Fundamentals Of Electrochemistry, Thermodynamics And

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Mitglied der Helmholtz-GemeinschaftFundamentals of Electrochemistry, Thermodynamicsand Solid State Chemistry for fuel cellsAugust 22, 2011 Ň / * - %HUW GH DDUWAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry, Thermodynamics andSolid State Chemistry for Fuel istryelectrochemical cellsoxidation and reductionanode and cathodecell and electrode potentialelectrolytic and galvanic cellsthermodynamicsNernst, standard and heating voltagecharge transportfuel utilisationoperation characteristics (IV curves)polarisation lossesefficienciesInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)ƔƔƔƔƔƔƔbasic characteristics and requirementsrequirements for materials / componentselectrolyte materialsionic conductivity in oxidescathode materialselectronic conductivity in oxidesanode materialsAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 2

ElectrochemistryElectrochemistry is the branch of physical chemistryƔ dealing with the interrelation of chemical and electrical effectsorƔ dealing with the study of chemical reactions as a results of the passage of current(conversion of chemical energy into electrical energy and vice versa)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)Fundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 3Electrochemical cellsElectrochemistry occurs in electrochemical cellsElectrochemical cells in their most simple form consist ofƔ two electronic conductorsÎ electrodesboth in contact withƔ one ionic conductor (or solution) Î electrolyteelectrodeInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)electrolyteelectrodeAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 4

Electrochemical cells: half-cellsIn electrochemical cells electrochemical reactions occurat the interfaces between the electrolyte and the electrodesEach electrode/electrolyte couple is referred to as half-cell;the electrochemical reaction occurring at its interface as half-cell n Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)Fundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 5Electrochemical cells: half-cell reactionsThe electrochemical reactions at the electrode/electrolyte interfacesinvolve electron transfer between the electrode and the electrolyte (or species in solution)There are two distinct types of half-cell reaction:Ɣ the electrolyte (or species in solution) donates electron(s) to the electrodeƔ the electrolyte (or species in solution) accepts electron(s) from the electrodehalf-cell(left)electron donation reactionhalf-cell(right)electron acceptance reactioneØreactant o product e reactant e o tute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)electrodeinterface(right)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 6

Electrochemical cells: oxidation and reductionelectron donation reactionelectron acceptance reactionreactant o product e reactant e o productOXIDATIONREDUCTION loss of electrons increase in oxidation statehalf-cell(left)half-cell(right) gain of electrons decrease in oxidation itute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)electrodeinterface(right)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 7Intermezzo: oxidation stateThe definition(1) as listed by IUPAC (International Union of Pure and Applied Chemistry)A measure of the degree of oxidation of an atom in a substance.It is defined as the charge an atom might be imagined to have when electrons are countedaccording to an agreed-upon set of rules:(1) the oxidation state of a free element (un-combined element) is zero;(2) for a simple (monatomic) ion, the oxidation state is equal to the net charge on the ion;(3) hydrogen has an oxidation state of 1 and oxygen has an oxidation state of -2 whenthey are present in most compounds. (Exceptions to this are that hydrogen has an oxidation state of -1in hydrides of active metals, e.g. LiH, and oxygen has an oxidation state of -1 in peroxides, e.g. H2O2);(4) the algebraic sum of oxidation states of all atoms in a neutral molecule must be zero,while in ions the algebraic sum of the oxidation states of the constituent atoms must beequal to the charge on the ion. For example, the oxidation states of sulfur in H2S, S8 (elementarysulphur), SO2, SO3, and H2SO4 are, respectively: -2, 0, 4, 6 and 6.The higher the oxidation state of a given atom, the greater is its degree of oxidation; thelower the oxidation state, the greater is its degree of reduction.(1) source: http://en.wikipedia.org/wiki/Oxidation stateInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 8

Intermezzo: oxidation stateAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)Fundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 9Electrochemical cells: oxidation and reductionelectron donation reactionelectron acceptance reactionmore formalreactant X o product (X n) n e reactant Y m e o product (Y -m) OXIDATIONREDUCTIONƔ loss of electronsƔ increase in oxidation statehalf-cell(left)half-cell(right)Ɣ gain of electronsƔ decrease in oxidation itute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)electrodeinterface(right)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 10

Electrochemical cells: oxidation and reductionelectron donation reactionelectron acceptance reactionreactant X o product (X n) n e reactant Y m e o product (Y -m) OXIDATIONREDUCTIONreductant X o product (X n) n e the reductant transferselectrons to anothersubstance, and is,thus, oxidized itself.And, because it "donates"electrons it is also calledan electron donor.oxidant Y m e o product (Y -m) eØeØelectrodeelectrolyteelectrodethe oxidant removeselectrons from anothersubstance, and is, thus,reduced itself.And, because it "accepts"electrons, it is also calledan electron acceptor.An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)Fundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 11Electrochemical cells: oxidation and reductionelectron donation reactionelectron acceptance reactionreactant X o product (X n) n e reactant Y m e o product (Y -m) OXIDATIONREDUCTIONreductant X o product (X n) n e oxidant Y m e o product (Y -m) reductant X o oxidant (X n) n e oxidant Y m e o reductant (Y -m) eØeØelectrodeInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)electrolyteelectrodeAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 12

Electrochemical cells: anode and cathodeelectron donation reactionelectron acceptance reactionreactant X o product (X n) n e reactant Y m e o product (Y -m) OXIDATIONREDUCTIONreductant X o product (X n) n e oxidant Y m e o product (Y -m) reductant X o oxidant (X n) n e oxidant Y m e o reductant (Y -m) eØeØred X o ox (X n) n e ANODEelectrodeelectrolyteox Y m e o red (Y-m) electrodeAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)CATHODEFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 13Electrochemical cells: anode and cathodeby definition:oxidation at the anodereduction at the cathodeOA RCtwo vowelstwo consonantseØred X o ox (X n) n e ANODEOXIDATIONInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)eØelectrolyteox Y m e o red (Y-m) CATHODEREDUCTIONAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 14

Electrochemical cells: net cell reactionm red X o m ox (X n) m n e multiply with mn ox Y n m e o n red (Y-m) multiply with n n oxY m redX o n red(Y-m) m ox( X n ) eØeØred X o ox (X n) n e ANODEelectrolyteOXIDATIONox Y m e o red (Y-m) CATHODEREDUCTIONAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)Fundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 15Electrochemical cells: cell potentialEcathode Eanodeǻ(cellby convention (IUPAC):switch is open; no current passing through the cellIVred X ox (X n) n e ANODEOXIDATIONInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)oxY m e red(Y-m) electrolyteCATHODEREDUCTIONAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 16

Electrochemical cells: cell potentialE eq,cathode E eq,anodeǻ( eq,cellby convention (IUPAC):with E eq electrode potential at current 0ªequilibrium at both electrode/electrolyte interfacesIVpotential (a.u.)E eq,catred X ox (X n) n e 'E eq,cellE eq,anANODEelectrolyteOXIDATIONCATHODEREDUCTIONAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)oxY m e red(Y-m) Fundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 17Electrochemical cells: cell potentialǻ( eq,cellby convention (IUPAC):E eq,cathode E eq,anodewith E eq electrode potential at current 0potential (a.u.)ªred X ox (X n) n e ox(X n) redX ox(X n) redX ox(X n) redX ox(X n) redX ox(X n) redX ox(X n) redX ANODEOXIDATIONInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)equilibrium at both electrode/electrolyte interfacesE eq,cat'E eq,cellE eq,anelectrolyteCATHODEREDUCTIONAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyoxY m e red(Y-m) Fundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 18

Electrochemical cells: electrode potentialelectrochemical (thermodynamic) equilibrium at the anode/electrolyte interface: of all species i must be equal in both phases (an,el)the electrochemical potential Pianabsolute potential (a.u.) Pired X ox (X n) n e Pi Q P ielox(X n) redX ox(X n) redX ox(X n) redX ox(X n) redX ox(X n) redX ox(X n) redX ANODEiQi0i PistoichiometriccoefficientsP 0T RT ln ai nFMchemicalpotentialMelP 0TaiManelectrolyteOXIDATIONchemical potential atstandard conditionsactivity of species i 1for solidsfor solutions fi c ifi activity coefficient 1 for diluted solutionsci concentration pi pressure for ideal gasesAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)electricalpotentialFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 19Electrochemical cells: electrode potentialelectrochemical (thermodynamic) equilibrium at the anode/electrolyte interface: of all species i must be equal in both phases (an,el)the electrochemical potential Pianabsolute potential (a.u.) Pired X ox (X n) n e Piielox(X n) redX ox(X n) redX ox(X n) redX ox(X n) redX ox(X n) redX ox(X n) redX ANODEOXIDATIONInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9) Q P iQi0i PistoichiometriccoefficientsP 0T RT ln ai nFMfor the anodic oxidation reaction given here:MelP 0T red RT ln ared nFMelP 0T ox RT ln aox nFManManMan Melelectrolyte'MT,eqP 0T ox P 0T red RT aox lnnFnF aredRT aox'M0T,eq lnnF aredAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 20

Electrochemical cells: electrode potentialin more general terms Q Oxii n e i Q Redjj'MT,eqjNOTE: now written as reduction reaction!absolute potential (a.u.)'M0T,eqox(X n) redX ox(X n) redX ox(X n) redX ox(X n) redX ox(X n) redX ox(X n) redX ª ared , j Q jRT « jln nF «« aox ,i Q i iº»»»¼however instead of absolute potentialselectrode potentials relative to a definedstandard reference electrode are preferredSHE: standard hydrogen electrodeMelH /H2 :aH E025qC,eq, H /H Man1 atm0 Volt2E T,eq, ox/red1; pH2ª ared , j Q jRT « jE0T,eq, ox/red lnnF «« aox ,i Q i iNernst potentialAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)º»»»¼Fundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 21Electrochemical cells: reduction potentialsstandard reduction potentials (relative to SHE)can be found in tables in most reference worksE T,eq, ox/redª ared , j Q jRT « jE0T,eq, ox/red lnnF «« aox ,i Q i iº»»»¼source:Vanýsek, Petr (2007). "Electrochemical Series",in Handbook of Chemistry and Physics: 88thEdition (Chemical Rubber Company).Institute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 22

Electrochemical cells: reduction potentialsan exampleCu2 HØ ĺ &X (0 Zn2 HØ ĺ Q (0 0.34 V-0.76 VexternalloadZn CuE0Cu/Cu2 E Zn/Zn2 E0Zn/Zn2 Cu2 SO42ØSO42Øelectrolyteǻ( eq,cellCATHODEREDUCTION Q ĺ Q2 HØCu2 HØ ĺ &Xǻ(0eq,cell ! 0RT ª c Zn2 ºln «»2F « c Cu2 ¼»RT ª c Zn2 ºln «»2F « c Cu2 ¼»Î a spontaneous reaction!An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)RT ª 1 ºln «»2F « c Zn2 »¼ 0.34 ( 0.76) 1 .1 OXIDATIONRT ª 1 ºln «»2F « c Cu2 »¼º»»»¼E eq,cathode E eq,anode'E eq,cellZn2 ANODEECu/Cu2 IeØV E T,eq,ox/redª ared , j Q jRT « jE0T,eq,ox/red lnnF «« aox ,i Q i iFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 23Electrochemical cells: electrolytic and galvanic cellsǻ(eq,cell 0 electrolytic cellǻ(eq,cell ! 0 galvanic cellƔ needs to be electrically drivenƔ not spontaneousƔ produces electrical energyƔ spontaneous powersourceexternalloadIeØV ANODEeØVeØIeØeØelectrolyteOXIDATIONInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9) CATHODEREDUCTIONeØ ANODEelectrolyteOXIDATIONAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, Italy CATHODEREDUCTIONFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 24

Electrochemical cells: electrolytic and galvanic cellsǻ(eq,cell 0 electrolytic cellǻ(eq,cell ! 0 galvanic cellƔ needs to be electrically drivenƔ not spontaneousƔ produces electrical energyƔ spontaneous powersourceexternalloadIeØVeØVeØIeØeØ ANODE electrolyte IONAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9) CATHODEREDUCTIONFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 25Electrochemical cells: galvanic cellsan example: the lead acid battery consists of Pb and PbO2 electrodes in sulphuric acidPbSO4 V HØ ĺ 3E V 6242Ø (aq)PbO2(s) SO42Ø(aq) 4 H HØ ĺ 3E624(s) 2 H2Oexternalloadduring discharging (electricity production)PbSO4 is formed on both electrodeseØV IPbPbO2 H ǻ( eq,cellE eq,cathode E eq,anodeǻ(0eq,cell00 EPbSOEPbO2 /PbSO 44 /Pb1.68 ( 0.36) Volt2.04 VoltSO42ØANODEelectrolyteOXIDATIONSO42Ø Pb(s) DT ĺ PbSO4 V HØ (E0 -0.36 V)(E0 1.68 V)CATHODEREDUCTIONPbO2(s) SO42Ø DT HØ ĺPbSO4(s) 2 H2OInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 26

Electrochemical cells: galvanic cellsan example: the lead acid battery consists of Pb and PbO2 electrodes in sulphuric acidPbSO4 V HØ ĺ 3E V 6242Ø (aq)PbO2(s) SO42Ø(aq) 4 H HØ ĺ 3E624(s) 2 H2O powersourceIPbSO4 during charging an external power sourcehas to apply a voltage higher than 2.04 VeØVPbO2PbH PbSO4 ǻ( eq,cellE eq,cathode E eq,anodeǻ(0eq,cell00 EPbOEPbSO4 /Pb2 /PbSO 4 0.36 (1.68) Volt 2.04 VoltSO42ØANODE(E0 -0.36 V)(E0 1.68 V)electrolyteCATHODEOXIDATIONREDUCTIONPbSO4(s) 2 H22 ĺPbO2(s) SO42Ø DT HØ PbSO4 V HØ ĺ Pb(s) SO42Ø DTInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 27Electrochemical cells: galvanic cellsanother example: the (solid oxide) fuel cellno standard reduction potentials(relative to SHE) availableO2 J HØ ĺ 22Ø (ad)H22 J HØ ĺ 2(g) O2Ø(ad)externalloadeØV'E0,cellO2H2H 2Oǻ( eq,cellI ANODEOXIDATIONH2(g) O2Ø DG ĺ H22 J HØ electrolyte E0O /O2- 2RT1 ln2F pO2 1/ 2§RT pH2 · EH0 2 /H2O ln 2FpH2O ¹ eØeØE eq,cathode E eq,anode'E eq,cellCATHODEE0O /O2- EH0 2 /H2O 2p H2 ORTln2F pO2 1/ 2 pH2REDUCTIONO2 J HØ ĺ O2Ø DGInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 28

Electrochemical cells: galvanic cellsanother example: the (solid oxide) fuel cellO2 J HØ ĺ 22Ø (ad)H22 J HØ ĺ 2(g) O2Ø(ad)externalloadI'E eq,cellE0O /O2- EH0 2 /H2O 'E eq,cell'E0eq,cell 2eØVO2H2H 2OH2(g) ½ O2 J ĺ 2O(g)eØ RTln2F pO2 1/ 2 pH2Nernst voltageeØANODEp H2 ORTln2F pO2 1/ 2 pH2p H2 O electrolyteOXIDATIONH2(g) O2Ø DG ĺ H22 J HØ CATHODEREDUCTIONO2 J HØ ĺ O2Ø DGInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 29Electrochemical cells and thermodynamicsGG H - TSGibbs free energyis the maximum amount of non-expansion workthat can be obtained from a closed systemHH U pVenthalpyis the internal energy of the system, including thework that the system has done on its surroundingsFirst Law of Thermodynamics'U Ufinal state - Uinitial stateQ WSentropyUinternal energyVTpvolumeabsolute temperaturepressureEnergy is conserved; it can be transformed (changed from oneform to another), but it can neither be created nor destroyed.The change in internal energy of a system (ǻU) equals the sum ofthe work done (W) and the heat transferred (Q) during the process.Institute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 30

Electrochemical cells and thermodynamics'U U2 - U1Q WG H - TSin fuel cells:volume workWVelectrical workheat transferWEQ'UH U pVWV p'VWE nF ǻ(Q T'S'GT,p'UT,p p'VT,p T'S T,p'UT,pT'S p'V nF 'E'GT,p'E T,p'HT,p T'S T,p'GT,p p'VT,p T'S T,p nF'E T,p 'GT,pnFFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)BdH, FZJ/IEK-9, Aug 22, 2011, sheet 31Fuel cells: Nernst, standard and heating voltage'E0'G'E0'H'ENernst 'G02Fstandard voltage (all activities 1)measure for the available energyfor 'H02Fheating voltage (based on enthalpy)measure for the maximum energycan be found inthermodynamic tablesin most reference works'E0'G p H2 ORTln2F pO2 1/ 2 pH2for'G0 and 'H0values at 25 C and 1 barH2(g) ½ O2 J ĺ 2O(g)Nernst voltage or Open Circuit Voltage (OCV)deviation from the standard voltage (concentration dependence)Institute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 32

Fuel cells: Nernst, standard and heating voltage'E0'G'E0'H 'G02Ftemperature dependence:'GT 'H2F0by useful approximation:ǻH and ǻS are temperature independent'GTfor'HT T'S T'G0 T 273 25 'S0'E0H2(g) ½ O2 J ĺ 2O(g)25 C800 C'G0 - 228.4 kJ/mol1.184 V1.006 V'H0 - 241.8 kJ/mol1.253 V1.253 V'S0 - 44.4 J/(mol K)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)Fundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 33Fuel cells: Nernst, standard and heating voltagevoltage vs. air / Volt1.3'E0'H 'H02F'E0'G 'G02F1.21.11.00.90.80100200300400500600700800900 1000temperature / CInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 34

Fuel cells: Nernst, standard and heating voltage'ENernst T'E0'G T p H2 ORTln2F pO2 1/ 2 pH2'E025 C800 C'E0'G1.184 V1.006 V'E0'H1.253 V1.253 V1.202 V1.071 V1.174 V0.970 V'ENforp H20.9 ; pH2O0 .1 ; p O 20.21 barp H20.5 ; pH2O0 .5 ; p O 20.21 barAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)Fundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 35Fuel cells: Nernst, standard and heating voltage1.3voltage vs. air / Volt'E0'H1.2 'H02F1.1'EN1.0'E0.90'Gp H20.9p H2 O0 .1 'G02F0.80100200300400500600700800900 1000temperature / CInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 36

Fuel cells: Nernst, standard and heating voltage1.3voltage vs. air / Volt'E 'H02F0'H1.21.1'EN1.0'E0.90 .1 'G02F0'G'EN0.9p H2p H2 Op H20.5p H2 O0 .50.80100200300400500600700800900 1000temperature / CFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)BdH, FZJ/IEK-9, Aug 22, 2011, sheet 37Fuel cells: Nernst voltageNernst voltage (or OCV) vs air / Volt1,15'ENernst,T'E0T 1,10p H2 ORTln2F pO2 1/ 2 pH2H2 ½ O2oH2O1,051,00watervapourpartial pressure/ bar0,950,020,150,350,550,750,900,85temperature800 0,250,450,650,850,90,10,30,50,70,91hydrogen partial pressure / barInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 38

Fuel cells: Nernst voltageNernst voltage (or OCV) vs air / Volt1,2'ENernst,T'E0T p H2 ORTln2F pO2 1/ 2 pH2H2 ½ O2oH2O1,1900 C1,00,9850 C800 C750 C700 Cwatervapourpartial pressure0,03 bar0,80,00,1650 C600 C0,20,30,40,50,60,70,80,91,0hydrogen partial pressure / barAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)Fundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 39Fuel cellswell let’s start doing some actual workthe switch is closed; current is passing through the cellIeØVH2H 2OeØO2O2 ØeØ ANODEOXIDATIONH2(g) O2Ø DG ĺ H22 J HØ electrolytetransport of electric chargeƔ via ions in the electrolyteƔ via electrons in the outer circuitƔ via charge transfer across theelectrode/electrolyte interfaces CATHODEREDUCTIONO2 J HØ ĺ O2Ø DGInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 40

Fuel cells: charge transport or electric currenttransport of electric charge via charge transfer across the electrode/electrolyte interfacesª implies the occurrence ofelectrochemical reactionsat the interfacesIVH2H 2OeØANODEI total current [A] electrolyteOXIDATIONH2(g) O2Ø DG ĺ H22 J HØ ª the current corresponds tothe consumption of fuelO2O2 ØeØ ª the current corresponds tothe rates of the reactionseØj I/A current density [A/cm²]CATHODEA effective electrode area [cm²]REDUCTIONO2 J HØ ĺ O2Ø DGAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)Fundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 41Intermezzo: Faraday constantthe total charge Q transported by one mol of electrons is given by:withNAeAvogadro constant6.022 u 10 23 mol -1elementary charge 1.602 u 10 C-19NA eQ 96485 C mol -1this is theFaraday constantIeØVQF 96485 C mol -1H2H 2OeØO2 ØeØ ANODEOXIDATIONH2(g) O2Ø DG ĺ H22 J HØ 96485 A s mol -1O2electrolyte CATHODEREDUCTIONO2 J HØ ĺ O2Ø DGInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 42

Fuel cells: fuel utilisation uF Hthe maximum current that can be drawn from a hydrogen supply n2(in [mol/s])is given by ImaxH2eØH 2OeØ ANODEelectrolyteOXIDATIONH2(g) O2Ø DG ĺ H22 J HØ uFO2O2 ØeØ(n 2)the fuel utilisation uF is defined as the ratiobetween the actual current drawn (I) and themaximum current (Imax) that can be reachedIV2F n H2 Z IImaxZ I2F n H2where Z is the number of cells in a stackCATHODEREDUCTIONO2 J HØ ĺ O2Ø DGAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)Fundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 43Fuel cells: operation characteristic (IV-curve)'ENcell voltage / Vvoltage losses00current density / A/cm²Institute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 44

Fuel cells: operation characteristic (IV-curve)Ohmic lossescell voltage / V'EN00current density / A/cm²An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyInstitute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)Fundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 45Fuel cells: operation characteristic (IV-curve)Ohmic losses'ENpolarisationanodiclossescell volatge / Vcathodic'E j'EN j x R: Kc Ka00current density / A/cm²Institute of Energy and Climate Research– Principles of Electrochemistry (IEK-9)An Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, ItalyFundamentals of Electrochemistry,Thermodynamics and Solid State ChemistryBdH, FZJ/IEK-9, Aug 22, 2011, sheet 46

Fuel cells: operation characteristic (IV-curve)'E j'ENR: j x R: REmaterials:design:Kc , KaRCKc Ka RA Rcontactsspecific conductivitygeometric sizescharge rials:design:combination electrode/electrolytetriple phase boundaryAn Introduction toSOFC TechnologyAug 21 – 27, 2011Viterbo, I

Fundamentals of Electrochemistry, Thermodynamics and Solid State Chemistry Institute of Energy and Climate Research – Principles of Electrochemistry (IEK-9) An Introduction to SOFC Technology Aug 21 – 27, 2011 Viterbo, Italy BdH, FZJ/IEK-9, Aug 22, 2011, sheet 3 Electrochemistry Elec

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