double layer and adsorbtion sähkökemian peruseet ke-31.4100 tanja kallio [email protected]...
TRANSCRIPT
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Electrical double layer
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0 x1x2
X = 0 interphaseX = x1 inner Helmholtz layerX = x2 outer Helmholtz layer
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Potential distribution at the interphase (1/3)
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met
al
elec
trol
yte
pote
ntia
l0 x2
OH
L
+distance from the interphase
Potential distribution at the interphase (2/3)
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sem
icon
duct
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elec
trol
yte
pote
ntia
l
distance from the interphase0 x2
OH
L
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Potential distribution at the interphase (3/3)
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-el
ectr
olyt
e II
pote
ntia
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distance from the interphase0
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elec
trol
yte
I
Gibbs adsorption isotherm (1/5)
i
ii
dnn
GdP
P
GdT
T
GdG
i
ii
dnn
GdP
P
GdT
T
GdG
Phase a and b in contact. Differentials of Gibbs energies for this phases are
Let us consider a system at constant temperature and pressure and so the first two terms on the right-hand side can be omitted.
phase a phase b
interfacial zone
For the whole system a new force g, surface tension, must be taking into account
i
iiidn
n
GdA
A
GdP
P
GdT
T
GdG
Gibbs adsorption isotherm (2/5)
By subtracting Gibbs energies of the phase a and b from that of the whole system Gibbs energy of the interphase, dGs, is obtained
i
iiii nnnddAdG
Surfaces at the interphase have either higher or lower number of species compared to the bulk phase. This difference is surface concentration or surface excess
in
iiii nnnn
So dG s can be written
i
iidndAdG (5.7)
Gibbs adsorption isotherm (4/5)
When a surface is formed between two phases via infinitesimal changes Gibbs energy of an interphase is obtained by integrating the previous equation
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n
ii
AG i
dndAdG000
Thus
i
iinAG
iii
iii dnAddndAdG
By differentiating
(5.10)
Gibbs adsorption isotherm (5/5)
As equations (5.7) and (5.10) must be equivalent the sum of the last two term in eq (5.10) must be zero. When surface excess is given per surface unit
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iidd Anii /where
Gibbs adsorption isotherm
Adsorption in diluted solution: relative surface excess
Gibbs-Duhem equation is valid in bulk phase
1 1
1i
ii dn
nd
iiidn 0
11
111
1 ii
ii
iii d
n
nddd
ii
solvent
Inserting the Gibbs-Duhem eq in the Gibbs adsorption isotherm
relative surface excess s
for diluted solution n1>>ni and thus
The electrocapillary equation (1/3)
Pt(s) | H2(g) | HCl(aq) | Hg(l) | Pt(s)
ClClH
Hg
eeHgHg~~~~ ddddd HCl
H
Surface tension is obtained by applying Gibbs adsorption isotherm for the interphase between the Hg electrode and HCl electrolyte
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iim FFz
eHg
ClHFml
Excess charge density on the metal, sm, is
Equal, but opposite, charge density, sl, resides on the solution side
RE WE
The electrocapillary equation (2/3)
Combining the equations we obtain
Hg
eHClHHClClHgHg
~~ ddF
dddm
From the equilibriums at the interphasesrPt,
e
H
e
HCl
H
H
H
wPt,
e
Hg
e~~;~~;~~ 22
As the composition of the H2(g) in the RE does not change and thus, for the equilibrium reaction H2 2 H+ + 2 e– can be written
02H d
22 He
HH
~~ dd
Inserting electrochemical potentials in the above most eq and applying dG = -nFdE for the last term we obtain
The electrocapillary equation (3/3)
D.C. Grahame, Chem. Rev. 41 (1947) 441
dEddd m HClσClHg
σHg
Lippmann equation orelectrocapillary equation
Capacitance of the double layer is (compare to a planar capasitor)
T
m
dl EC
,
Adsorption of organic molecules
D.C. Grahame, Chem. Rev. 41 (1947) 441