1. 2 Structure of electrified interface
1. The electrical double layer
2. The Gibbs adsorption isotherm
3. Electrocapillary equation
4. Electrosorption phenomena
5. Electrical model of the interface

2. 2.1 The electrical double layer
Historical milestones
The concept electrical double layer Quincke – 1862
Concept of two parallel layers of opposite charges Helmholtz 1879 and
Stern 1924
Concept of diffuse layer Gouy 1910; Chapman 1913
Modern model Grahame 1947

3. Presently accepted model of the electrical double layer

4. 2.2 Gibbs adsorption isotherm
Definitions a
G – total Gibbs function of the system
Ga,Gb,Gs - Gibbs functions of phases a,b,s s
Gibbs function of the surface phase s:
Gs = G – { Ga + Gb } b

5. Gibbs Model of the interface

6. The amount of species j in the surface phase:
njs = nj – { nja + njb}
Gibbs surface excess Gj
Gj = njs/A
A – surface area

7. Gibbs adsorption isotherm
Change in G brought about by changes in T,p, A and nj
dG=-SdT + Vdp + gdA + Smjdnj
– surface energy – work needed to create a unit area by cleavage
- chemical potential
dGa =-SadT + Vadp + + Smjdnja
dGb =-SbdT + Vbdp + + Smjdnjb
and
dGs = dG – {dGa + dGb}= SsdT + gdA + + Smjdnjs

8. dg = - Gjdmj Derivation of the Gibbs adsorption isotherm
dGs = -SsdT + gdA + + Smjdnjs
Integrate this expression at costant T and p
Gs = Ag + Smjnjs
Differentiate Gs
dGs = Adg + gdA + Snjsdmj + Smjdnjs
The first and the last equations are valid if:
Adg + Snjsdmj = or
dg = - Gjdmj

9. Gibbs model of the interface - Summary

11. 2.3 The electrocapillary equation
Cu’ Ag AgCl KCl, H2O,L Hg Cu’’

12. sM = F(GHg - Ge) +

14. Lippmann equation

18. Differential capacity of the interface

21. Capacity of the diffuse layer
Thickness of the diffuse layer

24. 2.4 Electrosorption phenomena

26. 2.5 Electrical properties of the interface
In the most simple case – ideally polarizable electrode the
electrochemical cell can be represented by a simple RC circuit

27. Implication – electrochemical cell has a time constant that
imposes restriction on investigations of fast electrode process
Time needed for the potential across the interface to reach
The applied value :
Ec - potential across the interface
E - potential applied from an external generator

28. t = RuCd Time constant of the cell
Typical values Ru=50W; C=2mF gives t=100ms

29. Current flowing in the absence of a redox reaction – nonfaradaic current
In the presence of a redox reaction – faradaic impedance is connected in parallel
to the double layer capacitance. The scheme of the cell is:
The overall current flowing through the cell is :
i = if + inf
Only the faradaic current –if contains analytical or kinetic information