double layer lectures
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Structure of Electrified Interfaces
(The Electrical Double Layer)
Types of interfaces
Models of M/S interface
Validation of the models
⇩
Surface tension varies with potential and electrolyte composition
Ideally-polariable interface (!"/Solution)
Electrocapillary phenomena
Lippmann e#uations
$ibbs adsorption isotherm
Impro%ements in the M/S model
&hen M/S interface is mobile
⇩
Electro'inetic () phenomena
pplications
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The interface
1- Complete charge transfer from one phase to the other phase:
M+
M+
M+
M+
M+
M+
M+
M+
M e t a l ( M )
S o l u t i o n ( S )
M e t a l ( M )
S o l u t i o n ( S )
X-
X-
X-
X-
X-
X-
2- Specific adsorption of ionic species:
3- Oriented adsorption of polar species:
Vacuum
i!uid
Vacuum
Solution
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"hen t#o different metals are immersed in an electrol$tic solution
⇓
%otential difference e&ists 'et#een the terminals of the t#o metals
"hen t#o identical metals are immersed in an electrol$tic solution
⇓
o potential difference
The conclusion %otential difference must e&ist at an$ M*S interface
The electrical analogue to the M/S interface
%arallel-plate condenser is candidate to descri'e the M*S interface
!M + - !S
Is the M/S interface really a parallel-plate condenser?
The ans#er is the models of the proposed structure of the M*S interface
The decision is 'ased on ho# capacitance of the M*S interface
,aries #ithpotential and electrol$te composition
1- elmholt. Model
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M*S interface resem'les a parallel-plate condenser of t#o charged
la$ers
/&le:
0i&ed positi,e
charges are created
on the metal
surfaces
due to
the natural tendency
of the deposition of
metal ions as metal
atoms
to achie,e the electrical neutralit$
la$er of anions in solution is arranged in a ro# close to the metal surface
%otential difference /M*S 'et#een the metal and the solution:
/M*S + /M - /S
The capacitance according to the model
ε
=
/
!)m0(C
o
S*M
M2
o + 4516-12 C2-1m-2
S o l u t i o n
M e t a l
/S+6
/M
0
/M*S
7istance from
metal surface
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ε 8 4 -9 and 8 16-16 m (the ionic radii)
⇓
C 8 -44µ
0cm-2
C ,alue is close to the e&perimental ,alue o'ser,ed sometimes But
The model fails to e&plain the dependence of C
on potential and electrol$te composition
2- ou$ and Chapman ModelThe electrical dou'le la$er cannot 'e fi&ed in position due to
the thermal motion of the electrol$tic species instead a diffuse la$er of
point-charge is proposed in the model
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/M*S deca$s e&ponentiall$ as the distance from the metal surface
increases
The model does not reflect the general C-/M*S feature
o'ser,ed e&perimentall$but
it ma$ 'e accepted #hen the electrol$te concentration is ,er$ lo#
S o l u
t i o n
M e t a l
/M
/S+66
/M*S
7istance from
metal surface
3- Stern Model
Stern model is a compromise 'et#een elmholt. and ou$-Chapman
models
;ons of the first ro# are fi&ed and stuc< close to the metal surface
and
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the rest of the ions are scattered in a cloud-li
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7istance from
metal surface
6
/M
M e t a l
S o l u t i o n
/S
ζ
(/:)
/M*S
*o specific adsorption
/
urther
The first ro# ions can 'e attracted to the metal surface
by
electrostatic attraction
or/and by
forces of specific adsorption
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ζ
/M*S
S o l u t i o n
M e t a l
/M
6
7istance from
metal surface/S
ζ
/M*S
S o l u t i o n
M e t a l
67istance frommetal surface
/S
/M
Specifically adsorbed anions Specifically adsorbed cations
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Validation of models of the structure of the M*S interface
"e should search for a surface (or an interfacial) propert$
;nterfacial tension of the g*solution interface responses to
,ariation of /M*S and the solution composition
The phenomenon is
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;deall$ polari.a'le and ideall$ non-polari.a'le electrodes
%olari.ation occurs #hene,er the current ; > 6
The passing current causes /M*S to de,iate from its e!uili'rium ,alue
/
C
u r r e n t
;deall$ polari.a'le
electrode
;deall$ non-polari.a'le
electrode
/re,
OO
C
R
0R
C
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The electrocapillar$ phenomena
%otentiometer?eference
electrode
g manometer
2 gas
g capillar$ electrode
/lectrol$te
g
gra,it$ force +
π
r2 h d g
surface tension force +
2 π r γ cos θ
height of g column
h
radius of the capillar$
r
θ
/lectrol$te
le,el
+ @ h r g d
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"hat did #ippmann and other scientists find?
-E
γ γ γ
-E -E
KNO3KNO3 KNO3
+ amyl alcohol
Tl+
(C3H7)4 N+Cl
-
-
!" -
pzc (ecm)
(a) (#) (c)
pzc (ecm)
pzc (ecm)
$ualitati!e e%planation of electrocapillary cur!e
-/
γ
p&c
g
Solutio
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$uantitati!e e%planation of electrocapillary cur!e
A$ anal$.ing the thermod$namics of the M*S interface
⇓
7eduction of the electrocapillar$ cur,e ( -/ cur,e)
Thermod$namics of M*S interface
0undamental thermod$namic e!uation of the polari.a'le M*S interface
The general electrocapillar$ e!uation
∑
µ
iii B
B
M
M dd0n
!d/!d
$
n
$
n oiii −=Γ
'ependence of interfacial tension on electrode potential
The first #ippmann (quation
t constant electrol$te composition ⇒ dµi + 6 and dµ B + 6:
Mcompconst !)
/(
−
∂
γ
)cmC(166!)mV(/
)cm*d$ne(2
M
−
µ
∂
γ
The second #ippmann (quation
C/
!
/
M
2
2
=
∂
∂
−
∂
γ
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)cm0(C)V(/
)cmC(!
/
2
2
M
2
2
−
−
µ
∂
µ
−
∂
γ
(c)(')(a)
-/-/
!C
-/
+
,
-
ecm
ecm ecm
;deal
%ara'ola
7ifferentiation 7ifferentiation
dγ /dE-#M
The differential capacitance
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-/ V
C 1
0
pzc
/&perimental cur,es
6661M
661M
61M
16M a0
p&c
C 1
0
-/ V -/ V
C 1
0
p&c
:ou$-Chapman
model
elmholt. model
661M a0
6661M
'ependence of surface tension on the solution composition
)ibbs adsorption isotherm
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"e use one and the same electrol$te for 'oth electrodes:
g*solution electrode and the reference electrode
The electrocapillar$ cur,es at different electrol$te concentrations are recorded
using the same electrol$te concentration for the reference electrode
;n order to remem'er that the reference electrode contains the same electrol$te
used in the cell for g* electrol$te interface
we will use
the s$m'ol /= (#hen = ions used in the h$drogen electrode for e&le)
and
/- (#hen Cl- ions used in the calomel electrode for e&le)
The surface e%cess of an anion
/=(V !s ?/)
γ
3%0 N HCl
0%& N HCl
&%0 N HCl
0%0& N HCl
Consider the e&le of g*Cl interface and #e #ant to calculate the surface
e&cess of Cl- ions at the g*Cl interface
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∑
µ
iii B
B
MM dd
0n
!d/!d
−
µ
ClCl
M
M ddd0
!d/!d
t constant /=
−
µ
ClCl
M ddd0
!d
A$ definition: −µClCl
−
µ
Cl--Cl ddd
)dd(dd0
!d
ClCl
M
µ
µ ClM
ClCld)
0!(dd
;t can 'e pro,ed that: 60
!Cl
M=
−
This is 'ecause: !M + - !S + -(!= = !-) + -( −ΓCl 00 )
"here != + n=0 = and !- + n-0 -
n= + 1 and n- + -1
;e != + ! + -0 and !- + −Cl! + - −Cl0
Thus: −
Γ
µ
γ
Cl/
-Cl
)(
'"om th( #a)i) o* th("mo+ynamic),
CloClCl aln?T
Aut: 2 ClCl aa±
CloClCl an?T2 ±
ClCl an?Td2d ±
−
Γ
∂
γ
±
Cl
/-Clan?T2
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The last e!uation is the i''s adsorption isotherm
The unit of ? in i''s isotherm + 315169 erg mol-1 D -1
The surface e%cess of a cation
−
Γ
∂
γ
±
-
/-Clan?T2
The surface e%cess of a neutral molecule
i
1/i Ban?T2
Γ
∂
γ
µ
(!idences of specific adsorption
!M + - !S + - (!= = !-) + 0 = - 0 -
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66
C h a r g e d e n s i t $ 1 m C c m
- 2
-/ V
=,e
-,e
p&c
!S
!=
!-
electrode is -,el$ charged
e l e c
t r o d e
i s = , e l $
c h a
r g e d
' a c
7ependence of the charge densities on the cell ,oltage
for the g*16 M aCl interface
*oint +a, is at p&c +ecm, where .g surface is neutral
!= > 6 and !- > 6
although
!M + 6 and !S + 6
"h$E
The reasona'le e&planation is that
one ionic form (either anion or cation) is held at g*S interface
'$ a different
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(specific adsorption forcesE)
The counter ions are also included
to achie,e the electrical neutralit$ (!- + !=)
"hich is the ion specificall$ adsor'ed hereE *oint +b, when .g is positi!ely charged
;f onl$ the electrostatic forces #ould operate
⇩
!S + !- + 0 −Cl
Aut the figure sho#s that != + 0 a > 6
This means that some a= cations are in,ol,ed
to partiall$ neutrali.e the specificall$ adsor'ed Cl- ions
This means accumulation of Cl- ions in the interface relati,e to the 'ul
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C is lo#er than C
⇩
C F C
⇩
'iffuse layer dominates the structure of M/S interface near p&c
Since ζ potential is a significant part of /M*S
;n concentrated solutions
C is larger than C
⇩
C F C
elmholt. model #or
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;t is not the charges an$#a$
Capacitance can also originate due to adsorption of dipole molecules
such as #ater molecules
;t is assumed that Metal is full$ co,ered '$ a monola$er of #ater dipolein electrol$tic solutions
;n the presence of some specificall$ adsor'ed species
some #ater dipoles are replaced
The center of this monola$er of oriented #ater molecules
form #hat is called inner elmholt. plane (;%)
1- The hydration of ions
%racticall$ all ions are h$drated in #ater
The result is that an increase in the radius of the 'are ion
due to the hydration
The center of the h$drated ion is called the outer elmholt. plane (O%)
Capacitance at more significantl$ negati,e potentials than p.c
sho#s a little dependence on the nature of electrol$te
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This is because the ion radius is a small fraction
of the +M 23.*, distance
o specific adsorption
M e a l
;% O%
7 i f f u s e a $ e r
Specific adsorption of anions
M e a l
;% O%
7 i f f u s e a $ e r
#ater molecules
M*S interface consists of t#o partsG
The dense part H(MI;%) = (;%IO%)J = diffuse part
;n concentrated electrol$tes (diffuse part ,anishes)
M*S interface K The dense part H(MI;%) = (;%IO%)J
The M*S capacitance in concentrated electrol$te is gi,en '$:
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O-%;-%;-%M
C
1
C
1
C
1
→
;n the presence of specific adsorption of organic molecules
⇩
CMI;% is significantl$ reduced and hence
C F CMI;%
"h$E
since ε decreases sharpl$
⇩
C F CMI;%
The decrease of CMI;% increases #ith surface co,erage #ith the
adsor'ed organic molecules θ
The /lectro
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nother condition to o'ser,e these phenomena in practice
is The tin$ si.e of the mo'ile dou'le la$er
"hen large mo'ile dou'le la$ers are in,ol,ed⇩
the electro
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⇩
STA;;T
.ow do the particles create the repulsion forces?
Colloid particles are charged particles surrounded '$ counter ions toachie,e the electrical neutralit$
Onl$ #hen the cloud of the counter ions is large in si.e
the repulsion of the clouds 'eat the forces of attraction
that wants particles to aggregate
arge si.e cloud of counter ions is fulfilled
#hen the .eta potential predominates /M*S
.eta potential is connected #ith the sta'ilit$ of the colloid
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"hen #e add a concentrated electrol$te
or in the presence of strong specificall$ adsor'ed species
.eta potential diminishes or ,anishes
and the dou'le la$er of according to elmholt. model predominates
The cloud of the counter ions is so small that
the aggregation forces (attraction) 'eat the repulsion forces
due to the dense thin dou'le la$er
% o t e n t i a l e n e r g $
d
0
repulsion force due to
the dou'le la$er
attraction forces
total otntial n".y / 0no coagulation
d
% o t e n t i a l e n e r g $
0
total otntial n".y 0
coagulation occurs
minimum distance 'et#eent#o coagulated particles
d
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The 0our /lectro
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%ore (capillar$) in the porous 'arrier
-,e electrode=,e electrode
charged li!uid la$er
charged inner surface
⇩
T#o phenomena are o'ser,ed
/lectroosmosis and Streaming %otential
(lectrophoresis
Mo,ement of charged (colloidal or suspension) particles
under the influence of an electric field
Aatter$
7ispersed
particles
7ispersion
medium
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Sedimentation potential
Creation of a potential difference on sedimentation (precipitation) of
charged particles (colloidal or suspension)
under the influence of the gra,it$
Voltmeter
7ispersed
particles
7ispersion
medium
(lectroosmosis
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Mo,ement of thin charged li!uid la$ers through
capillaries or pores of a solid phase (porous 'arrier la$er)
under the influence of an electric field
Aatter$
%orous 'arrier
Streaming potential
Creation of a potential difference on forcing thin li!uid la$ers to mo,e
through capillaries or pores of a solid phase (porous 'arrier la$er)
'$ appl$ing an e&ternal pressure
Voltmeter
pplied pressure
%orous 'arrier
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pplications of /lectro
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nal$sis of the cell potential
M M1
/M
/S
/Cell
/S1*M1
/P
/MQ
/M1
/MQ
/S1
S1
S
M
M1
MQ
MQ
/M*S
P
/M1*MQ
/MQ*M
a ' c d e
S S1
Pa e
dc
'
V
a- b- c- d- and e are the interfacial regions that determining the cell potential- ( Cell
/Cell
+ /MQ(a)*MQ(e)
+ /MQ*M
= /M*S
= /P
= /S1*M1
= /M1*MQ
/Cell + /M*S = /P = /S1*M11"actically2 EMM an EM&M 5"o V
n th a#nc o* th li6ui unction otntial2 E89/Cell + /M*S = /S1*M1
* M : M& an S : S& /Cell + .ero V
/MQ /M /S and /S1 are the internal potentilas of MQ M S and S1
/MQ*M /M*S /P /S1*M1 and /M1*MQ are the interfacial potential differences
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%ro'lems
1- Outline #ith dra#ing elmholt. model for the dou'le la$er structure
?efer to the applica'ilit$ of the model
2- Outline #ith dra#ing ou$-Chapman model for the dou'le la$er
structure ?efer to the applica'ilit$ of the model
3- Outline #ith dra#ing Stern model for the dou'le la$er structure
- Mention the factors missed in elmholt. and ou$-Chapman models
4- S
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13- %ro,e diagrammaticall$ that the .eta potential is essential for the
sta'ilit$ of a colloid
1- Sho# ho# the .eta potential can 'e estimated from the electro
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26- C + !M * /M*S
!M + C 5 /M*S + 194516-R 5 6946 + 131 5 16-R C cm-2
21- The electrocapillar$ measurements in Cl solutions #ith h$drogen
electrode in the same electrol$te as the reference electrode $ield thefollo#ing at 24 oC and a constant potential:
* d$ne cm-1 24 19 6 39
aUCl 663 61 69 1
0ind the surface e&cess of the Cl- ion at the studied potential
21- −
Γ
∂
γ
±
Cl/Cl
)an?T2
(
Slope of cur,e ( ,ersus ln a) + -R934 d$ne cm-1
−
Cl + -(slope* 2?T) + R934 * 2 5 31 5 169 5 2 + 13R 5 16-16 mol cm-2
0or another (appro&imate) solution t#o points ma$ 'e used as follo#s:
−
Γ
±
±
Cl/
1Cl
2Cl
12 )
JaH
JaHn?T2
(
216
9
cmmol1631
636
16n216312
2419 −×
×
−
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