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
Exchange rate of reaction
At equilibrium

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
How to explain these empirical formula?

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

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

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

9. 4.1.3 effect of overpotential on activation energy
transfer coefficient
polarization

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

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

12. 4.1.4 Effect of polarization on reaction rate
Marcus theory: transition state theory

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

14. At equilibrium

16. 4.2 Electrochemical polarization
4.2.1 Master equation
Master equation

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

18. Butler-Volmer equation

20. 4.2.3 discussion of B-V equation
1) Limiting behavior at small overpotentials
Current is a linear function of overpotential

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

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

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

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

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

26. 4.2.4 determination of kinetic parameters
For evolution of hydrogen over Hg electrode

27. 4.2.5 Exchange current density
1) The exchange currents of different electrodes differ a lot
Electrode materials
solutions
Electrode reaction
i0 / Acm-2 Hg
0.5 M sulfuric acid
H++2e– = H2
510-13 Cu
1.0 M CuSO4
Cu2++2e– = Cu
210-5 Pt
0.1 M sulfuric acid
110-3
110-3 M Hg2(NO3) M HClO4
Hg22++2e– = 2Hg
510-1

28. 2) Dependence of exchange currents on electrolyte concentration
Electrode reaction
c (ZnSO4)
i0 / Acm-2
Zn2++2e– = Zn
1.0
80.0
0.1
27.6
0.05
14.0
0.025
7.0
High electrolyte concentration is need for electrode to achieve high exchange current.

29. When i0 is large and i << i0, c is small.
When i0 = , c=0, ideal nonpolarizable electrode
When i0 is small, c is large.
When i0 = 0, c = , ideal polarizable electrode

30. 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.

33. 4.2 potential on electrode kinetics
Shift of potential
1 keeps constant
The nature of potential -dependence of rate

34. At equilibrium: cox(0,t)= cox0
i0,c=i0,a=i0
Master equation:

35. Master equation:
At equilibrium
Nernst equation

36. Master equation:
Butler-Volmer equation

37. Butler-Volmer equation
at small overpotentials
Charge transfer resistance

38. at large overpotentials
Tafel equation

39. 4.3 Diffusion on electrode kinetic
When we discuss situations in 4.2, we didn’t take diffusion polarization into consideration
When diffusion take effect :

40. At high cathodic polarization

41. Taking logarithm yields
Therefore:
Electrochemical term
Diffusion term
At this time the total polarization comprises of tow terms: electrochemical term and diffusion term.

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

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

44. 3. id  i >> i0 both terms take effect
4. i << i0, id no polarization

45. diff id
When id >>i0 ec 
1/2

46. id
diff  ec

47. Tafel plot under diffusion polarization
400
300
200
100
-100
-200
-300
-400
Tafel plot under diffusion polarization

48. i0 << i < 0.1 id Tafel plot with diffusion control:
Electrochemical polarization
i between 0.1id  0.9id mixed control
i >0.9 id diffusion control
How to overcome mixed / diffusion control?
The ways to elevate limiting diffusion current

49. 4.4.1 potential step 4.4 EC methods under EC-diff mixed control
Using B-V equation with consideration of diffusion polarization
at high polarization . c
c  constant
it  CO(0,t)

50. at low polarization :
is very small
Constant
Constant

51. i(0)= i is the current density at no concentration polarization at 1 2 3
0.5
2 t
is the current density at no concentration polarization at 
t=0
i(0)= i
no concentration polarization

52. at time right after the potential step : it t1/2 is linear
When it
at time right after the potential step : it t1/2 is linear
Extrapolating the linear part to y axes can obtain
Double-layer charge
i
EC control
diff control C

53. Making potential jump to different  can obtain i at different 
Making potential jump to different  can obtain i at different . Then plot i against c can obtain i~c without concentration polarization.
The way to eliminate concentration polarization effect
c  time constant s
it > i due to charge of double layer capacitor

54. 4.4.2 current step 3.8.2 Current step / jump iic t
c at different i0
cathodic current : 0  ic
3.8.2 Current step / jump

55.  t c c
c(0)
  transition time when potential step to next rxn.
i= i charge

56. The slope of the linear relationship between c (t) can be used to determine n and .
When t0 the second term = 0

57. 4.4.3 cyclic voltammetry (CV)
Typical CV diagram for reversible single electrode  I
Potential separation

58. For typical CV diagram of irreversible single electrode I
For typical CV diagram of irreversible single electrode
for fast EC reaction : i << i0 controlled by diffusion
0.1 i v
0.0
0.1
0.2
0.2

60. for the reversible systems , use the forward kinetics only :
can be only by numerical method:
Nicholson-Shain equation
 tramper coefficient
n – number of electrons involved in charge transfer step
is tabulated
x (bt) max =0.4958

61. For totally irreversible systems, peak potential shift with scan rate
0.1 i v
0.0
0.1
0.2
0.2
for slow EC reaction : ii0 ( 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 .

63. per decade of change in scan rate
drawn - out
ip COx0 lower due to 
if =0.5 n= 1

64. lnip  Ep E0 is linear with S= RT/nF, intercept is linearly proportional to k0

65. 4.4.4 effect of 1 potential on EC rate :x 1 
1=0, validate at high concentration or larger polarization
nF
effect of 1:
1.on concentration
2. =   1

66. When z0 <0 ( minus ) n  1 large
When z0 <0 ( minus ) n  1 large . For anion reduced on cathode , 1 effect is more significant.

67. 1 made c shift positively
When z0  n
1 made c shift positively
plus >0
minus <0
so: if 1 increases, i decreases +2 +4 2 4
+0.5
0.5
0.01M
0.1M 1M
0.001M
-0
without specific adsorption
 reduction of +1 cation
…… reduction of 1anion
1 accelerates reduction of cations slow reduction of anion
lgi

68. if: n =z Cu2+ +2e- = Cu
MnO4 +e = MnO42
= H+ +e- = 1/2 H2
if :z0 =0
adsorption of anion slow reaction

69. Electrochemistry of LB film

71. exam:
1.Draw the potential change versus distance away from electrode surface according to Stern electric double-layer and indicate 1 potential
2. When the electrode was positively charged, the surface concentration of action is still more than that of bulk solution. Explain this phenomenon using specific adsorption model
3.The differential double layer capacitance of Cu/H2O surface is 10-5 Fcm-2 while that for Cu/HS(CH2)11CH3 is 10-9Fcm-2 (can be taken as zero). If the differential Cdl for a Cu/HS(CH2)11CH3 system is measured to be 10-7 Fcm-2. Please calculate the coverage of HS(CH2)11CH3 on copper.

72. 4. Electro-capillary curves of Hg in KI and K2S solution are shown in the Figure.
Please indicate the PZC of Hg on the curves and explain the difference in PZC.
The curves coincide with each other when potential is quite negative but differ a lot when potential is positive, please give explanation. 
K2S KI 
5.Tell how to determine whether or not a electrode process is governed by diffusion. Given id for RDE can be expressed as id= 0.62 nF Di2/31/2-1/6 ci0

73. 6. This is a water drop with contact angle of  on Pt surface
6.This is a water drop with contact angle of  on Pt surface. When potential shift negatively, plot the change of  with potential, i.e.,  ~ . Pt 
7.Deposition of Cu nanowire in microspore of anodic alumina membrane (AAO) can be taken as ideal stable diffusion process. If the thickness of (AAO) is 1m =0.1 mol cm-1, =105cm2 s-1. Please calculate the limiting diffusion current.
8. Convection affects diffusion. If the slope of concentration gradient is ,The effective thickness of diffusion layer E=
and the dimity diffusion current id =

74. 9. a typical CV peak is shown in the figure
9.a typical CV peak is shown in the figure. Please Indicate EP, EP/2, Ere, and iP on it.
How can you determine whether or not this electrochemical process is electrochemical reversible?