Electrochemical reactions are interfacial reactions, the

structure and properties of electrode / electrolytic solution

interface greatly influences the reaction.

Influential factors:

1) Chemistry factor: chemical composition and surface

structure of the electrode: reaction mechanism

2) Electrical factor: potential distribution: activation energy

of electrochemical reaction

1) Chemistry factor: chemical composition and surface

structure of the electrode: reaction mechanism

2) Electrical factor: potential distribution: activation energy

of electrochemical reaction

Chapter 2

Electrode/electrolyte interface:

----structure and properties

For process involving useful work, W’ should be incorporated in the following thermodynamic expression.

dG = -SdT + VdP + W’+idni dG = -SdT + VdP + W’+idni

§2.1 Interfacial potential and Electrode Potential

For electrochemical system, the useful work is:

W’ = zieUnder constant temperature and pressure, for process A B:

1) Electrochemical potential

0

0 0

( )

( ) ( )

A B B A B Ai i i i

B B A Ai i i i

G z e

z e z e

Electrochemical potential

1) Definition:

zi is the charge on species i, , the inner potential, is the

potential of phase .

iii ez 0

A Bi i iG

In electrochemical system, problems should be considered using electrochemical potential instead of chemical potential.

0

0 0

( )

( ) ( )

A B B A B Ai i i i

B B A Ai i i i

G z e

z e z e

2) Properties:

1) If z = 0 (species uncharged)

2) for a pure phase at unit activity

3) for species i in equilibrium between and .

ii ,0

ii

ii 3) Effect on reactions

1) Reactions in a single phase: is constant, no effect

2) Reactions involving two phases:

a) without charge transfer: no effect

b) with charge transfer: strong effect

2) Inner, outer and surface potential

(1) Potential in vacuum:

the potential of certain point is the work done by transfer unite positive charge from infinite to this point. (Only coulomb force is concerned).

x xFdx dx

- strength of electric fieldF e

This process can be divided into two separated steps.

Vacuum, infinitecharged sphere

++

++

Electrochemical reaction can be simplified as the transfer of electron from species in solution to inner part of an electrode.ee

e

W2 +

10-6 ~ 10-7 m

W1

(2) Potential of solid phase

The work (W1) done by moving a test

charge from infinite to 10-6 ~ 10-7 m vicinity to the solid surface (only related to long-distance force) is outer potential.

Outer potential also termed as Volta Potential () is the potential measured just outside a phase.

10-6 ~ 10-7 m

W1

Moving unit charge from vicinity (10 –6 ~10-7 m) into inner of the sphere overcomes surface potential (). Short-distance force takes effect .

W2 +

W2

For hollow ball, can be excluded.

arises due to the change in environment experienced by the charge (redistribution of charges and dipoles at the interface)

(3) Inner, outer and surface potential

W2

10-6 ~ 10-7 m

W1

The total work done for moving unit charge to inner of the charged sphere is W1 + W2

= (W1+ W2) / z e0 = + The electrostatic potential within a phase termed the Galvani potential or inner potential ().

If short-distance interaction, i.e., chemical interaction, is taken into consideration, the total energy change during moving unite test charge from infinite to inside the sphere:

1 2W W 0 0 ( )ze ze

inner

hollow

10-6~10-7

0,, ii

infinite

ai

0ezi

0ezi0ezi

i

distance

workfunction eW

work function

the minimum energy (usually measured in electron volts) needed to remove an electron from a solid to a point immediately outside the solid surface

or energy needed to move an electron from the Fermi energy level into vacuum.

0i ieW z e

(4) Work function and surface potential

For two conductors contacting with each other at equilibrium, their electrochemical potential is equal.

e e

eΔ 0 e e

0

Δe

3) Measurability of inner potential

0e ee 0e e

e =

(1) potential difference

0e e( )e

0 0 0 0e ee e e e

0 0 0 0( ) ( ) ( )e e

e e e e

0eWee

0e

We

different metal with different eW

Δ 0 0e

W Therefore Δ 0

~ Δ ,not Δ nor Δe

V Conclusion

eΔ 0 Δ 0 Δ 0

ee

Ve0

No potential difference between well contacting

metals can be detected

0V

Galvanic and voltaic potential can not be measured using voltmeter.

If electrons can not exchange freely among the pile, i.e., poor electrical conducting between phases.

n

1

Fermi level

n

1

Fermi level

1’

11 1

1 0

11 1

1

Δ Δ

Δ Δ

n nne en i i

ni i n

Ve

1' 1

1 1

1 0

1

1

Δ Δ

Δ

ne en i i

ni i

Ve

(2) Measurement of inner potential difference

0e

V ee

V

Δ 0 Knowing V, can be only measured when

Δ 0

11 1

1 0

11 1

1

Δ Δ

Δ Δ

n nne en i i

ni i n

Ve

(3) Correct connection

n

1

Fermi level

1’

Consider the cell: Cu|Cu2+||Zn2+|Zn/Cu’

I S1 S2 II I’

IIIIIIIISSSSI

IIIIISSSSI

IIIIIII VV

'

'2

''

2211

211 )()()()(

For homogeneous solution without liquid junction potential

Δ Δ const.I II I S S IIV the potential between I and II depends on outer potential difference between metal and solution.

(4) Analysis of real system

Δ Δ const.I II I S S IIV

Using reference with the same Δ const.I II I SV

.11 constV SIIII .22 constV SIIII

)()( SIIIIV

The value of IS is unmeasurable but the change of is [ (I

S )] can be measured.

the exact value of unknown electrode can not be detected.

SI absolute potential

Chapter 2

Electrode/electrolyte interface: structure and properties

Cu

Zn

Zn2+ Zn2+ Zn2+ Zn2+ Zn2+

e- e- e- e- e- e- e- e-

1) Transfer of electrons

2.4 origination of surface potential

Cu

Cu2+ Cu2+(aq)

Cu

Cu2+

Cu2+

Cu2+

Cu2+

e-

e-

e-

e-

e-

e-

e-

e-

2) Transfer of charged species

AgI

AgI

AgI

I¯

I¯

I¯

I¯

I¯

I¯

I¯ +

+

+

+

+

+

+

3) Unequal dissolution / ionization

+

I¯

I¯

I¯

I¯

I¯

I¯

I¯ +

+

+

+

+

+

+

4) specific adsorption of ions

5) orientation of dipole molecules

–

–

–

–

+

+

+

+

+

+

+

+ –

+ –+ –

+ –

+ –

––

–––

–––

–

Electron atmosphere

6) Liquid-liquid interfacial charge

KCl HCl

H+K+

KCl HClH+

H+

H+

H+

Cl-

Cl-

Cl-

Cl-

Different transference number

1), 2), 3) and 6): interphase potential

4), 5) surface potential.

1) Transfer of electron1) Transfer of electron

2) Transfer of charged species2) Transfer of charged species

3) Unequal dissolution3) Unequal dissolution

4) specific adsorption of ions4) specific adsorption of ions

5) orientation of dipole molecules5) orientation of dipole molecules

6) liquid-liquid interfacial charge6) liquid-liquid interfacial charge

Cu

Cu2+

Cu2+

Cu2+

Cu2+

e-

e-

e-

e-

e-

e-

e-

e-

Electric double layer

– +++++++

– – – – – –

capacitor

Holmholtz double layer (1853)

Electroneutrality: qm = -qs

2.5 Ideal polarizable electrode and Ideal non-polarizable electrode

icharge

iec equivalent circuit

i = ich + iec

Charge of electric double layer Electrochemical rxn

Faradaic process and non-Faradaic process

an electrode at which no charge transfer across the metal-solution interface occur regardless of the potential imposed by an outside source of voltage.

ideal polarizable electrode

no electrochemical current:

i = ich

E

I

0

Virtual ideal polarizable electrode

Hg electrode in KCl aqueous solution: no reaction takes

place between +0.1 ~ -1.6 V

K+ + 1e = K

2Hg + 2Cl- - 2e- = Hg2Cl2 +0.1 V

-1.6 V

Electrode Solution

Hg

an electrode whose potential does not change upon passage of current (electrode with fixed potential)

ideal non-polarizable electrode

no charge current: i = iec

E

I

0

Virtual nonpolarizable electrode

Ag(s)|AgCl(s)|Cl (aq.)

Ag(s) + Cl AgCl(s) + 1e

For measuring the electrode/electrolyte interfac

e, which kind of electrode is preferred, ideal pol

arizable electrode or ideal non-polarizable elect

rode?

2.6 interfacial structure

surface charge-dependence of surface tension:

1) Why does surface tension change with increasing of surface charge density?

2) Through which way can we notice the change of surface tension?

Experimental methods:

1) electrocapillary curve measurement

2) differential capacitance measurement

interfaceInterphase Interfacial region

S S’

a a’

b b’

The Gibbs adsorption isotherm

iiii nnnn

iiii nnnn

in

A

i

iidndASdTdG

When T is fixed

i

iidndAdG

iinAG

dndnAddAdG iii

Integration gives

i

iidndAdG

0 dnAd ii Σ i id d

Σ i i e ed d d

Gibbs adsorption isotherm

Fdde

e

q

F

Σ i id d qd

qddd ii

When the composition of solution keeps constant

,,, 121

q

qdd

Lippman equation

Electrocapillary curve measurement

Electrocapillary curves for mercury and different electrolytes at 18 oC.

,,, 121

q

0q

Zero charge potential: 0

(pzc: potential at which the electrode has zero charge)

2

2 C

m

Electrocapillary curve

; ;d qd q C

d C d

0

dCd

m

2202

C

m

2

2 C

m Theoretical deduction of

Differential capacitance

Rs

Rct

Cdl

2

1

( )q c d

Differential capacitance

capacitor

–

+++++

– – – –

The double layer capacitance

can be measured with ease

using electrochemical

impedance spectroscopy

(EIS) through data fitting

process.

Measurement of interfacial capacitance

Integration of capacitance for charge density

Differential capacitance curves

Cd = C()

KF

K2SO4

KCl

KBr

KI

0.4 0.8 1.2 1.60.0

/ V

Cd

/ F

·cm

-2

20

40

60

Dependence of differential capacitance on potential of different electrolytes.

Differential capacitance curves

NaF

Na2SO4

KI

0.0 -0.4 -0.8 -1.20.4

/ V

q / C

·cm

-2

4

0

8

12

-4

-8

-12

Charge density on potential

differential capacitance curves for an Hg electrode in NaF aqueous solution

Dependence of differential capacitance on concentration

Potential-dependent

Concentration-dependent

Minimum capacitance at pote

ntial of zero charge (Epzc)

36 F cm-2;

18 F cm-2;

Surface excess

q

sz F z F q q

z+ z-M A M Av v

v v

v z v z

MAd v d v d

+

q qs

c0

0i id d i id qd d

qd d d

R.E.d z Fd

For any electrolyte

R.E.MA

v

R.E.MA

v

. . R.E.W Ed d d For R.E. in equilibrium with cation

MAd v d v d

KF

0.0 -0.4 -0.8 -1.20.4

/ V

q / C

·cm

-2

-2

0

-4

-6

2

4

6

KAc

KCl

KBr

KF

KAcKCl

KBr

Anion excess

cation excess

Surface excess curves

Electrode possesses a charge density resulted from excess charge at the electrode surface (qm), this must be balanced by an excess charge in the electrolyte (-qs)

2.7 Models for electric double layer

1) Helmholtz model (1853)

0

d

E

dA

C r 0 0 rVq

A d

q charge on electrode (in Coulomb)

2) Gouy-Chappman layer (1910, 1913)

Charge on the electrode is confined to surface but same is not true for the solution. Due to interplay between electrostatic forces and thermal randomizing force particularly at low concentrations, it may take a finite thickness to accumulate necessary counter charge in solution.

0

d

E

Plane of shear

RT

FCxC x

exp)( 0

RT

FCxC x

exp)( 0

Boltzmann distribution

Poisson equation

x

x

E

x

42

2

)()( xCxCFx

Gouy and Chapman quantitatively described the charge stored in the diffuse layer, qd (per unit area of electrode:)

RT

F

RT

FFC xx

x

expexp0

RT

F

RT

FFC

xxxx

expexp4 0

2

2

22

2

1

2x x

xx x

RT

F

RT

FFC

xxxx

x

expexp8 02

Integrate from x = d to x =

RT

F

RT

FRTcq

2exp

2exp

211

0

For 1:1 electrolyte

For Z:Z electrolyte

RT

Fz

RT

FzRTcq

2exp

2exp

211

0

RT

zFCRTqd 2

sinh8 02

1*

Experimentally, it is easier to measure the differential capacitance:

RT

zF

RT

CzFCd 2

cosh)2( 0

2

1*

2sinh

xx eex

Hyperbolic functions

For a 1:1 electrolyte at 25 oC in water, the predicted capacitance from Gouy-Chapman Theory.

1) Minimum in capacitance at the potential of zero charge

2) dependence of Cd on concentration

2) Gouy-Chappman layer (1910, 1913)

3) Stern double layer (1924)

Combination of Helmholtz and Guoy-Chapman Models

The potential drop may be broken into 2:

2 2( ) ( )m s m s

2 2( ) ( )m s m s

Inner layer + diffuse layer

This may be seen as 2 capacitors in series:

dit CCC

111

Ci: inner layer capacitance

Cd: diffuse layer capacitance-given by Gouy-Chapman

Ci Cd

M S

Total capacitance (Ct) dominated by the smaller of the two.

dit CCC

111

Ci Cd

M S

At low At low cc00 At high At high cc00

CCdd dominant dominant CCii dominant dominant

CCd d CCt t CCi i CCt t

1

qCi

RT

F

RT

FRTc

Ci 2exp

2exp

2

1 110

1

Discussion:

When c0 and are very small

011 22

1c

RT

FRT

Ci

Stern equation for double layer

Discussion:

When c0 and are very large

01

011

2exp

2

1

2exp

2

1

cRT

FRT

C

cRT

FRT

C

i

i

RT

F

RT

FRTc

RT

F

d

dqCd 2

exp2

exp22

110

1

Cd plays a role at low potential near to the p. z. c.

Fitting result of Stern Model.

Fitting of Gouy-Chapman model to the experimental results

4) Gramham Model-specific adsorption

0

d

E Triple layer

Specifically adsorbed anions

Helmholtz (inner / outer) plane

5) BDM fine model

Bockris-Devanathan-Muller, 1963

00

0

4 41 1 1 ii

d i

d d

C C C

4i i

di

C Cd

If rH2O = 2.7 10-10 m, i=6

-2 -220 F cm 18 F cmdC

-236 F cmdC

di i =5-6 do i =40

1) Helmholtz model

2) Gouy-Chappman model

3) Stern model

4) Graham model

5) BDM model

What experimental phenomenon can they explain?

The progress of Model for electric double layer

2.8 Fine structure

of the electric double layer

Without specific adsorption

– BDM model

With specific adsorption

– Graham model

Who can satisfactorily explain all the experimental phenomena in differential capacitance curve?

Models of electric double layer

As demonstrated last time, Stern Model can give the most satisfactory explanation to the differential capacitance curve, but this model can not give any suggest about the value of the constant differential capacitances at high polarization.

Stern model: what have solved, what not?

At higher negative polarization, the differential

capacitance, approximately 18-20 F cm2, is independent of

the radius of cations. At higher positive polarization,

differential capacitance approximates to be 36 F cm2.

As pointed out by Stern, at higher polarization, the

structure of the double layer can be described using

Helmholtz Model. This means that the distance between the

two plates of the “capacitor” are different, anions can

approach much closer to the metal surface than cations.

d i d o

i = 5-6 i = 40

o

o

i

i

oic

dd

CCC

44111

i

iic dCC

4

Capacitance of compact layer mainly depends on inner layer of water molecules.

If the diameter of adsorbed water molecules was assumed as 2.7 10-10 m, i = 6, then

2811

20107.21416.34

6

109

1

4

Fcm

dC

i

ic

The theoretical estimation is close to the experimental results, 18-20 F cm-2, which suggests the reasonability of the BDM model.

Weak Solvation and strong interaction let anions approach electrode and become specifically adsorbed.

Primary water layer

Secondary water layer

Inner Helmholtz plane 1

Outer Helmholtz plane 2

Specially adsorbed anion

Solvated cation

4. BDM model

– Bockris, Devanathan and Muller, 1963

Summary:

1. A unambiguous physical image of electric double layer

2. The change of compact layer and diffusion layer with concentration

3. The fine structure of compact layer

For electric double layer without specific adsorption