1. 22. Processes at electrodes

2. The electrode-solution interface
Electrical double layer diffuse double layer (Helmholtz layer model) (Gouy-Chapman model)

3. Stern model
Helmholtz layer model : 단단한 이온분위기 Gouy-Chapman model : 이온의 이동성 강조.
Stern model Helmholtz layer model + Gouy-Chapman model

4. Electric potential at the interface

5. 25.9 The rate of charge transfer
A first-order heterogeneous rate law Product flux = k[J] vOx = kc[Ox] vRed = ka[Red]
Reaction at the electrode in which an ion is reduced by the transfer of a single electron in the rate-determining step. cathodic current density jc = Fkc[Ox] for Ox + e- → Red anodic current density ja = Fka[Red] for Red → Ox + e-
Net current density j = ja – jc = Fka[Red] – Fkc[Ox]

6. The activation Gibbs energy
선형적 potential 변화.
Gibbs energy of the transition state depends on the extent to which the latter resembles the species at the inner or outer planes.
Rate constants k = Be-∆‡G/RT
j= FBa[Red]e-∆‡Ga/RT - FBc[Ox]e-∆‡Gc/RT
Ja > jc : anodic current jc > ja : cathodic current

7. The Butler-Volmer equation
Transition state resembles a species that has undergone reduction
a) Zero potential difference b) nonzero potential difference

8. Transition state resembles a species that has undergone oxidation
a) Zero potential difference b) nonzero potential difference

9. } j = ja-jc ja = FBa[Red]e-∆‡Ga(0)/RTe(1-α)f∆Φ
Transition state is intermediate in its resemblance to reduced and oxidized species
Activation Gibbs energy for reduction
∆‡Gc = ∆‡Gc (0) + αF ∆Ф
Activation Gibbs energy for anodic process
∆‡Ga = ∆‡Ga (0) + (1-α)F ∆Ф
α : transfer coefficient(0< α <1)
ja = FBa[Red]e-∆‡Ga(0)/RTe(1-α)f∆Φ
jc = FBc[Ox]e-∆‡Gc(0)/RTe-αf∆Φ
(f = F/RT)
} j = ja-jc
a) Zero potential difference b) nonzero potential difference

10. Ex) calculate the change in cathodic current density at an electrode.
Potential difference changes from 1.0V to 2.0V
∆Ф’-∆Ф = 1.0V , T=298K, typical α = 0.5
(1J = 1VC)

11. Exchange current density j0
ja = FBa[Red]e-∆‡Ga(0)/RTe(1-α)fE
jc = FBc[Ox]e-∆‡Gc(0)/RTe-αfE
If the cell is balanced against an external source, Galvani potential difference(∆Φ) can be identified as the (zero-current) electrode potential, E.
ja=jc=j0
Overpotential, η.
Zero current value E → New value E’ η = E’ - E
ja = j0e(1-α)fη , jc = j0e-αfη
j = j0{e(1-α)fη – e-αfη} → Butler-Volmer equation

12. The low overpotential limit
fη ≪ a (in practice, η less than about 0.01V)
j = j0{1+(1-α)fη+···-(1- αfη+···)} ≈ j0fη (taylor series)
Low overpotential 에서는 계면이 Ohm’s law에 따르는 도체의 성질을 나타냄.
Needed potential difference that must exist if a current density j has been established by some external circuit
EX) The exchange current density of a Pt(s)│H2(g)│H+(aq) electrode at 298K is 0.79mAcm-2. Therefore, the current density when the overpotential is +5.0mV is obtained by using above equation.
The current through an electrode of total area 5.0cm2 is therefore 0.75mA.

13. The high overpotential limit
When overpotential is large and positive (in practice, η≥0.12V)
When overpotential is large but negative (in practice, η≤-0.12V)
Tafel plot
The plot of the logarithm of the current density against the overpotential
The overpotential is obtained by taking the difference between the potentials measured with and without a flow of current through the working circuit.

14. EX)
The data below refer to the anodic current through a platinum electrode of area 2.0cm2 in contact with an Fe3+, Fe2+ aqueous solution at 298K. Calculate the exchange current density and the transfer coefficient for the electrode process.
η/mV 50
100
150
200
250
I/mV
8.8
25.0
58.0
131
298
Anodic process is the oxidation Fe2+(aq) → Fe3+(aq) +e-. Make a Tafel plot. The intercept at η=0 is lnj0 and the slope is (1-α)f.
η/mV 50 10
150
200
250
j/(mAcm-2)
4.4
12.5
29.0
56.6
149
ln(j/mAcm-2)
1.48
2.53
3.37
4.18
5.00
Intercept : 0.88, line slope ln(j0/(mAcm-2))=0.88 , j0=2.4mAcm-2 (1-α)F/RT= , α=0.58
At low overpotential, we cannot apply Tapel plot.

15. Voltammetry Polarization Concentration polarization
Non-polarizable : calomel and H2/Pt electrode Polarizable
(Criterion for law polarizability is high exchange current density.)
Concentration polarization
At high current density, we cannot apply the assumption in the derivation of the Butelr-Volmer eq.
Diffusion of the species towards the electrode from the bulk is slow.
Rate determining step!!
ηc : polarization overpotential

16. E0 : formal potential , (a=γc)
Mz+ ze- → M
Net current density : 0
EΘ : Standard emf
E0 : formal potential , (a=γc)

17. Fick’s first law
eq(36)
C’=0 : maximum diffusion rate
Limiting current density
With eq(36)
Expression for the overpotential in terms of the current density
j↑ → c’↓

18. Experimental techniques
Linear-sweep voltammetry
Differential pulse voltammetry

19. Cyclic voltammetry
Reversible reaction : symmetrical voltammmogram Irreversible reaction : unsymmetrical shape
Scan rate effect at fast sweep rates, irreversible reaction does not have time to take place, so the voltammogram will be typical reversible shape.

20. EX) The electroreduction of p-bromonitrobenzene in liquid ammonia is believed to occur by the following mechanism :
BrC6H4NO2 + e- → BrC6H4NO2- BrC6H4NO2- → ·C6H4NO2 + Br- ·C6H4NO2 + e- → C6H4NO2- C6H4NO2- + H+ → C6H5NO2
Suggest the likely form of the cyclic voltammogram expected on the basis of this mechanism.
At slow sweep rates, the second reaction has time to occur, and a curve typical of a two-electron reduction will be observed, but there will be no oxidation peak on the second half of the cycle because the product, C6H5NO2, cannot be oxidized
At fast sweep rates, second reaction does not have time to take place before oxidation of the BrC6H4NO2- intermediate starts to occur during the reverse scan, so the voltammogram will be typical of a reversible one-electron reduction

21. Electrolysis
Applied potential difference to bring about a nonspontaneous cell reaction > zero-current potential + cell overpotential.
Relative rate of gas evolution or metal deposition during electrolysis
Butler-Volmer equation and exchange current density table
j’ : metal deposition
j : gas evolution
j = -j0e-αfη
Exchange current density depends on
- nature of the electrode surface (in metal/hydrogen electrode : Platinum vs lead)
- crystal face exposed (copper deposition on copper) [(100) j0=1mAcm-2, (111) j0=0.4mAcm-2 ]

22. Working galvanic cells
M│M+(aq)║M’+(aq)│M’
X: right, left electrode
Apply Butler-Volmer equation -electrode area : A -transfer coefficient : ½ -an electron move at rate determining step
Concentration polarization ⇒

23. Impact on technology Fuel cells 2H2(g)+O2(g) → 2H2O(l) Hydrogen/Oxygen
Anode : 2H2(g) → 4H+(aq) + 4e-
Cathode : O2(g) + 4H+(aq) + 4e- → 2H2O(l)
Methanol/Oxygen
Anode : CH3OH(l) + 6OH-(aq) → 5H2O(l) +CO2(g) + 6e-
Cathode : O2(g) + 4e- + 2H2O(l) → 4OH-(aq)

24. Corrosion A A’ Fe2+(aq) + 2e- → Fe(s) EΘ = -0.44V In acidic solution
(a) 2H+(aq) + 2e- → H2(g) EΘ=0V
(b) 4H+(aq) + O2(g) + 4e- → 2H2O(l) EΘ=1.23V
In basic solution
(c) 2H2O(l) + O2(g) + 4e- → 4OH-(aq) EΘ=0.40V A A’
pH effect
E(a) = EΘ(a) + (RT/F) ln a(H+) = -(0.059V)pH
E(b) = EΘ(b) + (RT/F) ln a(H+) = 1.23V - (0.059V)pH
The rate of corrosion

25. Protecting materials against corrosion
1) Reduce the exposed surface area
2) Reduce the potential difference between anode and cathode in similar exchange current density
3) Coating of an iron object with zinc
4) Cathodic protection (magnesium is sacrificial anode)
5) Impressed-current cathodic protection