Double layer and adsorbtion

Sähkökemian peruseetKE-31.4100

Tanja Kalliotanja.kallio@aalto.fiC213

CH 5 – 5.2

+

Electrical double layer

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-

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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

troly

te

pote

ntia

l0 x2

OH

L

+distance from the interphase

Potential distribution at the interphase (2/3)

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-

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sem

icon

duct

or

elec

troly

te

pote

ntia

l

distance from the interphase0 x2

OH

L

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--

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--

-

Potential distribution at the interphase (3/3)

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-el

ectro

lyte

II

pote

ntia

l

distance from the interphase0

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elec

troly

te I

Gibbs adsorption isotherm (1/5)

i

iidn

nGdP

PGdT

TGdG

i

iidn

n

GdPPGdT

TGdG

Phase and 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 phase

interfacial zone

For the whole system a new force g, surface tension, must be taking into account

i

iiidn

nGdA

AGdP

PGdT

TGdG

Gibbs adsorption isotherm (2/5)

By subtracting Gibbs energies of the phase and from that of the whole system Gibbs energy of the interphase, dGs, is obtained

s gi

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 s

in

s iiii nnnn

So dGs can be written

ss gi

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

ss

s sgi

n

ii

AG idndAdG

000

Thus

ss gi

iinAG

gg sss

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

gi

iidd Anii /swhere

Gibbs adsorption isotherm

Adsorption in diluted solution: relative surface excess

Gibbs-Duhem equation is valid in bulk phase

1 1

1i

ii dnn

d i

iidn 0

g

11

111

1 ii

ii

iii d

nn

ddd

ii s

solventInserting 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

HgeeHgHg

~~~~ g ssss ddddd HClH

Surface tension is obtained by applying Gibbs adsorption isotherm for the interphase between the Hg electrode and HCl electrolyte

s sss

i

iim FFz

eHg

ss ss

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

sg

ss Hge

HClHHClClHgHg

~~ ddF

dddm

From the equilibriums at the interphasesrPt,

e

H

eHClH

H

HwPt,

eHge

~~;~~;~~ 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 msg HClσClHg

σHg

Lippmann equation orelectrocapillary equation

Capacitance of the double layer is (compare to a planar capasitor)

T

mdl EC

,

s

Adsorption of organic molecules

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