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

2.1 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

a

s

b

Definitions

G – total Gibbs function of the system

Ga,Gb,Gs - Gibbs functions of phases a,b,s

Gibbs function of the surface phase s:

Gs = G – { Ga + Gb }

Gibbs Model of the interface

Con

cent

ratio

n

Distance

Surface excess

Hypothetical surface

The amount of species j in the surface phase:

njs = nj – { nj

a + njb}

Gibbs surface excess Gj

Gj = njs/A

A – surface area

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

jinpTj

j nG

=,,

m - chemical potential

dGa =-SadT + Vadp + + Smjdnja

dGb =-SbdT + Vbdp + + Smjdnjb

and

dGs = dG – {dGa + dGb}= SsdT + gdA + + Smjdnjs

npTAG

,,

=g

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 + Smjdnj

s

The first and the last equations are valid if:

Adg + Snjsdmj = 0 or

dg = - Gjdmj

Gibbs model of the interface - Summary

2.3 The electrocapillary equation

Cu’ Ag AgCl KCl, H2O,L Hg Cu’’

sM = F(GHg - Ge)+

Lippmann equation

Differential capacity of the interface

2

2

dEd

dEdC M gs

==

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

dCqIRE +=

} dtCRtCRECidt

CqE

t

dudu

d

t

dc ===

00

/exp/

} duc CRtE /exp1 =

Time constant of the cell

t = RuCd

=

duduc CR

tCREE exp1

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

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