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Chapter 3 Kinetics of Electrode Reactions

Electrochemical Camp. Chapter 3 Kinetics of Electrode Reactions. Speaker: Chen-Ya Tseng Advisor: Kuo-Chuan Ho August 11, 2011. Electro-Optical Materials Laboratory, Department of Chemical Engineering, National Taiwan University. Outline. Review homogeneous and heterogeneous kinetics

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Chapter 3 Kinetics of Electrode Reactions

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  1. Electrochemical Camp Chapter 3Kinetics of Electrode Reactions Speaker: Chen-Ya Tseng Advisor: Kuo-Chuan Ho August 11, 2011 Electro-Optical Materials Laboratory, Department of Chemical Engineering, National Taiwan University

  2. Outline • Review homogeneousand heterogeneous kinetics • Derive the current - overpotential equation and explain the meanings of each term • Approximated forms of the current – overpotential equation (One step process) • Multistep process

  3. Electrode reaction • A heterogeneous reaction appearing at electrode-electrolyte surface. • Reaction rate bears the units of mol s-1 cm-2. ( cf. homogeneous reaction rate mol s-1 cm-3) • Electrochemical reaction rate is a function of concentration, temperature, and applied potential. Pathway of a general electrode reaction 不改變活化能 改變活化能

  4. ka B A kf, kb [=] s-1 CA, CB [=] mol/cm3 Vf, Vb, Vnet [=] mol/s cm3 kb 1st order homo. rxn. 一階均相反應 Dynamic equilibrium Equilibrium: Consider a simple, unimolecular elementary reaction (1) At equilibrium, Vnet = 0 (2) Nonzero rates of conversion of A to B and vice versa, but those rates are equal The exchange velocity of the reaction, V0 (交換速度) (3)

  5. A: Frequency factor EA: Activation energy T: Temperature EA,f EA,b The Arrhenius equation and potential energy surfaces (4) • Both reactants and products occupy minima on the energy surface. • The path along the reaction coordinate connects two minima. It must rises, passes over a maximum, then falls into the product zone. Simple representation of potential energy changes during a reaction

  6. κ : Transmission coefficient (from 0 to 1) K : Boltzmann const. h : Plank const. △G≠: Standard free energy Transition state theory • Reactions proceed through a well defined transition state (過度狀態) or activation complex (活化錯合物). • The activated complex (or transition state) is the configuration of maximum free energy. Free energy changes during a reaction (5)

  7. kf R O + ne kb Essentials of electrode reactions At equilibrium: ObeysNernst equation (6) Nonequilibrium: Obeyscurrent (i) – overpotential (η) relationship For many reactions taking with an appreciable current, the overpotential can be expressed by an empirical equation named Tafel equation(塔弗方程式). A successful electrode kinetic model / theory must predict Nernst equation (6) and explain the frequent validity of Tafel equation (7). (7)

  8. kf R O + ne ka kf, kb [=] cm/s CA, CB [=] mol/cm3 Vf, Vb, Vnet [=] mol/s cm2 1st order hetero. rxn. 一階異相反應 Electrochemical reaction (Heterogeneous rate expression) (8) 異相反應速率表示式中的濃度是表面的濃度 !! (9) (10)

  9. Effects of potential on energy barriers 氧化還原能量障壁相同，整個系統處於平衡狀態，E = Eeq。 電位調得較正，E > Eeq氧化(還原)的能障降低 (提高)，淨反應是氧化。 電位調得較負，E < Eeq還原(氧化)的能障降低(提高)，淨反應是還原。 Simple representation of standard free energy changes during a faradic process

  10. Derive an equation relating potential to rate constant (1) • If the potential is shifted to a more positive value, the free energy of electrons is lowered by nF(E-E0’). (ΔG = -nF(E-E0’)) • In developing a theory of electrode kinetics, it is convenient to express potential against a point of significance to the chemistry of the system. • Two natural reference points (a) The equilibrium potential Eeq (b) The formal potential E0’ Effects of a potential change on the standard free energies of activation for oxidation and reduction.

  11. Derive an equation relating potential to rate constant (2) (11) (12) (13) (11)代入(14) (12)代入(13) 令f = F/RT (14) (15) kf, kb寫成阿瑞尼士 方程式的型式 !! (16)

  12. The current – potential characteristic 利用k0對(15)(16)進行代換 (17) The current-potential equation (電流電位表示式) (18) 將(17)(18)代入(10) (19) Fundamental equation for electrochemical kinetics

  13. Interpretation of the standard rate constant k0 (1) Further insight into the boxed regions in (15) (16) (1) Independent of potential (2) Equal to the rate constant at E = E0’ Consider a special case (under two conditions) (1) Electrochemical reaction is at equilibrium. (能士特方程式適用) (2) The same concentration of O and R in the bulk solution. (Co* = CR*) E0’ is the potential where the forward and reverse rate constants have the same value, which is called the standard rate constant, k0 (標準速率常數).

  14. Interpretation of the standard rate constant k0 (2) • A measure of thekinetic facilityof a redox couple. (The larger the k0, the shorter the time required to achieve equilibrium.) • A process witha simple electron transferusually hasa large k0, while that involvesmolecular rearrangement upon electron transferusually hasa small k0. • Ranges from10 to 10-9 cm/s.

  15. ｝ (20) Interpretation of the transfer number α (1) Relationship of the transfer coefficient to the angles of intersection of the free energy. α, transfer number (轉移係數)

  16. Interpretation of the transfer number α (2) • A measure of the symmetry of the energy barrier. • It is a potential dependent factor. In most systems, it turns out to lie between 0.3 and 0.7, and can usually be approximated by 0.5 in the absence of the measurements. • In the great majority of the experiment, the applied potential over which kinetic data can be collected is narrow, so α can be regarded as a constant.

  17. Test the validity of the current – potential equation (1) At equilibrium: 1. Net current is zero (i = 0) 2. Nernst equation holds (Eeq vs. CO* and CR*) From equation (19) (21) (23) (22) Current – potential equation has passed the first test of compatibility at equilibrium !! 熱力學上的能士特方程式可以由動力學的式子在平衡的條件下得到。

  18. The exchange current i0 • At equilibrium, i = 0, we define ic = ia = i0 (交換電流) (24) (22)式兩邊冠上-α次方，對(24)式進行代換 (25) 整體濃度Co*及CR*固定，交換電流 (密度)io或jo就固定了。 (26) i0或j0與k0密切相關，也是衡量 電化學學反應發生快慢的指標。 (27)

  19. Test the validity of the current – potential equation (2) Non-equilibrium conditions: Obeys the i – ηrelationship 將(19)式除以(26)式 (28) 利用(22)式代換 (29) Current – overpotential equation (電流過電位方程式) (30) η = E - Eeq

  20. i/il ilc = il Total current i0 ic Eeq η, mV -i0 ia ila = -il The current – overpotential curve • For large negative η, ia isnegligible; hence the total current is almost ic. • For large positive η, ic is negligible; hence the total current is almost ia. • At extreme η, the current levels off, and is limited by mass transfer rather than heterogeneous kinetics. Current – overpotential curves for the system O + e = R with α = 0.5, T = 298 k, ilc = -ila = il, and i0/il = 0.2

  21. Special cases of the i – η equation (1) Case (a) No mass transfer effects Criteria: 對溶液充分攪拌，電極反應電流足夠小的前提下成立。 Equation (30) becomes Butler – Volmer equation 巴特勒 - 伏耳末 方程式 (31)

  22. j, μA/cm2 (a) (b) (c) η, mV Effect of j0 on η required to deliver j j0is a measure of any systems ability todeliver a net current density without a significant energy loss due to activation. η = η ct. + η conc. Concentration 濃度過電位 (質傳過電位) Charge transfer 電荷傳遞過電位 (活化過電位) (a) j0 = 10-3 A/cm2 (b) j0 = 10-6 A/cm2 (c) j0 = 10-9 A/cm2 O + e = R T = 298 K α = 0.5 (Neglect mass transfer effects)

  23. α= 0.75 j = μA/cm2 α= 0.5 α= 0.25 η, mV Effect of α on j – η curve α = 0.25 α = 0.50 j0 = 10-6 A/cm2, T = 298 K, O + e = R

  24. Applicable when Special cases of the i – η equation (2) Case (b) Linear characteristic at small η Neglect higher order terms (32) 交換電流愈大， 電荷傳遞阻力愈小 電極反應動力愈快 (33)

  25. logl i l Slope = (1-α)nF/2.303RT Slope = -αnF/2.303RT logi0 η, mV Special cases of the i – η equation (3) (7) Case (C) Tafel behavior (31) For large values of η, one of the bracketed terms becomes negligible (1) Cathodic, η < 0, i > 0 (34) (2) Anodic, η > 0, i < 0 (35) Tafel plot α= 0.5, T = 298 k, O + e = R

  26. Special cases of the i – η equation (4) Case (C) Tafel behavior Criteria: The back reaction contributes less than 1 % of the current Cathodic current dominates Anodic current dominates

  27. Characteristics of Tafel equation • Absence of mass transfer effects. • The electrode kinetics is sluggish, that is to say, no significant current can be observed except at high overpotential. • The faradic process is effectively unidirectional, and, therefore, chemicallyirreversible.

  28. ｛ Slope: -αnF/2.303RT Intercept: log i0 Special cases of the i – η equation (5) Case (d) Quasi-reversible Rearrange the Butler – Volmer equation (31) This approach has the advantage of being applicable to electrode reactions that are not totally irreversible. (36) A plot of log[i / 1-enfη] vs. η gives We can calculate α and i0 from the slope and intercept.

  29. Special cases of the i – η equation (6) Case (e) Reversible behavior (Very facile kinetics) When i0 >> i, equation (30) gives (37) 電極表面 的濃度 利用能士特方程式的 指數形式進行代換 (38)

  30. Characteristics of the reversible system • No kinetic parameters are present since the kinetics are so facile that no experimental manifestations can be seen. • The electrode potential (E) and surface concentration of O and R, regardless of the current flow, are linked by an equation of the Nernst form. • An electrochemical system in which the charge transfer interface is always at equilibrium can be called a reversible or a nernstian system(可逆的、能士特的系統).

  31. Special cases of the i – η equation (7) Case (f) Taking mass transfer effects into account According to equation (30) (30) 利用第一章的(1.4-9), (1.4-10)進行代換 (39) (38) (40)

  32. Concentration overpotential dominates Activation overpotential dominates Special cases of the i – η equation (8) Case (f) Taking mass transfer effects into account At small overpotentials (αnfη<< 1), the complete Taylor expansion of equation (30) gives 對於多變數方程式的泰勒展開式。附錄A.2 P.777-778 (41) (42) (43)

  33. Special cases of the i – η equation (9) Case (f) Taking mass transfer effects into account At large overpotentials (40) (1) Cathodic, η < 0, i > 0 (44) (2) Anodic, η > 0, i < 0 (45)

  34. Example 1 – Problem 3.2 (a) (b) (c)

  35. Example 2 – Problem 3.5 (1)

  36. Example 2 – Problem 3.5 (2)

  37. Multistep process • Most electrode processes are mechanisms of several steps. • Electrode reactions show complex behavior, and one can obtain a relation between current and potential, in which we have to take into account the potential dependences of all steps and the surface concentrations of all intermediates. • One can simplify the analysis by recognizing the rate determining step (RDS).

  38. Rate – determining electron transfer • If the mechanism is an electrode process, the RDS can be a heterogeneous electron – transfer reaction. • Truly elementary electron – transfer reactions always involve the exchange of one electron. • A rate – determining electron transfer is always one electron process, and the results we have derived for one step process can be used to describe the RDS.

  39. Quasireversible and irreversible multi - step process • If a multistep process is neither nernstian nor at equilibrium, the details of the kinetics will affect its behavior in electrochemical experiments. • For most mechanism, equation (5) is of limited direct utility, for O' and R' are intermediates, whose concentration cannot be controlled directly. • One can use the presumed mechanism to re-express O’ and R’ in terms of controllable species, such as O and R .

  40. Summaries • Most electrode processes are mechanisms of several steps. • One can simplify the analysis by recognizing the RDS. • Multistep process at equilibrium---Nernst equation • Very facile multistep process---Equation of Nernst form • Quasi-reversible and irreversible. Thanks for your attention！

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