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

17. 5.2 Homogeneous proceding surface reactions
place
homogeneous ( region close to electrode surface)
heterogeneous ( adsorption, desorption, new phase formation )
time
Foregoing / preceding
Post, succeeding
parallel
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. Mechanism with single electrochemical step (2) EC – following reaction
H2O EC

20. For evolution of hydrogenEC
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 1 than 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
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. Depends on cre not on diffusion
When K=10-3, kf =10-2 s-1 kb = 10 s-1, v=0.01~10 V s-1,  = 26 ~
v / Vs-1
lg
control
effect of preceding 10
-1.6 DP
Less effect (1) 1
-0.6 KI
0.01
1.6 KP
Depends on cre not on diffusion

30. v 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 2 4 6 8 10
0.5
1.0
1.5
2.0 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. 5.3 Reaction mechanism-succeeding/parallel reaction
5.3.1 For EreCcat
Electrocatalysis
Assuming [S] >> [O]
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. Increasing  
diffusion
ECcat

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

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

44. Diagnostic Criteria for EreCir mechanism:
180
120 60
60
0.2
0.0
0.2
0.4
(e)
Normalized current
(   1/2) n / mV
 = 10
0.1
0.01
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)
0.2
0.4
0.6
0.8
1.0
lgv
Ip,c/Ip,c

45. Electrochemical dimerization

46. 5.4.1 Conversion involving adsorption
Osol
Oads
Rads
Rsol
sol
ads
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

52. When bO bR,
Reversible, Nernstian, Langmuir, Monolayer

53. Electrochemistry of LB film

54. Dynamics of Br electrosorption on single-crystal Ag(100)
Journal of Electroanalytical Chemistry Volume 493, Issues 1-2, 10 November 2000, Pages 68-74

56. If bO >> bR
If bR >>bO
Pre-wave
post-wave
Dash line: without adsorption
Solid line: with adsorption

57. 5.5 Other mechanisms
5.5.1 EreEre mechanism

58. When  > 125 mV, two peaks becomes distinguishable
Shoulder
Changing shapes of cyclic voltammograms for the Er Er reaction scheme at different values of E0
When  > 125 mV, two peaks becomes distinguishable

59. CVs for the reduction of di-anthrylalkanes (An-(CH2)n-An) in 1:1 benzene/acetonitrile containing 0.1 M tetrabutylammonium perchlorate at a Pt electrode.

60. EreCreEre mechanism
It is much easier for C to be reduced than A

61. O  R
S  T
The figure shows the voltammogram for an ECE mechanism where the product (S) is more difficult to reduce than the starting material (O).

62. If the product (S) is more easy to reduce, slightly different behaviour is seen

63. 0.00
0.60
4.00
3.00
2.00
1.00
3.00
2.00
1.00
Current  = 0
(a) E
0.10 II I
Current  = 0.40
(c)
III IV
Current  = 0.05
(b)
5.00
(d)
CVs for the EreCirEre case obtained by digital simulation for E10 = 0.44 V, E20 = 0.20 V for different values of  =(kb/v)(RT/F); n1=n2=1.(a)  =0 (unperturbed Nernstian reaction ); (b) 0.05 ;(c) 0.40 ;(d) 2.

64. The ECE mechanism

65. CV of 4-Aminophenol
cyclic voltammograms recorded using a highly doped diamond electrode in an aqueous solution containing 3  10-3 mol dm‑3 4-aminophenol ( C6H4(OH)(NH2) ), and 0.5 mol dm‑3 sulphuric acid (H2SO4).4-aminophenol is an aromatic organic molecule, which may undergo a two step oxidation. The cyclic voltammograms show two oxidation peaks and two reduction peaks per scan
Figure 5.5 – CV of sample B67 in 3  10-3 mol dm-3 4-aminophenol & 0.5 mol dm-3 H2SO4 Various scan rates, Ag dag contact, geometric area of working electrode = 20 mm2

66. Diffusion equation (all x and t)
Summarization
Cre Ere
(as above)
Cre Eir
Diffusion equation (all x and t)
Reaction
Case

67. (as above, with kb = 0)
(equation for cY not required )
Ere Cir
Ere Cre

68. Ere C2ir

69. CreEre reaction diagram with zones for different types of electrochemical behavior as a function of K and  (defined in the following table).
Here,
The zones are DP, pure diffusion: DM, diffusion modified by equilibrium constant of preceding reaction: KP pure kinetics: and KI, intermediate kinetics.

70. Treatment depend on scan rate and on particular technique :
Dimensionless Parameters for Voltammetric Methods
Technique
Time
Parameter (s)
Dimensionless Kinetic parameter, , for CE EC
Chronoamperometry
and polarography t
(kf +kb ) t
k t
k Cz* t
Linear sweep and cyclic voltammetry
1/
[(kf +kb )/v] (RT/nF)
(k/v )
(RT/nF)
[(kcz* )/v]
Chronopotentiometry 
(kf +kb )  k
k Cz*
Rotating disk electrode
1/
(kf +kb )/ 
k/ 
k cz* /

71. for large kf and kb, p will be displaced as a function of v .
(30/n mV per 10 times v)

72. 5.5 Methods for mechanism study
Tafel Equation - “Simple” Electron Transfer
Assuming that ==0.5
For a simple 1 electron process
slope = 1 / 120 mV
For a simple 2 electron process
slope = 1 / 60 mV

73. Using the Butler-Volmer and Tafel Equation to Determine Multistep Reaction Mechanisms
Mechanism (A):
Cu2+ + 2e = Cu or
Mechanism (B):
Cu2+ + e = Cu+
Cu+ + e = Cu
For mechanism (A): n = 2 ,  = 0.5
Plotting logi against  gives a straight line with a gradient of - [60 mV]-1.
Similar arguments for reverse reaction: Cu  Cu2+ + 2e, gives a straight line with a gradient of [60 mV]-1.

74. Mechanism B (Forward Reaction)
Cu2+ + e = Cu+
Cu+ + e = Cu
assume (1) is rate determining step (r.d.s.):
For mechanism (B): n = 1 ,  = 0.5
Hence, for Cu deposition with Cu2+ + e  Cu+ (r.d.s.)
Cathodic section of Tafel plot (logi vs. )
gives a slope of - 1 / 120 [mV]

75. Mechanism B : Reverse Reaction
Cu2+ + e = Cu+
Cu+ + e = Cu
Reverse: Cu+  Cu2+ + e also r.d.s.
rapid step (2) in equilibrium. Can use Nernst eq. to find [Cu+]:
Tafel slope = 1 / 40 [mV]

78. 5.7 determination of intermediate
Rotating Ring-Disk Electrodes
Reversal techniques are obviously not available with the RDE, since the product of the electrode reaction, R, is continuously swept away from the surface of the disk.
addition of an independent ring electrode surrounding the disk.

79. By measuring the current at the ring electrode with the potential maintained at a given value, some knowledge about what is occurring at the disk electrode surface can be obtained.
For example, if the potential of the ring is held at a value at the foot of the O+ ne → R wave, product R formed at the disk will be swept over to the ring by the radial flow streams where it will be oxidized back to O (or “collected”).

80. The theoretical treatment of ring electrodes is more complicated than that of the RDE, since the radial mass transfer term must be included in the convective-diffusion equation.
The current at the ring electrode is given by
The solution to these equations yields the limiting ring current:

81. Levich equation for disk electrode:
Notice that for given reaction conditions (co0 and ) a ring electrode will produce a larger current than a disk electrode of the same area. Thus the analytical sensitivity of a ring electrode (i.e., the current caused by a mass-transfer-controlled reaction of an electroactive species divided by the residual current) is better than that of a disk electrode, and this is especially true of a thin ring electrode. However, constructing a rotating ring electrode is usually more difficult than an RDE.

82. RRDE experiments are usually carried out with a bipotentiostat,
which allows separate adjustment of ED and ER.
Several different types of experiments are possible at the RRDE:
Collection experiments, where the disk-generated species is observed at the ring
Shielding experiments, where the flow of bulk electroactive species to the ring is perturbed because of the disk reaction, are the most frequent.

83. Example for a collection experiment: the ring (b) measures the reduction of peroxide produced at the disk (a) during the electroreduction of oxygen.

84. the ring current is related to the disk current by a quantity N, the collection efficiency ; this can be calculated from the electrode geometry, since it depends only on r1, r2, and r3 and is independent of c, , DR,DO

85. 5.6.3 detection of intermediates using the same electrode (CV)
5.6.4 detection of intermediates using thin-layer cell and spectroscopy