Presentation on theme: "Chapter 4 Electrochemical kinetics at electrode / solution interface and electrochemical overpotential."— Presentation transcript:
1 Chapter 4Electrochemical kinetics at electrode / solution interface and electrochemical overpotential
2 Effect of potential on electrode reaction Thermodynamic aspectIf electrode reaction is fast and electrochemical equilibrium remains, i.e., Nernst equation is applicable. Different potential corresponds to different surface concentration.2. Kinetic aspectIf electrode reaction is slow and electrochemical equilibrium is broken. Different potential corresponds to different activation energy.
3 4.1 Effect of potential on activation energy 4.1.1 basic conceptsFor Elementary unimolecular processRate expressionsAt equilibriumExchange rate of reaction
4 Some important empirical formula: Arrhenius equationAccording to Transition State Theory:Corresponding to steric factor in SCT
5 For electrode reactions For reversible stateNernst equationFor irreversible stateTafel equation (1905)OverpotentialHow to explain these empirical formula?
6 Potential curve described by Morse empirical equation Activated complexReactantproductReaction coordinateStandard free energyIn electrochemistry, electrochemical potential was used instead of chemical potential (Gibbs free energy)
7 4.1.2 net current and exchange current Fe3+Fe2+Net current:Net current:
8 If cOx = cRed = activity = 1 at re At equilibrium conditionstandard exchange currentThen i net = 0
9 4.1.3 effect of overpotential on activation energy OxRedNa(Hg)xNa+ + eOxNa(Hg)xNa+ + eThe energy level of species in solution keeps unchanged while that of the species on electrode changes with electrode potential.RedNa+ + eNa(Hg)x
32 4.2.5 Exchange current density 1) The exchange current of different electrodes differs a lotElectrode materialssolutionsElectrode reactioni0 / Acm-2Hg0.5 M sulfuric acidH++2e– = H2510-13Cu1.0 M CuSO4Cu2++2e– = Cu210-5Pt0.1 M sulfuric acid110-3110-3 M Hg2(NO3) M HClO4Hg22++2e– = 2Hg510-1
33 2) Dependence of exchange currents on electrolyte concentration Electrode reactionc (ZnSO4)i0 / Acm-2Zn2++2e– = Zn1.080.00.127.60.0514.00.0257.0High electrolyte concentration is need for electrode to achieve high exchange current.Use of Ag/AgCl electrode.
34 When i0 is large and i << i0, c is small. When i0 = , c=0, ideal nonpolarizable electrode, basic characteristic of reference electrode.When i0 is small, c is large.When i0 = 0, c = , ideal polarizable electrode
35 The common current density used for electrochemical study ranges between 10-6 ~ 1 Acm-2. If exchange current of the electrode i0 > 10~100 Acm-2, it is difficult for the electrode to be polarized.When i0 < 10-8 Acm-2, the electrode will always undergoes sever polarization.For electrode with high exchange current, passing current will affect the equilibrium a little, therefore, the electrode potential is stable, which is suitable for reference electrode.
38 Influence of impurity If an impurity undergoes reduction at electrode The influence of impurity on equilibrium is negligible.IfIfOxidation of electrode and reduction of impurity take place. There is net electrochemical reaction.
39 Single/couple electrode and Mixed potential IcorroElectrode with exchange current less than 10-4 A cm-2 is hard to attain equilibrium potential.
40 4.3 Diffusion on electrode kinetic When we discuss situations in 4.2, diffusion polarization is not take into consideration.When diffusion take effect :
41 At high cathodic polarization Therefore:Electrochemical termDiffusion termThe total polarization comprises of tow terms: electrochemical term and diffusion term.
42 Discussion :1. id >> i >> i0No diffusionec polarizationAt large polarization:At small polarization :cii0c
43 2. id i << i0diffusionNo ecis invalidi idilog i
44 3. id i >> i0 both terms take effect 300200100-100-200-3003. id i >> i0 both terms take effect4. i << i0, id no polarization (ideal unpolarizable electrode)
45 When id >>i0, diffusion control ec1/2At half wave potentialThe half wave potential depends on both id and i0
47 Tafel plot without diffusion polarization -100-200-300300200100Tafel plot without diffusion polarization-100-200-300300200100400-400Tafel plot under diffusion polarization
48 Tafel plot with diffusion control: i0 << i < 0.1 idElectrochemical polarizationi between 0.1id 0.9idmixed controli >0.9 iddiffusion controlQuestion:How to overcome mixed / diffusion control?please summarize the ways to elevate limiting diffusion current
49 4.4 EC methods under EC-diff mixed control potential stepUsing B-V equation with consideration of diffusion polarizationat high polarization cAt constant c, it cOx(0,t)
50 at low polarization :is very smallConstant for potential step
51 Numerical solution: i(0)= i is the current density at no concentration polarization at That is1230.52 tAt t = 0i(0)= ino concentration polarization
52 at time right after the potential step : it t1/2 is linear Whendiff controlEC controlDouble-layer chargeitCiat time right after the potential step : it t1/2 is linearExtrapolating the linear part to y axes can obtain
53 The way can be used to eliminate concentration polarization. Making potential jump to different can obtain i at different . Then plot i against c can obtain i~c without concentration polarization.The way can be used to eliminate concentration polarization.diff controlEC controlDouble-layer chargeitCic time constant sit > i due to charge of double layer capacitor
54 4.4.2 current step i ic cathodic current : 0 ic t Record c at different iccurrent stepcathodic current : 0 icconstant transition time when potential steps to next reaction.
55 i= ichargetccc(0)The slope of the linear par of c (t) can be used to determine n and .cc(0)When t0 the second term = 0
56 4.4.3 cyclic voltammetry (CV) for reversible single electrodeIPotential separation
57 for the reversible systems , use the forward kinetics only : can be solved only by numerical method:Nicholson-Shain equationfor fast EC reaction : i << i0 controlled by diffusion tramper coefficientn – number of electrons involved in charge transfer step0.1iv0.00.10.20.2is tabulatedx (bt) max =0.4958
60 For totally irreversible systems peak potential shift with scan ratefor slow EC reaction : ii0 ( quasi reversible, irreversible) in comparison to the same rate, equilibrium can not establish rapidly. Because current takes more time to respond to the applied voltage, Ep shift with scan rate .0.1iv0.00.10.20.2
62 4.5 effect of 1 potential on EC rate : 1=0, validate at high concentration or larger polarizationG = nFx1effect of 1:1. on concentration2. = 1
63 This means 1 has same effect on the forward (reduction) and reverse (oxidation) reaction.
64 When zO <0 ( minus ), n zO is large, therefore, for anion reduced on cathode , 1 effect is more significant.When zO n1 made c shift positivelyso: if 1 increases, i decreases
65 if: n = zO Cu2+ +2e- = CuMnO4 +e = MnO42 = H+ +e- = 1/2 H2if :zO = 0adsorption of anion slow reaction
66 without specific adsorption reduction of +1 cation…… reduction of 1 anion1 accelerates reduction of cation, slows reduction of anion
67 Rotation rate of RDE on reduction of 110-3 mol/L K2S2O8 without supporting electrolyte
68 Effect of potential of zero charge on polarization curve of RDE for reduction of K2S2O8 without supporting electrolyteOnly when the electrode potential is near to the potential of zero charge, 1 has large effect on the reaction rate, while at higher polarization, 1 take less effect.
69 Effect of concentration of supporting electrolyte (sodium sulfate) on the polarization curve of RDE for reduction of K2S2O8 .1: 0; 2: 2.8 10-3; 3: 0.1; 4: 1.0 mol/L Na2SO4Problem: how to eliminate the effect of 1?
70 4.6 EC kinetics for multi-electron process For a di-electron reactionOx + 2e RedIts mechanism can be described byAt stable state
75 At higher overpotential For cathodic currentFor anodic current
76 4.7 Marcus theory for electron transfer Effect of reactant, solvents, electrode materials and adsorbed species on electrochemical reaction.Electron-transfer between two coordination compounds.MOuter-sphere reactionMinner-sphere reactionNo strong interaction between electrode surface and reactant.Reduction of Ru(NH3)63+reactant, intermediate and product interact with electrode surface strongly.Reduction of O and oxidation of H
77 Microscopic theories of electron transfer Electron transfer reaction, a radiationless electronic rearrangement, sharing commonalities with radiationless deactivation of excited molecules.For a homogeneous redox reaction :O + R’ R + O’Electron transfer between tow isoenergetic points ----isoenergetic electron transfer
78 Franck-Condon principle: Nuclear coordinates do not change on time scale of electronic transitions.Reactants and products share common nuclear configuration at moment of transfer.Deduce expression for standard Gibbs energy of activation as a function of structural parameters of reactant, so as to calculate rate constant of the reaction.activation
79 Transition stateisoenergetic electron transferg: global reaction coordinate for 1 dimensional process, related to solvation.
82 Work of assemblying reactants, i. e Work of assemblying reactants, i.e., ion pair + electrostatic work to bring charged species next to charged electrode, wO and wR not considered.Improved modelPredictions from Marcus theory½ factor seems like first order term in expansion of , rest are correctionsClassical Butler-Volmer theory regards as constant, cannot predict potential dependence of .
83 Electron transfer occurs between empty levels of electrode (or species in solution) and filled levels of species in solution (or electrode) of the same energy.For reduction - energy of occupied level of electrode must match energy level of empty state of species in solution.For oxidation - energy of empty level of electrode must match energy level of occupied state of species in solution.Energy levels of metal and species in solution form a continuumOverall rate must be evaluated by summing or integrating over all energy matched pairs.
84 Since filled electrode states overlap with (empty) O states, reduction can proceed. Since the (filled) R states overlap only with filled electrode states, oxidation is blocked.
85 Number of electronic states of electrode in energy range E and E + dE is area of the electrodedensity of statesTotal number of states of electrode in given energy rangeAt absolute zero, energy of highest filled state is called Fermi level, At higher temperatures, thermal energy promotes electrons to higher levels Electron distribution given by Fermi function f(E)
86 concentration density function Number concentration of R species in the range between E + dE is
88 Rate Constant for Reduction Rate Constant for OxidationFURTHER CONSIDERATIONS• Electron transfer occurs almost entirely at the Fermi level• Rate constant proportional to local rate at Fermi level.• Integrals reduce to single value