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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
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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
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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
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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
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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
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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
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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
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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
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inner
hollow
10-6~10-7
0,, ii
infinite
ai
0ezi
0ezi0ezi
i
distance
workfunction eW
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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
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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
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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
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~ 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.
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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
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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’
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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
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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
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Chapter 2
Electrode/electrolyte interface: structure and properties
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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
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Cu
Cu2+ Cu2+(aq)
Cu
Cu2+
Cu2+
Cu2+
Cu2+
e-
e-
e-
e-
e-
e-
e-
e-
2) Transfer of charged species
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AgI
AgI
AgI
I¯
I¯
I¯
I¯
I¯
I¯
I¯ +
+
+
+
+
+
+
3) Unequal dissolution / ionization
+
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I¯
I¯
I¯
I¯
I¯
I¯
I¯ +
+
+
+
+
+
+
4) specific adsorption of ions
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5) orientation of dipole molecules
–
–
–
–
+
+
+
+
+
+
+
+ –
+ –+ –
+ –
+ –
––
–––
–––
–
Electron atmosphere
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6) Liquid-liquid interfacial charge
KCl HCl
H+K+
KCl HClH+
H+
H+
H+
Cl-
Cl-
Cl-
Cl-
Different transference number
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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
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Cu
Cu2+
Cu2+
Cu2+
Cu2+
e-
e-
e-
e-
e-
e-
e-
e-
Electric double layer
– +++++++
– – – – – –
capacitor
Holmholtz double layer (1853)
Electroneutrality: qm = -qs
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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
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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
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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
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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
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For measuring the electrode/electrolyte interfac
e, which kind of electrode is preferred, ideal pol
arizable electrode or ideal non-polarizable elect
rode?
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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
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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
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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
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qddd ii
When the composition of solution keeps constant
,,, 121
q
qdd
Lippman equation
Electrocapillary curve measurement
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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
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; ;d qd q C
d C d
0
dCd
m
2202
C
m
2
2 C
m Theoretical deduction of
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Differential capacitance
Rs
Rct
Cdl
2
1
( )q c d
Differential capacitance
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capacitor
–
+++++
– – – –
The double layer capacitance
can be measured with ease
using electrochemical
impedance spectroscopy
(EIS) through data fitting
process.
Measurement of interfacial capacitance
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Integration of capacitance for charge density
Differential capacitance curves
Cd = C()
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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
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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
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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;
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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
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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
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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
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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
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dA
C r 0 0 rVq
A d
q charge on electrode (in Coulomb)
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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
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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:)
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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 =
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RT
F
RT
FRTcq
2exp
2exp
211
0
For 1:1 electrolyte
For Z:Z electrolyte
RT
Fz
RT
FzRTcq
2exp
2exp
211
0
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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
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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)
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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
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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
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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
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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
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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.
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Fitting result of Stern Model.
Fitting of Gouy-Chapman model to the experimental results
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4) Gramham Model-specific adsorption
0
d
E Triple layer
Specifically adsorbed anions
Helmholtz (inner / outer) plane
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5) BDM fine model
Bockris-Devanathan-Muller, 1963
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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
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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
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2.8 Fine structure
of the electric double layer
Without specific adsorption
– BDM model
With specific adsorption
– Graham model
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Who can satisfactorily explain all the experimental phenomena in differential capacitance curve?
Models of electric double layer
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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?
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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.
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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.
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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.
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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
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4. BDM model
– Bockris, Devanathan and Muller, 1963
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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