Review: Fermi level Electrochemical potential Inner, outer, surface potential, work function Inner potential difference, correct connection, absolute potential,

Review:

Fermi level

Electrochemical potential

Inner, outer, surface potential, work function

Inner potential difference, correct connection, absolute

potential, relative potential (standard potential)

Cu

Zn

Zn2+ Zn2+ Zn2+ Zn2+ Zn2+

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

1) Transfer of electrons

§2.2 Structure of Electrolyte/electrode surface

Cu2+(aq)

Cu

Cu2+

Cu

Cu2+

Cu2+

Cu2+

Cu2+

e-

e-

e-

e-

e-

e-

e-

e-

2) Transfer of charged species

2.2.1 Surface charge

Review:

AgI

AgI I¯

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-

Review:

Cu

Cu2+

Cu2+

Cu2+

Cu2+

e-

e-

e-

e-

e-

e-

e-

e-

2.2.2 Electric double layer

– +++++++

– – – – – –

capacitor

Holmholtz double layer (1853)

Electroneutrality: qm = -qs

Review:

1) Ideal polarizable electrode

E

I

0

E

I

0

Review:

2.2.4 Interfacial structure: experimental

1) Experimental methods:

(1) electrocapillary curve measurement

(2) differential capacitance measurement

Σ i id d qd Lippman equation

Review:

When the composition of solution keeps constant

2) Experiment equipmenti id d qd

1 2 1, , ,

d qd

q

Review:

Electrocapillary curves for mercury and different electrolytes at 18 oC.

0q

Zero charge potential: 0

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

Electrocapillary curve3) Experiment results

1 2 1, , ,

q

2

2m

C

Review:

1) Measurement method

Rs

Rct

Cdl

2.6.3 differential capacitanceoscillograph

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

3) Experimental results

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

Review:

differential capacitance curves for an Hg electrode in NaF aqueous solution

Potential-dependent

Concentration-dependent

Minimum capacitance at pote

ntial of zero charge (Epzc)

36 F cm-2;

18 F cm-2;

Review:

§2.3 Models for electric double layer

1) Helmholtz model (1853)

0d

E

0

4rq

V d

4d

dqC

dV d

Review:

0

d

E

Plane of shear

2) Gouy-Chappman layer (1910, 1913)Review:

Boltzmann distribution

Poisson equation

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

0( ) exp xFC x C

RT

0( ) exp xFC x C

RT

2

2

4 xE

x x

( ) ( )x F C x C x

+

q qs

c0

Review:

2 08exp expx x x

x

F FC F

x RT RT

1* 2

0(2 )cosh

2d

zFzF CC

RT RT

0 exp expx xx

F FC F

RT RT

2 0

2

4exp expx x xF FC F

x RT RT

22

2

1

2x x

xx x

Review:

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

Review:

3) Stern double layer (1924)

Combination of Helmholtz and Guoy-Chapman Models

The potential drop may be broken into 2:

1 1( ) ( )m s m s

Review:

1 1( ) ( )m s m s Inner layer + diffuse layer

This may be seen as 2 capacitors in series:

Ci Cd

M S1 1 1

t i dC C C

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

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( )i

dqC

d

1

d

dqC

d

1

Stern Fitting of 0.0001 mol·L-1 HClFitting result of Gouy-Chapman

Stern model: what have been solved, what have not?

experimental

calculation

Review:

1) Helmholtz model

2) Gouy-Chappman model

3) Stern model

The progress of Model for electric double layer

At higher negative polarization, the differential capacitance,

approximately 18-20 F·cm-2, is independent of the radius of

cations. At higher positive polarization, differential capacitance

approximates to be 36 F·cm-2.

what have been solved,

what have not?

4) BDM model

Bockris-Devanathan-Muller, 1963

Electrostatic adsorption Nom-electrostatic adsorption

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

Primary water layer

Secondary water layer

Inner Helmholtz plane IHP 1

Outer Helmholtz plane, OHP, 2

Specially adsorbed anion

Solvated cation

00

0

4 41 1 1 ii

d i

d d

C C C

4i i

di

C Cd

di i =5-6 do i =40

Dielectric saturation

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

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

211 8

1 620μF cm

4 9 10 4 3.1416 2.7 10i

ci

Cd

0.0

-0.4 -0.8 -1.20.4

M / C

·cm

-

2

-2

0

-4

-6

2

4

6

0.8

K+

F

E-EPZC / V

0.0 -0.4 -0.8 -1.20.4

-5

0

-10

-15

5

10

15

0.8

K+

Br

E-EPZC / V

M / C

·cm

-2

0

d

E

What have been solved, what have

not?

Surface excess curves

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

For any electrolyte

R.E.MA

v

R.E.MA

v

For R.E. in equilibrium with cation

R.E.d z Fd

MAd v d v d

ln1OxaRT

z F

y

R.E.d z Fd

5) Gramham Model-specific adsorption

= 0

1

+

+ 1

+

++ +

Specific adsorption due to chemical adsorption of anions

+

+

+

+

+

+ +

+

+

+

+

+

++

Overload adsorption

Normal adsorption due to electrostatic attraction of cations

0

dE

Triple layer

Specifically adsorbed anions

Helmholtz (inner / outer) plane

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

§2.4 1 potential

1 = 0 validate only at hig

h concentration or larger p

olarization

1 potential at outer Helmholtz plane

x

1

-1

GCS model

1

1 1( )

01 1

1

1exp exp

2 2 2i

F FRTc

C RT RT

When electrode bear negative charge218μF cmiC

Discussion: When c0 and are very small

When c0 and are very large

011

1

2 2i

FRTc

C RT

0 01 11

1 1exp exp

2 2 2 2i i

F FRT RTc c

C RT C RT

Influential factors: concentration and potential

-0.1

-0.2

0.0-0.5 -1.0 -1.5

1 / V

/ V

0.001

0.01

0.1

1.0

Dependence of 1 on c

10

2.3030.059V

lg

RT

c F

Hg in NaCl solution

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

0.2

0.4IHP

OHP

/

V

d / Å

Dependence of 1 on

x

1

-1

effect of 1

01exp( )i

i i

z FC C

RT

1. on concentration

01ln

z nRTi const i

nF n

2. on reaction rate

3. on polarization

01lnc

z nRTconst i

nF n

Chapter 2

Electrode/electrolyte interface: structure and properties

§2.3 Models for electric double layer

1) Helmholtz model (1853)

2) Gouy-Chappman model

3) Stern double layer (1924)

4) BDM model

5) Gramham Model

Primary water layer

Secondary water layer

Inner Helmholtz plane IHP 1

Outer Helmholtz plane, OHP, 2

§2.4 1 potential

2.5 Potential at zero charge (PZC, PZC)

Definition: potential at which the electrode bears no

charge.

2.4.1 Determination of PZC

(1) electrocapillary curve

(2) differential capacitance curve (most accurate )

(3) contact angle of gas bubble on the metal surface

(4) surface hardness

(5) wetting of surface

1) Experimental method

00.5 0.5 1.0

/ Nm

-1

0.3

0.4

q / Cm

-2

0.3

0.3

E / V vs. SCE

0q

Metals Metals Electrolyte Electrolyte PZCPZC

HgHg NaFNaF -0.193-0.193

Bi (multicrystal)Bi (multicrystal) KF (0.002)KF (0.002) -0.39-0.39

Bi (111 surface)Bi (111 surface) KF (0.01)KF (0.01) -0.42-0.42

Ag (111) Ag (111) KF (0.01)KF (0.01) -0.46-0.46

Ag(100)Ag(100) NaF (0.005)NaF (0.005) -0.61-0.61

Ag (110)Ag (110) NaF (0.005)NaF (0.005) -0.77-0.77

CdCd NaF (0.001)NaF (0.001) -0.75-0.75

2) Some experimental results of PZC

When the electrode potential is more positive than potential at zero charge, how is the electrode charged, positive or negative?

3) Difficulties in measuring PZC

1) purification of electrolyte and metal (why do we usually use mercury? )

2) specific adsorption (includes adsorption of hydrogen)

Hg-like metal: Cd, Sn, Pb, As, Sb, Bi; Ga, In, Tl

Pt-like metal: Ni, Pt, Pd; Co; Rh, Ir; Ru. Os

3) crystal facet and multi-crystal

Different crystalline facet has different differential capacitance and thus different potential of zero charge

Differential capacitance curves of different crystal facets of Ag in 0.01 mol dm-1 NaF solution. 1. (100); 2. (100), 3. (111).

,multi ,singled i dC C

For multi-crystal, its differential capacitance is the sum of all the differential capacitance of the surface of single crystal times their fraction.

AgAg

(111)(111) 0.001 mol0.001 moldmdm-3-3 KF KF -0.46-0.46

(100)(100) 0.005 mol0.005 moldmdm-3-3 NaF NaF -0.61-0.61

(110)(110) 0.005 mol0.005 moldmdm-3-3 NaF NaF -0.77-0.77

(MC)(MC) 0.005 mol0.005 moldmdm-3-3 Na Na22SOSO44 -0.7-0.7

AuAu

(110)(110) 0.005 mol0.005 moldmdm-3-3 NaF NaF +0.19+0.19

(111)(111) 0.005 mol0.005 moldmdm-3-3 NaF NaF +0.50+0.50

(100)(100) 0.005 mol0.005 moldmdm-3-3 NaF NaF +0.38+0.38

MCMC 0.005 mol0.005 moldmdm-3-3 NaF NaF +0.25+0.25

4) Application of PZC

0; ( ) 0M SPZC q

Surface potential () still exists due to the specific adsorption, orientation of dipoles, polarization of surface atoms in metal electrode, etc.

Therefore:

0 0 0( ) [( ) ( ) ] 0M S M S M Sq q q

PZC can not be taken as the absolute zero point for the interphase potential. M S

?M S

0( ) 0M Sq

Potential standard:

Potentials refereed to PZC as zero point (E-EPZC) are

named as rational potential standard.

1) potential versus reference electrode (0);

2) potential versus PZC (PZC)

5) Relationship between PZC and We

PZC,vs SCEeW C -1.0 -0.5 0.0

4.0

4.5

5.0

Ti

CdIn

GaZn

Ag

Sn

Bi

HgSb

CuAu

PZC vs. SCE/ V

e/ eVW

For mercury-like metals:

+

+

+

FE

Vacuum

-

M

eW

FE

M

SHE

-

SHE

eW

M0 0e

M0

0q

-

SHE

e4.6 0.2eVW

Theoretical calculation of electrochemical potential

2.6 Interface adsorption and Graham Model

Electrocapillary curve and differential capacitance curve in electrolytes with same valence type and concentration should be similar and neutral molecules have little effect on the curves.

The former four models for electric double layer are all electrostatic models without consideration of non-electrostatic interaction between species and electrode surface.

influential factors: 1) valence type; 2) concentration; 3) size of solvated ions; 4) potential related to PZC

Capillary curves of Hg in 0.01 mol dm-3 NaCl, NaBr and KI solution.

2.6.1 Some experimental phenomena

0.0 0.2 0.4 0.6 0.8 1.0

-0.8

-0.7

-0.6

-0.5

PZC

/ Vvs

. SC

E

c / mol dm-3

NaF

NaCl

KBr

KI

Dependence of PZC on anion and concentration

(1) Effect of ion on PZC

HS¯ > I¯ > Br¯ > Cl¯ > OH¯ > SO4¯ > F¯

K+Ta+

N(C3H7)4+

Special adsorption of cations:

Capillary curves of Hg in 0.01 mol dm-3 NaCl containing t-C5H11OH of different concentration.

C- curve for n-pentanol at a dropping Hg electrode in 0.1 M KCl

(2) Effect of surface active agent on PZC

(1) Adsorption of organic molecules

At PZC, surface tension decrease dramatically, but at higher polarization, no significant change can be observed.

2.6.2 discussion

Effect of potential on surface adsorption: around PZC, the adsorption attain maximum.

At high potential, water may replace organic molecules already adsorbed on the electrode surface. And the arrangement of water molecules on the electrode surface may change accordingly.

As concentration of surface active reagent increases, the surface tension decreases, and finally attains a limiting value.

Adsorption peaks appearing in differential capacitance curve

Where Ci is integration capacitance

When adsorption/desorption occurs, d(Ci)/d becomes astonishingly large – false capacitance. The peak of false capacitance marks the adsorption/desorption of the surface active reagent.

( ) ( )i id i

d C d CdqC C

d d d

(2) Degree of coverage

1 0(1 )q q q

0 1

1 0

1 0 0 1

(1 ) ( )

(1 ) ( )

d

dq dq dq dC q q

d d d d

dC C q q

d

can be used to characterize the formation of self-assembled monolayer, to evaluate the defect in polymeric coatings and determine the wetted area on substrate metal surface or water sorption of polymer materials.

0(1 )adC C C 0

0 ad

C C

C C

S-Y ZHANG, et al., "Evaluation of thin defect-free epoxy coatings using electrochemical impedance spectroscopy", Journal of Applied Electrochemistry, 1998， 28(11): 1277~1281

1) Concentration change in solution;

2) Electrochemical oxidation or reduction of adsorbed

species (coulomb);

3) Radioactive marks (radiation counter)

4) EQCM: Electrochemical quartz crystal micro-balance

(gravimetric method)

2.6.3 Other ways to measure adsorption