2 structure of electrified interface
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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. 2.1 The electrical double layer. Historical milestones

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2 Structure of electrified interface

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2 structure of electrified interface

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 structure of electrified interface

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


2 structure of electrified interface

Presently accepted model of the electrical double layer


2 structure of electrified interface

2.2 Gibbs adsorption isotherm

Definitions

a

G – total Gibbs function of the system

Ga,Gb,Gs - Gibbsfunctions of phases a,b,s

s

Gibbs function of the surface phase s:

Gs= G – { Ga + Gb }

b


2 structure of electrified interface

Gibbs Model of the interface


2 structure of electrified interface

The amount of species j in the surface phase:

njs = nj – { nja + njb}

Gibbs surface excess Gj

Gj = njs/A

A – surface area


2 structure of electrified interface

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


2 structure of electrified interface

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 = 0 or

dg = - Gjdmj


2 structure of electrified interface

Gibbs model of the interface - Summary


2 structure of electrified interface

2.3 The electrocapillary equation

Cu’ Ag AgCl KCl, H2O,L Hg Cu’’


2 structure of electrified interface

sM = F(GHg - Ge)

+


2 structure of electrified interface

Lippmann equation


2 structure of electrified interface

Differential capacity of the interface


2 structure of electrified interface

Capacity of the diffuse layer

Thickness of the diffuse layer


2 structure of electrified interface

2.4 Electrosorption phenomena


2 structure of electrified interface

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


2 structure of electrified interface

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


2 structure of electrified interface

Time constant of the cell

t = RuCd

Typical values Ru=50W; C=2mF gives t=100ms


2 structure of electrified interface

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


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