.

PEMFC contains a single CL with an ionomer content of 34 wt %. The third PEMFC contains four CLs (CL1 through CL4) containing 22 wt%, 26 wt%, 30 wt%, and 34 wt% of ionomer respectively. From the VeI curves, it is observed that the single CL PEMFC containing 34 wt% ionomer showed good performance at low and medium current densities. While at higher current densities, the performance dropped drastically. As discussed before, this drop in performance is because of a high mass transfer resistance. In the PEMFC with 22 wt% ionomer, the ionic losses are more than that in the previous case. Hence, at low and medium current densities the performance is inferior to the previous case. However at high current density when the mass transfer resistance plays a dominant role, the higher voidage becomes advantageous and the performance is improved. To trade-off between the ionic and mass transfer losses, a reaction medium of four CLs is considered. This distribution provides a gradual increase in ionomer volume from MPL/CL1 to CL4/membrane region. This configuration provides better performance than that of a single CL throughout the entire polarization range. Distributions of ionomer potential and the concentration of oxygen in reaction medium for these three cells are shown in Figs. 5 and 6 respectively. In Figs. 5 and 6, the divisions marking CL1 through CL4 are applicable only to the PEMFC with four layers of CL. For other PEMFCs with a single CL, “thickness ¼ 0” indicates the CL/MPL interface and “thickness ¼ 20 mm” indicates CL/membrane interface. Fig. 5 represents ionomer potential distribution at a voltage of 0.6 V. In the PEMFC with 22 wt% ionomer, the gradient of ionomer potential keeps increasing towards the CL/membrane interface. Fig. 5 also shows that the loss in voltage due to movement of protons is more in the PEMFC with four CLs compared to that of the single CL PEMFC with 34 wt% ionomer. In spite of this, the cell with four CLs performs better. This is due to the gain in the performance resulting from reduction of mass transfer losses. The profile of partial pressure of O2 at 0.4 V is shown in Fig. 6. The concentration gradient does not change much in the PEMFC with 22 wt% ionomer loading. However,

Fig. 5 e Distribution of ionomer potential for single and multiple CLs at 0.6 V.

the fall in the concentration gradient is rapid in case of the PEMFC with 34 wt% ionomer loading. In the cell with four CLs, the concentration gradient falls slowly in the first three CLs, and then falls sharply in the last CL. In this sensitivity study, a uniform gradient of 4% has been considered for the weight fraction of ionomer. Fig. 6 suggests that a variable gradient of ionomer weight fraction may reduce the mass transport losses in all the CLs particularly in the fourth CL. The optimal value of a variable gradient can be determined through an optimization study. Such a study is under progress.

3.3.2.

Graded weight fraction of platinum on carbon ( fpt)

If the platinum loading remains unchanged, an increase in the fpt causes ionomer and solids fractions to decrease. Therefore, void fraction increases. As a result, ionic and electric losses increase whereas mass transport losses diminish. Fig. 7 shows comparison of performance curves between PEMFCs with single CL and PEMFCs with multiple CL. Two single CL PEMFCs are considered here with fpt of 20 wt% and 35 wt% platinum

Fig. 6 e Distribution of oxygen concentration for single and multiple CLs at 0.4 V.

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Fig. 7 e Polarization curves for single and multiple CLs with graded wt% of Platinum.

respectively. Two multiple CL PEMFCs are considered e one with a uniform gradient of 5 wt % and another with a nonuniform gradient with fpt of 20%, 22%, 25%, and 35% in CL1, CL2, CL3, and CL4 respectively. From the results, it is observed that there is a reasonable increase in the cell performance especially at high current densities with multiple CLs. Single CL PEMFC with 20 wt% fpt performs better at low and medium current densities because of low activation and ohmic losses. Due to lower void fraction, limiting current density is reached at a voltage of 0.4 V. In contrast to this, the PEMFC with 35 wt% fpt performs well at higher current densities, but poor at higher voltages. The overpotential due to these two limiting regions is reduced considerably with a uniformly graded four CL reaction medium. From the Figure, it is also observed that the cell with non uniform graded CLs performs better than the cell with uniformly graded CLs. It can be mentioned that an improvement in the cell performance not only depends on this gradient, but also depends on other design parameters used in making the CL. Under certain circumstances, higher

Fig. 9 e VeI curves for single and multiple CLs for case 2.

gradients may give worse performance due to decreased three phase contact. A simultaneous optimization study can help in finding the optimum combination of these parameters.

3.3.3.

Non uniform platinum loading

The increase in platinum loading enhances the extent of ORR and hence the performance especially at higher voltages. For medium and high current densities, this beneficial effect is outweighed by a dominating concentration polarization. In this study, each CL is loaded with different amounts of platinum by keeping the total loading constant. The graded CLs with different platinum loadings show better performance than the single CL. In case 1, platinum and ionomer weight fractions are 0.35 and 0.34 respectively with a platinum loading of 0.4 mg cm2 for a single CL of 20 mm. Since the area of the cell is 14 cm2, the total platinum used is 5.6 mg. The same amount of platinum is distributed among the four CLs keeping other design parameters constant. The platinum loading is gradually increased from CL1 to CL4. In case 2, similar study is carried out with decreased ionomer and platinum weight fractions. The performance curves for both the cases are shown in Figs. 8 and 9 respectively. In both the cases, an improvement in performance is observed throughout the polarization range. However the improvement is significant at higher current densities. The design parameters and the platinum distributions for these cases are shown in Table 4.

Table 4 e Design parameters of platinum loading studies. fpt

mpt (mg cm2)

fionomer CL1

Fig. 8 e VeI curves for single and multiple CLs for case 1.

CL2 2

CL3

CL4

Case 1:

0.35 0.35

0.34 0.34

0.4 mg cm 0.08

(single CL) 0.09

0.11

0.12

Case 2:

0.2 0.2

0.22 0.22

0.4 mg cm2 (single CL) 0.08 0.09

0.11

0.12

6364

4.

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Conclusions

A two-dimensional two-phase steady state model of a PEM fuel cell cathode is developed. The developed model with single CL is validated with experimental data available in the open literature. Instead of a single CL used traditionally in a PEMFC, four CLs are considered in this study. Four CLs, each of thickness 5 mm, are used as a replacement of a 20 mm thick single CL. In each layer, different design parameters are chosen such that the CL near the MPL contains more void volume and the CL near the polymer membrane contains more ionomer volume. First, the performance of a four CL PEMFC with graded weight fraction of ionomer is compared with two single CL PEMFCs having 22 wt% and 34 wt% ionomer respectively. The cell with 22 wt% ionomer shows good performance at high current densities whereas the cell with 34 wt% ionomer performs well at low and medium current densities. Compared to these single CL PEMFCs, the four CL PEMFC generates higher current densities throughout the entire operating range. Similar studies are done with graded platinum fractions. The four CL PEMFCs, both with uniform and non-uniform gradients in platinum fraction, outperform the single CL PEMFCs. In comparison to uniform gradient, a non-uniform gradient in platinum fraction gives improved current densities. To study the effect of platinum loading gradient, platinum loading is varied from CL1 to CL4 by keeping the total amount of platinum same as a single CL. For this study, two different base cases are considered. In one of the base cases, ionomer and platinum weight fractions are decreased. In both the cases, the performance of a multiple CL cell is superior to that of a single CL cell. The sensitivity studies presented in this work confirm the superior performance of a multiple layer CL compared to that of a single layer CL. In this work, only a single design parameter is varied at a time keeping other design parameters constant. The results indicate the existence of an optimum combination of the design parameters in each catalyst layer that can significantly improve the performance of a PEMFC. The advantage of a multiple CL configuration is its flexibility in terms of optimizing the design parameters of each layer that can cater to the requirement of that particular layer. Further, the thickness of an individual CL and the total number of layers can be jointly optimized with the other design parameters. Such an attempt will of course need a mixed integer non-linear optimization. This work is under progress.

Nomenclature apt Cki CO2 jns Cmem W eff ;k

Di Dmem O2 Dmem W E fionomer fPt

Specific surface area of platinum (m2 Pt (Kg Pt)1) Concentration of species i in region k (mol m3) Concentration of dissolved oxygen at the ionomer and the spherical agglomerate Interface (mol m3) Concentration of liquid water in the membrane (mol m3) Effective diffusivity of the species i in region k (m2 s1) Diffusivity of oxygen in ionomer (m2 s1) Diffusivity of liquid water in the membrane (m2 s1) Activation energy (J mol1) Weight fraction of ionomer in the catalyst layer Weight fraction of platinum on carbon

F Faraday’s constant (C mol1) HO2 ;mem Henry’s constant for air-ionomer interface (atm m3 mol1) Henry’s constant for air-water interface HO2 ;W (atm m3 mol1) Local current density (A m2) ia Cell current density (A m2) icell Exchange current density for oxygen reduction on io platinum (A m2 (kg Pt)1) ref Reference exchange current density for oxygen io reduction on platinum (A m2 (kg Pt)1) k Local flux due to diffusion of species i in region k Ji (mol m2 s1) Condensation constant (s1) kc Evaporation constant (atm1s1) kv Permeability of liquid water inside porous region k at Kwo;k 100% saturation (m2) Platinum loading inside the catalyst layer mPt (Kg Pt (m2 CL)1) n Number of electrons taking part in the oxygen reduction reaction Net electro-osmotic drag coefficient nd Flux of liquid water in region k (mol m2s1) NW;k Partial pressure of water vapor (atm) pw Saturation pressure of water vapor (atm) psat Capillary pressure (atm) Pc Agglomerate radius (m) ragg R Universal gas constant (J mol1K1) Rate of oxygen reduction reaction per unit RO2 volume of the catalyst layer (mol m3s1) Interfacial transfer of water between liquid and Iw vapor (mol m3s1) Liquid water saturation level in region k sk Source term Sf Thickness of the catalyst layer (m) tCL Cell temperature (K) Tcell Volume occupied by the carbon inside vc catalyst layer (m3) Volume of the catalyst layer (m3) vCL vionomer Volume occupied by the ionomer inside catalyst layer (m3) Volume occupied by the platinum inside catalyst vPt layer (m3) Volume of solids inside catalyst layer (m3) vs Void volume inside catalyst layer (m3) vV Cell voltage (V) Vcell Mass of carbon inside the catalyst layer (kg) wc wionomer Mass of ionomer inside the catalyst layer (kg) Mass of platinum inside the catalyst layer (kg) wPt Greek letters b Cathode transfer coefficient Void fraction inside region k 3k Fraction of volume occupied by the ionomer inside 3ionomer the catalyst layer Effective proton conductivity in the catalyst keff ;c layer (mho m1) eff ;mem Effective proton conductivity in the membrane k (mho m1) k Electric conductivity in region k (S m1) kele

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eff ;k

kele lw

rc rionomer rPt rw s qc

Effective electric conductivity in region k (S m1) Water content in the membrane (mol H2O (mol SO3)1) Density of carbon (kg m3) Density of ionomer (kg m3) Density of platinum (kg m3) Density of water (kg m3) Surface tension (N m1) Contact angle

Subscripts i Index for the species: O2, N2, H2O k Index for the region: diffusion layer, micro-porous layer, catalyst layer l Index for the region: catalyst layer, polymer membrane

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