introduction double layer

7/29/2019 Introduction Double Layer

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Introduccin a la doble capaelctrica

MF Surez


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Cmo podemos

medir el pH deuna solucinacuosa?


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Sensor de pH

Sensor de Temperatura


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Unin p-n


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Energy Levels


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Debye-Hckel


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Doble capa elctrica


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2

=div grad=

zr 0 E=grad=

2=2

x22

y22

z2=

1

r2

d

dr[r2

ddr

]=zr 0

Ci r=C*exp zi er kT

( )kT

xez

xi

xii

en

n

=

,

,

Liquids, Solutions, and InterfacesFrom Classical Macroscopic Descriptions to Modern Microscopic DetailsW. RONALD FAWCETT, University of California, Davis, Oxford University press, 2004

Interacciones ion-ion de acuerdo ala teora de DebyeHckel


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=z+FC+*exp

z+er kT z -FC-

*exp

z- er kT

=i=1

n

z iFCi*

exp

zi er

kT 1

r2

d

dr

[r2 d

dr

]=

1

r 0i=1

n

z iFCi*exp

zi er

kT


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=i=1

n

ziFCi*

i=1

n

z i2

F

2

Ci*

rRT

Expansin en una seriede Taylor

I=1

2

i=1

n

z i2

Ci* Fuerza inica

1

r2

d

dr

[r2 d

dr

]=

r 0=

2F2I

r 0R T

=2


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y= r dydr=r d

d r d2y

dr2=2 d

d rr d

2d r

2

1r2 ddr [

r2 ddr ]=2r

dd r d

2

d r

2

d2y

dr2 =2

y

y= r=k1exp r k2expr = k1rexp r


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=r 0

2

a

4 r2d r=zi e

a

4 r k1r 02exp r d r=zi e

k1=zi e0expa

4r 0 1

1a =

zi e0exp r 4r0 r

exp a1a


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self=zi e0

4r 0 r

El potencial debido nicamente a la atmsfera inicaa una distancia igual al radio inico es igual a:

atm=zi e0exp a

4r 0 a exp a

1 a zi e0

4r0 a

atm=zi e0

4r 0 1 a


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0

z i e0

atm d zi eo= zi

2

e02

8r 0 1 a

RTlni=NLzi2

e02

8r 0 1 a

2F2

r 0R T

1

2i=1

n

zi

2C

i

*

=


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D bl l t i


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Doble capa elctrica(Tratamiento fsico)

d2

dx

2 = 1r 0i=1

n

z iFCi*exp

z i ex

kT Para un ion monovalente se obtiene:

d2

dx2=

FC*

r 0 [expex

kT exp ex

kT ]d2

dx

2=2FC

*

r 0sinh

ex kT


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d2

dx2 =

[d

d dd x ][

dd x ]=

1

2 [d

d dd x

2

]1

2

[d

d

d

d x

2

]=

FC*

r 0

[exp

ex

kT

exp

ex

kT

][ dd E2]=2FC*

r 0 [exp ex

kT expex

kT ]E

2= 2FC*kT

r 0 e [expex

kT expex

kT 2]lim0

E=0


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ex

2e

x

2

2

=exex2

E=2FC

*kT

r0 e

[exp ex2kT exp

ex

2kT ]

E=8C

*RT

r 0 [senhex

2kT ]E

2FC*

kT

r 0 e [ex

kT ]


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dd x

2FC

*

kTr 0 e [

exkT ]

0

d

0

x

2FC*

kT

r 0 e [e

kT

]dx =

2FC*

e

r 0 kT

ln

ln0x 0exp x


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q=0E.ds


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M=

sol=8r 0C

*RT

[senh z e02kT

]

q=0

Ex=0

A

dM

d0=Cd=

2r0z2

C*F

2

RT

[cosh

z e0

2kT

]


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Differential capacitance vs. potential for

NaF solutions in contact with mercury at

25C. [Reprinted with permission from D.

C. Grahame, Chem. Rev., 41, 441 (1947).

Copyright 1947, American Chemical

Society.]


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(a) A view of the differentialcapacitance in theGouy-Chapman-Stern (GCS)model as a series network ofHelmholtz layer and diffuse-

layer capacitances.

(b) Potential profile through thesolution side of the doublelayer, according to GCS theory.

Calculated for 1x10-2 M 1:1electrolyte in water at 25C.


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Expected behavior of Cd according to GCS theoryas the electrolyte concentration changes.

I i li id


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Ionic liquids


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Schematic representation of thedifferent type of interactions

present in imidazolium based ILs


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Full lines describe the predicted dependence on

charge of the capacitance of the outer element,

the inner layer, and the overall double layer, for a

(metal)/(ionic liquid) interface. Dashed lines show

corresponding predictions for a (metal)/

(electrolyte solution) interface, the inner

capacitance being the same for both systems.Parameters for both media: ionic and molecular

radii, r = 1.00 nm; permittivity, 1.77 x 10-10 F m-1;

bulk ionic concentration, c = 180 mM;

temperature, T = 298 K.

K.B. Oldham / Journal of Electroanalytical Chemistry 613 (2008) 131138

introduction double layer

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