Chapter 4

1. Chapter 4 Electrochemical kinetics at electrode / solution interface and electrochemical overpotential

2. Effect of potential on electrode reaction • Thermodynamic aspect • If electrode reaction is fast and electrochemical equilibrium remains, i.e., Nernst equation is applicable. Different potential corresponds to different surface concentration. 2. Kinetic aspect If 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 concepts For Elementary unimolecular process Rate expressions At equilibrium Exchange rate of reaction

4. Some important empirical formula: Arrhenius equation According to Transition State Theory: Corresponding to steric factor in SCT

5. For electrode reactions For reversible state Nernst equation For irreversible state Tafel equation (1905) Overpotential How to explain these empirical formula?

6. Activated complex Standard free energy Reactant product Reaction coordinate Potential curve described by Morse empirical equation In electrochemistry, electrochemical potential was used instead of chemical potential (Gibbs free energy)

7. Fe3+ Cu Cu2+ Fe2+ 4.1.2 net current and exchange current Net current: Net current:

8. If cOx = cRed = activity = 1 at re At equilibrium condition standard exchange current Then i net = 0

9. 4.1.3 effect of overpotential on activation energy Ox Red Na(Hg)x Na+ + e Ox Na(Hg)x Na+ + e The energy level of species in solution keeps unchanged while that of the species on electrode changes with electrode potential. Red Na+ + e Na(Hg)x

10. transfer coefficient polarization

11. Fraction of applied potential alters activation energy  for oxidation and  for reduction Anode side cathode side

12.    x  is usually approximate to 1/2

13. 4.1.4 Effect of polarization on reaction rate Marcus theory: transition state theory

14. No concentration polarization If initial potential is 0, then

15. At equilibirum

16. 0

17. 4.2 Electrochemical polarization 4.2.1 Master equation Master equation

18. Theoretical deduction of Nernst equation from Mater equation At equilibrium Nernst equation

19. 4.2.2 Butler-Volmer model and equation Butler-Volmer equation

21. 4.2.3 discussion of B-V equation 1) Limiting behavior at small overpotentials Current is a linear function of overpotential

22. i / A Cathode Net current  / V Anode Charge transfer resistance False resistance

23. i / A Cathode Net current  / V Anode 2) Limiting behavior at large overpotentials One term dominates Error is less than 1% When cathodic polarization is larger than 118 mV

24. Taking logarithm of the equation gives: Making comparison with Tafel equation One can obtain

25. 0 -100 -200 -300 300 200 100 At 25 oC, when n = 1,  = 0.5 The typical Tafel slope

26. log i0 re Tafel plot:  log i plot

27. 4.2.4 determination of kinetic parameters For evolution of hydrogen on Hg electrode

28. lgi i i    active dissolution active dissolution:

29. transfer coefficient

30. Anode side cathode side

31. Master equation Nernst equation Butler-Volmer equation Tafel equation

32. 4.2.5 Exchange current density 1) The exchange current of different electrodes differs a lot

33. 2) Dependence of exchange currents on electrolyte concentration High 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 Acm-2. If exchange current of the electrode i0 > 10~100 Acm-2, it is difficult for the electrode to be polarized. When i0 < 10-8 Acm-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. If If Oxidation of electrode and reduction of impurity take place. There is net electrochemical reaction.

39. Single/couple electrode and Mixed potential Icorro Electrode 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 term Diffusion term The total polarization comprises of tow terms: electrochemical term and diffusion term.

42. i c Discussion : 1. id >> i >> i0 No diffusion ec polarization At large polarization: At small polarization : i 0 c

43. i  id i   log i 2. id i << i0 diffusion No ec is invalid

44. 0 -100 -200 -300 300 200 100 3. idi >> i0both terms take effect 4. i << i0, id no polarization (ideal unpolarizable electrode)

45. diff id ec  1/2 When id >>i0, diffusion control At half wave potential The half wave potential depends on both id and i0

46. diff id ec   ec diff lgid lgi0

47. Tafel plot without diffusion polarization 0 -100 -200 -300 300 200 100 -100 -200 0 -300 -400 300 200 100 400 Tafel plot under diffusion polarization

48. Tafel plot with diffusion control: Question: 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 4.4.1 potential step Using B-V equation with consideration of diffusion polarization at high polarization c At constant c, it  cOx(0,t)

50. at low polarization : is very small Constant for potential step