Computational Modeling Aspects of PEFC Durability

Computational Modeling Aspects of PEFC Durability

Chapter 9 Computational Modeling Aspects of PEFC Durability Yu Morimoto* and Shunsuke Yamakawa Toyota Central R&D Labs. Inc., Nagakute, Aichi, Japan ...

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Chapter 9

Computational Modeling Aspects of PEFC Durability Yu Morimoto* and Shunsuke Yamakawa Toyota Central R&D Labs. Inc., Nagakute, Aichi, Japan

1. INTRODUCTION This entire book is dedicated to various aspects of the degradation of polymer electrolyte fuel cells. This last chapter describes an approach to this issue using computer modeling. This approach is a very effective and powerful tool, for two main reasons. Firstly, degradation issues in PEFCs are very complex. Therefore, observable phenomena are only the final results of multi-step chemical and thermodynamic reactions. The influences of PEFC operational conditions, such as temperature, pressure and humidification, on the final degradation frequently seem inconsistent. This can happen because a PEFC operational condition that can accelerate one step may decelerate another. Therefore, a total quantitative understanding is very difficult without help from computer modeling studies which describe the balances of all elemental steps and their dependencies on PEFC operational conditions. Secondly, the elemental steps themselves sometimes are not observable, hence their nature often cannot be experimentally defined. A quantum chemical approach can be an effective tool for these problems. In this chapter, the two modeling approaches, chemical engineering macroscopic modeling and molecular-level quantum chemical microscopic modeling for computational studies on PEFC durability and degradation are first reviewed. Secondly, recent works on macroscopic degradation of platinum catalysts in PEFCs are presented.

2. SIGNIFICANT LITERATURE 2.1. Macroscopic Models of Chemical Membrane Degradation Membrane degradation has been a focal issue, since it results not only in gradual performance loss but also sudden failure by gas cross Polymer Electrolyte Fuel Cell Degradation. DOI: 10.1016/B978-0-12-386936-4.10009-0 Copyright Ó 2012 Elsevier Inc. All rights reserved.



Polymer Electrolyte Fuel Cell Degradation

leakage. The basic mechanisms of the chemical degradation of the membrane are: 1. PFSA membrane is chemically decomposed by peroxide radical attack, 2. Peroxide radicals are generated on Pt when both H2 and O2 exist. There are, however, unanswered questions such as: 1. Is the peroxide radical generated directly on Pt or through hydrogen peroxide with help from transition metal ions? 2. On which platinum (in the cathode, anode or Pt band) is the peroxide radical and/or hydrogen peroxide generated? In spite of the low level of the understanding of the degradation mechanism, there has been one model published for the chemical membrane degradation [1]. Figure 9.1 shows the domain for the model. The assumed phenomena in this study are: 1. 2. 3. 4. 5. 6.

hydrogen crossover from the anode to cathode, peroxide radical formation on the cathode/membrane interface, membrane degradation caused by the radical attack, fluoride formation and transportation, membrane thinning, and OCV change by hydrogen crossover increase and electrochemical Pt area loss.

While there is a good agreement in fluoride emission, the model seems to need various refinements, and further advancement in the understanding of the mechanism.

FIGURE 9.1 Domains for chemical degradation model of reference [1]. Reproduced by permission of The Electrochemical Society.

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2.2. Microscopic Models of Membrane Degradation As indicated previously, the mechanism of peroxide radical formation is not fully understood. Atrazhev et al. [2] proposed that the peroxide radical can be formed directly on a Pt surface – as shown in Fig. 9.2 – instead of through hydrogen peroxide, using a density function theory calculation. This mechanism allows peroxide radicals to be formed on the cathode, whose potential is too high to form hydrogen peroxide, by the two electron reduction of oxygen. This could explain some experimental results which suggest radical formation on the cathode [3,4,5]. Chemical degradation mechanisms of polymer membranes were studied quantum-chemically for hydrocarbon membranes [6] and for perfluorinated membranes [7]. The latter showed a possible new decomposition mechanism of peroxide radical attack at undissociated SO3H side chain terminals, as shown in Fig. 9.3. Hydrogen radicals, which can be formed by the reaction between a hydrogen molecule and a peroxide radical, may attack any position on the polymer, in addition to the previously proposed mechanism [8] of peroxide radical attack at any remaining, non-fluorinated, main chain terminals, which would be followed by unzipping reactions.

2.3. Macroscopic Models of Mechanical Membrane Degradation Membrane failure means a large gas cross-leakage through a pinhole or tear. It is believed to be initiated chemically and to be finished mechanically: i.e. a pinhole or tear is formed by mechanical stress on a chemically degraded membrane. The major source of mechanical stress is RH cycling because

FIGURE 9.2 Direct peroxide formation scheme [2]. Reproduced by permission of The Electrochemical Society.


Polymer Electrolyte Fuel Cell Degradation

FIGURE 9.3 Peroxide attack on undissociated sulfonic acid end group to form sulfonyl radical and decomposition propagation scheme from sulfonyl radical to main chain scission [7]. Reproduced by permission of The Electrochemical Society.

a polymer electrolyte membrane, whether perfluorinated or hydrocarbon, swells at a high RH and shrinks at a low RH. X. Huang et al. [9] employed a finite element code to predict the tensile strain caused by RH cycling using experimental stress-strain data, and showed that a large strain is induced at the corner of a MEA, as shown in Fig. 9.4.

2.4. Macroscopic Models for the Mechanical Degradation of Catalyst Layer and Interface The catalyst layer has a microstructure of ionomer, Pt-deposited carbon, and pores and this can be changed by various means. Since fuel cell performance is significantly influenced by this microstructure, changes in it are important. Rong et al. [10,11] presented an FEM model to describe debonding and delamination between ionomer and C/Pt agglomerate during humidity and temperature cycles. Figure 9.5 shows their model for the contact between ionomer and catalyst powder, and Fig. 9.6 shows their microstructure model of a catalyst layer. They estimated the strain in the ionomer phase as caused by humidity cycles, predicted the initiation time of delamination between the ionomer and carbon and showed that these mechanical changes can happen, and can affect fuel cell performance. Delamination can also be an issue when water in the catalyst layer freezes. He et al. [12,13,14] presented a 1D transient model for this phenomenon.

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FIGURE 9.4 Model predicted distribution of maximum principal tensile strain in the MEA and edge seals as a result of RH variation from 75 to 0% [9].

Figure 9.7 shows the locations of ice lens formation. The authors showed that ice lens formation between the catalyst layer and the electrolyte membrane, or between the diffusion medium and the catalyst, can cause unrecoverable damage.

2.5. Models of Contamination Various types of contamination can be introduced into a PEFC from fuel and air flow, and by the corrosion or decomposition of fuel cell materials. Although CO is a common contaminant in the fuel flow, and its poisoning is a serious issue for reformate-fueled FCs, this is a performance issue rather than a degradation issue, since CO is a standard component in a reformate, and such poisoning is recoverable. H2S in the fuel flow, however, is a cumulative poison that is not easily removed, and therefore contamination by it can be regarded as a degradation issue. This issue was modeled by Shah and Walsh [15]. Their model assumed that H2S is adsorbed on Pt in the anode, forming Pt-S and predicted


Polymer Electrolyte Fuel Cell Degradation FIGURE 9.5 Model region for the contact between ionomer and catalyst powder; dark gray domain (domain 2) represents the C/Pt agglomerate and the light gray domain (domain 1) represents ionomer [10].

general dependency on temperature and relative humidity. Cation contamination, which could happen through introduction of salt-containing air, was modeled by Weber and Delacourt [16], who considered potassium contamination of the electrolyte, and its transportation causing the proton concentration at the cathode to become zero.

FIGURE 9.6 Model region for the contact between ionomer and catalyst powder; the dark gray domain represents the C/Pt agglomerate and the light gray domain represents ionomer [11].

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FIGURE 9.7 Illustration showing locations of ice lenses [13]. Reproduced by permission of The Electrochemical Society.

2.6. Macroscopic Models of Carbon Corrosion The mechanism of rapid carbon corrosion during start-stop was first presented in a simple model by Reiser et al. [17], in which carbon in the cathode catalyst layer is quickly corroded when hydrogen occupies only a part of the anode as shown in Fig. 9.8. A detailed mathematical model was subsequently developed by Meyers and Darling [18] to quantitatively study the influence of the operating conditions on the degree of the degradation, not only for start-stop but also for local anode flooding and hydrogen maldistribution. Figure 9.9 shows simulated, transient, carbon corrosion current density during start-up. Fuller and Gray expanded this model to 2D [19] to

FIGURE 9.8 Potential distributions along anode flow path during reverse current conditions [17]. Reproduced by permission of The Electrochemical Society.


Polymer Electrolyte Fuel Cell Degradation

FIGURE 9.9 Time trace of a fuel into air start. Step 1: Air on both electrodes. Step 2: Fuel is introduced to anode. Step 3: Fuel on anode, stagnant air on cathode. Step 4: Flowing air on cathode. Step 5: Load is gradually increased from open circuit to 1 A/cm2. Step 6: Current is maintained at 1 A/cm2. Note that as fuel is introduced, the carbon corrosion rate increases sharply and is sustained as long as there is a fuel-air front in the cell. The corrosion rate then drops sharply again, after the fuel-air front passes through the cell [18]. Reproduced by permission of The Electrochemical Society.

simulate the potential distribution in the membrane and both the electrodes as shown in Fig. 9.10. A 3D CFD model was developed by employing these concepts [20]. Various mitigation techniques, such as using a catalyst with high oxygen evolution

FIGURE 9.10 Simulated 2D potential distribution for partial fuel starvation [19]. Reproduced by permission of The Electrochemical Society.

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FIGURE 9.11 Average reversal current density as a function of O2 diffusivity in membrane [21]. Reproduced by permission of The Electrochemical Society.

reaction (OER) activity, a membrane of low O2 diffusivity, corrosion-resistant carbon support and high proton conductivity in the catalyst layer, were evaluated through a 2D model [21]. Figure 9.11 shows the effect of O2 diffusivity on a membrane. Franco and Gerard [22] integrated a 1D carbon corrosion model into a fuel cell performance model by estimating the thickness of catalyst layers, the surface area of Pt and the contact resistance between the cathode and a GDL.

2.7. Microscopic Models on Platinum Dissolution There are only a few reports of microscopic model studies for platinum dissolution. Tian and Anderson [23] showed, by a first principle calculation, that Co is oxidized before Pt on a Pt-Co alloy, and that Pt edge sites are more easily to be oxidized than Pt on the terrace. The latter result suggests that Pt dissolution is initiated at the edge site. Zhou [24] carried out a molecular dynamic (MD) simulation for a charged Pt surface in contact with Nafion containing water. The simulation suggested that Pt disintegration was caused by the interaction between Pt and the sulfonic acid terminal of Nafion, and by an instantaneous temperature rise at the interface of up to 2,000 K. This temperature rise, however, seems too high to be realistic.


Polymer Electrolyte Fuel Cell Degradation

2.8. Macroscopic Models of Catalyst Degradation The loss of area of electrochemically active Pt is one of the most serious degradation symptoms in PEFCs. A similar phenomenon was known in phosphoric acid fuel cells. Bett et al. [25] fitted the surface area decay curve and suggested that Ostwald ripening contributes to the surface area loss. (The term Ostwald ripening is generally used for a phenomenon in which a component species separates, dissolves, or evaporates from smaller particles, and then transfers through a medium and attaches, deposits, or condenses onto larger particles. It results in the disappearance of smaller particles and growth of larger particles.) Their idea suggests that the component species in this case is Pt atom, which transfers onto the surface of carbon. In PEFCs, the first mathematical model was presented by Darling and Meyers [26]. They consider Pt ion dissolution and its diffusion in the ionomer phase, rather than Pt atom separation and transfer. The phenomana included in the models are electrochemical Pt dissolution into the ionomer, Pt oxide formation and the chemical dissolution of Pt oxide. The rate of Pt dissolution was described as a function dependent on the coverage of Pt oxide and the Pt particle size, using a modified Butler-Volmer equation as follows: "   aa;1 n1 F ðF1  F2  U1 Þ r1 ¼ k1 qvac exp RT !  # ac;1 n1 F CPt2þ ðF1  F2  U1 Þ  (9.1) exp  RT CPt2þ ;ref U1 ¼ U1q 

aPt MPt 2FrPt r

The platinum oxide formation reaction rate is described as: "     aa;2 n2 F uqPtO r2 ¼ k2 exp  ðF1  F2  U2 Þ exp RT RT !  # 2 CH þ ac;2 n2 F ðF1  F2  U2 Þ  qPtO exp  2 RT CH þ ;ref U2 ¼ U2q þ

aPtO MPtO aPt  2FrPtO r 2FrPt r


(9.3) (9.4)

Figure. 9.12 shows simulated PtO coverage at a potential sweep. The same authors [27] then expanded their model to describe Pt movement in a fuel cell. Their new model includes Pt ion diffusion through the electrolyte membrane and the anode ionomer, and simulations were carried out assuming a bimodal particle-size distribution. The results successfully predicted that electrochemically active area loss is much quicker during potential cycling than potential

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FIGURE 9.12 Comparison of equilibrium oxide coverage to predicted oxide coverage [25]. Reproduced by permission of The Electrochemical Society.

FIGURE 9.13 Oxide coverage and soluble platinum concentration during square-wave cycling from 0.87 to 1.2 V with a period of 60s [26]. Reproduced by permission of The Electrochemical Society.

holding at any given potential. Figure 9.13 shows the Pt concentration change during potential cycling. Franco and Tembely [28] utilized a similar Pt dissolution/deposition model and simulated the electrochemical impedance spectroscopic responses based on ionomer/Pt interface. Bi and Fuller [29] added the phenomenon of Pt-band formation as a result of the chemical reduction of diffused Pt ion by cross-over hydrogen at a specific plane in the membrane. Holby et al. [30,31,32] used a similar model, and simulated electrochemically active area loss assuming various particle size distributions for the initial


Polymer Electrolyte Fuel Cell Degradation

condition. They concluded that the initial particle size distribution significantly affects electrochemically active area loss, and that hydrogen crossover accelerates this loss – presumably because hydrogen reduces Pt ion to Pt metal.

3. OUR RECENT APPROACHES TOWARD MACROSCOPIC MODELS OF CATALYST DEGRADATION 3.1. Simplified Model We (the authors of this chapter) [33] used a TEM observation-determined particle size distribution and applied a simple Pt dissolution/diffusion/deposition model, in which the dissolution/deposition is treated like the vaporization/ condensation of a vapor/liquid using a Kelvin type equation and Pt ion diffusion equation. The dissolution/deposition rate was set to be proportional to the difference between the saturated Pt ion concentration, determined as a function of particle size, and the actual concentration.

3.2. Integrated Model We have recently upgraded the simplified model to the integrated model, using the modified Butler-Volmer equation of Darling and Meyers [26]. The parameters for Pt oxide formation and reduction were determined to reproduce the cyclic voltammograms measured with various scan rates. The parameters for Pt dissolution and deposition were determined, in order to reproduce the total surface area reduction that had been measured experimentally. The diffusion coefficient of Pt ions was determined to reproduce the Pt mass loss rate. We assumed that Pt ions transported into the membrane were chemically reduced, and formed a Pt band at a position 1 mm away from the catalyst layer/ membrane interface. The simulation results are compared with the results of an experiment using the conditions shown in Table 9.1. Table 9.2 shows the parameters used for this simulation by the integrated model, in comparison with the other reference parameters [26, 29]. To obtain a good fit with the cyclic voltammograms for Pt oxide formation and reduction, the rate constant for the Pt oxide formation/reduction reaction needed to be set to a higher value than that estimated by Darling and Meyers [26]. Furthermore, a much faster Pt dissolution/deposition rate was also suggested.

4. RESULTS AND DISCUSSION The particle size distribution was simulated by the simplified model in various positions in a catalyst layer from the electrolyte membrane side to the GDL side, in which the initial size distribution was determined by TEM observation and particle size distribution change was simulated. Resulting platinum size distributions before and after degradation at positions near the membrane and

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TABLE 9.1 Condition Values of Voltage Cycling Condition


Lower voltage limit (V)


Upper voltage limit (V)


Holding time at upper / lower voltage (s)


Sweep rate (V/s)


Temperature ( C)


Thickness of cathode catalyst layer (mm) 2


Cathode Pt loading (mg/cm )


Ionomer / carbon weight ratio


Initial state of mean Pt particle diameter (nm)


near the GDL are shown in Fig. 9.14. Near the membrane, particles smaller than 5nm quickly diminish, and even larger particles decrease in size. Near the GDL, in spite of the similar relative particle size distribution, larger particles show actual growth in size. These simulation results show that relative particle size distribution measurement does not give the overall picture of catalyst degradation unless it accompanies a quantitative analysis of platinum distribution.

TABLE 9.2 Fitting Parameter Values Parameter

Fitted Value 10

Reference Value 9

w 310

3.41013 [25], 31010 [28]

Pt dissolution reaction rate constant (mol/cm2s)


Pt oxidation reaction rate constant (mol/cm2s)


1.361011 [25], 71010 [28]

Pt ions diffusion coefficient (cm2/s)


1106 [25], 1.5109 [28]


*) Values in this range were applicable according to supposed effective PtO coverage. Best-fitted value is still rather vague.


FIGURE 9.14 Distribution of Pt surface area per unit geometric area over particle size at the initial state and at the instances when the total Pt surface area becomes 2/3 and 1/3 of the initial state by potential cycling. (a) at the interface with the electrolyte membrane. (b) at the interface with the GDL.


Pt surface area per unit geometric area / -


Polymer Electrolyte Fuel Cell Degradation



at ECSA=2/3


at ECSA=1/3

10 5 0 0







particle size /nm

Pt surface area per unit geometric area / -

(b) 25 Initial at ECSA=2/3 at ECSA=1/3

20 15 10 5 0 0







paticle size /nm

FIGURE 9.15 Platinum surface area and loading losses during voltage cycling in the range of 0.72–0.955 V at 80 C under fully humidified H2(anode)-N2(cathode). ECSA was estimated from the total charge of hydrogen deposition reaction on Pt by CV. Pt Loading was estimated by using EPMA.

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Computational Modeling Aspects of PEFC Durability


Using the integrated model with the parameters shown in Table 9.2, the particle size distribution is simulated as a function of time and position, and the total surface area and total Pt loading can be calculated. Figure 9.15 shows that the experimental and simulated reduction trends of ECSA and total mass (loading) of platinum are in good agreement. The much smaller loading loss than the ECSA loss shows that the ECSA loss is mainly caused by the mechanism of Ostwald ripening through Pt ion diffusion, rather than by Pt ion effluence to the membrane. Simulated and experimental particle size distributions are shown in Fig. 9.16 for positions near the GDL and near the membrane after the potential cycling. At both the positions, particles smaller

FIGURE 9.16 Size distribution of platinum particles suffering voltage cycles. Corresponding ECSA remaining is 40%. In the two figures, (a) and (b) show the particle distributions near the membrane and gas diffusion layer, respectively. Filled black and gray squares denote results of simulation and experimental values measured from TEM micrographs, respectively.


Polymer Electrolyte Fuel Cell Degradation

FIGURE 9.17 Percentage of Pt loading relative to initial state at positions away from the catalyst layer/membrane interface. Lines of different gradations correspond to different ECSA remaining.

than 5 nm, which are initially dominant in number, diminish, but larger particles are more prominent in the GDL side. The simulated platinum mass distribution shown in Fig. 9.17 indicates that mass loss is seen only near the membrane. These results clearly indicate the significance of Ostwald ripening for the platinum catalyst degradation.

5. SUMMARY AND FUTURE CHALLENGES While computational modeling has been widely used in PEFC technological development for performance enhancement, its application to degradation issues has only just begun. This chapter provided a concise review and our studies were presented. As stated previously, a wide variety of degradation studies have been performed, and used for understanding the phenomena and improving the durability of PEFC cells. However, there are a lot of areas needing further study, in order to understand what is really happening, and to plan mitigation strategies. Areas that would benefit from further research include: 1. Macroscopic model of chemical degradation of membrane: this model should include the influence of formation of Pt band and its effect. 2. Performance prediction modeling, including the effects of membrane degradation, the effect of membrane thinning, and also the catalytic effects of decomposition products. 3. Microscopic Pt dissolution model: this model should elucidate the particle size effect on Pt dissolution, because the particle size term in the modified Butler-Volmer equation by Darling and Meyers [26], which we used in our study also, has not been validated theoretically or experimentally. 4. Performance prediction model including the catalyst degradation: this model should include Pt surface area loss, particle size distribution change,

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and decomposition products if membrane decomposition happens simultaneously. As the wider commercialization of PEFCs comes closer in automobile and static applications, durability issues become increasingly important, because PEFCs with low-cost constitutions such as low Pt loading and hydrocarbon electrolytes need to be operated under harsher conditions, such as high temperature and low humidity. Computational modeling studies in this area will increase in importance, and will play a crucial role in tackling this challenge for years to come.

ACKNOWLEDGMENTS The authors are deeply grateful to Professor M. Mench for his invitation and warm encouragement. Our gratitude also goes to our colleagues in Toyota Central R&D Labs. Inc., especially Dr S. Hyodo for his support for modeling studies and Mr T. Takeshita, Dr H. Murata, and Mr T. Hatanaka for their experimental contribution and fruitful discussions.

NOMENCLATURE Ci F ki MPt MPtO Ni r ri R t T Ui

concentration of species i, mol/cm3 Faraday’s constant, 96,487 C/equiv rate constant for reaction i in the forward direction, mol/cm2 s molecular weight of Pt, 195 g/mol molecular weight of PtO, g/mol number of electrons in reaction i particle radius, cm rate of reaction i, mol/cm2 s universal gas constant, J/mol K time, s temperature, K thermodynamically reversible potential for reaction i, V

GREEK aa,i ac,i F1 F2 qPtO qVac rPt rPtO sPt u

anodic transfer coefficient for reaction i cathodic transfer coefficient for reaction i solid-phase potential, V membrane-phase potential, V fraction of platinum surface covered by PtO fraction of platinum surface not covered by PtO density of platinum, 21.0 g/cm3 density of platinum oxide, 14.1 g/cm3 surface tension, J/cm2 PtO-PtO interaction parameter, J/mol


Polymer Electrolyte Fuel Cell Degradation

REFERENCES [1] S. Kundu, M. Fowler, L.C. Simon, R. Abouatallah, N. Beydokhti, Degradation analysis and modeling of reinforced catalyst coated membranes operated under OCV conditions, J. Power Sources 183 (2008) 619. [2] V. Atrazhev, E. Timokhina, S.F. Burlatsky, V. Sultanov, T. Madden, M. Gummalla, Direct Mechanism of OH Radicals Formation in PEM Fuel Cells, ECS Trans. 6 (25) (2008) 69. [3] N. Miyake, M. Wakizoe, E. Honda, T. Ohta, High Durability of Asahi Kasei Aciplex Membrane, ECS Trans. 1 (8) (2006) 249. [4] N. Hasegawa, T. Asano, T. Hatanaka, M. Kawasumi, Y. Morimoto, Degradation of Perfluorinated Membranes Having Intentionally Formed Pt-Band, ECS Trans. 16 (2) (2008) 1713. [5] V.O. Mittal, H.R. Kunz, J.M. Fenton, Membrane Degradation Mechanisms in PEMFCs, J. Electrochem. Soc. 154 (2007) B652. [6] A. Panchenko, DFT investigation of the polymer electrolyte membrane degradation caused by OH radicals in fuel cells, J. Membrane Sciences 278 (2006) 269. [7] F.D. Coms, The Chemistry of Fuel Cell Membrane Chemical Degradation, ECS Trans. 16 (2) (2008) 235. [8] D.E. Curtin, R.D. Losenberg, T.J. Henry, P.C. Tangeman, M.E. Tisack, J. Power Sources 131 (2004) 41. [9] X. Huang, R. Solasi, Y. Zou, M. Feshler, K. Reifsnider, D. Condit, S. Burlatsky, T. Madden, Mechanical Endurance of Polymer Electrolyte Membrane and PEM Fuel Cell Durability, J. Polymer Science Part B-Polymer Physics 44 (2006) 2346. [10] F. Rong, C. Huang, Z.-S. Liu, D. Song, Q. Wang, Microstructure changes in the catalyst layers of PEM fuel cells induced by load cycling Part I. Mechanical model, J. Power Sources 175 (2008) 699. [11] F. Rong, C. Huang, Z.-S. Liu, D. Song, Q. Wang, Microstructure changes in the catalyst layers of PEM fuel cells induced by load cycling Part II. Simulation and understanding, J. Power Sources 175 (2008) 712. [12] S. He, M.M. Mench, Degradation of Polymer-Electrolyte Membranes in Fuel Cells I. Experimental, J. Electrochem. Soc.,153 A1724 (2006). [13] S. He, S.H. Kim, M.M. Mench, One-Dimensional Transient Model for Frost Heave in Polymer Electrolyte Fuel Cells II. Physical Model, J. Electrochem. Soc. 154 (2007) B1024. [14] S. He, S.H. Kim, M.M. Mench, 1D Transient Model for Frost Heave in PEFCs III. Heat Transfer, Microporous Layer, and Cycling Effects, J. Electrochem. Soc. 154 (2007) B1227. [15] A.A. Shah, F.C. Walsh, A model for hydrogen sulfide poisoning in proton exchange membrane fuel cells, J. Power Sources 185 (2008) 287. [16] A.Z. Weber, C. Delacourt, Mathematical Modeling of Cation Contamination in a Protonexchange Membrane, Fuel Cells 6 (2008) 459. [17] C.A. Reiser, L. Bregoli, T.W. Patterson, J.S. Yi, J.D. Yang, M.L. Perry, T.D. Jarvi, A ReverseCurrent Decay Mechanism for Fuel Cells, Electrochem. Solid-State Lett. 8 (2005) A273. [18] J.P. Meyers, R.M. Darling, Model of Carbon Corrosion in PEM Fuel Cells, J. Electrochem. Soc. 153 (2006) A1432. [19] T. Fuller, G. Gray, Carbon Corrosion Induced by Partial Hydrogen Coverage, ECS Trans. 1 (8) (2006) 345. [20] K. Jain, A. Gidwani, S. Kumar, J.V. Cole, CFD Study of Carbon Corrosion in PEM Fuel Cells, ECS Trans. 16 (2) (2008) 1323.

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[21] J. Hu, P.C. Sui, N. Djilali, S. Kumar, Modelling and Simulations on Mitigation Techniques for Carbon Oxidation Reaction Caused by Local Fuel Starvation in a PEMFC, ECS Trans. 16 (2) (2008) 1313. [22] A.A. Franco, M. Gerard, Multiscale Model of Carbon Corrosion in a PEFC: Coupling with Electrocatalysis and Impact on Performance Degradation, J. Electrochem. Soc. 155 (2008) B367. [23] F. Tian, A.B. Anderson, Theoretical Study of Early Steps in Corrosion of Pt and Pt/Co Alloy Electrodes, J. Physical Chem. C 112 (2009) 18566. [24] X.Y. Zhou, Degradation of Pt Catalysts in PEFCs: A New Perspective from Molecular Dynamic Modeling, Electrochem. Solid-State Lett. 11 (2006) B59. [25] J.A.S. Bett, K. Kinoshita, P. Stonehart, Crystallite growth of platinum dispersed on graphitized carbon black II. Effect of liquid environment, J. Catalysis 41 (1976) 124. [26] R.M. Darling, J.P. Meyers, Kinetic Model of Platinum Dissolution in PEMFCs, J. Electrochem. Soc. 150 (2003) A1523. [27] R.M. Darling, J.P. Meyers, Mathematical Model of Platinum Movement in PEM Fuel Cells, J. Electrochem. Soc. 152 (2005) A242. [28] A.A. Franco, M. Tembely, Transient Multiscale Modeling of Aging Mechanisms in a PEFC Cathode, J. Electrochem. Soc. 154 (2007) B712. [29] W. Bi, T. Fuller, Modeling of PEM fuel cell Pt/C catalyst degradation, J. Power Sources 178 (2008) 188. [30] E. Holby, Y.S. -Horn, D. Morgan, 211th ECS meeting Abstract #907, The Electrochemical Society, Pennington, NJ, 2007. [31] E. Holby, Y.S. -Horn, A. Sheng, D. Morgan, 212th ECS meeting Abstract #391, The Electrochemical Society, Pennington, NJ, 2007. [32] E. Holby, Y.S. -Horn, A. Sheng, D. Morgan, 214th ECS meeting Abstract #798, The Electrochemical Society, Pennington, NJ, 2008. [33] T. Takeshita, H. Murata, T. Hatanaka, Y. Morimoto, Analysis of Pt Catalyst Degradation of a PEFC Cathode by TEM Observation and Macro Model Simulation, ECS Trans. 16 (2) (2008) 367.