Elementary Reaction Models for CO Electrochemical Oxidation on an Ni/YSZ Patterned Anode

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Citation Shi, Yixiang, et al. “Elementary Reaction Models for CO Electrochemical Oxidation on an Ni/YSZ Patterned Anode.” ASME 2010 8th International Fuel Cell Science, Engineering and Technology Conference: Volume 2, 14-16 June, 2010, Brooklyn, New York, ASME, 2010, pp. 159–66. © 2010 by ASME

As Published http://dx.doi.org/10.1115/FuelCell2010-33205

Publisher ASME International

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Citable link http://hdl.handle.net/1721.1/119260

Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Proceedings of the ASME 2010 Eighth International Fuel Cell Science, Engineering and Technology Conference FuelCell2010 June 14-16, 2010, Brooklyn, New York, USA

FuelCell2010-33205

ELEMENTARY REACTION MODELS FOR CO ELECTROCHEMICAL OXIDATION ON AN NI/YSZ PATTERNED ANODE

Yixiang Shi1,2 Won Yong Lee Ahmed F. Ghoniem 1 Department of Mechanical Engineering Department of Mechanical Engineering Department of Mechanical Engineering Massachusetts Institute of Technology, Massachusetts Institute of Technology, Massachusetts Institute of Technology, Cambridge, MA, USA, 02139 Cambridge, MA, USA, 02139 Cambridge, MA, USA, 02139 2 Department of Thermal Engineering, Tsinghua University, Beijing, China, 100084

measurements for CO electrochemical oxidation on ABSTRACT nickel/yttria-stabilized zirconia (Ni/YSZ) patterned anode, and examine Analysis of recent experimental impedance spectra and possible limiting steps in CO oxidation kinetics. We consider four polarization curves of nickel/yttria-stabilized zirconia (Ni/YSZ) possible reaction mechanisms for CO electrochemical oxidation at Ni/YSZ anode, as shown in Table 1. Mechanism I is taken from Etsell patterned anode of a solid oxide fuel cell (SOFC) are used to determine 12 the limiting steps in CO electrochemical oxidation kinetics. A and Elengas , and involves gaseous species or species adsorbed on the surface of the electrode and/or the electrolyte. In mechanism II, the comprehensive 1D model is proposed for the prediction of the 2- steady-state polarization curve of a patterned anode SOFC. The model oxidation of adsorbed CO by O in the electrolyte is proposed. incorporates gas species adsorption/desorption with surface diffusion Mechanism Is and IIs are constructed by adding the surface diffusion and one of two possible charge transfer reaction steps: O charge steps to Mechanism I and II, respectively. These kinetic mechanisms transfer reaction [O2-(YSZ)+(Ni)↔(YSZ)+O(Ni)+2e-], or CO charge are illustrated in Fig. 1, in which the geometry is similar to that used in 2- - the experimental setup of the patterned Ni anode button cell on a YSZ transfer reaction [O (YSZ)+CO(Ni)↔(YSZ)+CO2(Ni)+2e ]. We show single crystal with LSM/YSZ porous cathode investigated by that the mechanism incorporating charge transfer between adsorbed CO 11 and oxygen vacancy is able to better predict the experimental data. We Habibzadeh et al. estimate some of the model parameters, such as the exchange current density and charge transfer coefficient by fitting the simulation of the polarization curves to the experimental data. Key Words: solid oxide fuel cells, carbon monoxide oxidation, patterned electrode, charge transfer, surface diffusion

1. Introduction Solid oxide fuel cells (SOFCs) are known for their fuel flexibility and tolerance to carbon monoxide, CO. Thus, syngas can be used in an SOFC directly in generating electricity. Syngas, a mixture of carbon monoxide, CO, and hydrogen, H2, is derived from steam reforming of coal, biomass, methane, or other hydrocarbons.1 In order to optimize the anode performance, it is important to construct Figure 1. Patterned Ni patterned anode geometry and elementary comprehensive electrochemical oxidation models H2 and CO near the three-phase boundary (TPB) of the SOFC, based on sound reaction pathways experimental data and kinetic mechanisms. Compared with the systematic experimental and theoretical studies of H2 electrochemical We propose an 1D comprehensive electrochemical oxidation oxidation 2,3,4,5,6,7,8,9,10, few studies have been performed for the CO model for the prediction of the steady-state polarization curve of a electrochemical oxidation mechanism. patterned anode SOFC. The model utilizes one of the CO Different reaction mechanisms have been proposed for CO electrochemical oxidation mechanism described in Table 1 and electrochemical oxidation, depending on the experimental conditions incorporates either of the two charge transfer steps shown in Table 1, and the cell material. To reduce the effects of gas-phase mass transport that is: the O charge transfer or the CO charge transfer, as well as on the impedance, and eliminate some of the ambiguities in the analysis surface diffusion processes. Some of the model parameters are given of electrochemical oxidation rates, Habibzadeh 11 studied the CO and others are adjusted to match experimental polarization curves. We electrochemical characteristics on a Ni patterned anode. In this paper, use the experimental data to determine the electrochemical mechanism we use their experimental impedance spectra and polarization curve most likely to predict the measurements accurately.

Downloaded From: https://proceedings.asmedigitalcollection.asme.org on 11/20/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use occupied by a single CO molecule. Table 1 CO electrochemical oxidation mechanisms (7) The microstructure of the cathode is stable and homogeneous. The distributions of the two conducting phases (electronic and CO adsorption CO(g)+(Ni) ←⎯⎯⎯→⎯ CO(Ni) ionic) in the electrodes are assumed to be uniform. O charge transfer In order to simplify the calculation, the three-dimensional domain 2- - O (YSZ)+(Ni) ←⎯⎯⎯→⎯ O(Ni)+(YSZ)+2e shown in Fig. 1 is mapped onto a one-dimensional computational I adsorbed CO reaction domain as shown in Fig.2. In this figure, the model structures, calculation domains and boundaries are labeled schematically, as CO(Ni)+O(Ni) ⎯⎯→ CO (Ni)+(Ni) ←⎯⎯ 2 described later. ⎯⎯→ CO2 desorption CO22 (Ni) ←⎯⎯ CO (g)+(Ni) Is Mechanism I with adsorbed species surface diffusion CO adsorption CO(g)+(Ni) ←⎯⎯⎯→⎯ CO(Ni) CO charge transfer II 2- ⎯⎯→ - CO(Ni)+O (YSZ) ←⎯⎯ CO2 (Ni)+ (YSZ)+2e ⎯⎯→ CO2 desorption CO22 (Ni) ←⎯⎯ CO (g)+(Ni) IIs Mechanism II with adsorbed species surface diffusion The model equations and parameters are described in detail in Section 2. The results are obtained and discussed in Section 3. Finally conclusions are stated in Section 3.

2. Model development Model geometry and assumptions The model assumptions are: Figure 2. Representation of the 3D cell using a 1D calculation domain (1) Gases are modeled as ideal gases. (2) The temperature of the cell is uniform. All parameters are evaluated Using the above assumptions and the simplified model at the given temperature. (3) The electrochemical mechanism is modeled using a set of geometry, a 1D SOFC model is formulated considering elementary reactions that represent chemical reactivity at the anodic heterogeneous chemistry, electrochemistry, charge molecular scale. Heterogeneous thermochemical and and mass balance, as described in the following sections. electrochemical reactions are assumed to take place on both of the Ni surface and YSZ surface. (4) The charge transfer reaction is assumed to be a surface spillover Governing equations reaction taking place at the TPB as shown in Fig. 1. Two different reaction pathways are studied. A. Anode heterogeneous chemistry (5) Surface diffusion is one-dimensional and is modeled as Fickian Heterogeneous chemistry at the catalytic surface of the anode is diffusion along the surface in the direction perpendicular to the used. Ni is an effective catalyst for surface reactions, especially for B. hydrocarbon fueled SOFC. A simplified heterogeneous mechanism 13 14 15 (6) One adsorbed CO molecule occupies one vacant position on the from Hecht et al. , Janardhanan et al. and Zhu et al. is used, as surface, neglecting the possibility of two vacant positions being shown in Table 2.

Table 2 Heterogeneous reactions mechanism on the Ni surface a a a -1 Reaction A (cm, mol, s) n E (kJ mol ) Adsorption −02 b 1f O2 + Ni(s) + Ni(s) → O(s) + O(s) 1.000×10 0.0 0.00 −05 b 2f CO2 + Ni(s) → CO2(s) 1.000×10 0.0 0.00 3f CO + Ni(s) → CO(s) 5.000×10−01 b 0.0 0.00 Desorption +23 1b O(s) + O(s) → Ni(s) + Ni(s) + O2 4.283×10 0.0 474.95 +07 2b CO2(s) → CO2 + Ni(s) 6.447×10 0.0 25.98 3b CO(s) → CO + Ni(s) 3.563×10+11 0.0 111.27 c θCO(s) −50.00 Surface reactions

Downloaded From: https://proceedings.asmedigitalcollection.asme.org on 11/20/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use 4f C(s) + O(s) → CO(s) + Ni(s) 5.200×10+23 0.0 148.10 4b CO(s) + Ni(s) → C(s) + O(s) 1.354×10+22 −3.0 116.12 c θCO(s) −50.00 +19 5f CO(s) + O(s) → CO2(s) + Ni(s) 2.000×10 0.0 123.60 c θCO(s) −50.00 +23 5b CO2(s) + Ni(s) → CO(s) + O(s) 4.653×10 −1.0 89.32 a Arrhenius parameters for the rate constants are written in the form: k = AT n exp(−E/RT). b Sticking coefficient. c Coverage-dependent activation energy. The surface adsorbates are assumed to be uniformly distributed 0 The sticking coefficient Si is temperature dependent and is expressed over the Ni surface. The species molar production rates depend on the as gaseous species concentrations and the surface species concentrations, 0 b ⎛⎞d which are expressed by the coverage. The coverage θk is the fraction of i i SaTii=−exp⎜⎟ (6) the surface sites covered by the adsorbed species k. It is assumed that ⎝⎠RT the total number of surface active sites is conserved and the saturation where ai and bi are dimensionless parameters and di has units of RT. sorbent capacity is described by the maximum surface sites density Γ16. The parameters are listed in Table 1. The uncovered Ni surface is treated as a dummy surface species. For the YSZ surface, few validated reaction mechanisms are The gaseous adsorption-desorption reactions and surface reactions available in the literature. Vogler et al.10 considered molecular are written in the general form: adsorption and desorption of water, water dissociation, and KK++KK gs gs bulk-surface exchange. In this study, we neglect CO and CO2 ′′′ ∑∑ν kkχν⇒ kkχ (1) adsorption and desorption on the YSZ surface, and only consider the kk==11 bulk-surface exchange of oxygen. Transport of bulk oxygen species where χk is the kth species, ν k′ and ν k′′ are the stoichiometric takes place by a vacancy diffusion mechanism. The reaction formula and reaction data is given by coefficients of the reactants and products, Kg and Ks are the k 2- YSZ,1f 2- number of gaseous species and surface species, respectively. The net O (YSZ)+(YSZ,bulk) ←⎯⎯⎯⎯ ⎯⎯→ (YSZ)+O (YSZ,bulk) (7) YSZ,1b

molar production rate sk of a gaseous species or a surface species in where, kYSZ,1f is determined from mass action

a heterogeneous reaction are written as: ⎛Ei ⎞ 2 kinetics, kk=−exp with ki,0 = 1.6e22 cm /(mol s), and N KKgs+ ii,0 ⎜⎟ ν ′ ⎝⎠RT ′′ ′ ki skk=−∑()ννikiikc∏ k (2) i=1 k =1 activation energy Ei=90.9 kJ/mol. kYSZ,1b is determined from the equilibrium constant. where N is the total number of reactions and ck is the concentration of the kth species. For all the surface reactions and desorption reactions, B. Anode electrochemistry Two charge transfer pathways, corresponding to mechanism I and the reaction rate constant ki for the ith reaction is presented in the Arrhenius form: II in Table 1, are considered in this study:

Ks ⎛⎞E ⎛ε θ ⎞ kct,O,f ni ikik 2- ⎯⎯⎯→ - kATii=−exp exp − (3) O (YSZ)+(Ni) (YSZ)+O(Ni)+2e ⎜⎟∏ ⎜ ⎟ ←⎯k ⎯⎯ ⎝⎠RTRk =1 ⎝T⎠ ct,O,b 8) where A , n and E are the pre-exponential factor, temperature exponent k i i i 2- ⎯⎯⎯ct,CO,f → - and activation energy listed in Table 1, R is the gas constant, T is the CO(Ni)+O (YSZ) ←⎯ ⎯⎯ CO2 (Ni)+ (YSZ)+2e kct,CO,b 9) temperature,ε describes the species coverage-dependency of the rate ki where, kct,O,f, kct,CO,f and kct,O,b, kct,CO,b are the forward and constant. For most reactions, which are independent of species backward reaction rates of O charge transfer reaction and CO charge transfer reaction, respectively. coverage, ε ki is zero. For reactions 3b, 4b and 5f, the reaction rate According to Faraday’s law, the current at the anode, and 17 constants depend on the CO(s) coverage, θCO(s). In this case, ε ki is depending on the charge transfer step, can be expressed as follows , listed in Table 1.

For adsorption reactions, the rate constants are expressed in terms iFLkcckcc=−2 2- f,O TPB( ct,f,O O(YSZ)(Ni) ct,b,O (YSZ) O(Ni) ) (10) of the sticking coefficient form [16] 0 iFLkcckcc=−2 2- (11) SRTi f,CO TPB( ct,f,CO O(YSZ)CO(Ni) ct,b,CO (YSZ) CO2 (Ni) ) ki = (4) Γγ 2πW where i is the area specific Faradaic current, F is the Faraday 0 constant, L is three phase boundary length per unit area. where Si is the initial sticking coefficient, W is the molecular weight TPB of the gas-phase species, and cO(Ni) , cCO(Ni) , and cNi(s) denotes the surface concentrations of O and CO adsorbed on the Ni surface, and the free surface sites, respectively. K 2- s c and c denotes the surface concentrations of the O ′ O(YS2- Z) (YSZ) γ = ∑ν ki (5) k adsorbed on the YSZ surface and the free surface sites on YSZ surface,

Downloaded From: https://proceedings.asmedigitalcollection.asme.org on 11/20/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use respectively. at the TPB and in the bulk, respectively, α is the charge transfer The forward and backward charge transfer reaction rates are coefficient, ne is the number of electrons participating in the reaction, written as follows: and ηca is the cathode local overpotential, which is defined as [19] η = VVV−− 0 ⎛−(1 −α ) zF ⎞ ca elec,ca ion,ca ref,ca (21) kkct,f,ii= ct,f , exp⎜⎟ηan (12) ⎝⎠RT where Vref,ca is the cathode local relative potential difference between the electronic conductors at a reference state. The cathode 0 ⎛⎞α zF reference potential Vref,ca equals to the actual cell open circuit voltage kkct,b,ii= ct,b, exp⎜⎟ηan (13) ⎝⎠RT (OCV). Essentially, the SOFC is a concentration cell of O2 and the 18 where αis the charge transfer coefficient and ηan is the anodic OCV are determined by Nernst equation: O2 overpotential. The anode local overpotential ηan used in Section 3 is RT⎛⎞ pca VOCV = ln ⎜⎟ (22) defined as O2 nFe ⎝⎠ pan

η =−−VVV O2 O2 an elec,an ion,an ref,an (14) where pca and pan are the equilibrium oxygen partial

In this study, the anode reference potential Vref,an was set to zero. O2 pressures in the cathode and the anode, respectively. pan can be The Velec,an is the electronic potential of nickel at the TPB interface and determined by the heterogeneous reactions and the compositions of fuel the Vion,an is the ionic potential at the TPB interface. in the anode. The parameters k 0 ,,,k 0 k 0 k 0 are calculated ct,f ,CO ct,b,CO ct,f ,O ct,b,O Heterogeneous reactions rates and electrochemical reactions rates from, depend on the concentration of surface species. In order to obtain the

0 i0,O 0 i0,O reaction rates at the anode, the effective reaction areas for all reactions kct,f,O = , kct,b,O = (15) 2FL c00 c 2FL c00 c per unit volume is needed. According to the model assumptions, the TPB O(YSZ)2- (Ni) TPB (YSZ) O(Ni) heterogeneous reactions and electrochemical reactions only take place i i at the Ni surface and TPB, respectively. Therefore, the Ni active surface k 0 = 0,CO , k 0 = 0,CO ct,f,CO 00 ct,b,CO 00 (16) area per unit volume, S , and the TPB active area per unit volume, S , 2FL c2- c 2FL c c Ni TPB TPB O(YSZ)CO(Ni) TPB (YSZ) CO2 (Ni) 0 in the anode should be specified. where i0 is the exchange current density, c denotes the species The area STPB is formulated using the particle coordination number surface concentrations at equilibrium. in binary random packing of spheres using the percolation theory 19,20 The exchange current density are written in the following form: 22 SrnnnZZPTPB = πθsin el t el io el io elPZ io / (23) ⎛⎞ΔGCO ⎛⎞ΔGO ik0,CO=− CO exp⎜⎟, ik0,O=− O exp⎜⎟ (17) where Z is the mean coordination number, rel is the mean radius ⎝⎠RT ⎝⎠RT of the electronic conductor particle, θ is the contact angle between the where, k and ΔG are treated as tuning parameters when electronic and ionic conductors particles, nt is the total number of comparing the simulated polarization curve with the experimental particles per unit volume, nel and nio are the fraction number of results. electronic and ionic conducting particles, Zel and Zio are the C. Charge balance coordination numbers of the electron and the ion conducting particles, For the anode, the charge balance equations considering the and Pel and Pio are the whole range connection probabilities of the same transient effects of the double-layer capacitance are formulated as particles. follows: The cathode exchange current density i0,ca is expressed as: 0.25 β RT⎛⎞ Eca O ∂Δ(CVdl,an TPB ) 2 (18) ip0,ca =−exp⎜⎟()ca (24) iiif= f,O++ f,CO 4FRT⎝⎠ ∂t -1 21 where Eca is 130,000 J mol , and β is 5.76e10 . where t is time, Cdl is the specific interface double-layer capacitance between Ni and YSZ. There are no double-layer capacitance effects or current sources or The cathode ionic charge and electronic charge equations are: sinks in the electrolyte. Thus, the electrolyte charge balance equation is reduced to ∂−CSdl,ca TPB,ca() V ion,ca V elec,ca eff ()eff ∇ ⋅−σ ∇V =0 +∇⋅() −σ ion,ca ∇VQ ion,ca = ion,ca ( ion,electrolyte ion,electrolyte ) (25) ∂t (19) eff TPB where σ ion,electrolyte is the effective ionic conductivity of ⎧⎪⎪cO ⎡⎤αηnF ⎡−()1 αηnF ⎤⎫ =−iS 2 exp eca−exp − eca 0,ca TPB,ca ⎨⎬bulk ⎢⎥⎢⎥ cRTRT⎣⎦ electrolyte and Vion,electrolyte is the ionic potential in the electrolyte. ⎩⎪ O2 ⎣⎦⎭⎪ D.Mass balance ∂−CS V V ()dl,ca TPB,ca() elec,ca ion,ca eff For the anode, the species production rates follow mass-action +∇⋅() −σ elec,ca ∇V elec,ca ∂t (20) kinetics, and the species transport on the Ni and YSZ surfaces can be described in the following form: ==−QQelec,ca ion,ca ∂θσiiSsurf where Vion and Velec are the electronic and ionic electric potential, =+∇⋅∇ΓsDii()()θi (26) eff ∂Γt respectively. σ is the corresponding conductor phase effective surf TPB bulk where, D denotes the surface diffusion coefficients.We have conductivity. c and c are the cathode oxygen concentrations O2 O2 collected a compilation of surface diffusion coefficients from various

Downloaded From: https://proceedings.asmedigitalcollection.asme.org on 11/20/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use literature sources and tried to set the lowest value and highest values In the cathode, the relationship between the mass balance source from literature as the estimation limits. term and the current source term is governed by Faraday’s law: The extended Fick’s model (EFM) is used to describe the mass Q transfer in the porous cathode, and the effect of finite pressure gradient R = elec,ca (29) is neglected. The EFM equation is written as follows:22, O2 4F ∂c k,g eff To simplify the calculations, the concentrations of ε +∇() −Dkk ∇cR,g = k ,g (27) ∂t interstitial oxygen and oxygen vacancy are treated as

where ε is the porosity of the electrode, ck,g is the gas molar constant. This is because the concentrations of interstitial concentration, Rk,g is the mass balance source term of the gaseous oxygen and oxygen vacancy in an ionic conductor are several eff species inside the porous medium, and Dk is the effective diffusivity orders of magnitude larger than the concentrations of gases of gaseous species k. Molecular diffusion and Knudsen diffusion are and surface species. dominant for large pore sizes and when the pore sizes are smaller than molecular mean-free path, respectively. The effective diffusivity Boundary conditions eff Dk is written as: The boundary conditions of the charge and mass balance partial −1 differential equations are specified in Table 2. The boundaries of the ⎛⎞11 Deff =+⎜⎟ (28) model geometry are labeled schematically in Fig. 2. k ⎜⎟eff eff ⎝⎠DDkk,mole ,Kn eff eff where Dk ,mole and Dk ,Kn is the effective molecular diffusion coefficient and effective Knudsen diffusion coefficient, respectively.

Table 1 Boundary conditions Boundary Ionic charge Electronic charge Surface species mass balance Gas mass balance

Ni/gas interface — Van Insulation cCO,cCO2 Molar flux CO(Ni): -iCO/2FLTPB O(Ni):i /2FL TPB iCO or iO -iCO or -iO O TPB Insulation C(Ni): Isulation CO2(Ni) : iCO/2FLTPB Cathode/electrolyte interface Continuity Insulation — Insulation

Cathode/gas interface Insulation Vca — cO2,ca, cN2,ca The boundary conditions “insulation” and “continuity” refer to a voltage Vca at rate of 10mV/s was used in the calculation, which was zero partial derivative and a continuous flux at the boundary, the same as that used to produce the experimental polarization curve. respectively. The difference between Van and Vca is the cell operating For the 1D SOFC model, the average current density at a given cell voltage. voltage was treated as that in the electrolyte.

Solution method 3. Simulation and discussions Calculations were performed using the finite element commercial ® software COMSOL MULTIPHYSICS , Version 3.2. The cell Model parameters performance was calculated at a given cell voltage Vca. In order to Table 3 lists the cell properties and some of the model parameters. compare with the experimental measurement, a linear scan of the

Table 3 Properties and parameters for model calculation Property and parameters Value or expression Unit 23 -1 YSZ ionic conductivity (σion) 3.34E4exp(-10300/T) S m 23 -1 LSM electronic conductivity (σelec) 4.2E7/Texp(-1150/T) S m 10 -2 Ni surface maximum surface sites density (ΓNi) 6.1E-5 mol m 10 -2 YSZ surface maximum surface sites density(ΓYSZ) 1.3E-5 mol m 24 Cathode porosity 0.364 24 Cathode tortuosity (τca) 3.0 24 -2 Anodic Interface double-layer capacitance (Cdl,an) 27 F m 24 -2 Cathodic Interface double-layer capacitance (Cdl,ca) 27 F m 25 -3 Concentration of oxygen in the YSZ ( c x ) 4.45E4 mol m OO

Downloaded From: https://proceedings.asmedigitalcollection.asme.org on 11/20/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use 25 -3 Concentration of oxygen vacancy in the YSZ ( c ⋅⋅ ) 4.65E3 mol m VO

10000 The parameters α, (i0,CO, Ds,CO(Ni)) and (i0,O, Ds,O(Ni)) are tuned to produce the best fit with the experimental results.

1000 Comparing Mechanisms I and II

A. Mechanism I - CO charge transfer based mechanism 100 There are three fitting parameters: the charge transfer coefficient, 725C,Exp 775C,Exp α, the exchange current density, i0,co, and the surface diffusion 10 Sim coefficient, Ds,CO(Ni). Coefficients in these parameters were varied until the model predictions give the best fit for the experimental results. pCO = 0.323 kPa, pCO2 =0.032 kPa These results are shown in Fig. 3. The resulting expressions for the 1 fitting parameters are as follows. Current density/Am-2 (based on Ni area ) area Ni on (based density/Am-2 Current α = 0.6 (30.a) 0.1 ⎛⎞-165615 -1 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 i0,CO =1.68e15exp⎜⎟ Am (30.b) ⎝⎠RT Overpotential/V

11 -5 ⎛⎞-160518 2 Figure 4. Experimental Tafel plots and simulated results using the CO Ds,CO(Ni) =×2.85 10 exp⎜⎟ m /s (30.c) ⎝⎠RT charge transfer mechanism

1 B. Mechanism II - O charge transfer based mechanism 1048.15K,Exp pCO = 0.323 kPa, 1023.15K,Exp The three fitting parameters are as follows. 0.9 pCO2 =0.032 kPa 998.15K,Exp α = 0.6 (31.a) 973.15K,Exp 0.8 Sim ⎛⎞-165615 -1 i0,O =1.68e15exp⎜⎟ Am (31.b) 0.7 ⎝⎠RT

0.6 -7 ⎛⎞-117400 2 Cell voltage/V Ds,O(Ni) =×610exp⎜⎟ m/s (31.c) 0.5 ⎝⎠RT

0.4 The surface diffusion coefficients of O(Ni) species was directly taken from Vogler et al 10 0.3 0 200 400 600 800 1000 1200 1400 While the CO charge transfer mechanism is able to reproduce the -2 experimental polarization curves rather well, this is not the case when Current density/Am (based on Ni area ) attempting to fit the polarization curves using a model considering the Figure 3. Experimental polarization curves11 and simulated results O charge transfer mechanism, as shown in Fig. 5. For instance, at using CO charge transfer mechanism 725ºC, we kept all the parameters the same as in CO charge transfer mechanism model. We got the “base case” curves shown in Fig. 5(a). It At 750ºC, the surface diffusion coefficient of CO(Ni), calculated can be seen that the simulated curve largely underestimate the from Eq. (30.c), is around 1.82e-13 m2/s. According to the published experimental results. Next, a parametric analysis of O(Ni) surface data in literatures26,27,28, the surface diffusion coefficient of adsorbed diffusion coefficients was carried out. It was found that the deviation CO on Ni surface is in the range of 2.5e-6 to 4.95 e -13 m2/s, depending between the simulated and the experimental results could be reduced by on the surface properties, crystal type, surface coverage as well as increasing the O(Ni) surface diffusion coefficient. However, even when measuring method. The value predicted from Eq. (30.c) is within the the value of O(Ni) surface diffusion coefficient was increased to (1e12) published range. times the value used in base case, the simulated polarization curves still To further check the model validity using the CO charge transfer underestimated the experimental measurements. In addition, when mechanism, the computed Tafel plots is compared with the O(Ni) surface diffusion coefficient was increased from (1e9) to (1e12) experimental results, as shown in Fig. 4. The model results agree well times the original value, the polarization curves hardly changed. Next, with the experimental data. we increased the value of i0,O to twice its base case value, as shown in Figure 5(b), and found that the curve moved close to the experimental curves. Although the model with the O charge transfer mechanism could now predict the experimental results better, the value of model parameters, e.g. O(Ni) surface diffusion coefficient, is not reasonable. Therefore, we concluded that the CO charge transfer mechanism could better predict the cell performance while using more physically

Downloaded From: https://proceedings.asmedigitalcollection.asme.org on 11/20/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use reasonable parameters. -4.5 ) -2 1 -4.55 998.15K,Exp -4.6 0.9 Base case Ds,O(Ni)=1e3*Ds,O(Ni),base Ds,O(Ni)=1e6*Ds,O(Ni),base -4.65 0.8 725C,Polarization = 200mV Ds,O(Ni)=1e9*Ds,O(Ni),base 725C,Polarization = 400mV Ds,O(Ni)=1e12*Ds,O(Ni),base -4.7 0.7 775C,Polarization = 200mV (a) -4.75 775C,Polarization = 400mV 0.6 -4.8 pCO = 0.323 kPa, 0.5 pCO =0.032 kPa Cell voltage/V 2 -4.85 Log surface concentration/log(mol m concentration/log(mol surface Log 0.4 -4.9 0.3 0.5 0.4 0.3 0.2 0.1 0 Distance from TPB/μm 0.2 0 200 400 600 800 1000 Current density/Am-2 (based on Ni area ) Figure 8. CO(Ni) surface concentration distribution near TPB

1 The results show that the surface concentration of CO(Ni) at 725 Ds,O(Ni)=1e12*Ds,O(Ni),base º 0.9 C, which is mainly determined by the adsorption/desorption 998.15K,Exp equilibrium, is higher than that at 775 C. On the other hand, it can be 0.8 i0,O,base case seen that the surface gradient is larger at lower temperature and higher i0,O=2*i0,O,base 0.7 polarization voltage. At lower temperature, the surface diffusion is (b) slower and the CO(Ni) surface concentration gradient is larger. At 0.6 higher polarization voltage, the consumption rate of CO(Ni) at the TPB

0.5 interface is faster, which also leads to larger CO(s) surface Cell voltage/V concentration gradient. This agrees well with the quantitative 0.4 conclusion from the experimental EIS spectra analysis by Matsuzaki et 29 0.3 al , and suggests that at lower temperature and higher polarization voltage, the surface diffusion may be an important limiting step. 0.2 0 200 400 600 800 1000 Current density/Am-2 (based on Ni area ) 4. Conclusion A 1D comprehensive electrochemical oxidation model is proposed 11 Figure 5. Experimental polarization curves and simulated results for the prediction of the steady-state polarization curve of a patterned using the O charge transfer mechanism (a) Parametric analysis of O(Ni) anode SOFC. The model incorporates either of the two charge transfer surface diffusion coefficient (b) Parametric analysis of exchange steps: O charge transfer and a CO charge transfer, and surface diffusion current density of the O charge transfer reaction processes. The model is used for the quantitative investigation of the cell performance as well as microscopic elementary reactions and Species surface concentration diffusion steps. The model is also used to predict the concentration Spatial profiles of the surface concentration of CO(Ni) and O(Ni) distribution of surface species near the three-phase boundary (TPB). species at 200 mV are shown in Fig. 8 at 725 ºC and 775ºC and The main conclusions of the paper are: different polarization voltage (200, 400mV), obtained using the CO (1) Both of the models with O charge transfer and CO charge charge transfer mechanism model. Simulated results show strong transfer mechanism are able to predict the experimental polarization concentration gradients within 3e-7 m of the TPB and at different curves. However, the model with CO charge transfer mechanism operating conditions. predicts the cell performance more accurately while incorporating physically reasonable values for the surface diffusion coefficient. (2) The surface concentration gradient is larger at lower temperatures and higher polarization voltages. Thus, surface diffusion may be one of the important limiting steps at lower temperature and higher polarization voltage.

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