Evaluation of Tafel–Volmer kinetic parameters for the hydrogen oxidation reaction on Pt(1 1 0) electrodes

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<ul><li><p>Journal of Power Sources 196 (2011) 47054713</p><p>Contents lists available at ScienceDirect</p><p>Journal of Power Sources</p><p>journa l homepage: www.e lsev ier .com</p><p>Evalua foreactio</p><p>R.F. ManDepartment of , Stati</p><p>a r t i c l</p><p>Article history:Received 25 JuReceived in re10 December 2Accepted 13 DAvailable onlin</p><p>Keywords:Hydrogen oxidPt(110) electrAnode polarizActivation polPEM fuel cellsModelling</p><p>beeimprodelse ignothe apthe hassesempiondittempolmenera</p><p>data for Pt(110) electrodes and further develop the modelling of anode activation polarization over therange of operating conditions found in PEMFC operation.</p><p>Crown Copyright 2010 Published by Elsevier B.V. All rights reserved.</p><p>1. Introdu</p><p>The bacpublished [eralized steconsists of(PEMFC) ba</p><p>V = E + ac</p><p>The specicviously pubreaction onresults intopolarizationular loss issince it is, nloss at the cactivation pcapability is</p><p> CorresponRoyalMilitary7B4 Canada. T</p><p>E-mail add</p><p>0378-7753/$ doi:10.1016/j.ction</p><p>kground for the present paper has been recently13]. Our long-term aim is to further develop our gen-ady-state electrochemical model, the GSSEM, whicha simple, 1-dimensional, model of a PEM fuel cellsed on</p><p>t,a + act,c + ohmic + conc,a + conc,c (1)</p><p>goal of the present paper is to further evaluate pre-lished work which studied the hydrogen oxidationPt(hk l) electrodes in dilute H2SO4 and to develop thea modelling approach for act,a, the anode activation, in PEMFCs. The quantitative prediction of this partic-generally not given much attention in a PEMFC modelormally, much less signicant than the correspondingathode. There are situations, however, where the anodeolarizations could become signicant and a modellingtherefore desirable.</p><p>ding author at: Department of Chemistry and Chemical Engineering,College of Canada, 11 General Crerar Crescent, Kingston, Ontario, K7Kel.: +1 613 541 6000x6981; fax: +1 613 542 9489.ress: thurgood-c@rmc.ca (C.P. Thurgood).</p><p>Our present interest is the anode activation polarization relatedto the hydrogen oxidation reaction (HOR) for which the overallhalf-cell reaction is</p><p>H2 2H+ +2e (2)</p><p>The reverse of reaction (2) is the hydrogen evolution reaction(HER).</p><p>The anode reaction occurs in the presence of a catalyst, typicallyPt if the anode feedstock is pure hydrogen.</p><p>There is broad support in the literature for the HOR on Pt to pro-ceed via a TafelVolmer reaction sequence, fully described recently[3]. There is not, however, complete agreement on the kineticmodel as literature support exists for both rds Tafelfast Volmerkinetics and for fast Tafelrds Volmer kinetics. Thesewere respec-tively referred to as Mechanism I and Mechanism II in our recentreassessment [3] of a body of work published by what we chose tocall the Markovic Group [49]. This group of publications includedextensive results for rotating disk electrode (RDE) studies of theHOR on single-crystal Pt(1 00), Pt(1 10) and Pt(111) electrodes indilute sulphuric acid electrolyte at 1, 30 and 60 C and corrected toapH2 of 1 atm. These publications [49] concluded that the Pt(110)results were best explained by rds Tafelfast Volmer kinetics, ourso-called Mechanism I.</p><p>The present paper, in Section 2, will review the detailed devel-opment of thermodynamic and kinetic equations for Mechanism</p><p>see front matter. Crown Copyright 2010 Published by Elsevier B.V. All rights reserved.jpowsour.2010.12.016tion of TafelVolmer kinetic parametersn on Pt(110) electrodes</p><p>n, C.P. Thurgood </p><p>Chemistry and Chemical Engineering, Royal Military College of Canada, P.O. Box 17000</p><p>e i n f o</p><p>ne 2010vised form010ecember 2010e 21 December 2010</p><p>ation reactionodesationarization</p><p>a b s t r a c t</p><p>Modelling of PEM fuel cells has longand stack operation, facilitate designactivation polarization inmost PEMmcommonlymuchsmaller and tend tobterm is being undertaken to broaden</p><p>Published work on the kinetics ofin dilute H2SO4 has been recently recurrentdensitiesweredevelopedandwere proposed for the experimental cPt(111) electrodes, pH2 of 1 atm, andPt(110) electrodes followed a TafelV</p><p>The aim of the present paper is to ge/ locate / jpowsour</p><p>r the hydrogen oxidation</p><p>on Forces, Kingston, Ontario, K7K 7B4 Canada</p><p>n an active research area to improve understanding of cellovements and support simulation studies. The prediction ofhas concentrated on the cathode losses since anode losses arered. Furtherdevelopmentof theanodeactivationpolarizationplication and usefulness of PEM models in general.ydrogen oxidation reaction (HOR) using Pt(hk l) electrodessed and published. Correlations for diffusion-free exchangerical predictive equations for the anodeactivationpolarizationions of the previously published work: Pt(100), Pt(1 10) anderatures of 1, 30 and 60 C. It was concluded that the HOR onr reaction sequence.lize these TafelVolmer correlations, apply them to published</p></li><li><p>4706 R.F. Mann, C.P. Thurgood / Journal of Power Sources 196 (2011) 47054713</p><p>Nomenclature</p><p>b Tafel slope, 2.3RT(F)1 (Vdec1)BV ButlerVolmerc concentration (mol cm3)cH2 concentration of dissolved hydrogen at the reaction</p><p>interface (molH2 cm3)CM concentration of active Pt sites [in sites cm2 (order</p><p>1015) or moles of sites cm2 (order 108)]E equilibrium EMF of a cell (V) or total anode polar-</p><p>ization, act,a +conc,a, in Refs. [49] (V)fI(,0) functions of and 0 in the general ButlerVolmer</p><p>equation (see following Eq. (25))F Faradays Constant (clbs equt1)GSSEM generalized steady state electrochemical modelH Henrys Law constant (atmcm3 mol1)HER hydrogen evolution reaction (reverse of Eq. (2))HOR hydrogen oxidation reaction (Eq. (2))i current density (A cm2)io exchange current density (A cm2)k chemical rate constantkads rate constant for the 2-site dissociative chemisorp-</p><p>tion of a hydrogenmolecule [cm5 s1 (mol of vacantPt sites)2]</p><p>kdes rate constant for the hydrogen molecule desorp-tion reaction [(molH2) cm2 s1 (mol of occupied Ptsites)2]</p><p>ket,fwd forward rate constant for the electron transfer(Vogel) reaction</p><p>ket,rev reverse rate constant for the electron transfer(Vogel) reaction</p><p>Kads adsorption equilibrium constant for chemisorbedhydrogen molecules (also equal to kads/kdes)[cm3 (molH2)1, the reciprocal of the units of cH2]</p><p>KetcH3O+,o equilibrium constant, representing</p><p>{k-etcH3O+,o(ket)1}, for the electron transfer</p><p>reactions, Eqs. (8) and (9)Mechanism I the rds Tafelfast Volmer HOR processn number of electrons being transferred for one act of</p><p>the overall reactionna number of electrons being transferred after the rdsnb number of electrons being transferred before the</p><p>rdsp partial pressure of a gas component (atm)r chemical reaction raterds rate-determining-step in the reaction sequence at</p><p>the anodeRDE rotating disk electrodeV cell voltage (V)</p><p>Greek letters transfer coefcient symmetry factor polarization (i.e. overvoltage or loss) (V) fractional surface coverage (generally of</p><p>chemisorbed hydrogen atoms) stoichiometric coefcient in Eq. (5) (number of</p><p>times that the rds must take place for the overallreaction to occur once)</p><p>Subscriptsa anode or activityact activationads adsorption</p><p>b bulkc cathodeconcdesetexplfwdH2HH3O+</p><p>iIMGohmico</p><p>predrevsatTVvac</p><p>I, the rdsthese equattion/recorreelectrodesSection 4 wcorrelationresentative</p><p>2. DevelopTafelVolm</p><p>2.1. Introdu</p><p>The basiespecially,decades. Thtion and mothat is as mapply as poanode activoperating p</p><p>The literbut there aof the procfrom the pand ReddySpringer et[18].</p><p>2.2. Fundam</p><p>Variousone combiUsing M telectron, th</p><p>(i) H2 +M(ii) M.H2 +</p><p>with(iii) H2 +2Mconcentration (relating to mass transfer losses)desorptionelectron transfer (as in the Volmer reaction)experimentalforwardhydrogen moleculehydrogen atomhydrated proton (i.e. H+:H2O)interfaceMechanism IMarkovic Group (authors of Refs. [48])relating to ohmic (i.e. iR) lossesat zero polarization and zero net current condition(i.e. at equilibrium)predictedreversesaturatedTafel reactionVolmer reactionvacant</p><p>Tafelfast Volmer HOR process. Then, in Section 3,ions will be applied to the further analysis and correla-lationof somepublished results for theHORonPt(110)and evaluation of the TafelVolmer, TV, parameters.ill then deal briey with the generalization of these</p><p>s to values of pH2 and temperatures that are more rep-of PEMFC modelling applications.</p><p>ment of mechanistic equations for aer HOR reaction</p><p>ction</p><p>c theories of activation polarizations for the HOR and,overvoltages for the HER have been established foris sectionwill summarize the development of a correla-delling approach for the anode activation polarizationechanistic as possible yet as simple to understand and</p><p>ssible. The goal is to develop a relationship linking theation polarization to the current density and the otherarameters of the fuel cell.ature dealing with both the HOR and the HER is vastppears to be general agreement on the main featuresess. Much of the following development has benetedrevious work of Parsons [10], Austin [11,12], Bockris[13], Gileadi et al. [14], the Markovic Group [49],al. [15], Camara et al. [16], Breiter [17] and Lasia</p><p>ental steps in the HOR</p><p>possible steps in the overall HOR have been suggested,nation being the so-called TafelVolmer sequence.o represent an active Pt atom and e to represent ane steps in this sequence are:</p><p>M.H2M2M.H(i) + (ii), the Tafel step, often simplyHad +Had</p></li><li><p>R.F. Mann, C.P. Thurgood / Journal of Power Sources 196 (2011) 47054713 4707</p><p>(iv) M.H+H2OH3O+ +M+e(v) H3O+ H+ +H2O</p><p>with (iv) + (v), the Volmer step, often simply(vi) Had H+ +e</p><p>2.3. The phy</p><p>At the gapH2 , is in eqgen accordihydrogenwvicinity of telectrolyte/through theby subtractanode polasolved hydrsimply, cH2)centrationthat at the ibulk electroferent thanthe reactionnal to the ehydratedprpolarizationbe denoted</p><p>2.4. Kinetic</p><p>Kinetic erate r, for tplest form a[17] and ap</p><p>For the Tmolecule o</p><p>rT = rT,adsFor the Vowould havmolecule o</p><p>rV = rV,fwd kV,</p><p>In Eqs. (parameter t</p><p>The trancan generalBased on eaGileadi et alNomenclatu</p><p> = [(n nIn kinetic exof the Pt siintroductiovac, the frato participaelectrode. Fdepend onHads , i.e. va(i.e. Hads) isHads .</p><p>Mechanistic equations for the general TafelVolmer reactionsequencewill nowbedeveloped in detail, enlarging on andmodify-ing theEqs. (3) and (4)proposedbyBreiter andutilizing thedetailedtreatment in Section 5.9.3 of Austen [11]. The special case, Mecha-</p><p>, rdsese</p><p>felV</p><p>Introfollod onPt sn ad</p><p>n asseticorpttudyded trumked apnd thm-athe rs andnF</p><p>to anParaeactour,tionsen preactlytelacedction</p><p>The T(3),o thearea</p><p>2Fk</p><p>2Fk</p><p>gestection, thewevious</p><p>H2(ccity, w</p><p>f thety. Ifrapi</p><p>The V(4),</p><p>ith thsionsr) rea</p><p>2Fk</p><p>2Fksical picture</p><p>s/electrolyte interface, a hydrogen gas partial pressure,uilibriumwith concentration cH2,sat of dissolved hydro-ng to a Henrys Law equilibrium expression. Dissolvedill undergo bulk diffusion through the electrolyte to thehe anode, delivering a bulk concentration cH2,b at thereaction boundary layer interface. If the mass transferelectrolyte is very rapid, or if it has been accounted for</p><p>ing the anode concentration polarization from the totalrization, cH2,b can be taken as equal to cH2,sat. The dis-ogen concentration at the reaction interface, cH2,i (or,may be different than cH2,b. Likewise, the proton con-</p><p>at the reaction interface will be denoted as cH3O+ andnterface between the electrical boundary layer and thelyte will be cH3O+,b. Again, cH3O+ may have a value dif-cH3O+,b. Just as cH2,b is a function of factors external toboundary layer, sowill cH3O+,b dependon factors exter-lectrical boundary layer, e.g. the diffusion rate of theotons through the electrolyte. At the zero-current/zero-situation, cH2 and cH3O+ at the reaction interface will</p><p>as cH2,o and cH3O+,b, respectively.</p><p>expressions for the Tafel and Volmer reactions</p><p>xpressions, initially in terms of the chemical reactionhe above reactions can initially be written in their sim-s follows, essentially using the nomenclature in Breiterplying LangmuirHinshelwood methodology:</p><p>afel, adsorption/desorption, reaction involving 1f H2:</p><p> rT,des = kT,fwdaH2(1 H)2 kT,rev2H (3)</p><p>lmer, electron transfer or ionization, reaction, whiche to occur twice (i.e. a stoichiometric number of 2) perf H2:</p><p> rV,rev = kV,fwdH exp[V,fwdF(RT)1]</p><p>rev(1 H)aH+ exp[V,revF(RT)1] (4)</p><p>3) and (4), the rate constants, ki, will include someo represent the catalyst concentration.sfer coefcient, , has recently been discussed [2,3] andly be expressed as a function of , the symmetry factor.rlier work, the following expression was proposed by. [14] with the symbols and subscripts as dened in there:</p><p>b na) + nb]()1 (5)pressions involving catalyst concentration, the fractiontes that are vacant is often required. This leads to then of the common LangmuirHinshelwood parameter,ction of the active sites that is vacant and therefore ablete in the chemisorption/dissociation reactions on eachor a feed that is free of impurities, this should simplythe fraction of the sites occupied by adsorbed H atoms,c = 1 Hads . Since the present paper considers that Hthe only adsorbed species, will be understood tomean</p><p>nism Ifrom th</p><p>2.5. Ta</p><p>2.5.1.The</p><p>is baseactivebetweeis ofteing kinchemisTheir sconcluideal FfollowHads athe atobeingkinetic</p><p>Thebased)added.at the rbehavicentrahydrogphaseelectrobe repthe rea</p><p>2.5.2.Eq.</p><p>leads tsurface</p><p>iT,ads =</p><p>iT,des =As sugthe reacannotcan, hoas prev</p><p>ratio {csimpli</p><p>valueobe uniciently</p><p>2.5.3.Eq.</p><p>and wexpresVolme</p><p>iV,fwd =</p><p>iV,rev =Tafel followed by fast Volmer, will then be developedgeneral equations.</p><p>olmer equations for the HOR</p><p>ductionwing development of equations to describe the HORchemisorption according to a Langmuir isotherm, i.e.ites energetically homogeneous and no interactionssorbed species. Although ideal Langmuir adsorptionumed because of the relative simplicity of the result-equations, the Markovic Group, in fact, did study theion of hydrogen on the various Pt(hk l) crystal faces.[5], in conjunction with the earlier work of Vetter [19],hat, although thePt(111)datawerebestttedbyanon-in isotherm, theHORon Pt(110) at lowoverpotentialsplication of the Langmuir ideal adsorption isotherm ofe ideal dual-site form of the TafelVolmer sequence,tom recombination step (i.e. the reverse Tafel reaction)ds. In addition, they concluded for Pt(110) that themechanisms of the HER and HOR should be the same.conversion from a chemical rate equation (mole-electrochemical rate equation (current-based) is now</p><p>meter CM represents the active catalyst concentrationion interface. Typically, for low-pressure and near idealactivities can be replaced by the corresponding con-. The aH2 in Eq. (3) will, therefore, be replaced by theartial pressure, pH2 , or, more appropriately for a liquid-ion, cH2 , the concentration of dissolved hydrogen in theat the reaction interface. Similarly, the aH+ in Eq. (4)willby cH3O+ , the concentration of the hydrated protons atinterface.</p><p>afel reaction for dissociative chemisorptionwith n=2 and with the renements described above,rates of adsorption and desorption (per unit catalyst), expressed as current densities, as follows:</p><p>adscH2[CM(1 )]2 = 2F(kadscH2C2M)(1 )</p><p>2 (6)</p><p>des(CM)2 = 2F(kdesC2M)2 (7)</p><p>d in Section 2.3,...</p></li></ul>

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