F344 Journal of The Electrochemical Society, 161 (3) F344-F353 (2014)0013-4651/2014/161(3)/F344/10/$31.00 © The Electrochemical Society

Simulation of Surface-Potential Driven ORR Kinetics on SOFCCathode with Parallel Reaction PathwaysMingyang Gong,a,b Randall S. Gemmen,a David S. Mebane,a,b Kirk Gerdes,aand Xingbo Liua,b,∗,z

aNational Energy Technology Laboratory, Morgantown, West Virginia 26507, USAbMechanical and Aerospace Engineering Department, West Virginia University,Morgantown, West Virginia 26506, USA

In this research, the polarization behavior and kinetic pathways of an SOFC cathode have been investigated with a 1-D continuummodel incorporating material physical properties and surface potential effects into a multi-step ORR kinetic formalism. It is foundthat (1) Two different types of 3PB-to-2PB pathway transitions can be identified. A strong 2PB pathway contribution leads to anexplicit transition, while an implicit transition implies more favorable 3PB kinetics. The predicted kinetic trends qualitatively agreewith literature results on single-phase LSM cathodes in different configurations and operation conditions; (2) The explanation forthe different transition modes concerns the fact that the mass transport limitation of the 3PB path is more easily reached (at loweroverpotential) when incorporation kinetics are favored by the material properties; and (3) The surface potential is found to stronglycontrol the oxygen adsorption by introducing a rate-limit for cathodes with lower oxygen coverage, and can drive the incorporationfaster under 3PB-favorable states.© 2014 The Electrochemical Society. [DOI: 10.1149/2.104403jes] All rights reserved.

Manuscript submitted February 11, 2013; revised manuscript received January 9, 2014. Published January 17, 2014.

Solid oxide fuel cells (SOFCs) are promising solid-state elec-trochemical devices for clean power generation from fossil energyresources. Despite the SOFCs’ unique fuel-flexible advantages, is-sues including manufacturing cost, reliability, and the public’s mis-perception of SOFC as a hydrogen technology remain obstacles tocommercialization.1 Research priorities are focused upon develop-ment of affordable SOFCs operating with hydrocarbon fuels at anintermediate temperature (IT) range of 700–850◦C. However, loweroperation temperature negatively affects cell performance. Especiallyfor the most common SOFCs with Sr-doped lanthanum manganite(LSM) as the cathode, a major portion of the total polarization resis-tance arises due to the sluggish oxygen-reduction reaction (ORR) onthe cathode side.2,3 Numerous research efforts have been devoted toidentifying the reaction mechanism and rate-limiting factors for theSOFC cathode materials, which are mixed ionic and electronic con-ductors (MIECs) at elevated temperature or under bias. Such mixed-conducting characteristics allow oxygen incorporation and transportto proceed in a parallel fashion along both a surface pathway across the“open” triple-phase-boundary (TPB or 3PB) as well as via bulk path-way across the “closed” two-phase boundary (2PB) between cathodeand electrolyte.4,5 For LSM-type perovskite cathodes with low intrin-sic ionic conductivity, the ORR process is generally confined to thesurface pathway near the 3PB.6,7 For the more ionically conductivematerials such as Sr- and Fe- doped lanthanum cobaltite (LSCF), bulkpathway reactions are more kinetically dominant and result in su-perior IT performance.8–10 LSM possesses technical value owing togood long-term stability, good electrolyte compatibility, and a body oftechnical research available to help understand reaction fundamentals,e.g. activation behavior.10 Recently, progress has been made to utilizeLSM for IT SOFCs by microstructural optimization11 and throughsurface modification in infiltrated electrodes with LSCF backbones toimprove performance and stability.12,13

Although much progress has been made, determination of thedetailed ORR mechanism remains elusive with respect to domi-nance/competition for particular kinetic pathways and steps. In con-ventional measurements with porous cathodes, more than one rate-limiting step (RLS) along the surface path has been proposed forLSM at 700–950◦C, including charge-transfer for oxygen dissociativeadsorption, surface diffusion, and 3PB charge-transfer.6,14–16 Uncer-tainties observed in regular electrode construction and testing havespawned further research using model electrodes. Dense, thin-filmelectrodes or patterned microelectrodes have been increasingly ap-plied to quantify critical geometrical effects (e.g. 3PB length) on

∗Electrochemical Society Active Member.zE-mail: xingbo.liu@mail.wvu.edu

the polarization resistance and rate-determining process. Early worksfrom Siebert and Van Herle reported a shift of the dominant kineticprocess from dissociative oxygen adsorption to bulk ionic transportbelow −0.2 V polarization as the electrode is reduced.17,18 With thin-ner LSM micro-electrodes (∼250 nm thick) at 800◦C, Brichzin alsofound bulk oxygen transport to dominate the ORR process below−0.2 V, with possible contributions from oxygen incorporation and2PB interfacial transfer.19 Such bulk-dominated ORR kinetics werealso confirmed by La O’ and co-workers for a patterned LSM electrode(240∼360 nm thick), but they attributed the RLS to an unspecifiedsurface chemical reaction at temperatures above 700◦C.20 In contrast,Radhakrishnan and Miara reported the ORR kinetics for thicker (0.5micron) LSM-type patterned electrodes to be 3PB-dominated, in away that surface diffusion and charge-transfer became rate-limiting at600 and 800◦C, respectively.21,22 These recent studies have progres-sively analyzed the governing ORR mechanism from quantitativelywell-defined parameters, yet the interaction of kinetic pathways de-pends on the geometry and surface chemistry of microelectrodes,5,19

properties that vary with composition and processing as in macro-electrodes. Unfortunately, quantitative measurement of surface vs bulkpath kinetics for porous cathodes is not well established,10 as the de-convolution of impedance spectra must take place under significantempirical uncertainty.20

Numerical modeling provides an alternative method to correlatethe mechanistic information from fundamental measurement and full-scale cathode performance. Kinetic models unveil the detailed ORRby computing the roles played by each reaction pathway and allowingidentification of the key reaction and transport parameters. The resultscan be integrated into multi-scale models to predict the interplay ofcathode geometry and material properties. In recent modeling works,the charge and mass transport mechanisms during the ORR processhave been thoroughly studied with respect to reaction driving forcesand kinetic scenarios.23–33 Within the established theoretical frame-work, continuum models covering both 3PB and 2PB kinetic paths areaddressed in analyzing cathode polarization, since the oxygen trans-port under different overpotentials is influenced by particular cathodegeometry and material properties.

Even though phenomenological changes in cathode polarizationbehavior are expected to correlate to transition of dominance amongcompeting reaction pathways, detailed parametric analysis has notdetermined how such pathway transitions respond to the evolutionof surface and bulk material properties. In our recent calculation, theamount of 3PB sites with a certain contact area of 2PB depends onparticle size of SOFC cathode, indicating higher specific surface areawould result in faster 3PB kinetics. However, the microstructural ef-fects of SOFC cathode are less addressed here. The major goal of the

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Journal of The Electrochemical Society, 161 (3) F344-F353 (2014) F345

Figure 1. Schematic description of bi-pathway ORR process on MIEC cathode (LSM) and spatial distribution of surface potential χs along cathode surface.

present work is to investigate the effects of surface reaction kineticsand material physical properties on the 3PB/2PB pathway transition,and to explore its relationship with cathode polarization behavior. A1-D dynamic continuum model is constructed with two parallel ORRpathways (3PB and 2PB) for analyzing the electrochemical activationand reaction rate/species distributions of LSM-type MIEC cathodes.The model applies a Butler-Volmer (B-V) description of surface oxy-gen reaction driven by surface electrostatic potential, which varies ac-cording to diffusion-induced profiles of surface oxygen intermediates.A parametric study of cathode surface processes with varied surfaceoxygen coverage, exchange rates and consequent surface potential ef-fects gives rise to two types of I-V polarization characteristics in thisstudy, which are compared to relevant experimental data in the liter-ature. Physical processes determining 3PB-to-2PB kinetic transitionsand cathode performance are also discussed, with detailed analysis ofsurface reaction rates.

Model Description

Physical model for bi-pathway ORR kinetics on MIEC cathode.—Fig. 1a schematically shows the ORR process in a model single-phaseLSM-type MIEC cathode in contact with a yittria-stablized-zirconia(YSZ) electrolyte. Oxygen transport and incorporation into the elec-trolyte proceed through the cathode surface (3PB) and bulk (2PB).The detailed reaction mechanism for this model has been publishedin a prior study, and involves six elementary reaction steps with anionic surface oxygen intermediate and a bulk oxygen vacancy as theactive electrode species.34 The 3PB pathway consists of reaction stepsS1-S4, corresponding to oxygen adsorption, surface electronation,surface diffusion and 3PB charge transfer, respectively. The 2PB path-way competes with the 3PB path, adding oxygen incorporation stepB3 and 2PB oxygen exchange step B4 as well as considering bulkoxygen vacancy diffusion. To address the surface potential effects,the model assumes that surface electronation can be rate-limiting foroxygen adsorption on a metallic cathode surface, and the surface oxy-gen ad-ions are sufficiently abundant to ignore kinetic contributionsfrom other minor neutral and charged surface species. The oxygendissociative adsorption can then be described by combining elemen-tary reaction steps S1 and S2 together as a half-reaction S2 in overalloxygen reduction:

S2 : 1/2O2 + e− kS2↔k−

S2

O−ad [1]

With Fleig’s approach,28 the model considers a Helmholtz doublelayer on the MIEC cathode comprised of the surface oxygen ion andthe bulk mirror charge. Fig. 1b illustrates a surface potential χs acrossthickness d between surface/bulk as prescribed by Poisson’s equation.The presence of the surface potential modifies reaction rates S2 andB3. Furthermore, variation of surface potential along the cathode

surface is modeled during the ORR process, as surface charge densityis affected by polarization.

Driving forces for the multi-step ORR reaction.— The derivationstarts with applying transition-state-theory (TST) analysis to the rateexpressions for charge-transfer reaction steps S2, B3, S4 and B4.28,30

We then further explicitly correlate the physically-derived drivingforce to experimentally measured overpotential. The net charge-transfer reaction is energetically driven by the electrostatic (Galvani)potential difference between reaction states. The surface potential ishereby defined as the electrostatic potential difference between reac-tant and product species across the gas/MIEC interface in reactionstep S2:

χS = ϕe(M)B − ϕe(M)S [2]

Here ϕe(M)B and ϕe(M)S are the electrostatic potentials at MIECcathode bulk and surface respectively. This surface potential also ap-plies to incorporation step B3, but rather adversely affects the reactionrate as for step S2.28,30 We directly apply the treatment and derive theelectric potential for 3PB charge-transfer of step S4 as:

χ3P B = ϕe(M)S + ϕe(M)B − 2ϕe(Y ) [3]

ϕe(Y ) is the electrostatic potential for the YSZ electrolyte. At 2PBthe electric potential for charge-transfer step B4 is the electrostaticpotential difference between the cathode and the electrolyte

E2P B = ϕe(M)B − ϕe(Y ) [4]

Hence at 3PB boundary the surface and bulk electric potentialswould satisfy

χ3P B = 2E2P B − χS [5]

If the overpotentials are defined as deviation of electric poten-tials χS , χ3P B , and E2P B from their respective equilibrium (opencircuit, OC) states (χOC

S , χOC3P B , and EOC

2P B), a special relationship atthe 3PB/2PB boundary can be obtained from Eq. 5 as

�χ3P B = 2η2P B − �χS [6]

Here �χS , �χ3P B , and η2P B represent the overpotentials at3PB/2PB interface defined by �E = E-EOC with E asχS , χ3P B , andE2P B . Next for a 3-electrode electrochemical system both referenceand working electrodes are assumed to be good metallic electricalconductors, so that their electron entropies are assumed unperturbedduring cathode (working electrode) polarization. The electrical fieldgradient inside the bulk MIEC, the electrolyte ohmic drop, and thecathode/electrolyte contact resistance are considered negligible, there-fore (details are shown in Appendix)

�χ3P B = 2ηapp − �χS [7]

Here ηapp = η2P B is the applied overpotential between working(cathode) and reference electrodes. Eq. 7 allows evaluation of all

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F346 Journal of The Electrochemical Society, 161 (3) F344-F353 (2014)

overpotentials via an experimentally measurable overpotential. Re-action rates for charge-transfer steps S2, B3, S4 and B4 can thenbe phenomenologically expressed in B-V style kinetics with separatedriving forces at different reaction interfaces

rS2 = rS2,0{exp(−αs f �χs) −CO−

ad

CO−ad ,eq

exp[(1 − αs) f �χs]} [8]

rS4 =rS4,0

{CO−

ad

CO−ad ,eq

exp(−α3P B f �χ3P B) − exp[(1−α3P B) f �χ3P B]

}[9]

rB3 =rB3,0

{CO−

adCV,M I EC

CO−ad ,eqCV,M I EC,eq

exp(αs f �χs)−exp[−(1−αs) f �χs]

}[10]

rB4 = rB4,0{exp(−2α2P B f η2P B)

− CV,M I EC

CV,M I EC , eqexp[2(1 − α2P B) f η2P B]} [11]

Where rS2,0, rS4,0, rB3,0 and rB4,0 are the exchange rates definedby a set of forward and backward rate constants, chemical constantsand equilibrium species concentrations for respective reactions; CO−

ad,

CV,M I EC and CV,Y SZ represent the concentrations for surface oxygenion, oxygen vacancy of MIEC cathode and oxygen vacancy of theelectrolyte, respectively. The symmetry factors α are taken as 0.5, andthermal factor f is given by f = F/RT with F as the faradaic con-stant, R the gas constant and T the temperature. Overpotentials satisfyEq 7. Langmuir-type isothermal adsorption is assumed here, so thatany kinetic effect of surface site restriction is considered negligi-ble. The kinetic expressions thus only contain overpotentials, surfaceoxygen ion concentration and bulk oxygen vacancy concentration asactive simulation variables. It should be emphasized that contradictoryviews among researchers exist about the issue that the surface processof SOFC cathode is chemical or electrochemical, which is related tothe validity of B-V descriptions in surface process. The employmentof B-V type equations for surface reaction kinetics of MIEC electrodewas first conducted by Fleig.28 Based on our theoretical understand-ing on the non-linear correlation among applied overpotential, surfaceelectrostatic potential and surface adsorbed oxygen concentration asshown in Fleig’s work, the B-V approach is thereby used to describethe surface processes in this work.

Dependence of surface potential on oxygen intermediates.— Asη2P B is the only variable with experimentally defined value in a fullcell (working electrode overpotential ηapp), the dependence of thesurface potential on the concentration of surface oxygen intermediatesis estimated to reduce simulation requirements. Such a relationshiphas been derived by Fleig with Poisson’s equation.28 Specifically,Poisson’s equation is solved using surface oxygen ion concentration torepresent charge carrier density and assuming a homogeneous chargedistribution across a surface Helmholtz layer, i.e. a “plate capacitor”model

χs = FCO−,ad

Cs[12]

Here Cs is the area-specific surface capacitance, which is equiva-lent to the ratio between the dielectric constant and ionic radius. Hencefor the surface overpotential (surface potential change) we have

�χs = χs−χs,eq =F

(CO−

ad− CO−

ad ,eq

)Cs

=FCO−

ad ,eq

Cs

(CO−

ad

CO−ad ,eq

− 1

)[13]

Substitution of equation 13 into equation 7 gives

�χ3P B = 2η2P B −FCO−

ad ,eq

Cs

(CO−

ad

CO−ad ,eq

− 1

)[14]

Therefore in this way the simulation variables in kinetic equations8–11 are reduced to CO−

adand CV,M I EC with η2P B as the overpotential

input.

Numerical formalism.—Governing equations and boundaryconditions.— The above analysis leaves CO−

adand CV,M I EC as the

two primary dependent variables for numerical simulation. Reactionsteps S2, B3 and B4 are set as RLSs with finite rates,34 since surfacereactionkinetics become dominant above 700◦C,20 and 2PB exchangeinvolving oxygen vacancy is kinetically limited for LSM-type cathodewith low intrinsic ionic conductivity.26,35 Reaction step S4 remains atquasi-equilibrium with net kinetic rates ignored. The coupled reactive-diffusion equations can then be developed with Fick’s 2nd law basedupon Eq. 8, 10 and 13:⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

∂Co−,x

∂t= Ds,chem

(∂2Co−,x

∂x2

)+ rS2−rB3 [15]

∂CV,M I EC

∂t= Db,chem

(∂2CV,M I EC

∂x2

)− �S

�VrB3 [16]

Ds,chem and Db,chem are the surface diffusivity for oxygen ad-ionsand bulk oxygen vacancy diffusivity respectively; and �S/�V is thevolume-specific surface area. The boundary conditions at the cath-ode/electrolyte (x = 0) are Dirichlet-type for surface oxygen ion de-fined by quasi-equilibrium reaction S4 with dynamic balance, andflux-type for oxygen vacancies determined by reaction B4:⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

CO−ad ,x=0

CO−ad ,eq

exp

[f FCO−

ad ,eq

Cs

(CO−

ad ,x=0

CO−ad ,eq

− 1

)]

= exp(2 f η2P B) [17]

Db,chem

(∂CV,M I EC,x=0

∂x

)= rB4,0

{ CV,M I EC

CV,M I EC , eq

× exp[2(1 − α2P B) f η2P B] − exp(−2α2P B f η2P B)}

[18]

Eq. 21 is obtained from Eq. 13 and 18, and is regarded as a LambertW function. The boundary concentration of surface oxygen ions canthen be conveniently computed with Matlab. On the cathode surface(x = lc as in Fig. 1a), a zero-flux boundary condition is assumedfor surface oxygen. A blocking boundary condition is used for bulkoxygen vacancies with the assumption that 2PB path is only partiallyactivated through the cathode bulk by an increase of vacancy concen-tration from thermodynamic equilibrium.⎧⎪⎪⎪⎨

⎪⎪⎪⎩Ds,chem

∂Co−,x=lc

∂x= 0 [19]

CV,M I EC,x=lc = CV,M I EC,eq [20]

Simulation method and parameters.— The model utilizes the finitevolume method and explicit integration from Patankar to numericallyobtain steady-state solutions for governing equations 15 and 16.36

The total simulation length is set as 2 μm from the 2PB/3PB in-terface (x = 0) to the end surface of the MIEC cathode (x = lc).The computation distance adopted reflects the widely accepted phe-nomenological assertion that surface diffusion and 2PB activationeffects primarily occur within 1 μm of the electrolyte for LSM-type MIEC cathodes.20,37 2PB overpotentials (η2P B) ranging between−0.3 V to + 0.1 V at 50 mV intervals are input to calculate the speciesconcentration profiles and fluxes. The first flux node is placed right at

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Journal of The Electrochemical Society, 161 (3) F344-F353 (2014) F347

Table I. Values of parameters used in the simulation cases (a detailed discussion of parameter values appears in 34).

Parameter Case 1 Case 2 Case 3 Case 4 Description

I Db,chem 10−6 cm2s−1 Surface oxygen diffusivityDs,chem 10−6 cm2s−1 Bulk vacancy diffusivity

CV,M I EC,eq 10−8 mol cm−3 10−8 mol cm−3 10−7 mol cm−3 10−8 mol cm−3 Equilibrium vacancy conc. in MIECCO−

ad ,eq 10−11 mol cm−2 10−10 mol cm−2 10−10 mol cm−2 10−10 mol cm−2 Equilibrium surface oxygen conc.

rS2,0 10−8 mol cm−2s−1 10−7 mol cm−2s−1 Exchange rate constant for S2rB3,0 10−6 mol cm−2s−1 10−7 mol cm−2s−1 Exchange rate constant for B3rS4,0 10−6 mol cm−2s−1 Exchange rate constant for S4rB4,0 10−7 mol cm−2s−1 Exchange rate constant for B4

�S(�V )−1 105 cm−1 Volume-specific surface areaCs 10−5 F cm−2 Surface capacitance

αs , α3P B , α2P B 0.5 Symmetry factorII � 10−9 mol cm−2 5 × 10−9 mol cm−2 Surface adsorption site density

θeq 0.02 0.05 Equilibrium oxygen coverageT 1073 K Temperature

p O2 0.21 atm Oxygen partial pressure

the MIEC cathode/electrolyte interface (x = 0), and hence the faradaiccurrents of 3PB and 2PB pathways are given by the correspondingdiffusional flux values at steady state,

i3P B = −2F�S

�VDs,chem

(∂CO−∂x

)|x=0 [21]

i2P B = 2F Db,chem

(∂CV,M I EC

∂x

)|x=0 [22]

Given the modeled overpotential and simulation distance range,calculation of faradaic currents from diffusion fluxes is consideredadequate. Mebane and Lynch have pointed out that sheet resistance as-sociated with electronic migration and bulk charge inhomogeneity willaffect cathode polarization of thin-film cathodes (<1 μm) at high over-potential (> −0.4 V),31,32 while Svensson estimated that for a thickercathode (>10 μm) the charge balance had little change at low to mod-erate overpotential and migration flux would become negligible.24,25

Other computation details are mentioned in a previously-publishedwork.34

Simulations are performed to examine the role of cathode proper-ties in determining performance. In particular, the influence of phys-ical properties and kinetic parameters is examined with respect topolarization and reaction pathway dominance (whether 2PB or 3PB).Four cases are conceived in this study, with parameter values listed inTable I. Type I parameters are directly included in numerical calcu-lation while type II parameters indirectly determine performance bydescribing the pertinent material physical and thermodynamic states.The bulk material properties for LSM, such as equilibrium vacancyconcentration and oxygen chemical diffusivity, are well-documentedexperimentally and theoretically, and thus our parameterization canbe conveniently based upon common dopant levels and material pro-cessing conditions. However, the parameters associated with surfaceproperties cannot be readily extracted from the experimentally well-defined and widely-utilized thermodynamic values such as oxygen ex-change coefficient. Despite such difficulty, fundamental analyzes andDFT calculations30–32,42 provide supports for our choice of dominatingsurface reactant species and corresponding exchange rate constants.Details about parameter enumeration have been thoroughly discussedin a prior work34 and Appendix B. Exchange reaction rates for dis-sociative oxygen adsorption (S2) and incorporation (B3) are variedbetween cases to investigate the relationship between surface potentialeffects and rate-limiting surface reactions. Besides, the physical im-plication of parametric study on material surface properties has beenprovided in Appendix B.

This study focuses on a parametric examination of cathode sur-face processes for various surface oxygen ionic coverages, surfaceexchange rates, and consequent surface potential effects. Case 1 isthe baseline, and case 2 has higher surface equilibrium oxygen ion

concentration, thus enhancing the driving force for oxygen transportacross the surface and into the bulk cathode. Case 3 has both highersurface equilibrium oxygen ion concentration and equilibrium bulkvacancy concentration, and case 4 has higher equilibrium bulk va-cancy concentration but the same surface equilibrium oxygen ionconcentration as case 1.

Results and Discussion

I-V relationship and pathway transition.— The current-voltageplots simulated in case 1 (baseline) and case 2 (higher surface equi-librium oxygen ion concentration) studies are respectively presentedin Fig. 2a and 2b. Generally the I-V responses of all simulations inthis study follow the trend previously reported by Coffey and our pre-vious modeling work.26,34 Specifically, 3PB currents tend to dominateORR kinetics at anodic and low cathodic overpotentials, but ORR ki-netics become eventually dominated by 2PB currents when cathodicoverpotential grows higher. Coffey pointed out this tendency for thecase where approximate parity exists between the 2PB and 3PB ex-change rates,26 and the claim is supported by experimental studieswith dense-film MIEC cathodes.

The results shown in Fig. 2 possess an additional critical meaningand provide a testable prediction. Specifically, Fig. 2 indicates thatthe equilibrium concentration of the surface oxygen ion changes thenature of the cathode polarization behavior and performance. For case1 with lower CO−

ad ,eq , the 3PB current reaches a maximum at approx-imately −0.1 V, and decreases at overpotentials >−0.15 V. On theother hand, 2PB current increases steadily without exhibiting a kineticlimit. The total current in Fig. 2a is consequently non-linear with acurrent-limiting “plateau” appearing between −0.1 V and −0.2 V ow-ing to opposing 3PB and 2PB kinetic response to overpotential. Themanifestation of the 3PB-to-2PB pathway transition is thus “explicit”via an abruptly observable total current increase above −0.2 V. Incontrast to case 1, the adoption of higher CO−

ad ,eq in case 2 results ina smooth “implicit” transition from 3PB to 2PB control, as depictedin Fig. 2b. The mass-transport limits in 3PB current now appear athigher cathodic overpotentials (above −0.2 V), and the suppressionof transport limitations results in higher 2PB and total currents withTafel-like overpotential response, and greater than 200% performanceincrease compared with case 1.

The smooth arc of total current density permits the drawing oftangent lines to extract exchange current densities from the interceptsat 0 V. The value of the 2PB exchange current i0,2P B(10−3.76 A/cm2)from Tafel analysis is considerably lower than that (10−2 A/cm2)directly given by the RB4,0 parameter. This indicates as in prior studiesthat activation of the 2PB path is kinetically sluggish. The extractedtotal exchange current (i0,tot ) is much higher than the observed 2PB

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F348 Journal of The Electrochemical Society, 161 (3) F344-F353 (2014)

Figure 2. Logarithmic current versus overpotential profiles for bi-pathway electrode kinetics with parameters for (a) case 1 with Co-,eq = 1 × 10−11mol cm−2,and (b) case 2 with Co-,eq = 1 × 10−10mol cm−2.

current (i0,2PB), indicating that the 3PB path strongly contributes tooverall electrode activation.

The above results indicate that increasing CO−ad ,eq improves both

3PB and 2PB currents, yet the transition point and modes are not pre-dictable a priori. An examination of various mass-transport parame-ters is conducted to elucidate the character of the resulting pathwaytransition. In the next sections, the species concentration profile, sur-face potential response, and distribution of surface reaction rates arecompared between cases 1 and 2.

Evolution of concentration profiles, surface potential and surfacereaction rates with applied overpotential.—Concentration profiles.—Figures 3a and 3b show the steady-state concentration profiles ofsurface oxygen ion and bulk oxygen vacancy respectively for cases 1and 2 as function of applied overpotential. The active reaction zonesnear the 3PB/2PB interface, where the largest deviations of CO−

adand

CV,M I EC occur, are qualitatively similar in both cases, and widen ascathodic overpotential increases. In case 1, both CO−

adand CV,M I EC

show strong curvature near the 3PB/2PB interface, which intensifiesas overpotential increases. The value of CO−

adat x = 0 is fixed by

the Dirichlet boundary condition, therefore the profile curvature isevidence of a surface-diffusion limitation. This simulation result isphysically consistent with the lower CO−

ad ,eq used in case 1, whichwould be expected to result in a relatively diminished CO−

adpopulation

as current density increases, and subsequently increased diffusionlength and diffusional resistance. As expected, the diffusion limitationin case 2 is delayed to a larger overpotential, and accordingly a negativeshift of the 3PB to 2PB transport control is observed.

Examination of oxygen vacancy profiles also demonstrates the im-pact of surface potential on oxygen incorporation rates. If the oxygenincorporation step B3 were a pure chemical reaction, lower oxygenvacancies would be expected for case 2, as more vacancies wouldbe consumed by increased numbers of surface oxygen ions. However,Fig. 3b indicates non-trivial differences in the oxygen vacancy profilesbetween the two cases. At an overpotential of −0.1 V, the oxygen va-cancy concentration in case 2 is actually higher than case 1 except forthe last computational node at the 2PB interface (x = 0). Although thisresult defies the general expectation of diminished CV,M I EC in case 2,application of greater overpotential (>−0.2 V) eventually producesthe intuitive result of lower CV,M I EC than in case 1 throughout the

Figure 3. Comparison of normalized concentration profiles in cases 1 & 2 under different overpotentials for (a) Surface oxygen ion CO-/CO-,eq, and (b) BulkOxygen vacancy Cv/Cv,eq.

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Journal of The Electrochemical Society, 161 (3) F344-F353 (2014) F349

Figure 4. Spatial distribution of surface overpotential �χs for case 1 and 2under different applied overpotentials.

bulk except for the 2PB boundary node (x = 0), where CV,M I EC incase 2 is slightly (∼8%) lower than that of case 1. Here, as the MIECbulk vacancy concentration decreases (lattice oxygen increases) theoxygen exchange rates increase across the 2PB, in accordance withEq. 11. From low to high overpotentials, the observed deviation ofvacancy profiles from those expected for a purely chemical reactionsuggest that surface potential effects determine surface reaction rates.

Surface overpotential.— The profile of surface overpotential(�χS) in Fig. 4 is qualitatively similar to that of the surface oxygenions in Fig. 3. This intuitively obvious result arises from the originalmodel assumption and leads to two important observations. First28,30

the amplitude of surface overpotential can diverge from the applied2PB overpotential. Even though surface oxygen is displaced less fromequilibrium in case 2 than in case 1 (higher ratio CO−

ad/CO−

ad ,eq ), thesurface polarization is more pronounced due to the increased mag-nitude of absolute surface charge density. Secondly, surface overpo-tential tends to be less dependent on the surface chemical potential(CO−

ad/CO−

ad ,eq ) as the cathode polarizes. For case 1, �χS becomes in-variant beyond 0.2–0.6 μm away from the 3PB when the applied 2PBoverpotential exceeds 0.1 V cathodic. This suggests that a maximumelectrochemical driving force for surface reactions can be approachedonce CO−

ad/CO−

ad ,eq drops to a very low level (below 0.1). Below thisthreshold some other driving force controls rates to maintain steadyoverpotential.

Surface reaction rates.— A comparison of reaction rates at thesurface between cases 1 and 2 is shown in Fig. 5. Fig. 5a suggests thathigher oxygen coverage gives rise to faster oxygen adsorption kineticsin case 2, due to the increase of surface overpotential and polarization.Case 1 shows notable adsorption limitations at higher overpotentials,with a rate plateau appearing near the 3PB. This finding implies that onan oxygen-depleted cathode surface, oxygen adsorption becomes rate-limiting, and the maximum rate is essentially determined by chemicalproperties as rS2,0 exp(α f χS,eq ). For the oxygen incorporation step B3at −0.1 V, case 1 is relatively faster near 3PB (∼0.15 μm). This ismainly attributed to a lower energy barrier (absolute value of �χS) totransfer of the oxygen anions into the bulk cathode,29 given that thesurface oxygen concentration CO−

ad/CO−

ad ,eq for case 1 at this moment(low polarization) is not much lower (> 0.1 as in Fig. 3a) than case 2.High polarization of −0.3 V in case 1 causes oxygen incorporation tobecome kinetically limited by depleting surface oxygen near the 3PB.Hence, the model predicts for the active regions next to the electrolytethat, both adsorption and incorporation become slower with reducingsurface oxygen coverage on the cathode, due to diminishing electri-cal and chemical driving forces respectively at higher overpotentials.Comparing Fig. 5b to Fig. 3b, the oxygen vacancy concentrations canbe regarded to mainly control surface exchange rates outside of suchactive reaction regions.

Furthermore, comparison of case 1 adsorption/incorporation rates(explicitly shown in Fig. 5b by dotted- and dashed plots at −0.3 V)reveals that bulk incorporation dominates the surface reaction processwith rates equal to or higher than adsorption rates near 3PB at higheroverpotentials. Consequently, the oxygen transport is preferred via theincorporation-active 2PB path and a surface diffusion limitation foroxygen ad-ion results. In case 2 with an oxygen-rich cathode surface,oxygen adsorption dominates the surface reaction kinetics except forthe 3PB proximal zone at −0.3 V only. Accordingly, the 3PB kineticsare more favored than in case 1 and the 3PB transport limit is initiatedat a more negative overpotential. Changes in surface oxygen coverageshift the dominant surface reaction step, thereby making either the3PB or 2PB path more kinetically competitive.

Effects of equilibrium vacancy concentration and surface ex-change rate constants.— In this section, two cases are developedwith a change of the bulk material parameter CV,M I EC,eq and sur-face exchange rates rS2,0 and rB3,0. As shown by the parameter list inTable II, the equilibrium bulk vacancy concentration CV,M I EC,eq forcase 3 is increased by 10 times over that of case 2. In case 4, theexchange rates rS2,0 for surface adsorption and rB3,0 for incorporationare increased and reduced respectively from case 2 by 10 times, to thevalue of 10−7 mol•cm−2s−1. Other parameters are kept the same asfor case 2.

Figure 5. Profiles of surface reaction kinetics in case 1 and 2 under different overpotential for (a) Oxygen adsorption rate RS2 (b) Oxygen incorporation rate RB3.

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F350 Journal of The Electrochemical Society, 161 (3) F344-F353 (2014)

Table II. Summary of V-I relationship and tafel analysis results for case 1 to case 4.

CaseCv,eq

(mol/cm3)CO-,eq

(mol/cm2)Transition

Voltage (V)Set-up of i0,3PB

(mA/cm2)Set-up of i0,2PB

(mA/cm2)Extracted i0,2PB

(mA/cm2)Extracted i0,TOT

(mA/cm2)iTOT at −0.3 V

(mA/cm2)

1 1 × 10−8 1 × 10−11 −0.13 1 100 N/A N/A 222 1 × 10−8 1 × 10−10 −0.15 1 100 1.8 7.2 703 1 × 10−7 1 × 10−10 −0.12 1 100 N/A N/A 844 1 × 10−8 1 × 10−10 −0.22 10 10 1.4 18 187

The I-V relationship for case 3 in Fig. 6a shows an “explicit” 3PB-to-2PB pathway transition as in case 1, and inhibited 3PB kineticscompared with case 2, with 3PB mass-transport limitations appearingat lower overpotentials (<−0.15 V). The dominance of 2PB kineticsin case 3 means that the electrode becomes electrochemically activeat higher overpotentials, as shown by the higher overall and 2PBcurrents at −0.3 V in Table II. Fig. 6b indicates both incorporationand adsorption kinetics are improved for case 3 with increase ofbulk oxygen vacancies. While it is natural to find faster incorporationfor more ionically conductive cathode is somewhat counter-intuitive.The enhancement of the surface adsorption rate is attributed to ahigher surface overpotential �χS, resulting from reduction of surfaceoxygen by the bulk vacancies. Also here, in analogy with case 1, thesurface oxygen exchange is more incorporation-active (i.e., at higheroverpotentials surface incorporation is faster than adsorption till adistance away from electrolyte), although the active reaction zoneexpands further from that of cases 1 and 2. Thus it is predicted thata cathode with higher ionic conductivity would be more active forsurface oxygen exchange.

In case 4, surface exchange rates are adjusted to make oxygenadsorption faster and incorporation slower. In Fig. 7b a narrower activereaction zone (0.4 ∼ 0.5 μm wide) is predicted for a case 4 cathode,but at regions close to 3PB (0.3 μm wide) surface oxygen reactionsare far more active, yielding the highest species fluxes toward theelectrolyte among all cases. Clearly, the enhancement of adsorption isfrom the increase of rS2,0, but faster incorporation is due to the controlof the surface reaction by the surface overpotential and oxygen ions.Thus, when the cathode adsorbs oxygen more easily, its ORR kineticswill be improved but confined closer to the 3PB and 2PB comparedwith other cases. With adsorption as the more active surface reactionprocess, 3PB path is kinetically favorable in case 4, and hence inFig. 7a surface transport limit is insignificant so that an “implicit”pathway transition results as seen in case 2.

Summarizing the simulation results for cases 1–4 (i.e., Figs. 2–4,5c and 7b), clearly correlations are shown between relative pathwaydominance, the active oxygen reaction zone and the pathway transitionstyle under polarization. Higher oxygen surface coverage and affinitypromotes adsorption-advantaged surface reactions and 3PB-inclinedORR kinetics, which give rise to implicit pathway transitions andcontraction of the active reaction zone.

Discussion and comparison of modeling results to experiment.—V-I relationship as function of kinetic pathway dominance.— Fig. 8ashows that pin-shaped and dense-film LSM electrodes exhibit similarpolarization behaviors as that simulated for cases 1 and 3, with abruptcurrent increases above certain overpotentials (−0.1 to −0.3 V), rep-resenting an “explicit” kinetic transition to the 2PB path at relativelylow overpotential.17,18 This trend can also be seen for LSM at loweroxygen partial pressure,16 which would reduce the concentration ofsurface oxygen ions while increasing the bulk vacancy concentration,thus favoring 2PB kinetics. On the other hand, results in Fig. 8b fortypical porous LSM electrodes in atmospheric conditions agree morewith cases 2 and 4, for which no obvious kinetic transition can beobserved even at much higher overpotentials (< −0.3 V).38,39 Despitethe discrepancies between simulation and literature results, which cancome from parameter uncertainty, the different kinetic behaviors forcases 1–4 do seem to reflect the experimental trends seen in Figs. 8aand 8b. Even though the microstructural and oxygen partial pressureeffects are not explicitly considered in the case study for this model,qualitative kinetic pathway dominance can be expected to depend onboth surface/bulk material properties and the microstructural/ambientstates of the electrode. The specific surface area �S

�V of MIEC cathodecan be expressed as40

�S

�V= 4ε

dp= πNpdpτ

A[23]

Figure 6. Simulation results of case 3 with Cv,eq increasing by 10 times from case 2 shown for (a) Pathway-constituted V-I relationship (b) Surface reaction rateprofiles.

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Journal of The Electrochemical Society, 161 (3) F344-F353 (2014) F351

Figure 7. Simulation results of case 4 with RS2,0 and RB3,0 changed by 10 times from case 2 shown for (a) Pathway-constituted V-I relationship (b) Profiles ofspecies concentrations and surface reaction rates at −0.3 V.

Where ε is the electrode porosity; dp and Np are the pore diameterand number of pores, τ and A the tortuosity and the electrode cross-section area respectively. A higher �S

�V predicted by Eq. 23 for moreporous electrode would directly promote 3PB current in Eq. 21, andcan benefit 2PB kinetics as well by increasing the incorporative termin Eq. 16. Such effects are qualitatively comparable to that broughtby increasing CO−

ad ,eq while keeping a constant surface area in case 2.On the other hand for electrode with dense microstructure and/or athigh temperatures, 2PB kinetics becomes dominant due to increasedionic conductivity and broadened contact area of the electrode withthe electrolyte.20,41 The 3PB kinetics of dense electrodes is inhibitedby low oxygen diffusivity inside pores and diminished local oxygenpartial pressure.40 Further Fig. 8a implies that even for fully-denseLSM cathode at very high temperature, 3PB kinetics does not becomenegligible during electrode polarization.

The above comparisons show that the pathway transition can bephenomenologically useful to probe relative 3PB or 2PB dominance inORR kinetics for LSM-type cathode, as both this study and prior workindicate the current-limiting behavior for electrode V-I plots at inter-mediate overpotentials comes from 3PB mass transport limitation.26

It should be pointed out that two types of pathway transition havealso been reported by Coffey’s modeling study,26 but in Coffey’s casethe kinetic disparity is caused by different magnitudes of exchange

currents between cases, whereas for 3PB and 2PB paths in each simu-lated case the exchange currents are kept essentially the same.26 Thisis in contrast to the present work, wherein the pathway transition ischanged by changes in the relative 3PB/2PB kinetic contributions as-sociated with the tuning of material physical properties from case tocase. For a practical MIEC cathode, the dependence between overall3PB and 2PB exchange currents is rather uncertain. The case studyresults here can be more conveniently correlated to the performanceoptimization routes of modifying the cathode material surface/bulkproperties. However, care must be taken of applying such 1-D simula-tion findings onto real cathode with 3-D network, as the kinetic effectsfrom the microstructure and ionic component of cathode should beexplicitly considered.

Implications for performance optimization.— Understanding thekinetic behavior for different types of cathodes, including the influ-ence of surface potential, can be important when choosing a strategyfor performance optimization. Comparisons among cases 2–4 implythat for LSM, modification of the surface catalytic activity by increas-ing of CO−

ad ,eq and χS can be more efficient than enhancing the ionicconductivity (with higher CV,eq ), in that the former methodology pro-motes overall performance without sacrifice of 2PB kinetics, while

Figure 8. Comparison of simulated V-I relationships to literature results for (a) Dense-structured LSM cathodes17,18 or porous cathode under low pO216;

(b) Porous LSM cathode28 and LSM-YSZ cathode29 under ambient pO2.

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F352 Journal of The Electrochemical Society, 161 (3) F344-F353 (2014)

the latter (case 3) leads to suppression of the 3PB path. (A similarconclusion was also drawn by Svensson.25)

Conclusions

The polarization behavior and kinetic pathways of an SOFC cath-ode have been investigated with a 1-D continuum model incorporatingmaterial physical properties and surface potential effects into a multi-step ORR kinetic formalism. The key findings can be summarized asfollows:

(1) Two different types of 3PB-to-2PB pathway transitions can beidentified. A strong 2PB pathway contribution leads to an explicittransition, while an implicit transition implies more favorable3PB kinetics. The predicted kinetic trends qualitatively agreewith literature results on single-phase LSM cathodes in differentconfigurations and operation conditions.

(2) The explanation for the different transition modes concerns thefact that the mass transport limitation of the 3PB path is moreeasily reached (at lower overpotential) when incorporation ki-netics are favored by the material properties.

(3) The surface potential is found to strongly control the oxygenadsorption by introducing a rate-limit for cathodes with loweroxygen coverage, and can drive the incorporation faster under3PB-favorable states.

Acknowledgment

This research is financially supported by U.S. Department of En-ergy’s SECA program in conjunction with National Energy Technol-ogy Laboratory’s Regional University Alliance (NETL-RUA) projectunder contract number (DE-AC26-04NT41817). The authors appre-ciate Dr. Harry Abernathy from NETL and Dr. Hui Zhang for valuablediscussions and technical contributions.

Appendix A - Derivation of surface and bulk overpotentials

If overpotentials are defined as potential deviation from equilibrium value at OCVsuch that �χ = χ − χeq and η2P B = E2P B − EOC

2P B , we know from Eq. 6 that

�χ3P B = 2η2P B − �χS [6]

Next the relationship between applied overpotential ηapp with �χ and η2P B needsto be identified. Assume a 3-electrode testing system; the measured open circuit potentialVOC between working electrode and reference electrode can be expressed as:27

FV OC = μOCe (r ) − μOC

e (M)L [A1]

In which μOCe (r ) and μOC

e (M)L are the equilibrium electrochemical potentials for electronat reference electrode and MIEC cathode surface respectively. Hence we have

F(V − V OC ) = Fηapp = [μe(r ) − μOC

e (r )] − [

μe(M)L − μOCe (M)L

][A2]

If it is assumed here that both reference and working electrodes are metallic electricalconductors, and their electron chemical potentials can be assumed as constant,30 thenEq. A2 changes to

Fηapp = −F{[ϕe(r ) − ϕe(M)L ] − [

ϕOCe (r ) − ϕOC

e (M)L]}

[A3]

And rearrangement of Eq. A3 gives

ηapp = [ϕe(M)L − ϕe(r )] − [ϕOC

e (M)L − ϕOCe (r )

][A4]

Where ϕe(r ) and ϕe(M)L are the electrostatic potentials at reference electrode and cathodesurface respectively. For simplicity point of view the electrical field gradient inside bulkMIEC and ohmic drop caused by electrolyte together with its contact resistance withworking electrode are considered negligible,27 then it follows,

ϕe(r ) = ϕe(Y ),ϕOCe (r ) = ϕOC

e (Y ),ϕe(M)L = ϕe(M)B , ϕOCe (M)L = ϕOC

e (M)B

[A5]In which ϕe(Y ) and ϕe(M)L represents the electrostatic potentials inside electrolyte andMIEC cathode bulk next to cathode/electrolyte interface respectively. Hence A4 can berewritten as

ηapp = E2P B − EOC2P B = η2P B [A6]

Appendix B - Correlation of parametric study to surfacethermodynamic property

As the simulation results of case 1–4 suggest cathode surface reaction kinetics togetherwith competition of kinetic pathways can depend upon certain surface material parameterssuch as equilibrium oxygen ion concentration (CO−

ad ,eq ), it is worthwhile to further discuss

the physical mechanism and kinetic implication underlying such parameter modification.Refer to the surface adsorption step in Eq. 6, the following relationship would exist forthe assumed reaction mechanism at equilibrium as is derived by Lynch [],

K ex = exp(−�G0

ads

RT) = kS2

k−S2

= p−1/2O2

CO−ad ,eq exp( f χS,eq ) [B1]

Where �G0ads is the standard oxygen adsorption energy for step S2. Hence increase of

CO−ad ,eq and associated χS,eq implies a reduction of oxygen adsorption energy and essential

enhancement of adsorption kinetics. This energy change may be physically correlated tothe presence of kinetically favorable coordination plane and cation composition on cathodesurface, as DFT calculation with TST surface model has suggested much lower adsorptionenergy for B-site cation such as Mn in perovskite structure.42 Therefore, the varied speciesconcentrations for case study would rather reflect fundamental change of surface structuralor catalytic properties. On the other hand, change of exchange currents in case 4 withconstant species equilibrium concentrations implies then the rate constants are modifiedby transition state energy specifically assumed while surface properties keep unchanged.It should be also mentioned here that in this study oxygen surface exchange is assumedto occur via surface oxygen ion (O−) as dominant reaction species, since recent DFTcalculation43 by incorporating the surface Galvani potential effect into the analysis foradsorption enthalpies of different surface oxygen species has suggested the equilibriumcoverages of super- and peroxygen ions would be orders of magnitude lower than that ofatomic surface oxygen ion on LSM electrode surface due to less exothermic adsorptionprocess.

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