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1、2011 Spring Fuel Cell and Electrochemistry,Lecture 9 Kinetics of electrode reactions,Dynamic Equilibrium,The 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 bot
2、h the approach to equilibrium and the dynamic maintenance of that state. Thermodynamics describe only equilibrium. Exchange velocity: equilibrium features nonzero rates of conversion of A to (and vice versa), but those rates are equal. v0,The Arrhenius Equation and Potential Energy Surfaces,A is the
3、 pre-exponential factor k is the reaction rate coefficient EA activation energy,Transition State Theory,we focus on the special condition in which the entire systemA, B, and all other configurationsis at thermal equilibrium,Essentials of electrode reactions,we always saw that current is often limite
4、d wholly or partially by the rate at which the electroreactants 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 determinin
5、g the current. Instead, it is controlled by interfacial dynamics.,Tafel equation,Butler-volmer model of electrode kinetics,Suppose the electrode potential is equal to E. The cathodic and anodic activation energies are,Where , the transfer coefficient,Standard Rate Constant,It simply is a measure of
6、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 sluggish. The largest measured standard rate constants are in the range of 1 to 10 cm/s, and are associated with particularly simple electron-transfer p
7、rocesses. Molecular rearrangement upon electron transfer or multistep process can be very sluggish,The Transfer Coefficient,In most systems a turns out to lie between 0.3 and 0.7, and it can usually be approximated by 0.5 in the absence of actual measurements.,The transfer coefficient,a should gener
8、ally 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.,Exchange cur
9、rent,At zero current,At equilibrium, the bulk concentrations of and R are found also at the surface,Exchange current,Exchange current density,The current-overpotential Equation,Current-overpotential Equation,The current-overpotential Equation,The solid curve shows the actual total current, which is
10、the sum of the components ic and ia, shown as dashed 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
11、same as ia. In going either direction from Eeq, the magnitude of the current rises rapidly, because the exponential factors dominate behavior At extreme overpotential, the current levels off. the current is limited by mass transfer rather than heterogeneous kinetics.,Approximate Forms of the i- Equa
12、tion,(1)No Mass-Transfer Effects,The 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.
13、Even 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 tha
14、t exceeds 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 cu
15、rrent without a significant energy loss due to activation.,Approximate Forms of the i- Equation,(2) Linear Characteristic at Small For small values of x, the exponential ex can be approximated as 1 + x,Approximate Forms of the i- Equation,(3) Tafel Behavior at Large at large negative overpotentials, exp(-f ) exp(l- )f ,Approximate Forms of the i- Equation,Tafel Plots,Exchange Current Plots,Very Facile Kinetics and Reversible Behavior,When i0 becomes very large compared to any current of interest, The ratio i/i0 then approaches zero,Effect of Mass Transfer,
