Seebeck coefficients of cells with lithium carbonate and gas electrodes

ContentslistsavailableatScienceDirect

Electrochimica Acta

jo u r n al h om ep a g e :w w w . e l s e v i e r . c o m / l o c a t e / e l e c t a c t a

Seebeck coefficients of cells with lithium carbonate and gas electrodes

M.T. Børset

^a

, X. Kang

^d

, O.S. Burheim

^c

, G.M. Haarberg

^b

, Q. Xu

^e

, S. Kjelstrup

^a,∗

aDepartmentofChemistry,NorwegianUniversityofScienceandTechnology,NO-7491Trondheim,Norway

bDepartmentofMaterialsTechnologyandEngineering,NorwegianUniversityofScienceandTechnology,NO-7491Trondheim,Norway

cFacultyofTechnology,Sør-TrøndelagUniversityCollege,Trondheim,Norway

dSchoolofMaterialsScienceandMetallurgy,NortheasternUniversity,Shenyang,Liaoning,110819,China

eSchoolofMaterialsScienceandEngineering,ShanghaiUniversity,Shanghai,200072,China

a r t i c l e i n f o

Articlehistory:

Received19May2015

Receivedinrevisedform18August2015 Accepted16September2015

Availableonline21September2015

Keywords:

Seebeckcoefficient Transportedentropies thermoelectricity Moltencarbonate

a b s t r a c t

TheSeebeckcoefficientisreportedforthermoelectriccellswithgaselectrodesandamoltenelectrolyte ofonesalt,lithiumcarbonate,atanaveragetemperatureof750^◦C.Weshowthatthecoefficient,which is0.88mVK⁻¹,canbefurtherincreasedbyaddinganinorganicoxidepowdertotheelectrolyte.We interpretthemeasurementsusingthetheoryofirreversiblethermodynamicsandfindthattheincrease intheSeebeckcoefficientisduetoareductioninthetransportedentropyofthecarbonateionwhen addingsolidparticlestothealkalicarbonate.Oxidesofmagnesium,ceriumandlithiumaluminateleadto areductioninthetransportedentropyfrom232±12toaround200±4JK⁻¹mol⁻¹.Thisisofimportance fordesignofthermoelectricconverters.

©2015TheAuthors.PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Renewableenergytechnologiesarehighontheglobalresearch agendaasoneofthemeanstomeetenergysecurityandtheglobal warmingchallenge[1–3].Thermoelectricpowergeneratorspro- duceelectricitydirectlyfromheatviatheSeebeckeffect.Thepower canbegeneratedfromvariousheatsourcesandwithnomoving parts.Thedevicesareexpectedtotakepartbothinprimarypower productionandtobeabletoimprovetheoverallenergyefficiencyof existingplants[4,5].Mostoftheresearchactivityhasbeenconcen- tratedontheuseofsemiconductors[4,6],withtheaimtoincrease theefficiencyofthethermoelectricmaterialsitself.However,the successfuldeploymentdependsalsoonthecostperwattproduced [7,8].

Ahighthermoelectricconversionefficiency,asmeasuredbythe so-calledfigureofmerit,isobtainedwhenthesystemhasahigh Seebeckcoefficient,alowthermalconductivityandalowelectri- calresistivity[9].TheSeebeckcoefficientisdirectlyrelatedtothe Peltierheat,throughirreversiblethermodynamictheory,seee.g., Agar[10],deGrootandMazur[11]orFørlandet.al[12].ThePeltier heatisthereversibleheatchangeattheinterfaceswhencharge istransferred fromone phasetoanother. Semiconductorshave

∗Correspondingauthor.

E-mailaddresses:[email protected] (M.T.Børset),[email protected](X.Kang),[email protected]

(O.S.Burheim),[email protected](G.M.Haarberg),[email protected] (Q.Xu),[email protected](S.Kjelstrup).

Seebeckcoefficients oftypically 200VK⁻¹,butgiganticvalues have beenreported,e.g.45mVK⁻¹ in stronglycorrelated semi- conductorFeSb2[13],850VK⁻¹foratwo-dimensionalelectron gasinSrTiO₃[14]and450VK⁻¹at900KforSrTiO₃/SrTi_0.8Nb_0.2O₃ superlattices[15].Inelectrochemicalsystems,theSeebeckcoeffi- cientcanbemuchlarger,whentheentropychangeoftheelectrode reactionislarge.Especiallyforcellsinvolvingcomplexformationor withgaselectrodes.Forexample,Bonettiet.al.[16]reportedaSee- beckcoefficientnear7mVK⁻¹fornon-aqueouselectrolytesatlow temperatures(30-40^◦C).Forsystemswithionicliquids,Abraham and co-workersreportedSeebeckcoefficientsof 1.5-2.2mVK⁻¹. Formoltensalts,Flemet.al[17]reportedSeebeckcoefficientsup to1.8mVK⁻¹foroxygenelectrodesinanelectrolytewithmolten cryoliteand oxidesat960^◦C. JacobsenandBroers[18] reported valuesaround1.2mVK⁻¹at800-1150Kforequimolarmixturesof alkalicarbonatesandgaselectrodes.Salesandco-workersexplored capacitivemembrane technologyforthermal energy harvesting from small temperature differences [19]. There are two main reasonswhy wefind itinteresting toinvestigateelectrochemi- calsystemsaspotentialthermoelectricpowergenerators:1)the potentialforlargeSeebeckcoefficientscombinedwith2)thepos- sibilitytoavoidtheuseoftoxicandrareelements.Pursuingthis pathway,weaimtofindasafeandpotentiallycheapthermoelectric powergenerator.

We seek electrochemical systems with higher Seebeck coefficientsthan semiconductors,targeting heatrecoveryin the metallurgicalindustry[20].Inthisindustry,heatisavailableattem- peraturesfrom1600^◦Canddowntoroomtemperature[21–23].

http://dx.doi.org/10.1016/j.electacta.2015.09.091

0013-4686/©2015TheAuthors.PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.

0/).

Wehavechosentoinvestigatecarbonatesandelectrodesreversible tocarbonateionsascandidatesystemsastheyarestableliquids atintermittenttemperatures(400^◦Cto800^◦C).Thechoicewas motivatedbytheearlyresultsformixturesofalkalicarbonatesby JacobsenandBroers[18].Alkalicarbonatesareusedaselectrolytes inmoltencarbonatefuelcellsandhavebeenstudiedextensively sincethe1960’s.Thus,forsystemsdevelopment,weexpecttodraw onthisknowledge.

Here, we combinetheoreticaland experimentalstudies and starttobuildsystematicknowledgeabouttheSeebeckcoefficient.

Weapplythemethodofirreversiblethermodynamicstoestablish thetransportequationsforthesystem.Thistheoryhasprogressed overthelastfewyearstobeabletodealwithheterogeneoussys- tems[24].Yet,fewapplicationsof this newmethodhavebeen madetothermoelectricphenomena.Thetransportequationsgive aframeworkthathelpstodefineconditionsthatgiveswelldefined experiments.Also,theseequationsgivesinformationontempera- tureprofilesandelectricpotentialprofilesaswellasaframework suitableforoptimizationofaworkingunit.WeexpresstheSeebeck coefficientintermsofthethermodynamicentropiesofthecompo- nentsandthetransportedentropiesofthechargecarriers.While afewmodelsexiststoexplainthereversibleheateffect,orthe transportedentropiesofsemiconductors,modelsarenotavailable forthetransportedentropyofions.Overtheyears,thetransported entropyofanionhasmostoftenbeencomparedtothethermo- dynamicentropyofanion.Thedifferencebetweenthetwoisthe Eastmanentropy.Listshavebeenmadeofsingleelectrodeheats, foroneortwo-componentelectrolytes,butwethinkitisfairto saythatthereisasofyetnodetailed modelabletopredictthe magnitudeofthetransportedentropy.

JacobsenandBorers[18]addedpowderofmagnesiumoxideto theliquidmixturesoftwoorthreealkalicarbonates,givingamore viscouselectrolyteeasiertohandle.Wechoosetostartsimplewith asinglealkalicarbonateaselectrolyte,purelithiumcarbonate.A seriesofinorganiccompoundsisnextintroducedinthemoltencar- bonate,MgO(s),CeO₂(s)andLiAlO₂(s).Theadditionofapowderin thesolidstatedoesnotaltertheexpressionfortheSeebeckcoef- ficient,butitdoeshaveanimpactonthevalueofthecoefficient, causedbyvariationsinthetransportedentropyofcarbonateions.

ThepresenceofLiAlO₂(s),butnotCeO₂(s),altersthesymmetryof thecarbonateion[25,26].WeuseMgO(s)tobeabletocompare withearlierresults[18].WealsoconsideredtoaddSiO₂,butthis iswasnotfeasibleasSiO₂greatlyenhancethedecompositionof lithiumcarbonate[27].

Thepaperisorganizedasfollows.In thetheoreticalpart,we dividethetotalcellintofivesubsystems.Foreachsubsystemwe establishtheentropyproductionandgivethefluxequationsthat followfromthis.Fromthefluxequations,wefindthecontribu- tionfromthesubsystemstothecell’sSeebeckcoefficient.Next, wereporttheexperimentaltechniquealongwithmeasurements thatverifyandconfirmthereliabilityofthetechniqueused.We seethatthelargeSeebeck coefficientforthe singlecomponent electrolytecanbeenhancedbymakinguseofadispersionofpar- ticularsolidinorganicoxides.Theadditiveleadstoareductionin thetransportedentropyofcarbonateions.

2. Theory

2.1. Systemdescription

Considertheconversionofthermalenergyintoelectricenergy intwocellswithelectrodesreversibletothecarbonateion:

Au

s,T^s,a

|CO₂(g),O₂(g)|Li₂CO₃(l)|CO₂(g),O₂(g)|Au

s,T^s,c

(LC) Au

s,T^s,a

|CO₂(g),O₂(g)|Li₂CO₃(l),XO (s)|CO₂(g),O₂(g)|Au

s,T^s,c

(LC-XO) Here thecells labelsrefer to theelectrolyte used, LCdesig- natepuremoltenlithiumcarbonatewhileLC-XOisa dispersion ofmoltenlithiumcarbonateandanoxide(XO)inthesolidstate, whereXOrepresentstheoxidesMgO,CeO₂ orLiAlO₂.Thecells havetwocarbondioxide|oxygenelectrodes,keptattemperatures T^s,aandT^s,c.Theelectrodegasesarebubbledoverelectronconduc- torsofgold,immersedinanelectrolyteofuniformcomposition.

JacobsenandBroers[18]usedplatinumelectrodes,butweusegold electrodes.Bothplatinumandgoldhaveproventobestable,repro- ducibleandreversibleinmoltencarbonates[28].Thevalueofthe Seebeckcoefficientisnotaffectedbythechoiceofelectrodemate- rial,giventhattheelectrodereactionisthesame,asthetransported entropyoftheelectronissmallandnegligibleinbothmetals.We shallseebelowthatthepresenceoftheoxideXOintheelectrolyte willhavenoeffectonthetheoreticalexpressionoftheSeebeck coefficient,butwillchangethevalueofthecoefficientevenifits solubilityintheelectrolyteisnegligible.Theadditionofoxidecould affectthesolubilityofthegasesintheelectrolyte,however,only thegasstateofcarbondioxideandoxygenenterstheoverallelec- trochemicalreaction.ThisiswhycellsLCandLC-XOcanbeusedto learnaboutthetransportedentropyofthecarbonateion.

Theoverallelectrochemicalreactionattheleft-handsideis[29]:

1

2CO²₃⁻→1

2CO₂(g)+1

4O₂(g)+e⁻ (1)

whiletheoppositereactiontakesplaceattheothersideofthecell.

Tofacilitatethetheoreticaldescription,wedividecellsLCand LC-XO into five subsystems, consisting of three homogeneous phasesandtwointerfaces;theanodeconductor(a),thetwoelec- trodesurfaces(s,a ands,c), theelectrolyte (e)and the cathode conductor(c).ThesymbolsandnotationareillustratedinFig.1a.

ToestablishtheexpressionfortheSeebeckcoefficient,weneed anexpressionfortheemfmeasuredbetweentwoCuwiresattached totheAuconductorsatroomtemperature(T^a,o=T^a,o=T⁰)when thetwoelectrodesareattemperaturesT^s,aandT^s,c.TheSeebeck coefficientisdefinedasthepotentialdifferencedividedbythetem- peraturedifferencebetweentheelectrodesinthelimitsj→0and T^s,c−T^s,a=T→0:

˛S≡

T

j→0,T→0= a+c

T +a,e+e,c T +e

T (2) whereweusedthatthemeasuredemfisthesumofthepotential differenceacrosseachsubsystemandthattheelectrodesarether- mostatted,i.e.T^a,e=T^s,a=T^e,aandT^e,c=T^s,c=T^c,e,c.f.Fig.1a.Weshall findanexpressionforfromnon-equilibriumthermodynamics theoryforheterogeneoussystemsasoutlinedin[24].

2.2. Applicationofnon-equilibriumthermodynamics

We shall evaluate thecontribution fromeach subsystemto thecellpotential,andhencetheSeebeckcoefficient,seeEq.(2).

Foreachsubsystemweestablishtheentropyproductionandgive thefluxequationsthatfollows.Fromthefluxequationswefind theexpressionforthepotentialdifferencethatentertheSeebeck coefficientforcellsLCandLC-XO.TheequationsfortheAu(s)con- ductors(aandcinFig.1a)havebeengivenelsewhere(seee.g., chapter9in[24]).Theequationsfortheelectrodesurfaces(s,aand s,c)andtheelectrolyte(e)havenotbeenestablishedbefore.

2.2.1. Theconductorsconnectingthecell

Byintegratingtheexpressionfortheelectricpotentialfromthe temperatureofthesurroundings,T⁰,totheelectrodetemperature

Fig.1. Aschematicpictureofthecell(a)andacrosssectionoftheexperimentalcellwithelectrodes(b).Ina)weshowthefivesubsystemsofthecellandthenotationused fortransportproperties.Thefirstsuperscriptreferstothephaseinquestion,andthesecondtotheneighboringphase.Awithonesubscript,i,denotesthedifferenceacross phasei.Awithtwosubscripts,i,k,denotesthevalueinphasekminusthevalueinphasei.Inb)weshowacrosssectionofthecellusedintheexperiments.Theelectrodes consistofagoldwirewhichispoint-weldedtoagoldplate(theelectrodesurface).WeusedafiveboreAl2CO3asinsulationforthermocouplesandelectrodes,cross-section showninthefigure.

T^s,aonthelefthand-side,andfromtheelectrodetemperatureon theright-handside,T^s,c,toT⁰,wefindthecontributionsfromthe conductorstotheSeebeckcoefficient(seechapter9in[24]):

a+c T =−1

FSe^∗ (3)

Here S^∗e is thetransported entropy of theelectron, this was assumedconstantin thetemperatureintervalT.Theoriginof thisexpressionwillbeexplainedbelow,inthesectiondescribing theelectrolyte.

2.2.2. Theelectrodesurfaces

Thesurfaces(s,aands,cinFig.1a)canberegardedasindepen- dentthermodynamicsystems.Thethermodynamicpropertiesof thesurfacearethendescribedbyexcessdensities,asexplainede.g.

by[24](chapter5).Theexcessentropyproductionintheanode surface(s,a)hascontributionsfromheatfluxesintoandoutofthe surface,fromfluxesofoxygenandcarbondioxideoutofthesurface, fromafluxoflithiumcarbonateintothesurface,fromtheelectric currentdensityacrossthesurfaceandtheelectrochemicalreaction inthesurface(seeEq.(1)):

^s,a =Jq^a,ea,s

₁

T

+J^e,aq s,e

₁

T

− 1

T^s,aJ^e,a_O2s,eO2,T

T^s,a

− 1

T^s,aJ_CO^e,a₂s,eCO2,T

T^s,a

− 1

T^s,aJ^e,a_Li2CO3s,eLi₂CO₃,T

T^s,a

− 1

T^s,aja,e+r^s

− 1 T^s,anG^s,a

(4)

HereJqisthemeasurableheatfluxandJ_j isthefluxofcom- ponentj,j,Tisthechemicalpotentialofcomponentjevaluated at constanttemperature T, jis theelectric current density and a,eisthepotentialdropacrossthesurface.Fig.1agivesfurther explanationsofthenotation.Withthermostattedelectrodes,we

haveconstanttemperatureacrosseachsurface(i.e.fors,awehave T^a,e=T^s,a=T^e,a).Weassumealsochemicalequilibriumforadsorbed components(i.e.^s,a_j =^e,a_j ).Bothconditionsapplytoreversible conditions(^s,a=0).Wemeasuretheemfwhenaverysmallelec- triccurrentispassingtheelectrode,andthesurfacereactionrate isr^s=j/F.For^s,a=0thepotentialdropacrosstheanodesurfaceis:

a,e=−1

FnG^s,a (5)

HerenG^s,ahascontributionsfromtheneutralgascomponents CO₂andO₂totheelectrodereaction:

nG^s,a=1 2^s,a_CO2

T^s,a

+1 4^s,a_O2

T^s,a

(6) WeintroduceEq.(6)intoEq.(5)andexpressthepotentialdrop acrosstheanodesurfaceintermsofthechemicalpotentialsofthe neutralcomponents:

a,e=−1 F

₁

2^s,a_CO2

T^s,a

+1 4^s,a_O2

T^s,a

(7) Thesameanalysisappliestotheotherelectrodesurface.The totalcontributionfromtheelectrodereactionstothecellpotential isthen:

a,e+e,c =−1 F

₁

2

^s,a_CO2

T^s,a

−^s,c_CO2

T^s,c

+1 4

^s,a_O2

T^s,a

−^s,c_O2

T^s,c

=−1 F

₁

2SCO2+1

4SO2 T^s,c−T^s,a

(8)

We used the relation

∂j/∂T

p,ni=−Sj to obtain the last equality.WeshallevaluateS_jfortheaveragecelltemperature.The contributionfromthesurfacestotheSeebeckcoefficient(Eq.(2)) is:

a,e+e,c T =−1

F

₁

2SCO₂+1 4SO₂

(9) 2.2.3. One-componentelectrolyte

TheelectrolyteofcellLCispuremoltenlithiumcarbonateand thepressureisconstant throughoutthesystem.Thus, onlytwo thermodynamicforcescontributetotheentropyproductioninthe electrolyte(e):thethermalforceandthegradientintheelectric potential.Theentropyproductionis:

^e=Jq^e

∂

∂x 1 T +j

−1 T

∂

∂x (10)

Fig.2.ThechargetransporttakingplaceincellsLCandLC-XObytransferenceof 1Fpositivechargesfromlefttorightinsidethecell.Thetransportnumbertiisthe fractionofcurrentcarriedbytheioni.

Thefluxequationsfortransportofheatandchargeintheelec- trolytefollowfromtheentropyproduction:

Jq^e=L^eqq

−1 T²

dT dx

+L^e_q

−1 T

d dx

(11)

j=L_q^e

−1 T²

dT dx

+L^e

−1 T

d dx

(12) Thecoefficients(L’s)dependonstatevariables,butareindepen- dentoftheforces.TheyarerelatedthroughtheOnsagerrelations asL_q=L_q.Thecoefficientsarephenomenologicalandmustthere- forebedeterminedfromexperiments.Wesolveford/dxfrom Eq.(12),integrateacrosstheelectrolyteforj≈0,andexpressthe contributionfromtheelectrolytetotheSeebeckcoefficientas:

e T =−^e

TF (13)

where Fis Faraday’s constant and we tookthe ratio^e/T con- stantoverthetemperatureinterval.ThePeltiercoefficientofthe electrolyte,^e,describestheheattransportedwiththecurrentat uniformtemperatureandcomposition(i.e.atreversibleconditions):

^e≡

Jq^e

j/F _dT=0,d

T=0

=FLq

L =

T

J_S^e−SLi₂CO₃JLi₂CO₃

j/F

dT=0,d_T=0

(14)

whereJ_S^eistheentropyfluxinabsenceofafluxofLi₂CO₃ when chargeistransportedintheelectrolyte.

Weneedamoredetailedexpressionfor^e.Thiscanbefound fromthedefinitioninEq. (14),byconsideringtheentropybal- anceofavolumeelementintheelectrolyteatreversibleconditions (isothermalconditions).Todescribethemovementofionsinthe electrolyte(Li⁺andCO²⁻₃ )andthecomponent(Li₂CO₃)weneeda frameofreference.Wefollowthegeneralprocedureoutlinedin Ref.[30]andtakeeitherthecationsortheanionsastheframeof reference,i.e.tLi⁺=0ort_CO²−

3 =0(seeFig.2).Thisgivestwoequiv- alentexpressionsforthePeltiercoefficient,becauseboththe andtheTinEq.(13)areindependentoftheframeofreference.

Thetransferencecoefficientofthelithiumcarbonateisdefinedas:

tLi₂CO₃≡

JLi2CO3

j/F _dT=0,d

T=0

=L_q^e

L^e (15)

Inacationframeofreference[30],thetransportnumberofthe carbonateionisunityandthetransferencecoefficientofthesalt, tLi2CO3=0.Then,allentropy,orequivalently,heat,istransported

bythecarbonateionandthePeltiercoefficientcanbeexpressedby thetransportedentropyofthecarbonateion:

^e=−T1 2S_CO^∗ 2−

3

(16) Heretheconventionusedfortransportofchargegivestheminus sign(c.f.Fig.2).

Inananionframeofreference[30],thetransportnumberof thelithiumionisunityandthetransferencecoefficienttLi₂CO₃= 1/2.FromEq.(15)thePeltiercoefficientthenequalsthedifference betweentheentropytransported withLi⁺,S_Li^∗+,andtheentropy transferredwithLi₂CO₃:

^e=T(S^∗_Li+−1

2SLi2CO3) (17)

AsdiscussedaboveEqs.(16)and(17)mustbeidenticalandwe findtherelationbetweenthetransportedentropyoftheionsand thethermodynamicentropyoftheLi2CO3:

S^∗_CO2− 3

+2S^∗_Li+=SLi2CO3 (18) The relation between transported entropies and thermody- namicentropieswasalreadyshown,seee.g.,Agar[10],deGroot andMazur[11]andFørlandet.al[12].

2.2.4. Dispersionsoflithiumcarbonateandaninorganicoxide Inorganic oxides in thesolid state can be added to molten lithiumcarbonateelectrolyte,asincellLC-XO,withoutalteringthe formofthetheoreticaldescriptionofthecellemf.WetakeMgO asanexampletoseethatthisstatementistrue.Anequilibrium canbeestablishedbetweenMgO(s)andCO₂(g)inthemelttogive MgCO₃(l)accordingtoEq.(19)

MgO (s)+CO₂(g)MgCO₃(l) (19)

Van Velden [31] studied the equilibrium between alkali- magnesiumcarbonatemelts,carbondioxidegasandmagnesium oxide.ThemolefractionofMgCO3(l)inthecarbonatemelt was about0.12 at450^◦Cand 0.03 at750^◦C,when themeltwasan equimolarmixtureoflithium-,sodium-,andpotassium carbon- ate[31].Largelithiumcontentandhightemperaturereducedthe MgCO₃contentinthemelt,favoringtheMgO(s)-phase.Wethere- foreexpectaverysmallamountofMgCO₃inthemoltenLi₂CO₃in thepresenceofMgO(s).Thiswasalsothecase whenweinves- tigated. Nevertheless, the electrolyte of cell LC-XO has for the conditionsusedheretwochemicalcomponents.

However,aslongasthesolidphaseofMgO(s)exists,thereis only oneindependent component according tothe Gibbs phase rule.ThechemicalpotentialofMgCO₃(l)isdictatedbytheequilib- rium(19)andthegaspressure.ThechemicalpotentialofMgO(s) is

MgO,T(s)=⁰_MgO,T(s)

.Then,withequilibriuminEq.(19)and dpCO₂=0,d2,T=dMgCO3,T=0.This,togetherwiththeGibbs- Duhem relationfor the electrolyte, gives (n1d1,T+n2d2,T=0), dLi₂CO₃,T=d1,T=−n2d2,T/n1=0.Therefore, theexpression fortheentropyproductionwillbethesameastheentropyproduc- tionfortheone-componentsystem,Eq.(10).Thisgivesthesame expressionfortheSeebeckcoefficientofcellsLC-XOandLC.What willchange,asweshallsee,isthevalueofthetransportcoefficients.

Thesamereasoningappliestoalltheoxidesusedinthepresent cell.WeshallinvestigatetheoxidesMgO(s),CeO2(s)andLiAlO2(s).

2.3. TheSeebeckcoefficientofcellsLCandLC-XO

WeaddthecontributionfromthefivesubsystemstotheSee- beckcoefficientforthecellsLCandLC-XO,seeEq.(2).Wechoose thecationframeofreferencefortheelectrolyteandaddEqs.(3),(9) and(13).Atreversibleconditions,thechoiceofframeofreference

forthemassfluxeswillnothaveanimpactontheexpressionfor thepotentialdropacrossthesurface.Theresultis:

˛S = (T^s,c−T^s,a)

=−1 F

1 2S_CO⁰₂+1

4S⁰_O2−R

2lnp^u_CO2−R 4lnp^u_O2−

1 2S^∗_CO2−

3

−S_e,Au^∗

(20)

whereweassumedidealgasandusedtherelationSj=S_j⁰+lnp^u_jfor theentropiesofthegases.IntheEq.abovep^u_j isthefractionofthe partialpressureandthestandardpressurep⁰ofcomponentjand S⁰_j isthepartialmolarentropyofcomponentjattemperatureTand standardpressurep⁰.Theentropiesandthetransportedentropies aregenerallyfunctionsoftemperature.Intheexperiments,wekeep theaveragetemperatureconstantanduseT<20^◦Ctoavoidtem- peraturecorrections.Theentropiesofthecomponentsvaryless than1%witha20degreetemperaturevariation,whichisnegli- giblecomparedtotheexperimentalaccuracy.FromEq.(20),and knownvaluesoftheentropies,thegaspartialpressuresandthe transportedentropyoftheelectroningoldwecancalculatethe transportedentropyofthecarbonateion.WedothisinSections 4.2and4.3.Apositivemeansthatthesystemproduceswork fromthetemperaturedifferencebetweentheelectrodesurfaces, orthatheatflowsfromthehightemperaturetothelowtempera- ture.Inthissituation,thetemperaturedifferenceT=T^s,c−T^s,ais negativeandconsequentlytheSeebeckcoefficientisnegativefora systemthatproduceswork.

FromEq.(20),wecanpredictthepressurevariationoftheSee- beckcoefficient.Forafixedvalueoftheoxygenpressure,wehave:

d˛S

dlnp^u_CO2

p^u O2

= R

2F =0.043mVK⁻¹ (21)

3. Experimental

Anexperimentalroutinewasmadetoestablishthemeasure- mentprocedure,andtolearnabouttheeffectonthetransported entropyofcarbonateioninadispersion.Asexternalagentswere addedMgO,CeO₂andLiAlO₂.

3.1. Materials

Lithiumcarbonate(Li2CO3)withpurity>99%,magnesiumoxide (MgO)withpurity>99%,ceriumoxide(CeO₂)withpurity>99.9

%and lithium aluminate(LiAlO₂,lot number:21804PRV)were acquiredfromSigmaAldrich.Chemicalswereusedwithoutfur- therpurification.Thespecificsurfaceareasofalloxidesaregiven inTable1.

Pre-made gasmixtures of oxygen and carbon dioxidewere obtainedfromYaraPraxair.Threegasmixtureswereusedcontain- ing66%CO₂ and34%O₂,20%CO₂and33%O₂,7.3%CO₂ and 33%O₂,therestwasHe(g).Experimentswereperformedinacon- trolledatmosphereofN2(g)ofpurity≥99.999%.Thegasmixtures Table1

TheSeebeckcoefficient(˛S)andthetransportedentropyofthecarbonateion.The uncertaintyinthecalculatedresultstemsfromindependentmeasurements.XOis theaddedoxideincellLC-XOandthesurfaceareaisdeterminedbyBETanalysis.

Cell ˛S S^∗_CO2−

3

XOsurfacearea mVK⁻¹ JK⁻¹mol⁻¹ m²g⁻¹ LC −0.88±0.06 232±12 -

LC-MgO −1.04±0.02 201±4 120

LC-CeO2 −1.05±0.02 200±4 4

LC-LiAlO2 −1.00±0.02 209±4 1

wasexposedto1barpressureinthesurroundings,meaningthat thetotalpressureinthecell(thesumofthepartialpressures)was constantandalwaysequalto1bar.

GoldwasobtainedfromK.A.Rasmussen,Norway.Aluminatubes andcrucibleswereacquiredfromMTCHaldenwanger,Germany.

3.2. Apparatus

Allexperimentswereperformedinastandardlaboratoryverti- caltubularfurnace[32].Thecell,shownindetailinFig.1b,consisted ofanAl2O3crucible,withelectrodesimmersedinamoltencarbon- ateelectrolyte.Eachgoldelectrodewasinsertedintothecenter bore(diameter2.3mm)ofa5-boreAl₂O₃tubeandthegoldsheet waspoint-weldedtothewire.Thethermocouple(Pt-Pt10%Rh)was insertedintotwooftheotherholes(diameter0.75mm)andthe junctionwaspositionedasnearaspossibletothegoldsheet.Gas wassuppliedthroughtheboresoftheceramictube.Thetemper- aturesandcellemfwererecordedeverythird secondbyadata acquisitionunit(Agilent,34972A).

3.3. Procedure

Theelectrolytewaseitherpurelithiumcarbonateoradispersion electrolyteofLi2CO3andoneoftheoxidesMgO,CeO2orLiAlO2.For alldispersions,thevolumefractionoftheliquidphasewas0.62.The dispersionelectrolyteswerepreparedbymixingtheLi₂CO₃with theoxidepowderbyhandinamortar.Thelithiumcarbonateorthe mixturewerepre-heatedmorethan48hoursat200^◦Cinamuffle furnace.Afterdrying,theelectrolytewasmeltedundernitrogen atmosphereat750^◦Cintheverticaltubefurnaceandkeptatthis temperatureforatleast48hourstoensurestableconditions.Next, thegasmixture(inmostcaseswiththecomposition66%CO₂and 34%O₂)waspassedthroughthe5-boreceramictubeforatleast 5hoursbeforetheexperimentstarted.Atthestartofeachexperi- ment,weadjustedthegasflowratetogivestablemeasurements.

Aslowflowrate,adaptedforgoodgas-metal-electrolytecontact wasused.WithSEM-imaging,wevisuallyinspectedthesolidified electrolyteofcellLC-MgO.Thesepicturesshowedhomogeneously distributedparticlesofgrainsizearound1-2m.

Theexperimentstartedwhenthetemperaturesandtheelectric potentialwerestable.Atemperaturedifference(T)wasestab- lished between theelectrodes bypositioning them at different heightsinthecrucible.Theaveragecelltemperaturewaskeptat 750^◦Cand thetemperaturedifferencewasalwayssmallerthan 20^◦C,toavoidtheneedfortemperaturecorrectionsintheSeebeck coefficient.Theelectromotiveforcebetweentheelectrodeswas measuredasafunctionofthetemperaturedifference,bygradually firstincreasingandthen decreasingthetemperaturedifference, seeFigs.3and4.Afteranequilibrationperiodof10-20min,the cellwasagainstable,anda measurementwithanewtempera- turedifferencewasdone.Recordingsweremadeovertimetomake surethatthesituationwasstable,andtoeliminateeffectsofminor instabilitiesordriftduetovoltagefluctuationsinthemains.The techniquedemonstratedinthesefigureswasusedtoobtainthe Seebeckcoefficient.

FromFigs.3and4,weseethatthepresenceofMgOhasacertain stabilizingeffectonthevoltagerecordings.Thevoltagefluctuation islargerinthefirstcasegivingahigheruncertaintycomparedto thecaseswheninorganicpowderwasadded.Addingparticlesto theliquidincreasetheeffectiveviscosityandpreventsconvection, resultinginmorestableconditions.

Weestimatedtheaccuracy(adoublestandarddeviation)from repeatedmeasurements.ForcellLC,theSeebeckcoefficientwas determined for three different gas flows (i.e. different outlet pressuresfromthegasbottle).Thisgaveadoublestandarddevia- tionof±0.06mVK⁻¹.ForcellLC-XOoneseriesofmeasurements

0 5000 10000 15000 20000 -20

0 20 -20 0 20 40

t / s

Δφ / mV ΔT / K

Fig.3.Themeasuredpotentialdifference()thatfollowfromvariationsinthe temperaturedifference(T)asafunctionoftime,inthecellLC.Theelectrodes wereofgold,theaveragetemperaturewas750^◦C,p^u_CO

2=0.66andp^u_O

2=0.34.

0 5000 10000 15000 20000 25000

-20 0 20 -20 0 20

t / s

Δφ/ mV ΔT / K

Fig.4.Themeasuredpotentialdifference()andthemeasuredtemperaturedif- ference(T),c.f.3,asafunctionoftimeforthecellLC-MgO.Theelectrodeswereof gold,theaveragetemperaturewas750^◦Candp^u_CO

2=0.66andp^u_O

2=0.34.

Fig.5.TheSeebeckcoefficientforcellLC-MgOasafunctionofthepartialpressure ofCO2,keepingthepartialpressureofoxygenconstantat0.33bar.Theelectrodes wereofgoldandtheaveragetemperaturewas750^◦C.Thelinerepresentsthelinear regression.

wasreproduced three times, replacing theelectrolyte between eachexperiment.Theuncertainty,±0.02mVK⁻¹,waslargerthan thedoublestandarddeviationfromlinearregression.

Inaparallelstudy,weusedalsoplatinumaselectrodematerial [33].Withintheaccuracyoftheexperiment,thetwometalsgave thesameSeebeckcoefficient.

3.4. Solubilityofmagnesiumoxideinlithiumcarbonatewith carbondioxidepresent

Wedidanindependentmeasurementtodeterminethesolubil- ityofmagnesiumoxideinlithiumcarbonatewhencarbondioxide waspresent,seeEq.(19).Pelletsofmagnesiumoxidewasaddedto thelithiumcarbonate.Thegaswassuppliedatthebottomofthe crucible,bubblingoverthepelletsincontactwithlithiumcarbon- ate.Sampleswerecollectedfromthemoltenphaseandanalysed formagnesiumcontent(ICP-MS).Asreference,wetookasample fromthemoltenlithiumcarbonatewhennomagnesiumoxidewas present.Thistestconfirmedthatmagnesiumoxideisonlyslightly soluble in lithium carbonateat ourconditions, increasingfrom 0.007to0.013wt%.

4. Resultsanddiscussion

4.1. TheSeebeckcoefficientdetermination

Figs.6and7givetheemfplotted vsthetemperaturediffer- encebetweentheelectrodesforcellsLCandLC-XOwithMgO(s) andCeO2(s).Thevaluesareaveragesofvaluesmeasuredovera periodintimewhenthepotentialwasstable.WefoundtheSee- beckcoefficients(˛S,seeEq.(2))astheslopesoftheseandsimilar plots.ThecoefficientsobtainedinthismanneraregiveninTable1.

The lines in Figs. 6 and 7 do not cross theorigin, meaning thatthere isa biaspotentialbetweentheelectrodes.Thevalue oftheSeebeckcoefficientis,however,notaffectedbyanystable, systematicerrorintheabsolutepotential.JanzandSaegusa[28]

reportedstablebiaspotentialsoftheorder±5mVafteraninitial agingperiodforanO2/Auelectrodeinmoltencarbonatesat600^◦C.

BoruckaandSugiyama[29]reportedthetimestabilitytobewithin

±2mVfortheequilibriumpotentialsofO₂/CO₂/Auelectrodesin moltencarbonates.Inourexperiments,thethermocoupleswere positionedcloseto,butnotattheelectrodesurface.Asystematic differencebetweenthemeasuredandactualsurfacetemperature

-30 -20 -10 0 10 20 30

-20 0 20 40

Δφ / mV

Δ T / K Δ φ =( 9.6 ± 0.4) - ( 0.88 ± 0.03 )Δ T

Fig.6. Themeasuredpotentialdifference()asafunctionofthetemperature differencebetweentheelectrodes(T)incellLC.Theelectrodeswereofgold,the averagetemperaturewas750^◦C,p^u_CO

2=0.66andp^u_O

2=0.34.

-30 -20 -10 0 10 20 30 -40

-20 0 20 40

-30 -20 -10 0 10 20 30

-40 -20 0 20 40

Δ T / K

Δ φ / mV Δ φ (A)= ( 8.2± 0.2) - (1.04± 0.01) Δ T

Δ φ (B)=( -0.6 ± 0.2) - (1.05± 0.01) Δ T B A

Fig.7. Themeasuredpotentialdifference()asafunctionofthetemperature differencebetweentheelectrodes(T)incellLC-MgO(A)andforcellLC-CeO2(B).

Theelectrodeswereofgold,theaveragetemperaturewas750^◦C,p^u_CO2=0.66and p^u_O

2=0.34.

maythereforealsoarise.Thismaygiveasystematicerrorinthe Seebeck-coefficient,astherealtemperaturedifferencediffersfrom themeasured.BasedontheobservedSeebeckcoefficients,1mVoff- setcorrespondstoaconstanttemperatureoff-setbiasof1K.This isaround2%oftheoveralltemperaturerange.Also,anysmallvari- ationingasconcentrationorsurfaceconcentrationisrepresented bythebiaspotentialanddoesnotaffecttheresultsfortheSeebeck coefficient.Agingofelectrodescouldcauseadrift,butthiswasnot observed.

AsshownbyEq.(21),theslopeofaplotoftheSeebeckcoeffi- cientversusthelnp^u_CO2 is0.043mVK⁻¹fortheelectrodereaction inEq.(1).TheplotshowninFig.5confirmstheexpectedtheoreti- calslopeofEq.21,withintheaccuracyoftheexperimentandthus theelectrodereaction.ThisallowedustouseEq.(20)toanalyse thecontributionstotheSeebeckcoefficientandtocalculatethe transportedentropyofthecarbonateion(seeSections4.2and4.3).

4.2. Thetransportedentropyofthecarbonateioninpurelithium carbonate

FromEq.(20),wecalculatedthetransportedentropyofthecar- bonateion. StandardentropiesoftheCO2(g),O2(g)and lithium carbonateat750^◦Cwere271,244and309JK⁻¹mol⁻¹(HSCchem- istry).Thetransportedentropyoftheelectroninthegoldconductor was0.4JK⁻¹mol⁻¹[34].Withthis,wecalculatedthetransported entropyofthecarbonateionforthecellsLCandLC-XO,seeTable1 forresults.Thelargestvaluewasobtainedforpuremoltenlithium carbonate,232±12JK⁻¹mol⁻¹.

Thetransportedentropy isanenergy carriedalong withthe chargecarrier,anenergyofatypethatdrawsfromorder-disorder transitionsasthechargeiscarriedalong.Thecarbonateionhas rotationaldegreesoffreedominthecarbonatemeltwhichcanbe influencedbythesurroundings[35].Thispropertycouldtherefore beconnectedtoahighvalueofthetransportedentropy.

4.3. Thetransportedentropyofthecarbonateioninadispersion WeseefromTable1thatthetransportedentropyofthecarbon- ateiondecreasessubstantiallywhensolidMgOoranotheroxideis addedtotheelectrolyte.Thesmallertransportedentropyiscom- patiblewithalargervalueoftheSeebeckcoefficient.Fromthepoint

Table2

Thermodynamicandtransportedentropiesat750^◦C.Thethermodynamicentropy appliestoabulkliquid.ThetransportedentropyoflithiumisfoundfromEq.(20) withmeasuredvaluesoftheSeebeckcoefficient.

cell SLi₂CO3 S^∗

CO²⁻

3

S^∗

Li²⁺

JK⁻¹mol⁻¹ JK⁻¹mol⁻¹ JK⁻¹mol⁻¹

LC 309 232±12 39±12

LC-LiAlO2 287^* 209±4 39^*

*Estimated

ofviewofapplications,asmallervalueisthereforemostinteresting.

Thefactorsthataffectthevariationarethereforeofinterest.

Itisclearfromthetheoreticalderivations,thatthesolereason forthevariationinthetransportedentropyofcarbonateioncomes fromthefactthattheliquidelectrolyteisincludedinadispersion.

ThefactthatgoldandplatinumelectrodesgavethesameSeebeck- coefficient,see[33],excludesanimpactoftheelectrodematerial.

Theelectrodereactionisthesameinthepresenceandabsenceof theoxideintheelectrolyte.Theelectrodereactionshowsfurther- moretheexpecteddependenceonthepartialpressureofcarbon dioxide.FromtheBETsurfaceofalloxides(seeTable1)andSEM imaging,itseemsclearthatthemoltenlithiumcarbonateisnotin abulkstateinsidethedispersions.

GiventhatthepresenceofLiAlO₂(s),butnotCeO₂(s),altersthe symmetryofthecarbonateion[25,26],onewouldexpectavaria- tioninthetransportedentropyofthecarbonateionbetweenthe twodispersions.Theresults200and209JK⁻¹mol⁻¹differwithin theuncertaintyintheresults,butbarelyso.Iftheabilitytopolarize leadstoanincreasingvalue,theresultsindicatethatLiAlO2hasthe highestpolarizingabilityoftheoxidesused.Also,LiAlO₂hadthe smallestBETsurfacearea,seeTable1.

Blinovetal.[36]calculatedthetransportedentropyofleadion inmixtureswithalkalichlorides,andfoundavalue,affectedby thefieldstrengthofthealkalimetal,orthepolarizingpower.The transportedentropyofleadionwaslargerinthepresenceofLi⁺ thanofCs⁺.Thisvariationcanbesaidtosupportourfinding.The morepolarizingthesurroundingsare,thelargeristhenumberof statestoexploreupontransport,andthehigherbecomesthevalue oftransportedentropy.

Capillaryeffectsareexpectedinthedensedispersions.Mizuhata et.al.[37]foundthattheenthalpyofmeltingofLi2CO3wasreduced with50-80%ofthenormalvaluebyincludingthesaltinadisper- sionwithLiAlO₂.Reductionsinthefreezingpoint couldalsobe seen[37].Thereductionsweredependentontheratioofmolten carbonateandthetotalsurfaceareaofthesolidphase.Alowering oftheenthalpyofmelting,indicatesthattheentropyoftheliq- uidphasebecomeslower.Thevalueoftheentropyofthesaltin theporousmaterialwillthereforedifferfromthebulkvalue.The relationinEq.(18)canbeusedusedtoarguewhyS^∗_CO2−

3

obtainsa reduction.Janzandco-workers[38]reportedanenthalpyofmelt- ingof44.8kJmol−1andthemeltingpoint726^◦CforpureLi₂CO₃. Fora50%reductionintheenthalpyofmeltingforthepuresalt, thisgivesareductionof22JK⁻¹mol⁻¹intheentropyat750^◦C.The observedreductionisfrom232to209JK⁻¹mol⁻¹or23JK⁻¹mol⁻¹. Theloweringintheentropyofthesalt,compatiblewithamore orderedstructureinsidethedispersion,canexplainthelowering inthetransportedentropyofthecarbonateionseeninTable2.

Thenumbersare,however,uncertainandtherecouldalsobean increaseinthetransportedentropyofthelithiumion.

Thevalues from theBET experimentsshowthat additionof thesolidphasecreatesextrasurfacesinthesystem,varyingwith thegrainsizeofthepowdersadded.Suchaddedsurfaceislikely tohaveanimpactontheelectricalandthermal conductivityof themelt,propertieswhichplayanimportantroleinthefigureof merit.Introducingtheelectricallynon-conductingsolidphaseto