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-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

Presently accepted model of the electrical double layer

2.2 Gibbs adsorption isotherm

Definitions

G – total Gibbs function of the system

GGG - Gibbsfunctions of phases

Gibbs function of the surface phase

G = G – { GG }

Gibbs Model of the interface

Con

cent

ratio

n

Distance

Surface excess

Hypothetical surface

The amount of species j in the surface phase:

njnj – { nj

+ nj

Gibbs surface excess j

j = njs/A

A – surface area

Gibbs adsorption isotherm

Change in G brought about by changes in T,p, A and nj

dG=-SdT + Vdp + dA + jdnj

– surface energy – work needed to create a unit area by cleavage

jinpTj

j n

G

,,

- chemical potential

dG =-SdT + Vdp + + jdnj

dG =-SdT + Vdp + + jdnj

and

dG = dG – {dGdGSdT + dA + + jdnj

npTA

G

,,

Derivation of the Gibbs adsorption isotherm

dG = -SdT + dA + + jdnj

Integrate this expression at costant T and p

G = A + jnj

Differentiate G

dG = Ad + dA + njdj + jdnj

The first and the last equations are valid if:

Ad + njdj = 0 or

d= - jdj

Gibbs model of the interface - Summary

2.3 The electrocapillary equation

Cu’ Ag AgCl KCl, H2O,L Hg Cu’’

M = F(g - e)+

Lippmann equation

Differential capacity of the interface

2

2

dE

d

dE

dC M

Capacity of the diffuse layer

Thickness of the diffuse layer

2.4 Electrosorption phenomena

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

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 reachThe applied value :Ec - potential across the interfaceE - potential applied from an external generator

Time constant of the cell

RuCd

duduc CR

t

CR

EE exp1

Typical values Ru=50 C=2F gives =100s

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