电极过程动力学 (7).pdf
5-1 CHAPTER 5:OVERPOTENTIALS AT POLARIZED ELECTRODES 1.The Overpotential and its components 2.The activation overpotential 3.The concentration overpotential 4.The ohmic overpotential 5.Polarization curves under mixed overpotential control 5-2 CHAPTER 5 OVERPOTENTIALS AT POLARIZED ELECTRODES 1.The Overpotential And Its Components Processes taking place at an appreciable rate,i.e.all practical processes where current is flowing,deviate from thermodynamic equilibrium.This deviation from reversibility is associated with an overpotential,i.e.,a potential in excess of the equilibrium potential E,required to drive the reaction at the specified rate.Hence,the potential difference,V,applied across the electrodes in a current carrying electrochemical cell is given by:V=E+Of the two components on the right,is by far the more intriguing one since it provides the driving force for the current flow and is intimately linked to the current distribution.A current carrying electrode is said to be“polarized”or to exhibit overpotential.The overpotential can be regarded as the penalty we pay in order to drive the reaction away from equilibrium.The higher the current density,the larger the overpotential required.The overpotential is consumed in the electrochemical cell by various dissipative processes associated with different resistive mechanisms for current passage.Although numerous dissipative processes can be identified,it is convenient,particularly for engineering purposes to consider the overpotential in terms of three components:activation,concentration,and ohmic,each acting in dif-ferent regions of the cell.a.Ohmic(i-r)overpotential:.Associated with ohmic losses mainly in the bulk of the electrolyte phase,but occasionally also significant in the electrodes and leads.After i-r drops in bulk phases and leads taken into account,some i-r drop may persist-associated with electrode surfaces.Most commonly caused by some type of oxide film,which is poor conducting.b.Activation overpotential:caused by limiting rate at which some steps in electrode reactions can proceed.Energy barrier and hence activation energy are involved.c.Concentration overpotential:arises from decrease in concentration of reactants and increase for products relative to bulk phase,because of mass transport limitations.These resistive mechanisms or overvoltages depend on the current density(often non-linearly),and different mechanisms are dominant at different regions of the electrochemical cell.The current is adjusted along the electrodes such that at any local point the overall voltage balance is maintained,Note that a is limited to the surface and does not extend beyond the double layer,i.e.,100 A.The concentration overpotential C,is at the surface and typically extends to few mm or less depending on the convective flow.In stagnant electrolyte C changes with time and will eventually extend between the electrodes 5-3 Since the expressions for the overpotentials involve the current implicitly,the resulting expression relating the local current to the applied voltage is not simple.Rather than solving it rigorously,the concept of controlling overpotential is conveniently introduced.Accordingly,the current distribution is specified mostly by only one dominant overpotential model referred to as the controlling overpotential.Notice:Overpotentials are losses,therefore,a close circuited battery will operate at a voltage lower than its open circuit EMF.Similarly,an electrolysis or plating cell will require voltage higher than what is indicated from thermodynamic analysis.Sign Convention:Overpotentials are dissipative always working against us.+Anodic overpotentials and current densities:Positive-Cathodic overpotentials and current densities:Negative 5-4 5-5 Polarization Curves aCaARTFRTFeeii0 Alternate form:aaRTFnRTFneeii0 A +C n o Transfer Coefficients:+1 o i0(exchange current density):100 10-16 A/cm2 5-6 THE BUTLER-VOLMER EQUATION aCaARTFRTFeeii0 Approximations:(1)Tafel(High Field):|a|RT/F 0.12 V or i i0 ibaiFRTiFRTiiFRTaalnlnlnln00 (2)Linear(Low Field):|a|RT/F 0.02 V or i i0 ibiiFnRTiiFnRTa00 (3)Linear Extrapolation:a=a”+b”i A +C nTransfer Coefficients:a”=a0 0.343 b b”=0.343 b/i0 b=2.3 RT/F-Tafel Slope iV Tafel Tafel Linear 5-7 5-8 5-9 The Exchange Current Density i0 The electrode-electrolyte interface involves a dynamic current balance:Equilibrium Anodic Current Cathodic Current i0 varies across a very broad range:103 10-16 Nickel:i0 10-6 A/cm2 i 10-1 10-2 A/cm2 Zinc:i0 10-1 A/cm2 i 10-1 10-2 A/cm2 Li:i0 1-10 A/cm2 i 10-2 10-3 A/cm2 i0=f(Ce,T,electrolyte composition,substrate only in redox reactions)CONCENTRATION EFFECT:i0 Ce,reactant for most di-valent ions i0,(Ce)=i0,(Creference)Ce/Creference i+i-i+=|i-|=i0 i+-i-=i(anodic,positive)i-=i+=i(cathodic,negative)5-10 The Transfer Coefficients A,C A&C represent the fraction of the overpotential that is spent in accelerating or decelerating the anodic and cathodic processes,respectively.In deposition:A decelerates the anodic process C accelerates the cathodic process.Typically,Temperature dependence:Theoretically -None or weak Practically -T(Since:F/RT is temperature independent)A +C n 5-11 5-12 SIGNIFICANCE OF THE ACTIVATION OVERPOTENTIAL Low overpotential sought for primary cell reaction to minimize energy loss High activation overpotential for suppressing competing reactions Corrosion protection is often based on arranging high overpotential for hydrogen evolution M Mn+ne nH+ne n/2 H2 M+nH+Mn+n/2 H2 In plating,high activation overpotential is desired for attaining level deposits Low i0 minimizes roughness and dendritic growth Low C corresponds to a high Tafel slope,indicating a large increase of the overpotential with the current density.This produces uniform thickness deposits(high throwing power,or high Wa number)In batteries,fuel-cells and industrial electrolysis it is essential to have low activation overpotential(high surface area electrodes are often employed)Alloy deposition is often based and controlled by activation overpotential The activation overpotential may extend the range of aqueous electrochemistry by suppressing hydrogen and oxygen evolution MEANS OF CONTROLLING AND MODIFYING THE ACTIVATION OVERPOTENTIAL Catalytic electrodes(only in redox reactions)Elevated temperature lowers a a can be enhanced by raising the interfacial concentration Additives and contaminants typically increase a 5-13 THE CONCENTRATION OVERPOTENTIAL BECCCnnFRT LBEiiCC1 LCiinnFRT1 Anodic:i,C are positive Cathodic:i,C are negative NrBLtnFDCi)1(NrEBtCCnFDi)1()(LCiinnFRT|1 C CB,B CE,E ViiL 5-14 SIGNIFICANCE OF THE CONCENTRATION OVERPOTENTIAL Maximum reaction rate Energy dissipation when i iL Minimal below iL Need for forced convection Source for roughness in plating and electroforming Porous structures A problem in dilute,stagnant electrolytes MEANS OF MINIMIZING THE CONCENTRATION OVERPOTENTIAL High bulk reactant concentration Effective agitation Reduce(eliminate)supporting electrolyte THE OHMIC OVERPOTENTIAL Linear with the current density Inversely proportional to the conductivity Strongly affected by the supporting electrolyte L the current path is not known a-priory,except in trivial geometries Li 5-15 Transport effects on the kinetically controlled current 5-16 5-17 Voltage Balance in Electrochemical Cells Wearequiteinterestedinthepotentialdistributioninelectrochemicalcells,since,itistheparameterwhichdeterminesthecurrentdistribution.Thepotentialappliedexternallybetweentheelectrodesincludes,aswehaveseen,athermodynamiccomponent(standardpotential,E0)andanoverpotentialwhichisdissipatedthroughoutthecellintermsofmainlythreedissipativemechanisms.Wecanformallywrite:AV=E+a+C+6-23 Aswehavediscussed,bothEandaarepresentonlyattheelectrode/electrolyteinterface,withintheextremelynarrow,0,doublelayer.Theconcentrationoverpotential,C,insystemsinvolvingfreeorforcedconvectionpersistsacrossarelativelythin,0(m),masstransport(diffusion)boundarylayerneartheelectrodes.Theohmicoverpotential,ontheotherhand,isdissipatedthroughouttheelectrolyteintheinterelectrodegap.Consequently,wecanrewritemoreexplicitlyEquation623,associatingvariousoverpotentialswiththecorrespondingelectrodes:AAA CCCACAaCCaCVVVEE 6-24WeRecallthatthecathodicoverpotentialsarenegative,hencetheabsolutevaluesofalltheoverpotentialscontributetothevoltageacrossthecell:ACACAAA CCCaCaCVVVEE 6-24Here,thestandardpotentialsandtheoverpotentialsassociatedwitheachelectrodewerelumpedtogether.Theohmicoverpotentialwhichcannotbelinkedtoanyspecificelectrodestandsalone.Itshouldberememberedthattheoverpotentialsareallfunctionsofthecurrentdensity,andofpositioninthecell.WecanthereforerewriteEquation624:(,)(,)(,)(,)(,)ACACAAA CCCaCaCVVVEEi x zi x zi x y zi x zi x z Heretheactivationandconcentrationoverpotentialswereconsideredasessentiallytwodimensionalthinlayersontheelectrodesandtheohmicoverpotentialwasconsideredtovarythroughouttheentirecell.Recallthatoverpotentialarelossesandalwaysworkagainstus.Inaplatingcellorduringchargingofabatterywemustputinexcessvoltage,inabatterydischargeweobtainlessthanthestandardpotential.Thehigherthecurrentdensity,thelargerarethelosses.Inordertodecreaselosseswewanttolowerthecurrentdensity.Thisisachievedbyeitherloweringthecurrentorincreasingtheelectrodearea.Thepenaltyisalargercapitalequipmentinvestment.5-18 Synthesisofoverallpolarizationcurvefromitscomponents:Overpotentialcomponentsandtheirsynthesis(FromJ.Newman,ElectrochemicalSystems,JohnWiley,1968).Note:Wecansynthesizeacurvebypickingacurrentdensityandaddingtheoverpotentialcomponents,i.e.,IV.Thereverseprocedure(Vi)ismuchmorecomplex.Wecandothisalsonumerically,Calculate,e.g.,inExcelsheet,foranumberofgivencurrents,i1,i2,i3,:Anode OhmicCathode,11,101lnln(1)CAAaAAAALERTiFiRTinFi,11,101lnln(1)CCCaCCCCLERTiFiRTinFiAddingthecomponentsati1,i2,i3,etc.11,1,1,1,1,1ACACAAA CCCaCaCVVVEE1.11A Cli 5-19 Analysisofanoperatingcell:Effectofoperatingconditions(controllingmechanism)How can you tell experimentally where you are located?Ohmic control:Vary cell gap,add supporting electrolyte,look for linear dependence on current,insensitive to flow.Not very sensitive to T.Activation control:Very sensitive to T.Insensitive to cell geometry or gap.Sensitive to additives Mass transport control:Sensitive to agitation,reactant conc.Insensitive supporting electrolyte.V i V iV i V i 5-20 Operating Curves for a Process:Copper electrorefining:Cu+2e Cu EC=0.34 Cu Cu+2e EA=0.34 E=0.34 0.34=0 V Copper electrowinning:2Cu+4e 2Cu EC=0.34 2H2O O2+4H+4e EA=1.23 E=1.23 0.34=0.89 V +V I 0.34 V+V V I 0.34 V 1.23 V V Cu+2e Cu Cu Cu+2e 5-21 Water Electrolyzer:4H+4e 2H2 EC=0 2H2O O2+4H+4e EA=1.23 E=1.23 0=1.23 V H2-O2 Fuel Cell:2H2 4H+4e EC=0 O2+4H+4e 2H2O EA=1.23 E=0 1.23=-1.23 V +V I 0 V 1.23 V V 4H+4e 2H22H2 4H+4e+V I 0 V 1.23 V V 4H+4e 2H22H2 4H+4e O2+4H+4e H2O
