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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 to parallel layers of opposite char!es Helmholt" 18#$ and
Stern 1$2%-Concept of diffuse layer &ouy 1$1'( Chapman 1$1)-*odern model &rahame 1$%#
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Presently accepted model of the electrical double layer
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2.2 &ibbs adsorption isotherm
+efinitions
G total Gibbs function of the system
G,G,G- Gibbsfunctions of phases ,,
Gibbs function of the surface phase :
G! G " G + G#
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Gibbs $odel of the interface
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%oncentration
&istance
'urface e(cess
)ypothetical surface
The amount of species * in the surface phase+
n*= n* " n*, n*}
Gibbs surface e(cess *
* ! n*s
surface area
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Gibbs adsorption isotherm
%han/e in G brou/ht about by chan/es in T0p0 and n*
dG!-'dT , dp , d , *dn*
surface ener/y or needed to create a unit area by cleaa/e
jinpTj
jnG
=
,,
- chemical potential
dG!-'dT , dp , , *dn*
dG
!-'
dT ,
dp , , *dn*
and
dG! dG "dG + dG}= 'dT , d , , *dn*
npTA
G
,,
=
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&eriation of the Gibbs adsorption isotherm
dG! -'dT , d , , *dn*
nte/rate this e(pression at costant T and p
G! , *n*
&ifferentiate G
dG! d, d , n*d*, *dn*
The first and the last equations are alid if+
d, n*d*! 6 or
d ! - *d*
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&ibbs model of the interface , Summary
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2.3 The electrocapillary equation
%u7 / /%l 8%l0 )290: )/ %u77
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$ ! ;
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:ippmann equation
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&ifferential capacity of the interface
2
2
dE
d
dE
dC M
==
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%apacity of the diffuse layer
Thicness of the diffuse layer
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2.4 Electrosorption phenomena
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2.- lectrical properties of the
interfacen the most simple case ideally polari>able electrode the
electrochemical cell can be represented by a simple ?% circuit
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mplication electrochemical cell has a time constant that
imposes restriction on inesti/ations of fast electrode process
Time needed for the potential across the interface to reachThe applied alue +
Ec - potential across the interface
E - potential applied from an e(ternal /enerator
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Time constant of the cell
= ?u%d
=
dudu
cCR
t
CR
EE exp1
Typical alues ?u!56;%!2; /ies !166s
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%urrent floin/ in the absence of a redo( reaction nonfaradaic current
n the presence of a redo( reaction faradaic impedance is connected in parallel
to the double layer capacitance. The scheme of the cell is+
The oerall current floin/ throu/h the cell is +
i ! if, inf
9nly the faradaic current ifcontains analytical or inetic information