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Page 1: Influential factors:

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

Page 2: Influential factors:

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

Page 3: Influential factors:

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

Page 4: Influential factors:

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

Page 5: Influential factors:

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

Page 6: Influential factors:

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

Page 7: Influential factors:

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

Page 8: Influential factors:

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

Page 9: Influential factors:

inner

hollow

10-6~10-7

0,, ii

infinite

ai

0ezi

0ezi0ezi

i

distance

workfunction eW

Page 10: Influential factors:

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

Page 11: Influential factors:

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

Page 12: Influential factors:

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

Page 13: Influential factors:

~ 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.

Page 14: Influential factors:

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

Page 15: Influential factors:

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’

Page 16: Influential factors:

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

Page 17: Influential factors:

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

Page 18: Influential factors:

Chapter 2

Electrode/electrolyte interface: structure and properties

Page 19: Influential factors:

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

Page 20: Influential factors:

Cu

Cu2+ Cu2+(aq)

Cu

Cu2+

Cu2+

Cu2+

Cu2+

e-

e-

e-

e-

e-

e-

e-

e-

2) Transfer of charged species

Page 21: Influential factors:

AgI

AgI

AgI

I¯ +

+

+

+

+

+

+

3) Unequal dissolution / ionization

+

Page 22: Influential factors:

I¯ +

+

+

+

+

+

+

4) specific adsorption of ions

Page 23: Influential factors:

5) orientation of dipole molecules

+

+

+

+

+

+

+

+ –

+ –+ –

+ –

+ –

––

–––

–––

Electron atmosphere

Page 24: Influential factors:

6) Liquid-liquid interfacial charge

KCl HCl

H+K+

KCl HClH+

H+

H+

H+

Cl-

Cl-

Cl-

Cl-

Different transference number

Page 25: Influential factors:

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

Page 26: Influential factors:

Cu

Cu2+

Cu2+

Cu2+

Cu2+

e-

e-

e-

e-

e-

e-

e-

e-

Electric double layer

– +++++++

– – – – – –

capacitor

Holmholtz double layer (1853)

Electroneutrality: qm = -qs

Page 27: Influential factors:

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

Page 28: Influential factors:

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

Page 29: Influential factors:

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

Page 30: Influential factors:

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

Page 31: Influential factors:

For measuring the electrode/electrolyte interfac

e, which kind of electrode is preferred, ideal pol

arizable electrode or ideal non-polarizable elect

rode?

Page 32: Influential factors:

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

Page 33: Influential factors:

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

Page 34: Influential factors:

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

Page 35: Influential factors:

qddd ii

When the composition of solution keeps constant

,,, 121

q

qdd

Lippman equation

Electrocapillary curve measurement

Page 36: Influential factors:

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

Page 37: Influential factors:

; ;d qd q C

d C d

0

dCd

m

2202

C

m

2

2 C

m Theoretical deduction of

Page 38: Influential factors:

Differential capacitance

Rs

Rct

Cdl

2

1

( )q c d

Differential capacitance

Page 39: Influential factors:

capacitor

+++++

– – – –

The double layer capacitance

can be measured with ease

using electrochemical

impedance spectroscopy

(EIS) through data fitting

process.

Measurement of interfacial capacitance

Page 40: Influential factors:

Integration of capacitance for charge density

Differential capacitance curves

Cd = C()

Page 41: Influential factors:

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

Page 42: Influential factors:

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

Page 43: Influential factors:

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;

Page 44: Influential factors:

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

Page 45: Influential factors:

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

Page 46: Influential factors:

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

Page 47: Influential factors:

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

Page 48: Influential factors:

dA

C r 0 0 rVq

A d

q charge on electrode (in Coulomb)

Page 49: Influential factors:

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

Page 50: Influential factors:

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:)

Page 51: Influential factors:

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 =

Page 52: Influential factors:

RT

F

RT

FRTcq

2exp

2exp

211

0

For 1:1 electrolyte

For Z:Z electrolyte

RT

Fz

RT

FzRTcq

2exp

2exp

211

0

Page 53: Influential factors:

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

Page 54: Influential factors:

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)

Page 55: Influential factors:

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

Page 56: Influential factors:

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

Page 57: Influential factors:

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

Page 58: Influential factors:

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

Page 59: Influential factors:

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.

Page 60: Influential factors:

Fitting result of Stern Model.

Fitting of Gouy-Chapman model to the experimental results

Page 61: Influential factors:

4) Gramham Model-specific adsorption

0

d

E Triple layer

Specifically adsorbed anions

Helmholtz (inner / outer) plane

Page 62: Influential factors:

5) BDM fine model

Bockris-Devanathan-Muller, 1963

Page 63: Influential factors:

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

Page 64: Influential factors:

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

Page 65: Influential factors:

2.8 Fine structure

of the electric double layer

Without specific adsorption

– BDM model

With specific adsorption

– Graham model

Page 66: Influential factors:

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

Models of electric double layer

Page 67: Influential factors:

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?

Page 68: Influential factors:

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.

Page 69: Influential factors:

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.

Page 70: Influential factors:

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.

Page 71: Influential factors:

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

Page 72: Influential factors:

4. BDM model

– Bockris, Devanathan and Muller, 1963

Page 73: Influential factors:

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


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