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eview on the Properties of Nano-/icrostructures in the Catalyst

ayer of PEMFC

iao Yu

inliang Yuan1

-mail: [email protected]

engt Sundén

epartment of Energy Sciences,aculty of Engineering,und University,2100 Lund, Sweden

he catalyst layer (CL) of a proton exchange membrane fuel cellnvolves various particles and pores that span a wide range ofength scales, from several nanometers to a few microns. Theuccess of the CL design depends decisively on understanding theetailed structure in microscale or even in nanoscale. In this pa-er, the properties of nano-/microstructures are outlined, and thehysical and chemical processes are analyzed on the Pt surfaces.software package of automatic simulation environment is devel-

ped and applied to investigate the electronic structure of thet–H system. Then, the H2 dissociative adsorption process is ob-

ained using the nudged elastic band approach. The modeling ofhe nanocomposites in the CLs is a multiscale problem. The nano-cale models are used for investigating the structural evolutionnd the interactions between Pt/C particles and polymer compo-ents; while the microscale simulations, which aim to bridge mo-ecular methods and continuum methods, are extended to describehe morphology of heterogeneous materials and rationalize theirffective properties beyond length- and time-scale limitations ofhe atomistic simulations. However, there are still some majorhallenges and limitations in these modeling and simulations. Theultiscale modeling should be developed to demonstrate the use-

ulness for engineering design with the longstanding goal of pre-icting particle-structure-property. �DOI: 10.1115/1.4003170�

eywords: nanostructure, microstructure, property, multiscale,odel, PEMFC

IntroductionProton exchange membrane fuel cells �PEMFCs� are promising

lectrochemical devices for a direct conversion of the chemicalnergy of hydrogen into electrical work. It is supposed that theyould replace the internal combustion engines �ICEs� in light dutyehicles and offer benefits in transportation, stationary, and por-able power applications. Due to their high efficiency, fast andasy start-up, and environment friendliness, PEMFCs are distin-uished as a primary solution to vehicle development.

The basic component of PEMFCs is a membrane-electrode as-embly. A proton exchange membrane �Nafion type, for example�s in contact with the anode and cathode catalyst layers �CLs� andurther with two gas diffusion layers �GDLs�. The typical CLs areabricated as random heterogeneous composites to meet the mul-

1Corresponding author.Contributed by the Advanced Energy Systems Division of ASME for publication

n the JOURNAL OF FUEL CELL SCIENCE AND TECHNOLOGY. Manuscript received October3, 2010; final manuscript received November 5, 2010; published online March 1,
011. Editor: Nigel M. Sammes.
ournal of Fuel Cell Science and TechnologyCopyright © 20

ded 02 Mar 2011 to 130.235.81.195. Redistribution subject to ASM

tifunctional requirements of transport phenomena and electro-chemical activity. They are composed of Pt nanoparticles, carbon-aceous substrates, and Nafion ionomers to form a protonconduction network. A schematic representation of the CLs isshown in Fig. 1 �1�. Its structure involves various particles andpores that span a wide range of length scales, including Pt nano-particles on carbonaceous substrates and primary pores with sizesof 3–10 nm at the microscale. The agglomerates and the second-ary pores between agglomerates have sizes in the range of 10–50nm �2� at the mesoscale, and the catalyst layer as a complexcomposite medium has sizes of about 10 �m at the macroscopicscale.

The species and processes that occur in the CLs include elec-trochemical reactions, diffusion of hydrogen or hydrocarbon-based fuels �anode� and oxygen �cathode�, migration and diffusionof protons, migration of electrons, water transport by diffusion,permeation, electro-osmotic drag, and vaporization/condensationof water. Electrical current is generated/consumed at Pt nanopar-ticles, which are randomly dispersed on a high-surface carbonmatrix. During fabrication, the colloidal solution of carbon/Pt andan ionomer self-organizes into a phase-separated composite withinterpenetrating percolation phases for the transport of electrons,protons, and gases.

A main goal of studying CLs is to get a rapid and accurateprediction of the properties and features, which is very difficult toachieve with traditional modeling and simulation methods at asingle length and time scale with the current computer power. Thecatalyst layer models can be classified into two groups accordingto the level that these models are able to deal with �i� the macro-scopic models that have been developed to describe the fuel cellworking behavior, with a common assumption of infinitesimallythin CLs, and �ii� the microscopic or nanoscale models that con-sider the transport phenomena at the pore or even particle level.Therefore, it is expected to use the multiscale simulation strategiesto bridge the models and simulation techniques across a broadrange of length and time scales. Then, the macroscopic or mesos-cale behaviors of CLs can be addressed from a detailed descrip-tion of the nano-/microstructures, and the calculated parameters,properties, and numerical information can be efficiently trans-ferred across scales. It is so required because the observable prop-erties of the CLs depend on the inhomogeneous structures at dif-ferent length scales, such as chemical details and transportphenomenon at the nanoscale, aggregation, and self-organizingprocess at the microscale up to continuum phenomena at the mac-roscale. As a result, the complete description of the nano-/microstructures in the CLs typically requires a wide range oflength scales from the chemical bond, at around 1 Å in length, upto chain aggregates extending for many hundreds of angstromsand beyond.

In order to achieve the longstanding goal of predicting particle-structure-property in material design and optimization, this paperwill outline the properties of nano-/microstructures and analyzethe physical and chemical processes in the catalyst layer and thenprovide the basic theories and simulation approaches to solve themultiscale problems involved.

2 The Properties of Nano-/Microstructures

2.1 Challenges for the Structural Design. For the catalystlayer, the most important objective is to produce the highest cur-rent density with a minimum amount of the catalyst, which willgreatly reduce the cost �DOE targets of $30/kW by 2015� �3�. Thismeans a huge electrochemical active surface area, small kineticbarriers to bulk transport, and interfacial transfer of protons, elec-trons, and reactant gases.

The importance of the catalyst structure has been previouslydescribed by Vojislav et al. �4�. An enhanced activity was revealedfor specific crystal surfaces over that for Pt deposited on carbon�Pt/C�. United Technology Co. �UTC� Power and Brookhaven Na-
tional Laboratory �BNL� are developing core-shell structured Pt
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atalysts to reduce Pt content while increasing activity �3�. Twoajor improvements in the catalyst layer design have appeared by

ncorporation of Pt or Pt group metals �PGMs� with sizes on theange of 2–5 nm and by the impregnation of mixing large surfacearbon support with ionomer. The former way provides a greatnhanced electrochemical active surface area, while the latter en-ures uniform access of protons to active Pt atom surface through-ut the complete layer. As first demonstrated by Los Alamos Na-ional Laboratory �LANL� �5,6�, these methods enabled aramatic reduction of catalyst loading. Recent efforts in improv-ng the fabrication of CLs have explored ways to replace polytet-afluoroethylene �PTFE� by ionomer to form a major components a binder and a hydrophobizing agent �7�. In addition, Pt alloysre also being investigated for improved durability, as well asncreased activity. By these methods, the catalyst loadings haveeen reduced from about 4–10 mg Pt cm−2 �in 1980s� to about.2 mg cm−2 today �3�.

Naturally, the success of the CLs design depends decisively onnderstanding the detailed structure in the microscale or even inhe nanoscale with the assistance of supercomputers and the ad-anced experimental methods.

2.2 Experimental Methods for the Structural Properties.hysical properties of PEMFC CLs include measurement of theurface area, the electrochemical active surface area, the phasend composition of active components, the particle size and sizeistribution of active components, the morphology and crystallanes, and other features. Some of the related test methods areighlighted as follows.

2.2.1 MSCP. A method of standard contact porosimetryMSCP� was developed in the 1980s �8� and was discussed inetail in Ref. �9�. This method can be used to investigate theorous structure of fuel cell components; for example, the influ-nce of ionomer on the porous structure of ten different carbonubstrates �CSs� was investigated �10�.

The MSCP is based on the laws of capillary equilibrium. If twoor more� porous bodies partially filled with a wetting liquid are inapillary equilibrium, the values of the liquid’s capillary pressuren these bodies are equal. According to the Laplace equation, themount of a wetting liquid in the test sample �Vt� is measured.imultaneously, the amount of the same wetting liquid is mea-ured in a standard specimen of known porous structure �Vs�. Theiquids in both porous samples are kept in contact. After someime, a thermodynamic equilibrium is established. The measure-

ents are performed for different overall amounts of the liquid0=Vs+Vt. During measurements, this overall amount is changedy gradual evaporation of the liquid. This method can establish

ig. 1 Schematic illustration of a cathode catalyst layer †1‡.eprinted from Ref. †1‡ with permission from Elsevier.

he distribution of pore volume versus pore size of the test sample

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by comparing with the known specimen.MSCP has several substantial advantages over mercury poro-

simetry and other methods because of high accuracy �the error isless than 1%� and broader measurement range of pore radii from 1to 3�105 nm. Further, the method makes it possible to obtain agreat deal of diverse information about the porous structure, aswell as about sorption and hydrophilic–hydrophobic properties, ofall porous and disperse materials.

2.2.2 TEM. Electron microscopes use a beam of highly ener-getic electrons to examine objects on a very fine scale. The trans-mission electron microscope �TEM� was the first type of electronmicroscope developed by Knoll and Ruska �11� in Germany in1932, 35 years after Thompson’s discovery of the electron.

The TEM passes an accelerated electron beam through a thinsample �50–300 Å�. Some of the electrons are scattered by theatoms in the sample. A phase distortion is created, resulting in aphase contrast that is used to create an image. The TEM builds animage by means of differential contrast. Those electrons that passthrough the sample go on to form the image, while those that arestopped or deflected by dense atoms in the specimen are sub-tracted from the image. In this way, a black and white image isformed.

A much lower wavelength of electrons makes it possible toachieve a resolution a thousand times better than that of a lightmicroscope. It enables the operator to see the “inside” of thesample rather than the surface. The main use of the TEM is toexamine the structure, composition, or properties of a specimen insubmicroscopic detail in the order of a few angstroms. For theCLs of PEMFC, it is possible to study the microscopic morphol-ogy down to near atomic levels by the high resolution �HR�-TEM�12�.

2.2.3 XPS. X-ray photoelectron spectroscopy �XPS� has beenwidely used for the surface characterization of materials, espe-cially catalysts. It is the greatest applicability among all the meth-ods of electron spectroscopy for chemical analysis �ESCA�, whichis the most important and useful method for surface analysis. XPScan be used to study electrons in both valence band and core toidentify the atoms at surfaces by comparing the observed lineswith either calculated core level binding energies or experimen-tally derived spectra from standards. It is possible to examine thechemical elements present at successive depths within a sampleby running an electron spectrum after each short treatment withions. In addition to qualitative analysis, XPS can be applied for aquantitative analysis because the number of emitted electrons is afunction of the number of atoms on the surface.

It is clear that XPS analysis can give sufficient informationabout the qualitative and quantitative elemental surface composi-tion of a catalyst, the oxidation state of an atom, the chemicalenvironment, as well as the precise sites of atoms in relation tocrystal structures �13�.

For the fuel cell catalysts, the oxidation states of Pt and thecrystallites’ contents can be determined by XPS �14�. A surveyXPS scan on the nanocomposites can provide a qualitative analy-sis of the elemental composition on the CL surface �15�. It alsoprovides a better insight into the surface properties of the carbon-supported Pt-alloy electrocatalysts in relation to platinum metal�16�. The electrocatalysts were characterized by XPS to determinethe valence states of the elements, the compositions, and theatomic ratios of the metal components.

2.2.4 EDS. Energy-dispersive x-ray spectroscopy �EDS orEDX� is an analytical technique used for the elemental analysis orchemical characterization of a sample. It is one of the variants ofx-ray fluorescence spectroscopy, which relies on the investigationof a sample through interactions between electromagnetic radia-tion and matter, analyzing x-rays emitted by the matter in re-sponse to being hit with charged particles. Its characterization
capabilities are due in large part to the fundamental principle that
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ach element has a unique atomic structure allowing x-rays thatre characteristic of an element’s atomic structure to be identifiedniquely from one another �17�.

There are four primary components of the EDS setup: the beamource, the x-ray detector, the pulse processor, and the analyzer. Aumber of freestanding EDS systems exist. However, EDS sys-ems are most commonly found on scanning electron microscopesSEM-EDS� and electron microprobes. A broad area of small par-icles on the SEM or TEM images can be selected for EDS analy-es to obtain composition information for the selected region. El-ment mapping with EDS can be used to obtain the distribution oflements on the surface. The source of the x rays is manifested asgrouping of extremely bright dots against a dark background,

ndicating where that element is absent.For the fuel cells, EDS analysis has been used to investigate the

omposition of the alloy particles in the catalysts �18�. In addition,t can provide the distribution of active components on the surfacend through the cross-section of the membrane �19�.

2.3 The Structure of Pt-Based Nanocatalyst. The typicalLs are fabricated as random heterogeneous composites to meet

he multifunctional requirements of transport phenomena andlectrochemical activity. They are composed of Pt or Pt-alloyanoparticles, carbonaceous substrates, and Nafion ionomers toorm a proton conduction network. Considering various nanopar-icles and carbonaceous substrates, there are large differences forhe structures of Pt-based nanocatalysts.

2.3.1 Catalyst Supported on Carbonaceous Materials. Cur-ently, carbon black supports, Vulcan X �VC-X� and Ketjen BlackKB�, are widely used in platinum catalysts. TEM images providehe information of Pt particle size and distribution, as shown inig. 2 �20�. All prepared catalysts showed a good distribution andlear Pt lattice structures. It is found that the particle sizes are inhe range of 2–4 nm with different distributed networks.

However, recent publications suggest that novel carbon sup-orts, such as ordered mesoporous carbon �21�, carbon nanofibers

ig. 2 TEM images of the catalyst with different substrates: „a…t50/VC-X and „b… Pt33/KB †20‡. Reprinted from Ref. †20‡ withermission from Elsevier.

Fig. 3 TEM images of „a… ordered mand „c… CNTs †23‡. Reprinted from
Elsevier.
ournal of Fuel Cell Science and Technology


�CNFs� �22�, and carbon nanotubes �CNTs� �23�, may improve theefficiency of electrocatalysts, reduce Pt loading, and increase thesurface area of the catalysts, as shown in Fig. 3.

2.3.2 Pt-Based Electrocatalysts. Among metals, Pt exhibitsthe highest catalytic activity for low-temperature fuel cells. How-ever, Pt is expensive and rare, so its loading must be minimizedwithout weakening the cell performance. Thus, there has beengreat focus on synthesizing Pt nanoparticles on carbon to maxi-mize their surface availability �24�. A surfactant-stabilized colloi-dal method was used to control the sizes of the Pt particles, asshown in Fig. 4 �25�. The TEM image in Fig. 4�a� presents theparticle size and dispersion of the Pt/C catalyst prepared withsurfactants Brij 35 �B�+Tween 20 �T� at ten times of the criticalmicelle concentration �or 10�CMC�. These Pt nanoparticles arein the range of 1–4 nm with the average size of 2.4 nm. At amixed binary surfactant concentration of 10�CMC, Pt nanopar-ticles are surrounded by the surfactants to form spherical micelles,which inhibit aggregation �Fig. 4�b��. When the concentration isincreased to 50�CMC, severe aggregation of Pt nanoparticlesoccurs, as witnessed in Fig. 4�c�. When the surfactant concentra-tion is too high, the spherical micelles are converted to cylindricalmicelles, and hence tubular-shaped Pt nanoparticles are formed�Fig. 4�d��.

oporous carbon †21‡, „b… CNFs †22‡,efs. †21–23‡ with permission from

Fig. 4 „„a… and „c…… TEM images and „„b… and „d…… enlargedHR-TEM images of the Pt/C catalyst prepared with 10ÃCMCand 50ÃCMC of B+T, respectively †25‡. Reprinted from Ref.†25‡ with permission from Elsevier.

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In order to promote both the activity and the oxidation of thehemisorbed CO, the Pt-based alloy catalysts, which involve these of a secondary metal �e.g., Ru, Sn, Mo, and Cr�, have been theocus of extensive research in the past decade �26�. Figure 5�a�hows a HR-TEM image of the 3Pt1Sn/C catalyst. It was foundhat the PtSn nanoparticles, with an average particle size of 2.3m �Fig. 5�b��, were uniformly well-dispersed on the carbon sup-ort. By using XPS, the surface chemical state and bonding of thetSn catalysts were also analyzed �27�.Although the alloy catalysts show improved oxygen reduction

eaction �ORR� activity compared with Pt/C catalysts, their sta-ilities are still poor. Recently, the Pt/C catalyst adding metalxides has been extensively investigated for enhancing the ORRctivities �28�. In Fig. 6�a�, CeO2 nanoparticles can be found neart nanoparticles, as the crystal phases of Pt and CeO2 are identi-ed by lattice analysis. The lattice spacing of Pt and CeO2 is about.22 nm and 0.31 nm corresponding to Pt�111� and CeO2�111�,espectively. The EDS spectrum �Fig. 6�b�� of the0Pt–10CeO2 /C catalyst proves the coexistence of Pt and Ce onhe carbon support �29�.

Additionally, catalyst agglomeration could be avoided with theddition of polybenzimidazole �PBI�. Fujigaya et al. �30� discov-red that pyridine-containing compounds such as PBI �PyPBI�ould exfoliate and enwrap multiwalled carbon nanotubesMWCNTs�. Pt ions have been efficiently adsorbed onto PyPBIrapped MWCNTs via coordination, and subsequent reduction oft ions formed uniform Pt nanoparticles on the surface ofWCNT/PyPBI. Figure 7 shows HR-TEM results of the nano-

atalyst.

Fig. 5 „a… The HR-TEM image and3Pt1Sn/C catalyst †27‡. ReprintedElsevier.

Fig. 6 HR-TEM image of „a… 20Pt–1for the 20Pt–10CeO2/C catalyst †29‡
sion from Elsevier.
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3 Transport Phenomena and Chemical Reactions

3.1 Surface Adsorption. The embedding methods are em-ployed to investigate interactions between the surface and adsor-bates �31�, which work best if a strong chemisorption bound isformed so that other interactions are secondary. The adsorptionenergy is calculated by

E = E�adsorbate� + E�substrate� − E�adsorbed system� �1�

For the adsorption on metals, there is a model �32� to predict theadsorption bound strength based on the electronic properties ofthe metals,

Ed_hyb = − 2�1 − f�V2

��d − �a�+ 2�1 + f��V2 �2�

where Ed_hyb is the energy gained from hybridization of the ad-sorbate orbital with the metal d-band, �a is the adsorbate orbitalenergy, and � is a constant, which is independent of the metal butdepends weakly on the identity of the adsorbate. From this model,three surface properties contribute to the ability of the surface tomake and break adsorbate bonds: the energy center ��d� of thed-bands, the degree of filling �f� of the d-bands �number of delectrons�, and the coupling matrix element �V� between the ad-sorbate states and the metal d-states.

The interaction between the adsorbate states and the metald-states is an important part of the interaction energy because ofthe narrowness of the d-band. When the structure of the surfacechanges, the d-band center will alter due to the change in the

the particle size distribution of theRef. †27‡ with permission from

O2/C catalysts and „b… EDX patterneprinted from Ref. †29‡ with permis-

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umber of metal neighbors �the metal coordination number�. Theeneral rule is that the lower the coordination number, the smallerhe local bandwidth and the higher energy center �d. This is therigin of the reactivity difference due to the surface structure �33�.

3.1.1 Adsorption of H2 on Pt. In the adsorption, hydrogen isttached to the surface of a material either as hydrogen moleculesr as hydrogen atoms. In absorption, hydrogen is dissociated into

atoms, which are incorporated into the solid lattice framework.latinum is also of particular importance due to the central role itlays in hydrogenation reactions; hence, the interactions of hydro-en with Pt surfaces have been investigated in a large number oftudies �34�. Potential energy �PE� for H2 dissociative adsorptionn the Pt�111� surface is as functions of �1� the H2 interatomicistance r, �2� the distance Z from H2 center of mass �CM� to theurface, �3� the H2 polar and azimuthal orientations with respecto the surface normal and parallel, �4� the surface relative positionf the H2 CM, and �5� the surface coverage of H on Pt�111�, ashown in Fig. 8. It was found that the reaction paths were withoutr with very low barriers leading to dissociation of H2 on thet�111� surface �35�, and vacant sites increased the surface reac-

ivity of Pt�111� by lowering the activation barriers for the disso-iative adsorption of H2 on the substrate �36�. By performinguantum dynamics calculations on ab initio potential energy sur-aces �PESs�, Arboleda et al. �37� also investigated the effects ofhe initial kinetic and vibrational energies and the orientation ofhe incident hydrogen molecule �H2� on the dissociative adsorp-ion dynamics of H2 on a Pt�111� surface.

3.1.2 Diffusion of H Atom on Pt. A software package of Au-omatic Simulation Environmental �ASE� is developed and appliedo investigate the electronic structure of the Pt–H system. A 2

2 unit cell �corresponding to 0.25 ML coverage of adsorbates�s provided, which has a three-layer slab of the Pt�111� facet of aace-centered cubic �fcc� crystal of platinum atoms with the ex-erimental lattice parameter of 2.77 Å.

In order to speed up the calculations, all the adsorbates and theop layer of Pt�111� slab were relaxed to the equilibrium structure.he convergence criterion was that the force on all atoms shoulde less than a certain value. Initial estimates of transition states foreactions were obtained using the nudged elastic band �NEB� ap-roach, which could calculate the minimum energy path �MEP�or any given chemical processes when both the initial and finaltates were known. The NEB activation barrier was refined by

ig. 7 Typical HR-TEM image of the MWCNT/PyPBI/Pt. The Ptanoparticles are penetrated into the thin PyPBI-coating layero contact closely with the MWCNT surfaces †30‡. Reprintedrom Ref. †30‡ with permission from Elsevier.

inear interpolation of a set of images between the known initial



and final states, and each “image” corresponded to a specificbound length and energy. Thus, once the energy of the string ofimages got the minimum value, the true MEP was revealed.

When the H atom was set in the fcc position as the initial statesand the place where the atom moved to another fcc site by diffu-sion as the final states, the NEB approach could be used to calcu-late the MEP and got the images under the equilibrium states.

For the cases above, the energy changes look like two humpswith the maximum value of 0.089 eV �that is, 8.587 kJ mol−1�,which represents the diffusion barrier for the H atom in thePt�111� surface. It is smaller than that predicted by Blaylock et al.�38�, in which they got 13.4 kJ mol−1 for the H atom on the fccsite. As observed in Fig. 9, the H atom also reached a steady statewhen it passed through a cubic closest-packing �hcp� site, wherethe energy became nearly zero. Thus, fcc and hcp were both thepreferable sites for the H atom diffusion.

Fig. 8 Representations of the H2–Pt„111… systems. The inter-atomic distance r, the H2 CM distance Z from the surface, thepolar angle �, and the azimuthal angle � are illustrated in „a….The H2–Pt configurations are also shown for the adsorption ofH2 on the ideal surface „b… and on the defective surface withvacancies at sites „c… 1, „d… 2, „e… 3, and „f… 4. The surface unitcell is given in „b…, with a lattice constant of 2.772 Å †36‡. Re-printed from Ref. †36‡ with permission from Elsevier.

Fig. 9 The MEP for H atom diffusion on Pt„111… surface and
the images under the equilibrium states „the red dots…
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3.1.3 Adsorption of O2 on Pt. For the interaction of oxygenith the Pt�111� surface, three molecular O2 adsorption statesave been identified. When the surface temperature is below 30 K,weakly bound physically adsorbed species exists. At about 150

and higher temperature, the experiments at the platinum-ltrahigh frequency �UHV� interface have shown that there arewo different kinds of molecularly chemisorbed states, which haveeen characterized as peroxo-like �O2

−2� and superoxo-like �O2−�,

espectively �39,40�.To theoretically describe the adsorption process of O2 on

t�111�, we performed ab initio calculations of the atomic andlectronic structures of the adsorbate-substrate system using theienna ab initio simulation program �VASP� �41�. The superoxo-

ike �O2−� paramagnetic precursor was formed at the bridge site

s-b-t� with the molecule parallel to the surface. The O–O boundength was 1.39 Å, and the O–O stretching frequency was50 cm−1. The calculated adsorption energy was 0.72 eV. Theeroxo-like �O2

−2� nonmagnetic precursor was formed in thehreefold hollow, with the atom slightly canted in a top-hollow-ridge geometry. The O–O bond length was 1.43 Å for t-f-b �1.42

for t-h-b�, the O–O stretching frequency was 690 cm−1

710 cm−1 for t-h-b�, and the adsorption energy was 0.68 eV0.58 eV for t-h-b� �42�.

3.2 Activation Energy. The activation energy for the elemen-ary electron transfer step is a key to understand the electrocata-yzed reaction mechanism. For a multi-electron transfer reaction,t is a challenge to identify the rate determining step. Severalheoretical models to account for the electron transfer processave been developed since the initial work by Gurney �43�. Bock-is and Abdu �44� reported the first theoretical prediction of acti-ation energy for the first step of the ORR, based on Gurney’sodel. Anderson and Albu �45,46� introduced the local reaction

enter electron transfer theory. Thus, the activation energy, theransition state energy minus the reactant energy, can be predictedy this approach.

The theoretically predicted activation energies were comparedn a later paper with experimental data for platinum alloys �47�.verall agreement between the theoretical prediction and the mea-

ured current density was observed: �i� The first electron reductiontep, forming OOHads, was the rate-limiting step, and �ii� the ac-ive catalyst sites for the various catalyst systems were similar.he presence of alloying atoms adjacent to the active site did notramatically affect the activation energy.

To account for the electronic field, the O2+H+�H2O�3

e− /Pt�111� system was modeled in Ref. �48�. The study ob-erved that at first the proton transfer intermediate was formedapidly, similar to results reported by Jinnouchi �49�. The forma-ion of the end-on chemisorption precursor H–O–O–Pt had annergy barrier of about 0.4 eV. They suggested that the mecha-ism for the first electron transfer involved �1� proton transfer, �2�lectron transfer, and �3� dissociation and hydroxyl adsorption48�. Hyman and Medlin �50� reported an activation barrier for O2

rotonation and OOH dissociation. Using the H5O2+ model, the

2 protonation had a more stable precursor and a lower activationarrier �0.07 eV� than O2 dissociation �0.22 eV�.Activation energy studies suggest that with Pt as the catalyst,

roton transfer precedes O2 dissociation and is involved in the rateetermining step of the oxygen reduction reaction. Without cata-ysts, the third electron transfer step has the largest activationnergy, followed by the first electron transfer step. An efficientRR catalyst should activate the first and third electron transfer

teps.

3.3 Reaction Thermodynamics. The thermodynamics of theeactions was established as a function of voltage by calculatinghe stability of the reaction intermediate, and the overpotential ofhe reaction could be linked directly to the proton and electron
ransfer �51�. The procedure to calculate the free energy of the
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intermediates of the electrochemical reactions is outlined and dis-cussed below with different reaction mechanisms.

3.3.1 Hydrogen Reduction Reaction. The oxidation of hydro-gen occurs readily on Pt-based catalysts �52�. The kinetics of thisreaction is very fast on Pt catalysts, and in a fuel cell the oxidationof hydrogen at higher current densities is usually controlled bymass-transfer limitations. The oxidation of hydrogen also involvesthe adsorption of the gas onto the catalyst surface followed by adissociation of the molecule and the electrochemical reaction tohydrogen ion as follows:

2Pt�s� + H2 → Pt – Hads + Pt – Hads �3�

Pt – Hads → H+ + e− + Pt�s� �4�

where Pt�s� is a free surface site and Pt–Hads is an adsorbedH-atom on the Pt active site.

By the ASE software, the H2 dissociative adsorption process wassimulated in this paper using the NEB approach. In the initialstate, the molecule was adsorbed on the same Pt�111� surface, asdiscussed in Sec. 3.1.2. At the beginning, both of the H atomsmoved to the bridge site �shown as the arrow in Fig. 10� as themolecular status; after that, they were separated with large energychanges, and the dissociation process happened; at last, one Hatom went back to the fcc site, and another went to another fccsite to keep the whole system energy in a higher state. In suchcases, the system needed extra energy provided from the environ-ment, and the reaction barrier was 4.371 eV.

Although this reaction is fast on the Pt catalysts in PEMFCs,some problems may arise as to when impure hydrogen is used.Thus, some studies on various alloys have been carried out toimprove the catalyst activity with contaminated hydrogen �53,54�.

3.3.2 Oxygen Reduction Reaction. For some reasons, the ki-netics of the cathode reaction is much slower than the anode re-action. The ORR process is

12O2 + 2�H+ + e−� → H2O �5�

The simple dissociative mechanism was first introduced in �51�12O2 + � → O� �6�

O� + H+ + e− → HO� �7�

HO� + H+ + e− → H2O + � �8�

where � denotes a site on the catalyst surface. In the following

Fig. 10 MEP for H2 dissociative adsorption on the Pt„111…surface

section, the associative mechanism, where O2 does not dissociate



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efore it is hydrogenated, was described in detail. Several studies55� have suggested that oxygen reduction on Pt surfaces takeslace via peroxy intermediates, for example, in a reaction giveny the elementary steps:

O2 + � → O2� �9�

O2� + �H+ + e−� → HO2

� �10�

HO2� + �H+ + e−� → H2O + O� �11�

O� + �H+ + e−� → HO� �12�

HO� + �H+ + e−� → H2O+� �13�he last two steps are the same as the ones of the dissociativeechanism above. The new steps in Eqs. �9�–�11� involve adsorp-

ion of molecular O2 and direct proton/electron transfer to it ando OOH.

An alternative to form water in Eq. �11� is to form hydrogeneroxide. Therefore, the associative mechanism can also beermed as a peroxo mechanism. Figure 11 illustrates the possibleeaction pathways, and the possibilities of the ORR pathways areummarized as follows �56�:

1. a “direct” four-electron reduction to H2O �in acid media� orto OH− �in alkaline media�

2. a two-electron pathway involving reduction to hydrogen per-oxide

3. a “series” pathway with two- and four-electron reduction4. a “parallel” pathway that is a combination of 1–35. an “interactive” pathway in which the diffusion of species

from a series path into a direct path is possible

A four-electron oxygen reduction yields water, while a two-lectron reduction produces hydroxide, which not only reduceshe efficiency but also poisons the catalysis and cell because of itsigh oxidizability. The standard potentials for direct four-electron,wo-electron, and one-electron reactions involved in the ORR arehown as follows:

O2 + 4H+ + 4e− → 2H2O, 1.23 V �14�

O2 + 2H+ + 2e− → H2O2, 0.68 V �15�

H2O2 + 2H+ + 2e− → 2H2O, 1.77 V �16�

O2 + H+ + e− → HO2, − 0.13 V �17�here are three types of ORR catalysts used nowadays: transitionetals and alloys, non-noble metals and metal oxides, and

ransition-metal macrocyclic complexes. For transition-metal cata-ysts, two-electron reduction is reported for less active metals,uch as Au and Hg. For the most active catalyst, Pt, four-electroneduction is generally believed to occur. For the ORR on Pt, twoafel regions have been observed in both acid and alkaline solu-

ions. At low current densities, a Tafel slope of �60 mV/dec wasoted, and at the high current densities, the slope was �120 mV/ec �57�. The difference in Tafel slopes is attributed to a partialoverage of the Pt surfaces by intermediates, especially by PtO. Its reported that at a potential �0.8 V �NHE, normal hydrogen

Fig. 11 Oxygen reduction reaction pathways

lectrode�, the Pt surface coverage by PtO could be about 30%



�58�. Thus, the adsorbed intermediates and their coverage on Ptaffect the ORR kinetics dramatically.

4 Modeling and Simulation MethodThe major objective of CL modeling is to establish the relations

between the structures and the properties of the transport pro-cesses and the reactions. In the following, the modeling is sepa-rated into two levels: the nanolevel and the microlevel. The reasonis that the individual Pt nanoparticles and primary pores are in theorder of 1 nm, while the sizes of the secondary pores, Pt/C ag-glomerates, and polymer components are in the order of 100 nm.Hence, the modeling of the CL structure is a multiscale problem:The microscale model, extended to study the microscopic struc-ture of agglomerates and phase separation of the polymer nano-composites, is able to simulate the phenomena on the microlengthand time scales, while the nanoscale model with the resolution of1 nm is used for investigating the structural evolution and theinteractions between Pt/C particles and polymer components.

4.1 Nanoscale Theories and Simulations

4.1.1 MD. The molecular dynamics �MD� simulation was em-ployed to predict the time evolution of a system involving inter-acting particles and to provide insights into structural correlationsand transport properties of CLs, particularly in three-phase bound-aries �TPBs� of carbon/Pt, ionomer, and gas phase. Furthermore, itprovides the information about atomic positions, velocities, andforces. In classical MD simulations, the system is treated as a setof N interacting particles �59�. The atoms are presented by spheri-cal nuclei that attract and repel each other. After assigning pointcharges to each particle, the forces acting on the particles arederived from a combination of bonding, nonbonding, and electro-static potentials. The motions of the atoms are calculated using thelaws of classical mechanics. The result of a MD simulation is atrajectory in terms of positions and velocities of all N particles inthe system. The thermodynamic properties, spatial and temporalcorrelation functions, and transport properties can be exactly cal-culated when simulating with an appropriate time step and a suf-ficient time length.

Nowadays, computationally feasible time trajectories in atom-istic MD simulations extend from a few nanoseconds �ns� up tohundreds of nanoseconds. The time trajectory of an MD system isobtained from solving a system of second order differential equa-tions:

mid2rt

dt2 = �j

F�J + � Fk, i = 1, . . . ,N �18�

here i denotes the considered particle; mi and ri are the mass andthe position vector of this particle, respectively. The forces Fijrepresent two-body interactions between atom i and j. Forces Fkwere the action of external fields. The force field includes van derWaals interactions and electrostatic interactions, and it is the keyto get an accurate solution. Thus, by solving a set of the classicalNewtonian equations, the motions for all particles in the systemcan be established. The forces acting on the nuclei are derivedfrom the gradients of the potential energy function,

Fi = − �riV �19�

Such a force field may be obtained by the quantum theory �e.g.,ab initio �60��, the empirical method �e.g., Lennard–Jones �LJ�,Mores, and Born–Mayer� or the quantum-empirical method �e.g.,embedded atom model, glue model, and bond-order potential�. Itcan be split up into two contributions: nonbonded interactionsbetween all nuclei and bonded interactions between nuclei that arepart of the same molecule. The nonbonded interactions consist ofelectrostatic interactions, van der Waals interactions, and polariza-tion effects. Polarization effects are the result of varying electrondensities and cannot be described explicitly using force field
methods, which invariably ignore electron dynamics. It is com-
JUNE 2011, Vol. 8 / 034001-7


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on practice to include them implicitly in the van der Waals in-eractions. This leaves two terms for the nonbonded interactions.he first term corresponds to Coulomb interactions

V = �ij

qiqj

4��orij�20�

etween two charged spheres at a distance rij from each other. Inhis equation, qi represents the charge of particle i and �0 is theielectric permittivity of vacuum. The particles can be assignedartial charges or integer values in the case of ions.

The second type of nonbonded interactions corresponds to theispersion or the van der Waals forces. These are the interactionsetween the atoms that arise from �quantum� fluctuations of thelectronic charge densities. Both of these interactions are repre-ented in a second term for nonbonded interactions, for which these of the LJ potential has become a standard procedure in MDimulations,

V = 4��

r12

− ��

r6 �21�

n the equation above � represents the depth of the potential at theinimum �rmin=21 /6�� and � is the point at which V=0.There are some other bonded integrations that also need to be

alculated: bond stretching �two-body�, bond angle �three-body�,nd dihedral angle �four-body� interactions. The first two can beescribed by a harmonic potential, which can also be used toescribe the motion of a vibrating spring or a pendulum with theame mechanism. However, because of the rotational symmetry,he dihedral interaction can be described by a periodic functionnstead of harmonic potential. All these bonded interactions playn important role when simulating the hydrated Nafion ionomer61–65�.

In MD simulations, the molecular adsorption concept is used tonterpret the Pt–C interactions during the fabrication processes.he Pt complexes are mostly attached to the hydrophilic sites on

he carbon particles, viz., carbonyl or hydroxyl groups �66�. Thedsorption is based on both the physical and chemical adsorptions.any efforts have been done on the MD simulations of Pt nano-

articles adsorbed on carbon with or without ionomers �67–71�.he Pt–Pt interactions are modeled with the many-body Sutton–hen �SC� potential �72�, whereas a LJ potential is used to de-

cribe the Pt–C interactions. The SC potential for Pt–Pt and Pt–Cnteractions provides a reasonable description of the properties formall Pt clusters. Diffusion of platinum nanoparticles on graphiteas also been investigated, with diffusion coefficients in the orderf 10−5 cm2 s−1 �73�.As for the properties of hydrated Nafion membrane, the concept

f cluster formation for ionomers �74� was suggested for configu-ational dipole-dipole interactions of water and ions. One widelyccepted empirical model for hydrated Nafion is the cluster-etwork model proposed by Hsu and Gierke �75� on the basis ofmall-angle x-ray scattering �SAXS� experiments. In this model,pherical hydrophilic clusters �about 4 nm diameter� of water areurrounded by sulphonate groups connected through cylindricalhannels with �1 nm diameter. A two site model and a single-oint-charge �SPC� model are used for oxygen and water, respec-ively �70�. The dynamic behavior of water and O2 transport at thehree-phase interface gas/catalyst/hydrated membrane are investi-ated. The view in Fig. 12 shows the nanoparticle surface in de-ail. Further, the amount of water on the Pt�111� surface is appre-iable, and the water forms a network connected by hydrogenonds.

MD simulations can be performed in many different ensembles,uch as grand canonical ��VT�, microcanonical �NVE�, canonicalNVT�, and isothermal-isobaric �NPT� �76�. Applying MD into
olymer composites allows us to evaluate the effects of fillers on
34001-8 / Vol. 8, JUNE 2011


polymer structure and dynamics in the vicinity of the polymer-filler interface and to probe the effects of polymer-filler interac-tions on the materials properties.

4.1.2 DFT. Based on the MD simulation, density functionaltheory �DFT� has become a choice for large systems, especiallyfor solid-state surfaces. It came from the Hohenberg–Kohn theo-rem �77�. According to this, the electron density determines theground-state wave function and all other electronic properties ofthe system. The correct density is the case that has the minimumenergy. Because the electron density is a function of the position,the DFT approach could significantly reduce the computationaldemand. First, a fictitious reference system of noninteracting par-ticles was introduced to obtain the electron density. Its state can becalculated by solving a set of one-electron Schrödinger equations�78�,

�− 12�2 + vext�r� + vH�r� + vxc�r� i�r� = �ii�r� �22�

where the external potential is

vext�r� = − �a

za

�r − Ra��23�

and the Hartree potential reads

vH�r� =� �r��r − r��

d3r� �24�

while vxc�r� is the exchange-correlation potential.In principle, if the true exchange-correlation term is known, the

exact electron density could be obtained. However, in reality, theexchange-correlation term is unknown, and there is no systematicway of deriving it. There are several types of approximate func-tions, such as local density approximation �LDA� �79� and gener-alized gradient approximation �GGA� �80�. In general, as theexchange-correlation function contains both exchange and Cou-lomb correlation terms, the DFT provides better quality than thesingle determinant Hartree–Fock �HF� method, which does nothave a Coulomb correlation term.

Recent efforts employing DFT calculations focused mainly onmorphologies and electrocatalytic properties of small metal nano-clusters �81,82�. With the help of the density functional theory andclassical molecular dynamics simulations, the details of ionic andmolecular transport can also be elucidated. Balbuena et al. �71�illustrated the formation of ionic clusters in the vicinity of thecatalyst sites and revealed how the connectivity of these clustersmight determine the transport mechanism of protons and molecu-lar species.

4.2 Microscale Theories and Simulations. The modeling

Fig. 12 Details of the interface catalyst surface/water/Nafion„for a polymer content of 7 Nafion-4/cell, �=24… †70‡. Reprintedfrom Ref. †70‡ with permission from Elsevier.

and simulation at the microscales aim to bridge molecular meth-



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ds and continuum methods and avoid their shortcomings. Micro-cale simulations can describe the morphology of heterogeneousaterials and rationalize their effective properties beyond length-

nd time-scale limitations of atomistic simulations. Specifically, inanoparticle-polymer systems, the study of structural evolutioni.e., self-organized phenomenon� involves the description of bulkow �i.e., hydrodynamic behavior� and the interactions betweenanoparticles and polymer components. With the help of the mi-roscale models, it can elucidate whether or not ionomer is able toenetrate into primary pores inside Pt/C agglomerates. Note thathe hydrodynamic behavior is relatively straightforward to be pre-icted by the continuum theories but is very difficult and expen-ive to be treated by the atomistic methods. In contrast, the inter-ctions between the components can be examined at an atomisticevel but are usually not straightforward to incorporate at the con-inuum level. Therefore, various simulation methods have beenvaluated and extended to study the microscopic structure, ele-ent distribution, and phase separation of these polymer nano-

omposites, including Monte Carlo �MC� methods, dissipativearticle dynamics �DPD�, and the lattice Boltzmann methodLBM�. In these methods, a polymer system is usually treatedith a field description or microscopic particles that incorporateolecular details implicitly. Therefore, they are able to simulate

he phenomena on the length and time scales currently inacces-ible by the classical MD methods.

4.2.1 Monte Carlo Method. Monte Carlo methods �or Montearlo experiments� are a class of computational algorithms that

ely on repeated random sampling to calculate the properties ofnterest. It is extremely simple in principle: Choose a site at ran-om, propose a change in the sample, calculate the change innergy, �E, and accept or reject the change based on �E. Whenerforming such dynamics, it is required that a probability transi-ion function is defined. There are two common choices, the Me-ropolis function and the symmetric function. The Metropolisunction is

P��E� = �1, �E � 0

exp�−�H

kBT , �E � 0 � �25�

nd the symmetric function reads

P��E� =1

2�1 − tanh

�E

2kBT� �26�

here kBT defines a thermal energy of the simulation; it is analo-ous to the thermal energy of experimental systems but not di-ectly related. The choice of the probability function has no effectn the thermodynamics of the system, although the choice of theunctional form of P��E� does affect the dynamics of boundaryotion slightly. The basic algorithm to determine whether a

hange is accepted or not using the Metropolis scheme is dis-ussed below.

In an NVT ensemble with N atoms, a new configuration wasypothesized by arbitrarily or systematically moving one atomrom position i→ j. Due to such atomic movement, one can cal-ulate the change in the system Hamiltonian, �H,

�H = H�j� − H�i�

here H�i� and H�j� are the Hamiltonian associated with the origi-al and new configuration, respectively. This new configuration ishen evaluated according to the following rules. If �H 0, thenhe atomic movement would bring the system to a state of lowernergy. Hence, the movement is immediately accepted and theisplaced atom remains in its new position. If �H�0, the move-
ent is accepted only with a certain probability pi→j, as given by


Pi→j � exp�−�H

kBT �27�

where kB is the Boltzmann constant. According to Metropolis�83�, a random number � between 0 and 1 can be generated, and anew configuration will be determined by the following rule:

if � � exp�−�H

kBT, the movement is accepted �28�

if � � exp�−�H

kBT, the movement is not accepted

�29�

If the new configuration is rejected, one then counts the originalposition as a new one and repeats the process by using otherarbitrarily chosen atoms. While for a �VT ensemble, the compu-tational process is quite similar to an NVT ensemble.

Different from MD, which gives nonequilibrium as well asequilibrium properties, MC provides only the information onequilibrium properties �e.g., free energy and phase equilibrium�.In polymer CLs, MC methods have been used to generate a ran-dom distribution of three kinds of particles, i.e., Pt/C catalyst,Nafion, and poly-tetra-fluoro-ethylene �PTFE� �84�. Based onsuch a cluster model, the catalyst utilization was calculatedthrough counting the number of Pt/C clusters and Nafion particleclusters.

In chemistry, dynamic Monte Carlo �DMC� is a method formodeling the dynamic behavior of molecules by comparing therates of individual steps with random numbers. Unlike the Me-tropolis Monte Carlo method, which has been employed to studysystems at equilibrium, the DMC method is used to investigatenonequilibrium systems such as a reaction and diffusion �85�. Thismethod is mainly applied to analyze the adsorbates’ behavior onthe surfaces �86,87�.

Similar to the DMC method, the kinetic Monte Carlo �KMC�method is also a Monte Carlo method that intends to simulate thetime evolution of some processes occurring in nature. Typically,these processes occur with a given reaction rate. It is important tounderstand that these reaction rates are also the inputs to the KMCalgorithm because the KMC method itself cannot predict them.The main difference between KMC and DMC seems to be interminology and application areas: KMC is used mainly in phys-ics, while the “dynamic” method is mostly used in chemistry.KMC tools are well suited for studying on a time scale muchlonger than the nanosecond range covered by MD simulators andfor handling the extreme large number of molecules to accuratelysimulate pressures �88�. These models utilize physical propertydata generated by MD, or experimental analysis—typically in theform of activation energies, mobilities, sticking efficiencies, etc.KMC models cannot identify new reaction paths but rather focusattention on the complexities associated with the interaction ofmany individual processes. It has been widely developed to simu-late the cathode side of an yttria stabilized zirconia �YSZ� fuel cell�89,90�, or a so-called solid oxide fuel cell �SOFC�, for the objec-tive to determine overpotential limitations for the cathode/YSZperformance.

4.2.2 DPD. The DPD method was introduced by Hooger-brugge and Koelman for simulating the complex hydrodynamicbehavior of isothermal fluids �91� and was further developed byEspanol �92�, who included stochastic differential equations andconservation of energy. It can simulate both Newtonian and non-Newtonian fluids, including polymer melts and blends, on micro-scopic length and time scales. In DPD simulations, the particlesrepresent a small cluster of atoms or molecules, and the particle-particle interactions are much softer than the particle-particle in-
teractions used in typical molecular dynamics simulations. There-
JUNE 2011, Vol. 8 / 034001-9


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ore, it is feasible to take much larger particle size and mucharger time step, and DPD simulations are much more efficienthan MD simulations for the purpose of simulating macroscopicydrodynamics.

In general, the particles in the DPD method are defined by theirass Mi, position ri, and momentum pi. The interaction between

wo particles can be expressed as the sum of a conservative force

ijC, a dissipative force Fij

D, a random force FijR, and a harmonic

pring force FijS for the system,

fi = �j�i

�FijC + Fij

D + FijR + Fij

S� �30�

he positions and the velocities of the particles are solved inccordance with the above equations by implementing Newton’squation of motion and a modified version of the velocity. Whilehe interaction potentials in MD are high-order polynomials of theistance rij between two particles, in DPD the potentials are soft-ned so as to approximate the effective potential at microscopicength scales. The form of the conservative force is chosen inarticular to decrease linearly with increasing rij. Beyond a certainutoff separation rc, the weight functions and thus the forces arell zero. Because the forces are pairwise and the momentum isonserved, the macroscopic behavior directly incorporatesavier–Stokes hydrodynamics. However, energy is not conservedecause of the presence of the dissipative and random force terms.

Recently, DPD methods have been employed to model mor-hology evolution of a wide range of copolymer systems, includ-ng ionomers, during phase separation �93,94�. It could also besed to investigate the microscale structure of Nafion membranest various degrees of hydration �95�. Because the diffusion ofolecules in Nafion depends strongly on the time scale on which

t is measured, water within the pores is very mobile and re-embles that of pure water �96�. Thus, DPD simulations can besed at high water volume fractions for the objective to find alear relation between the shape of the pore networks and pre-icted water diffusion constants �94�.

DPD can be used to simulate complex fluid systems on physi-ally interesting and important length and time scales, and it rig-rously conserves both the number of particles �equivalently, theotal mass� and the total momentum of the system. Another ad-antage is that DPD is a Lagrangian method, the solid/fluid inter-ace and fluid/fluid interface move with the fluid particles so theres no need to track the interface explicitly. The microscale feature,ogether with the Lagrangian nature, makes the DPD method auitable choice for simulating small scale multiphase fluid flow.

4.2.3 LBM. LBM is another microscale method that is suitedor an efficient treatment of polymer solution dynamics. The ori-in of LBM can be traced back to the lattice-gas cellular automataLGCA�, in which a similar kinetic equation is shared �97�,

f i�x + ci�t,t + �t� = f i�x,t� + �i�f i�x,t��, i = 0,1, . . . ,k

�31�

typical lattice-gas automaton consists of a regular lattice witharticles residing on the nodes. A set of Boolean variable fi�x, t�i=1 , . . . ,k� describing the particle occupation is defined, where ks the number of directions of the particle velocities at each node;i is the particle velocity, and the last term �i in the equationepresents the collision operator in accordance with arbitrary col-ision rules.

During the evolution, each time step can be divided into twoubsteps: �i� streaming, in which each particle moves to the near-st node in the direction of its velocity, and �ii� collision, whichccurs when particles arriving at a node interact with each othernd then change their velocity directions according to scatteringules.

The main feature of the LBM method is to replace the particle
ccupation variables fi �Boolean variables� by single-particle dis-
34001-10 / Vol. 8, JUNE 2011


tribution functions fi= �fi� and neglect individual particle motionand particle-particle correlations in the kinetic equation, where � �indicates an ensemble average.

Recent lattice Boltzmann models are further simplified by re-placing the Boolean algebra with a continuous distribution func-tion and also by linearizing the collision operator by Bhatnagar–Gross–Krook �BGK� approximation �98� based on the idea thatthe rate at which collisions drive the distribution function towardthe local equilibrium value depends linearly on the deviation fromlocal equilibrium.

As an example, LBM provides an effective tool to investigatethe transport phenomenon at the pore-scale level. In the TPB offuel cells, several LB models �99� have been presented in theliterature to describe the diffusion process in complex pore struc-tures �as shown in Fig. 13�, while in the CLs, an interaction-potential-based two-phase LB model was developed to study thestructure-wettability influence on the underlying two-phase dy-namics �100�. Further, the possible contributions for the waterconfiguration, such as capillary pressure, gravity, vapor condensa-tion, wettability, and microstructures of the gas diffusion layer�GDL�, are discussed using the LBM �101,102�.

An important advantage of the LBM is that the microscopicphysical interactions of the fluid particles can be convenientlyincorporated into the numerical model. Compared with theNavier–Stokes equations, the LB can handle the interactionsamong fluid particles and reproduce the microscale mechanism ofthe hydrodynamic behavior. Therefore, it belongs to the MD innature and bridges the gap between the molecular level and themacroscopic level.

4.3 Challenges for Multiscale Modeling. One of the impor-tant goals about CL modeling is to rapidly and accurately predictthe properties and features, which is very difficult to achieve withtraditional modeling and simulation methods at single length andtime scales with the current computer power. However, severalchallenges, both experimental and theoretical, remain as a road-block to successful research and development, as summarized be-low.

4.3.1 The Length Scales. In particular, the smallest and largestlength scales present in the CLs may span three to four orders ofmagnitude, from about 1 Å �size of an atom� up to hundreds ofnanometers �end-to-end distance� �103�. This broad range oflength scales includes chemical details at the atomistic level, in-dividual chains, and microscopic features involving aggregates orself-organized chains, up to continuum phenomena at the meso-and macroscale. A proper study of the CLs requires suitable andsimplified models, which allow one to focus on essential features�76�. Then, it is expected to use the multiscale simulation strate-

Fig. 13 A conceptual representation of the implementation ofSOFC porous structures into a LBM model. „a… A representationof the pore structure where the white regions are the pore andthe black regions represent the dense Ni and YSZ materials. „b…A binary representation of this structure, as read by the LBM,where “1” is a pore and “0” is a dense region. „c… Discreteelectrochemical boundary conditions are implemented with aunique binary indicator, “2,” at the interface. False colors areused as a visual guide †99‡. Reprinted from Ref. †99‡ with per-mission from Elsevier.

gies to bridge the models, as seamlessly as possible, from one



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cale to another. The calculated parameters, properties, and nu-erical information can be efficiently transferred across the

cales.

4.3.2 The Time Scales. The broad range of length scales bringsbout a correspondingly wide range of time scales, with chemicalond vibrations occurring over tens of femtoseconds and, at thether extreme, collective motions of many chains taking secondsr much longer, while the time step in the continuum equations isoverned by the smallest element in the mesh. Therefore, if theesh is down to the atomic scale, the simulation will evolve very

lowly, and many time steps will be used to simulate the dynamicsn the areas of little interest. This problem will directly affect theomputational cost of the simulation. A means of avoiding thisssue by completely separating the two time scales would be nec-ssary. This way, there is no restriction on the mesh to be refinedo nanodimensions; therefore the continuum simulation canvolve on a larger time step.

4.3.3 The Integration Algorithms. Time integration algorithmsre based on finite difference methods, where the time is dis-retized on a finite grid. The time step is the distance betweenuccessive points on the grid. These algorithms are only approxi-ate and have two errors associated with them �104�. First, trun-

ation errors arise because these algorithms involve Taylor expan-ions that need to be truncated at a certain order. Second, round-ff errors arise from the implementation of the algorithms onperating systems, which use a finite number of digits in theirrithmetic operations. Both these errors can lead to a divergencef the solution. As very small time steps need to be used in thetomistic domain, the highly iterative nature of these multiscaleimulations can cause error amplification.

4.3.4 The Contact at the Interface. As with any nanosystem,ontact remains a critical issue. Small atomic-level changes in thetructure of the contact can have a significant impact on the con-act resistance, and very little characterization data exist on mostxperimental contacts. Besides, even though DFT methodologiesre becoming faster and more accurate, they are still too limited inealistically representing the contacts. In CNT-polymer compos-tes �105�, even if the CNTs are well dispersed, it is also needed toontrol and study the mechanical, electrical, and thermal couplingetween polymer and CNT in much more detail. For some appli-ations, it is necessary to design a truly multiscale method toddress the contacts in different length and time scales.

4.3.5 Degrees of Freedom to Design. One of the main goals ofultiscale modeling is to drastically reduce the number of degrees

f freedom of engineering problems while maintaining accuracyn regions of interest. So far, the developed methods have notchieved the goal of attaining large realistic system sizes. Evenith the use of parallel computing techniques, these methods still

equire a long time to simulate the problems of interest �104�.All single scale modeling methods provide the results that lead

o an understanding of the properties under specific conditions.his information is then passed on to designers to learn from and

ncorporate into future designs. Thus, the multiscale modelinghould be developed to demonstrate the usefulness for engineeringesign. Clearly, the results directing to real engineering problemsan be used to assist in CL design.

ConclusionIn this review, an overview of the nano-/microstructures of the

uel cell catalyst layer based on experimental analysis was pre-ented. The CLs can be considered as a highly dispersed interfaceetween Pt and electrolytes �ionomer or water�. Due to the ran-om composition and complex structure, the properties of physi-al and chemical processes on the Pt surface are outlined. Thesetructural properties include the adsorption energy, the activationnergy, and the reaction energy. The study of the adsorption abili-
ies �reactant, intermediate, and product� is widely employed to


understand the catalyst activity and the design of CLs. The inter-actions between the catalysts and the reaction species govern thereactions, and the adsorption energy is relatively easier to calcu-late than the reaction and activation energies.

The modeling of the nanocomposites in the CLs is a multiscaleproblem. Theoretical procedures have to provide quantitative pre-dictions about elementary processes at the nanoscale and also of-fer the morphology of heterogeneous materials �e.g., ionomers,Pt/C agglomerate� and rationalize their effective properties. In thispart, many traditional simulation techniques �e.g., MC, MD, andLB� have been employed, and some novel simulation techniques�e.g., DPD� have been developed.

Despite the significant achievements in recent years, there stillexist major challenges and limitations in modeling and simulation.Developing such a multiscale method needs new and improvedsimulation techniques at individual time and length scales. It isalso important to integrate the algorithms and explore the contactat a wider range of time and length scales. An ideal couplingmethod would incorporate all the positive aspects of each methodinto one sole approach. Therefore, when the computational burdenis decreased, it would be possible to reduce the degrees of free-dom. Once the efforts are directed to real engineering problems,the structural, dynamic, and mechanical properties, as well as op-timizing design can be explored more effectively.

AcknowledgmentThe European Research Council �ERC� supports the current

research.

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