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Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
Sustainable hydrogen and electrical energy storage batteries_lecture5
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Sustainable hydrogen and electrical energy storage batteries_lecture5

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  • 1. 20 March 20131Radiation, Radionuclides and ReactorsHydrogen and Electrical Energy StorageF.M. Mulder & M. Wagemaker
  • 2. 20 March 2013 2Program BatteriesLecture 1: History, Applications, basic Electrochemistry and thermodynamicsFeb 27 of batteries: Redox reactions, Gibbs free energy, chemical potential,Nernst.Lecture 2: Solid state electrode reaction mechanisms, phase diagrams, phase rule,March 6 Gibbs Free energy, voltage profiles, capacities and energy densities.Li-ion batteriesLecture 3: Continue topics Lecture 2.March 13 Electrolyte stability: Pourbaix diagram, band structure solids, Cycle life.Lecture 4: Kinetics, Buttler-Volmer, diffusion, solid state diffusionMarch 20 Discussion on Science paper 6 seconds discharge.Lecture 5: Super capacitorsMarch 27 Future systems: Li-air, Li-sulphurFlow-cellsCosts and Performance comparison batteries/systemsMaterial Abundance
  • 3. A C A CCell C A F Fe eE            Electrolyte-electrode stability diagram20 March 2013 3
  • 4. Example SEI Formation: Graphite20 March 2013 4
  • 5. 20 March 2013 5Demands Li-ion Electrolyte• Good (Li+) ionic conductor• Electronic Isolator• Stability window 5 V (depends on sys.)• Stable up to ~ 70 degree celcius• Cheap• Non toxicMostly applied: Non aqueous solvents:Ethylene Carbonate (EC), Dimethyl Carbonate (DMC)Good ionic conduction, stability ~ 0.8-4.5 V (vs Li/Li+)Medium toxic, flammable, unstable etc -> Casing battery should be very good (=expensive)-F(A-E)=-FA- +Anode CathodeLiLiLiLiLiLi+Li+Li+Ie-e-e-Li salts: LiClO4 or LiPF6: Toxic and expensive
  • 6. 20 March 2013 6Li-ion batteries, ionic liquidsIonic liquid: salt in the liquid state: electronic isolatorgood ionic conductorthermal stabilitynon-flammablechemically stable (large stability window)cheap?safe
  • 7. 20 March 2013 7Solid electrolytes:Less difficulty/cost associated with long termencapsulating liquid electrolytes (that may startleaking), freedom design of batteries, high temp.Example: polymer electrolytes like polyethyleneoxideBecause polymers can have intrinsic mobility ofthe polymer chains, a dissolved Li salt can alsomove through it. However, solid electrolytesshow much lower Li+ conductivities (low powerdensity)Li-ion batteries, solid electrolytesPoor ionic mobility, PEO LiIApplication limited to large systems that can bemaintained at high temperatures
  • 8. 20 March 2013 8Li-ion batteries, electrolytesOther strategy:Adding nano-particles increases theConductivity in PEO-LiClO4
  • 9. 20 March 2013 9Space chargesTwo ion conductors and poor electronic isolators:A > BLi+Li+Li+Li+Li+Li+Li+Li+Li+Li+Li+Li+Li+Li+Li+Li+Li+Li+Li+Li+Li+Li+Li+Li+A = B  A BA BA A B BA BFF F          F(A-B)=-(A - B)F xCreates vacancies in A!Is called “Space Charge”
  • 10. 20 March 2013 10For diffusion you need vacancies
  • 11. 20 March 2013 11Li-ion batteries, electrolytesLi+Li+Li+Li+Li+Li+I-I-I-I-I-I-I-I-Li+Li+Li+I-I-Li+Li+Li+I-I-Li+Li+I-I-“Space charge” due to difference in chemical potentialCreates vacancies that enhance the mobilityTiO2
  • 12. 20 March 2013 12Home assignmentsRead Chapters 3.1-3.3 ElectrochemistryRead Paper Ceder et al. Sciencex1 x2Composition xg2g1Gibbsfreeenergyg(x)J/molx3g3a) Sketch the voltage profile resulting from theGibbs Free energy diagramb) In which direction with this reaction proceedc) Calculate the voltage of the voltageplateau(‘s) if any.d) Sketch a phase diagram that could representthis Gibbs Free energy diagramExercise: g(x) is the Gibbs Free energy of the cathode duringdischarge, assume the potential of the anode to be 0and constant
  • 13. 20 March 2013 13Home assignmenta) Sketch the voltage profile resulting from the GibbsFree energy diagramb) Which direction will this reaction proceed?c) Calculate the voltage of the voltage plateau(‘s) if any.d) Sketch a phase diagram that could represent thisGibbs Free energy diagramg(x) is the Gibbs Free energy of the cathode duringdischarge, assume the potential of the anode to be 0and constantx1 x2Composition xg2g1Gibbsfreeenergyg(x)J/molx3g3x1 x2Composition xCellpotenitalx3E12E23a)b) In the direction of decreasing Gibbs Free energy: right
  • 14. 1,2 2 1common-tangent 122 12 112 1 22 112 1 212 1 223 2 323 2 3( )constant (x <x<x )( )(x <x<x )( )(x <x<x )AnodeAnodeg gg x x Cx xg ggx x xx g gEzF Fx g gEzF F            x1 x2Composition xCellpotenitalx3E12E23Home assignmentc)x1 x2Composition xg2g1Gibbsfreeenergyg(x)J/molx3g3d)20 March 2013 14
  • 15. Kinetics in batteriesCharge transport20 March 2013 15
  • 16. Charge transport, kinetics(1) (3)(2)(1) ionic conduction A+(2) Charge transport over the electrolyte-electrode interface(3) ionic conduction A or B(4) electronic conduction20 March 2013 16(4)
  • 17. Question kinetics 1If the charge transport kinetics is improved:a) The power density will improveb) The energy density will improvec) Both power and energy density will improved) No clue20 March 2013 17[ / ] [C/g V]CellCellxzFEnergyDensity J g capacityM   
  • 18. Question Energy Density26 Why do you think batteries have in practicerelatively thin electrodes?a) Difficult to makeb) Long (dis)charge timesc) Shorter cycle lifed) No clue~300 μm2L DtLtDL: diffusion length:D: diffusion coefficientt: diffusion timeElectrode 6 times thicker => takes 36 times longer to charge20 March 2013 18
  • 19. 20 March 2013 19Question kinetics 2Up till now we assumed no current wasrunning, resulting in the open cell potential(Equilibrium Thermodynamics).What is the consequence of the internalresistance during discharge on VB-VA (themeasured voltage over the battery)?a) VB-VA increasesb) VB-VA decreasesc) VB-VA remains constantd) No clue- ++-IRriVAVBdischarging- ++-IriVAVBchargingECellECell, 0: Battery B A CellR I V V V E     
  • 20. 20 March 2013 20Internal resistance- ++-IUp till now we assumed no current wasrunning, what is the consequence ofthat?RriVAVBB A Battery Cell iBattery CellV V V E IrV E   discharging- ++-IriVAVBchargingB A Battery Cell iBattery CellV V V E IrV E   iIr Definition overpotential or polarization:(deviation from equilibrium), 0: Battery CellR I V E   Charging:Discharging:Equilibrium:ECellECell
  • 21. Anodecathode-e-++++++porousbarrierZn2+Zn2+e-e-e-NO3-NO3-NO3-NO3-A EE CEC= C - C =Cu/Cu2++Non-equilibrium electrochemistryEA= E - A =-Zn/Zn2+e- Zn2+e- NO3-NO3-Equilibrium:A EE CNon-Equilibrium:Discharge CellC A     20 March 2013 21
  • 22. 20 March 2013 22Also capacity (energy density) and therefore the efficiency depend on the (dis)charge rate!Consequence of internal resistance: cell voltage will depend on currentChange in equilibrium potentialchargingdischargingDischargeCharge( ) : Capacity (Coulomb)( )( )Energy E Q dQ QE Q dQEfficiencyE Q dQEffect called: Polarization Galvanic cell (discharge): Discharge< CellElectrolytic (charge) : Charge> Cell
  • 23. Change in equilibrium potentialECell[V]Chargedischarge0Capacity [Coulomb]equilibriumDischargeCharge( ) : Capacity (Coulomb)( )( )Energy E Q dQ QE Q dQEfficiencyE Q dQ20 March 2013 23
  • 24. Different sources for theoverpotential/internal resistance(1) (3)(4)(2)1 2 3 4 , 1 2 3 4Total i Totalr r r r r           20 March 2013 24(1) ionic conduction A+ through the electrolyte(2) Charge transport over the electrolyte-electrode interface(3) solid state ionic conduction A or B(4) electronic conduction
  • 25. Ionic diffusion through the electrolyteIExample: Reduction: Cu2+ + 2e- -> Cu(s) (cathodic)e-NO3-NO3-NO3-NO3-NO3-NO3-e-e-H2OH2OH2OH2OresistanceCu2+NO3-H2OCu2+NO3-H2O1: resistance due to finiteconductivity electron/ion inthe electrode/electrolyteDiffusion of Cu2+ will be hindered by attractedmolecules increasing its effective radius andthereby increasing its resistance.Ohmic behaviour: 1 =Iri,1hydration sphere20 March 2013 25
  • 26. Mass transport through diffusion (related to overpotential 1)O + ze- -> RFlux OFlux RIonic diffusion through the electrolyte:Fick 1st law Flux (mol/s):I/nFRemember:  =  + RT lnc -> concentration gradient -> mass flowIonic diffusion through the electrolyteRedRedOxOxdcJ DdxdcIDzF dxdcIDzF dx   20 March 2013 26
  • 27. Distance to electrode: x dxFick 1st law:Time dependent mass transport (derive Fick 2nd law)Change in time dt of ci(x) equals the difference in Flux in and out:: Fick 2nd law22( ) ( ) ( ) ( )i i i idc x dc x dc x dx d c xD Ddt dx dx dx      Ionic diffusion through the electrolyte20 March 2013 27Flux in( )idc xDdxFlux out( )idc x dxDdx( )Flux = idc xDdx
  • 28. To be able to calculate the current, I, that the electrolyte can pass:(1) We need c(x): solution of differential equation, depends on conditions(2) We need D: Measured property (how to measure?)22( )( ) ( )ii idc xI zFDdxdc x d c xDdt dx Ionic diffusion through the electrolyte20 March 2013 28
  • 29. O + ne- → R (reduction)O + ne- <- R (oxidation)(Cu2+ + 2e- <-> Cu)Experiment: t=0 App = eqt>0 App < eqStarting concentration O: cOinfQuestions: (1) How does the current look as a function of time?(2) How to determine the diffusion coefficientIonic diffusion through the electrolyte20 March 2013 29cOxcOCu2+I/nF+
  • 30. 20 March 2013 30Cu2+I/nF+20ln CueqCucRTzF c       Question kinetics 3Suppose we impose what willhappen?a) netto reductionb) netto oxidationc) nothingd) no clueeqAppApp Eq Cu2+ + 2e- -> Cu (reduction)Cu2+ + 2e- <- Cu (oxidation)2202lnCu is converted to Cunetto reduction (cathodic current)CuApp eqCuCu CucRTzF cc c          
  • 31. O + ne- -> R (reduction)Experiment: t=0 App = eqt>0 App < eqStarting concentration O: cOinfQuestion: (1) How does the current look as a function of time?Ionic diffusion through the electrolyte20 March 2013 31cOxcOCu2+I/nF+22( ) ( )Solve ( ) from: i idc x d c xc x Ddt dx( )idc xI zFDdx 
  • 32. O + ne- -> R (reduction)Experiment: t=0 App = eqt>0 App < eqStarting concentration O: cO Boundary/initial conditions forInitial condition t=0:Boundary conditioncOxcOCharge transfer is not ratelimitingIonic diffusion through the electrolyte20 March 2013 3222( ) ( )i idc x d c xDdt dx( 0, )O Oc t x c 0 ( , 0) 0( , )OO Ox c t xx c t x c      
  • 33. Solutions of usually have the form of an error functionIt appears (can be derived via Laplace):0 10 20 30 40 500.00.20.40.60.81.0Oxidant concentration after potential stepcO(t=0) = 1 mol/lt=0.0 st=0.1 st=0.5 st=1.0 st=2.0 st=6.0 scO[mol/l]distance perpendicular electrode interface (m)0 0( , ) ( )4xc t x c erfDt21/ 202( ) exp( )xerf x t dt Ionic diffusion through the electrolyte20 March 2013 334Dt22( ) ( )i idc x d c xDdt dx
  • 34. Measurement of current after potentialstep leads to diffusion coefficient!21/ 2021/ 22( ) exp( )( ) 2exp( )xerf x t dtderf xxdx  02( , )exp4( 0)OOxOOOOOOdc t xIDzF dxc xI zFDD tD tDI x zFct            Ionic diffusion through the electrolyte20 March 2013 340 10 20 30 40 500.00000.00010.0002Current density after potential stepcO=1 mol/lD=1.0 10-6cm2/sD=2.0 10-6cm2/sD=0.5 10-6cm2/sCurrentdensityI(A/cm2)time [s]The current as a function of timeafter the potential step App < eq
  • 35. 20 March 2013 35Ionic diffusion through the electrolyte0( , )OOxdc t xIDzF dx      Higher concentrations -> larger gradients -> higher currents?Dependence D on Temperatureand concentration LiPF6 salt:
  • 36. Different sources for theoverpotential/internal resistance(1) (3)(4)(2)1 2 3 4 , 1 2 3 4Total i Totalr r r r r           20 March 2013 36(1) ionic conduction A+ through the electrolyte(2) Charge transport over the electrolyte-electrode interface(3) solid state ionic conduction A or B(4) electronic conduction
  • 37. What do we want?20 March 2013 37chargingdischargingPredict current given the overpotential: I()
  • 38. 20 March 2013 38Ie-+++NO3-NO3-NO3-NO3-++e-e-NO3-NO3-Kinetic electrochemistry, charge transferNO3-H2OZn2+Step 1: enter the electrical double layerand loose hydration sphereStep 2: electron transferExample: Reduction: Zn2+ + 2e- -> Zn(s) (cathodic)Electrochemical double layer
  • 39. 20 March 2013 39ICu2+LUMOe-e-e-EFermiStep 1: enter the electrical double layer andloose hydration sphereStep 2: electron transfere-e-e-Example: Reduction: Zn2+ + 2e- -> Zn(s) (cathodic)LUMO: Lowest unoccupied molecular orbitalKinetic electrochemistry, charge transfer
  • 40. 20 March 2013 40Kinetic electrochemistry, charge transferAlthough during discharge the charge transfer process is spontaneous, it doesneed to overcome a barrier (step 1 and 2).Relationship of the current density [A/cm2] with the activation barrier GA, Arrhenius law:c: concentration [mol/cm3], F: Faradays constant [C/mol] and k: rate constant [cm/s]AGRTi zFckeGAG
  • 41. 20 March 2013 4120 March 2013Outer Helmolz PlaneOxidation: M -> M+z + ze- (anodic)Reduction: M <- M+z + ze- (cathodic)e-Mz+ElectrochemicalDouble Layer(EDL)e-e- Mz+MMz+e-Mz+
  • 42. 20 March 2013 4220 March 2013Outer Helmolz PlaneM/Mz+MEOxidation: M -> M+z + ze- (anodic)Reduction: M <- M+z + ze- (cathodic)e- Mz+e- Mz+e- Mz+g zF     g0Oxg0RedM
  • 43. 20 March 2013 43Constant p and Tj j j jj jdG Vdp SdT dn dn EdQ          ////zzzj j M MzjM M MzMM M MzMM M MzMdG dn dQG n QG n znFg zFg zF                           Integrate over n molesDifference in chemical potenital is differencein Gibbs free energy per mol
  • 44. 20 March 2013OHPAEg0OxOxidation: M -> M+z + ze- (anodic)Reduction: M <- M+z + ze- (cathodic)Dynamic equilibrium:Zero netto current: inetto = iA - iC = 0definition exchange current density(equilibrium current): i0 = iA = iCRed00gRTC O Ci i zFc k e 00OxgRTA R Ai i zFc k e 44- +Situation:Equilibrium has established atopen circuit. The difference inchemical potential iscompensated by the field.Both reduction and oxidationoccur, in the same rate!g0Redg zF     M/Mz+
  • 45. 45Question Kinetics 4What will happen with the barrier forreduction, g0Red, if the over- potential will be applied?a) g0Red increasesb) g0Red decreasesc) g0Red remains the samed) No clueWhat will be the result?a) Effective oxidationb) Effective reductionc) Nothingd) No clue
  • 46. 46Question Kinetics 4What will happen with the barrier forreduction, g0Red, if the over- potential will be applied?a) g0Red increasesb) g0Red decreasesc) g0Red remains the samed) No clueWhat will be the result?a) Effective oxidationb) Effective reductionc) Nothingd) No clue
  • 47. 20 March 2013OHPM/M2+AEOxidation: M -> M+z + ze- (anodic)Reduction: M <- M+z + ze- (cathodic)RedgRTC O Ci zFc k eOxgRTA R Ai zFc k e47- +Situation:Polarized state, pumpingelectrons in the negativeelectrode (charging), gred :effectively reduction:The new barriers will be:gOxgRedzF1 0C Ai i0 (1 )Ox Oxg g zF     Red Red0g g zF    
  • 48. 20 March 2013 48In equilibrium, =0, iC=iA=i0 => iNetoo= iA - iC = 0in that condition we define iC=iA=i0 as the exchange current densityWhat is so important about the exchange current density i0?Quantitative measure of the amount of electron transfer activity at equilibriumio large  much simultaneous ox/red electron transfer (ET)  inherently fast ET (kinetics)io small  little simultaneous ox/red electron transfer (ET)  sluggish ET reaction (kinetics)Kinetic electrochemistry, charge transferRed0 00Oxg gRT RTA C O C R Ai i i zFc k e zFc k e    Fill in the barriers upon polarization:RedRed00gg zF zFRT RT RT RTC O C O Ci zFc k e zFc k e e i e        0 (1 ) (1 )0OxOxgg zF zFRT RT RT RTA R A R Ai zFc k e zFc k e e i e        
  • 49. 20 March 2013 49So for the netto current density (difference anodic and cathodic current at one electrode):Kinetic electrochemistry, charge transfer(1 )0( )zF zFRT RTnetto A Ci i i i i e e          This is the fundamental equation of electrode kinetics, relates the current density with theexchange current density, the overpotential  and the transfer coefficient.Remember, we only considered the charge transfer at the electrode-electrolyte interface ()Butler-Volmer equation
  • 50. 20 March 2013 50In practice the two following limiting cases of the Butler-Volmer equations are most important:(1) low overpotentials, ||=|Cell-eq|  10 mV(2) high overpotentials, ||=|Cell-eq| > 50 mVCase 1: Low OverpotentialHere we can use a Taylor expansion to represent ex:Ignoring higher order terms:so total current density varies linearly with the overpotential  near eqKinetic electrochemistry, charge transfer(1 )0( )zF zFRT RTi i e e       1 ...xe x  0 0(1 )1 1zF zF zFi i iRT RT RT                
  • 51. 20 March 2013 51Case 2: High Overpotentialwhat happens as  becomes a large negative value? => iC >> iAWe can neglect iA term as rate of oxidation becomes negligible:So, current density varies exponentially with , or taking the ln on both sides:This is the cathodic Tafel equationSimilar, if  becomes a large negative value (iA >> iC ) we find the anodic Tafel equation:0zFRTCi i i e  0ln( ) ln( )zFi iRT  0(1 )ln( ) ln( )zFi iRT  Kinetic electrochemistry, charge transfer(1 )0( )zF zFRT RTA Ci i i i e e         
  • 52. 20 March 2013 52Tafel Plots: Determine the exchange current density i0 and the transfer coefficient  [V]Eeqln|i|Cathodic Anodicln(io)High overpotential:Low overpotential:High overpotential:0ln( ) ln( )zFi iRT   0(1 )ln( ) ln( )zFi iRT  Kinetic electrochemistry, charge transfer0zFi iRT =0
  • 53. Question kinetics 5 [V]ln|i|Cathodic Anodic=0ABABWhich curve represents the mostsluggish reacting electrode?a) Ab) Bc) No clue
  • 54. Question kinetics 5 [V]ln|i|Cathodic Anodic=0ABABA: higher current at the same overpotential => a) curve A more sluggish
  • 55. Question kinetics 6 [V]ln|i|Cathodic Anodic=0ABABWhy do the curves deviate from the Buttler Volmer relation at high overpotential?a) Buttler-Volmer is not validb) No reacting species can be delivered due to the high ratec) Because of side reactionsd) No clue
  • 56. Question kinetics 6 [V]ln|i|Cathodic Anodic=0ABABCurrent doesn’t increase when increasing the overpotentialElectrolyte cannot provide Li-ions, mass transport limited => a) and b)
  • 57. Different sources for theoverpotential/internal resistance(1) (3)(4)(2)1 2 3 4 , 1 2 3 4Total i Totalr r r r r           20 March 2013 57(1) ionic conduction A+ through the electrolyte(2) Charge transport over the electrolyte-electrode interface(3) solid state ionic conduction A or B(4) electronic conduction
  • 58. 20 March 2013 58EA Li+Correlation time between jumps:Diffusion of Li+Through a lattice:Relation with diffusion coefficient:n: number of jump directionsl: jump distanceCharge Transport, Ion transport electrodeTypical D ~ 10-12 cm2/s (106 smaller thanin the electrolyte!)0AEkTCorrelation e CorrelationnlD0 00whereAEkTnlD D e D 0: attempt frequency, k: Boltzmann constant: Activation barrierIonic transport through the electrodesps Li-ion jump in TiO2 (rutile)
  • 59. Different sources for theoverpotential/internal resistance(1) (3)(4)(2)1 2 3 4 , 1 2 3 4Total i Totalr r r r r           20 March 2013 59(1) ionic conduction A+ through the electrolyte(2) Charge transport over the electrolyte-electrode interface(3) solid state ionic conduction A or B(4) electronic conduction
  • 60. 20 March 2013 60Charge Transport, Electronic transportElectronic transport through the electrodesMaterials having vacancies for Li-ions aretypically semiconductors (no interstitial spacein metals!), hence poor electronicconductors.F
  • 61. 20 March 2013 61Improvement electronic conductivity: Example LiFePO4Carbon coating nano particles (or coating with another conducting material):Fe-Map Carbon-Map50 nmCharge Transport, Electronic transportNote: the coating needs to be transparent for Li-ions!e-Li+
  • 62. Discussion Nature paper20 March 2013 62
  • 63. Question 1The diffusion coefficient of Li-ion diffusion is 1 million times smaller in theelectrode material (host material) compared to the electrolyte.What would your solution be achieve faster (dis)charge rates?a) Make the electrode more porous (more electrolyte, less storage material)b) Reduce the size of the storage particlesc) Increase the amount of carbond) no clue20 March 2013 63Li+D = 10-12 cm2/sD = 10-6 cm2/s
  • 64. 20 March 2013 64Question 12dDiffusion distance:Diffusion time:d Dt2dtDd = 1 mD = 10-12 cm2/sd = 43 nmD = 10-12 cm2/st ~ 1 hourt = 6 sLi+
  • 65. 20 March 2013 65Disadvantages AdvantagesNano particles have low packing density(results in low energy density electrode) (-)Shorter cycle life due to surface reactionsthat decompose the electrolyte (-)Nano particles are less stable resulting in ashorter cycle lifeSupercapacitive behavior (charge in the doublelayer that can be released very quickly) leadingto high powerNano particles can host more strain resulting ina longer cycle lifeReactions that are otherwise impossible arepossible when nano-structured (example:reconstitution-displacement reactions)Nano sizing, pro’s and con’s
  • 66. Question 2What charge transport mechanism does the paper claim to be ratelimiting?a) Electronic conduction in the electrodeb) Li-ion conduction through the electrolytec) Li-ion conduction over the surface of the electroded) Li-ion conduction through the electrode20 March 2013 66
  • 67. Question 3What problems may be encountered charging a battery of anelectrical car (~50 kWh) in 6 secondsa) No problemb) Heating up batteryc) Size of the electrical cables and connectorsd) Both b and ce) No clue20 March 2013 67
  • 68. 50 kWh in 6 seconds50 kWh ~ 180 MJ180 MJ in 6 seconds = 30 MW (power of a small power plant)At 4 Volts the charge that needs to pass is 180/4=45 106 CoulombIn 6 seconds that leads to a current of 7.5 106 Amperes=> Huge connectors=> Large heat production in the batteryQuestion 320 March 2013 68
  • 69. Question 4The voltage curves represent:a) chargingb) dischargingc) no clueThe meaning of 30C is:a) (dis)charging in 30 minutesb) (dis)charging in 2 minutesc) (dis)charging in 30 secondsd) (dis)charging in 5 minutese) no clue20 March 2013 69
  • 70. Question 4The voltage curves represent:a) chargingb) dischargingc) no clueThe meaning of 30C is:a) (dis)charging in 30 minutesb) (dis)charging in 2 minutesc) (dis)charging in 30 secondsd) (dis)charging in 5 minutese) no clueLower voltages with higher rates => dischargeDecreasing voltage => dischargeMeaning of 30C: thirty times the full capacity in 1 hour,so full capacity in 2 minutes => b) and b)20 March 2013 70
  • 71. Question 5How will the electrode loading (mg/cm2) will affect the chargingtime?a) No effectb) Increase charging timec) Decrease charging timed) no clue20 March 2013 71
  • 72. Question 520 March 2013 72
  • 73. Li+ Li+Li+ Li+Li+ Li+Question 5 Diffusion distance:Diffusion time:d Dt2dtD20 March 2013 73
  • 74. Question 6Assume the charging time increases with increasing electrode loading(mg/cm2) (equivalent with increasing electrode thickness). Which chargetransport step do you conclude could to be rate limiting:a) Electronic conduction through the electrodeb) Li-ion conduction through the electrolytec) Li-ion conduction over the surface of the electroded) Li-ion conduction through the electrodee) Both a) and d)f) No clue20 March 2013 74
  • 75. Li+ Li+Li+ Li+Li+ Li+Question 6 Resistance that scales with the electrode thickness:a) Electronic conduction through the electrodeb) Li-ion conduction through the electrolytec) Li-ion conduction over the surface of the electroded) Li-ion conduction through the electrodee) Both a) and d)20 March 2013 75
  • 76. Energy density: amount of active material① : Al Foil② : PositiveElectrode③ : Separator④ :NegativeElectrode⑤ : Cu Foil~20-25 μm~10 μm~10 μm~300 μm~100 μm~100 μm~25 μm~20-25 μm~25 μm~10 μm~10 μm~100 μm~300 μmIncreasing Energy Density20 March 2013 76
  • 77. Increasing electrodeloading/thicknessTime constant relatedto the (discharge time)Increasing electronicresistanceIncreasing ionicresistanceIonic versus electronic conduction ofthe electrode
  • 78. Question 7By adding relatively more carbon black faster charging may be theresult of:a) Better electronic conduction in the electrodeb) better Li-ion conduction through the electrodec) Less storage material (LiFePO4) in the electroded) Both a) and c)e) No clue20 March 2013 78
  • 79. Question 720 March 2013 79Li+ Li+Li+ Li+Yes: Better electronic conduction in the electrode => a)But also Less storage material (LiFePO4) in the electrodeResults in less Li-ion flux required through the electrode => c)So answer d) both a) and c)Note:Low energy density!
  • 80. ConclusionsHigh power density High energy densityThin electrodes Thick electrodesPorous electrodes Dense electrodesNano structured electrodes Large particles(low packing density) (large packing density)“Diluted” electrodes Concentrated electrodes(carbon addition) (pure storage material)
  • 81. Improving the electrode morphology
  • 82. 20 March 2013 82Summarize charge transport(1a) Ionic transport through electrolyte: No problem(1b) Ionic transport through the electrolyte in the electrode In practice rate limitingRequires smart electrode design(2) Charge transfer from electrolyte to the electrode: Usually not rate limiting in Li-ionbatteries, it usually is in othertypes of batteries.(3) Ionic transport through the electrodes: Often Rate limiting, not for smallparticles!(4) Electronic transport through the electrodes: Often Rate limiting, can besolved with carbon
  • 83. Program BatteriesLecture 1: History, Applications, basic Electrochemistry and thermodynamicsFeb 27 of batteries: Redox reactions, Gibbs free energy, chemical potential,Nernst.Lecture 2: Solid state electrode reaction mechanisms, phase diagrams, phase rule,March 6 Gibbs Free energy, voltage profiles, capacities and energy densities.Li-ion batteriesLecture 3: Continue topics Lecture 2.March 13 Electrolyte stability: Pourbaix diagram, band structure solids, Cycle life.Lecture 4: Kinetics, Buttler-Volmer, diffusion, solid state diffusionMarch 20 Discussion on Science paper 6 seconds discharge.Lecture 5: Super capacitorsMarch 27 Future large energy density systems: Li-airLi-sulfurBatteries for large scale applications: Lead-acidLi-ionFlow-cellsSodium aqueous batteriesCosts and Performance comparison batteries/systems
  • 84. To do for next weekRead review Li-air and Li-S (BB)Collect questions for the last battery lecture

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