review: fermi level electrochemical potential inner, outer, surface potential, work function inner...
TRANSCRIPT
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