double layer lectures

8/17/2019 Double Layer Lectures

1/38

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


2/38

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


3/38

"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


4/38

M*S interface resem'les a parallel-plate condenser of t#o charged

la$ers

/&ample:

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


5/38

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


6/38

/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


7/38

the rest of the ions are scattered in a cloud-li


8/38

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


9/38

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


10/38

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


11/38

;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


12/38

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


13/38

"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


14/38

$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


15/38

)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


16/38

-/ 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


17/38

"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&ample)

and

/- (#hen Cl- ions used in the calomel electrode for e&ample)

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&ample of g*Cl interface and #e #ant to calculate the surface

e&cess of Cl- ions at the g*Cl interface


18/38

∑

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


19/38

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 -


20/38

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


21/38

(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


22/38

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


23/38

;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


24/38

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$te is gi,en '$:


25/38

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


26/38

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


27/38

⇩

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


28/38

"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


29/38

The 0our /lectro


30/38

%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


31/38

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


32/38

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


33/38

pplications of /lectro


34/38

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


35/38

%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


36/38

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


37/38

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 −×

×

−


38/38

double layer lectures

Documents