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1、Towards a Sustainable Energy Future2011 SpringFuel Cell and ElectrochemistryLecture 9Kinetics of electrode reactionsEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004
2、-2011AsposePtyLtd.Towards a Sustainable Energy FutureDynamic EquilibriumEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Ener
3、gy FutureDynamic EquilibriumThe kinetic theory therefore predicts a constant concentration ratio at equilibrium, just as thermodynamics does;Kinetics describe the evolution of mass flow throughout the system, including both the approach to equilibrium and the dynamic maintenance of that state.Thermo
4、dynamics describe only equilibrium. Exchange velocity: equilibrium features nonzero rates of conversion of A to (and vice versa), but those rates are equal. v0Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesf
5、or.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureThe Arrhenius Equation and Potential Energy SurfacesAisthepre-exponentialfactorkisthereactionratecoefficientEAactivationenergyEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyrigh
6、t2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesf
7、or.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureTransition State Theorywe focus on the special condition in which the entire systemA, B, and all other configurationsis at thermal equilibriumEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile
8、5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureEssentials of electrode reactionswe always saw that current is often limited wholly or partially by the rate at which the ele
9、ctroreactants are transported to the electrode surface.This kind of limitation does not concern a theory of interfacial kinetics. More to the point is the case of low current and efficient stirring, in which mass transport is not a factor determining the current. Instead, it is controlled by interfa
10、cial dynamics.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureTafel equationEvaluationonly.CreatedwithAspose.Sl
11、idesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureButler-volmer model of electrode kineticsEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPr
12、ofile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureSupposetheelectrodepotentialisequaltoE.ThecathodicandanodicactivationenergiesareEvaluationonly.CreatedwithAspose.Slidesf
13、or.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureWhere , the transfer coefficientEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.C
14、opyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.
15、Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureStandard Rate ConstantIt simply is a measure of the kinetic facility of a redox couple. A system with a large k0 will achieve equilibrium on a short time scale, but a system with small k0 will be s
16、luggish. The largest measured standard rate constants are in the range of 1 to 10 cm/s, and are associated with particularly simple electron-transfer processes.Molecular rearrangement upon electron transfer or multistep process can be very sluggishEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5Cli
17、entProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureThe Transfer CoefficientInmostsystemsa turnsouttoliebetween0.3and0.7,anditcanusuallybeapproximatedby0.5intheabsence
18、ofactualmeasurements.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureThe transfer coefficienta should generally
19、 be a potential-dependent factor;In a typical chemical system, the free energies of activation are in the range of a few electron volts, but the full range of measurable kinetics usually corresponds to a change in activation energy of only 50-200 meV, or a few percent of the total.Evaluationonly.Cre
20、atedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureExchange currentAtzerocurrentAtequilibrium,thebulkconcentrationsofandRarefoundals
21、oatthesurfaceEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureExchange currentExchangecurrentdensityEvaluationon
22、ly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureThe current-overpotential EquationCurrent-overpotentialEquationEvaluationon
23、ly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyr
24、ight2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureThe current-overpotential EquationThe solid curve shows the actual total current, which is the sum of the components ic and ia, shown as d
25、ashed traces. For large negative overpotentials, the anodic component is negligible; hence the total current curve merges with that for ic. At large positive overpotentials, the cathodic component is negligible, and the total current is essentially the same as ia. In going either direction from Eeq,
26、 the magnitude of the current rises rapidly, because the exponential factors dominate behaviorAt extreme overpotential, the current levels off. the current is limited by mass transfer rather than heterogeneous kinetics.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright20
27、04-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureApproximate Forms of the i- Equation(1)No Mass-Transfer EffectsEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright20
28、04-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.
29、NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towar
30、ds a Sustainable Energy FutureThe exchange current can be viewed as a kind of idle current for charge exchange across the interface. If we want to draw a net current that is only a small fraction of this bidirectional idle current, then only a tiny overpotential will be required to extract it. Even
31、at equilibrium, the system is delivering charge across the interface at rates much greater than we require. The role of the slight overpotential is to unbalance the rates in the two directions to a small degree so that one of them predominates. On the other hand, if we ask for a net current that exc
32、eeds the exchange current, the job is much harder. We have to drive the system to deliver charge at the required rate, and we can only do that by applying a significant overpotential. From this perspective, we see that the exchange current is a measure of any systems ability to deliver a net current
33、 without a significant energy loss due to activation.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureApproximat
34、e Forms of the i- Equation(2) Linear Characteristic at Small For small values of x, the exponential ex can be approximated as 1 + xEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.
35、0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureApproximate Forms of the i- Equation(3) Tafel Behavior at Large at large negative overpotentials, exp(-f ) exp(l- )f Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly
36、.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureApproximate Forms of the i- EquationTafel PlotsEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspo
37、se.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011Aspos
38、ePtyLtd.Towards a Sustainable Energy FutureExchange Current PlotsEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy Futu
39、reVery Facile Kinetics and Reversible BehaviorWheni0becomesverylargecomparedtoanycurrentofinterest,Theratioi/i0thenapproacheszeroEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.
40、Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy Fut
41、ureEffect of Mass TransferEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Towards a Sustainable Energy FutureEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.
