2 Structure of electrified interface 1. The electrical double layer 2. The Gibbs adsorption isotherm...
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Transcript of 2 Structure of electrified interface 1. The electrical double layer 2. The Gibbs adsorption isotherm...
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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
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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
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Presently accepted model of the electrical double layer
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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 }
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Gibbs Model of the interface
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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
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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
,,
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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
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Gibbs model of the interface - Summary
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2.3 The electrocapillary equation
Cu’ Ag AgCl KCl, H2O,L Hg Cu’’
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M = F(g - e)+
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Lippmann equation
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Differential capacity of the interface
2
2
dE
d
dE
dC M
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Capacity of the diffuse layer
Thickness of the diffuse layer
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2.4 Electrosorption phenomena
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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
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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
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Time constant of the cell
RuCd
duduc CR
t
CR
EE exp1
Typical values Ru=50 C=2F gives =100s
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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