Chapter 5 Mechanism of complex electrode reaction

1. Chapter 5 Mechanism of complex electrode reaction

2. 5.1.1 B-V equation for multi-electron process For a di-electron reaction Ox + 2e  Red Its mechanism can be described by At stable state

3. If

4. Therefore

5. 5.1.2 important consideration Consider a multi-step electrochemical process proceeding via the following mechanism Net result of steps preceding rds (r.d.s.) Net result of steps following rds Note: n’+n’’+1 = n

6. Since preceding step is in equilibrium, one can write Similarly, the succeeding reaction is also assumed to be fast, i.e., at equilibrium

7. Replacing above

8. After very laborious algebra, one can show that This equation correctly accounts for influence of redox pre-equilibrium on measured value of Tafel slop for the reaction scheme. Tafel slope is not Tafel slope of rate determining step, , rather it is (n’+)

9. without considering concentration effects By making comparison with The effect of potential change on activation energy of the cathodic and anodic reaction differ from that of simple electrochemical reaction

10. At small overpotentials, i.e., in the linear regime: The exchange current is n times that of the current of the r.d.s. Therefore, charge transfer resistance for multi-step is: At higher negative polarization At higher negative polarization

12. For a multi-electron reaction Ox + ne  Red Its mechanism can be described by Steps before rds, with higher i0 at equilibrium Steps after rds, with higher i0 at equilibrium

13. Therefore At small overpotential

14. At higher overpotential For cathodic current For anodic current

15. 5.1.3 Stoichiometric number multi-electron process

16. Surface region Mass transfer Chem. rxn O* Os Ob Desorption/ adsorption O* Bulk solution EC rxn R* Desorption/ adsorption R* Rs Rb Mass transfer Chem. rxn 5.2 surface transitions reactions:

17. homogeneous ( region close to electrode surface) place heterogeneous ( adsorption, desorption, new phase formation ) Foregoing / preceding parallel time Post, succeeding 5.2 Homogeneous proceding surface reactions Electrochemical -chemical (EC) Chemical-Electrochemical (CE)

18. Classification of couple electrode  homogeneous : • Mechanism with single electrochemical step • (1) CE – preceding reaction • e.g. Reduction of formaldehyde on mercury Dominant, no EC rxn. Adifficult to be reduced CE

19. O O O H2O e- O O O • Mechanism with single electrochemical step • (2) EC – following reaction EC

20. For evolution of hydrogen EC 2 M  H  2M + H2  H+ + M +e M  H H+ + M  H + e  M + H2  EE Possible proceeding/succeeding reactions: dissociation, complexities, dimerization, isomerization , formation of new phase (gas bubble, metal plating, conversion layer).

21. Mechanism with single electrochemical step • (3) ECcat – catalytic reaction

22. 5.2 Reaction mechanism-proceeding reaction For CreEre reaction as If K <1, then O is the main reactant which can be reduced at potential 2, while O* is easier to be reduced at potential 1than O. This means at 2, both O and O* can be reduced. At 1, For slow chemical kinetics: At 1, For fast chemical kinetics, O* can be replenished in time: 1 2 Limiting kinetic current Ik

23. At 2, For slow chemical kinetics: Curves I and II can be described by normal diffusion current when O and O* become totally depleted, respectively. Curve III is different.

24. At electrode surface, the concentration gradient of O and O* can be described as: At stable state: Very small At 1 If: No concentration polarization of O at electrode surface.

25. For O* at complete concentration polarization, its boundary conditions are: At x = , At x = 0, surface concentration: Therefore, the concentration gradient at electrode surface is:

26. The thickness of reaction region

27. Less than the effective thickness diffusion layer, why? At incomplete polarization: The limiting current resulted for CE mechanism is usually much larger than that of merely diffusion control kinetics, Why?

28. Cyclic voltammograms for the CE case. A  B; B + e - C When  = 0 V, c0 = 1 mM , A= 1cm2, DA = DB = DC = 10-5 cm2 /s, K =103, kf = 10-2 s-1, kb =10 s-1, T =25 ℃, at scan rates ,v of (1) 10 V/s; (2) 1 V/s; (3) 0.1 V/s; (4) 0.01 V/s.

29. When K=10-3, kf =10-2 s-1kb = 10 s-1, v=0.01~10 V s-1,  = 26 ~ 0.026.

30. v 2.0 1.5 1.0 0.5 0 6 4 2 8 10 Some diagnostic criteria for a CE situation . 1) ip /v1/2 will decrease as v increases 2) ipa /ipc will become large for small K or for large v

31. Both O and O* can be reduced The first wave corresponds the reduction of Cd2+ which is governed electrochemically, while the second wave corresponds to reduction of CdX-. Wave III is oxidation of Cd(Hg) which is governed by diffusion.

32. Assuming [S] >> [O] 5.3 Reaction mechanism-succeeding/parallel reaction 5.3.1 For EreCcat Electrocatalysis Catalytic decomposition of hydrogen peroxide S is the substrate whose concentration is usually much higher than that of O and R. Therefore, I mainly depends on Id, O.

33. Assuming [S] >> [O]

34. Solution is When Concentration of R is very low

35. Catalytic current at complete concentration polarization Catalytic current at other polarization

36. diffusion ECcat Increasing  

37. Here both behaviors going on: we are consuming Red with rate constant k, this will shift the ratio [Red]/[Ox]. So we expect the half wave potential to shift. But, we also are generating Ox with rate k. So we expect the wave to get bigger.

38. 5.3.2 For EreCir reaction For ECir mechanism:

39. The kinetic current is If is negligible The thickness of the reactive layer

40. EreCir for the EC reaction when the electron transfer reaction is reversible and the chemical rate constant kEC is extremely large The reduction in size of the reverse peak occurs since much of the R produced electrochemically is destroyed by the chemical step.

41. Scan rates on voltammograms A/B * = 0 V, c0=1 mM, A =1 cm2, D = 10-5 cm2 /s, and kf = 10 s-1. The vertical scale changes from panel to panel.

42. Conversion rate constant on voltammograms http://www.nuigalway.ie/chem/Donal/Surfaces11.ppt#274,13,Catalytic

43. (e) 10  = 0.1 0.4 0.01 0.2 Normalized current 0.0 0.1 0.2 0.01 60 180 120 0 60 (  1/2) n / mV Normalized current for several values of . For small , reversible by nature. For large , no reverse current can be observed, i.e., irreversible.

44. (e) 10  = 0.1 0.4 0.01 1.0 0.2 0.8 Ip,c/Ip,c Normalized current 0.0 0.6 0.1 0.2 0.4 0.01 0.2 60 180 120 0 60 (  1/2) n / mV lgv Diagnostic Criteria for EreCir mechanism: 1) ipa / ipc will approach 1 as v increases 2) ipc proportional to v1/2 3) pc will be displaced in the anodic direction as v decreases (30/n mV per 10  in v)

45. Electrochemical dimerization

46. Osol Oads ads sol Rsol Rads 5.4.1 Conversion involving adsorption rad 10* 0 coverage rde  0* maximum coverage 0* at equilibrium at large negative polarization : rxn, fast

47. So When make adsorption .id = io

48. For proceeding reaction, its polarization curves is similar to that of diffusion-control kinetics.

49. post kinetic : Using similar treatment : so For succeeding reaction, its polarization curves is similar to that of electrochemistry-control kinetics.

50. 5.4.2 Conversion of surface species Since R and O are confined, no diffusion If we use the Langmuir isotherm to describe the coverages of O and R make use of the Nernstian criterion