Chapter 2
Electrode/electrolyte interface:
----structure and properties
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
§2.1 Interfacial potential and Electrode Potential
1) Electrochemical potential
For process involving useful work, W’ should be
incorporated in the following thermodynamic expression.
dG = -SdT + VdP + W’+idni
For electrochemical system, the useful work is:
W’ = zie
Under constant temperature and pressure, for process A  B:
GiAB  iB  iA  zi e0 ( B   A )
 ( iB  zi e0 B )  ( iA  zi e0 A )
GiAB  iB  iA  zi e0 ( B   A )
 ( iB  zi e0 B )  ( iA  zi e0 A )
1) Definition:



i  zi e0  i
Electrochemical
potential
zi is the charge on species i, , the inner potential, is the
potential of phase .
G
AB
i
 i  i


In electrochemical system, problems should be considered
using electrochemical potential instead of chemical potential.
2) Properties:
1) If z = 0 (species uncharged)
2) for a pure phase at unit activity
3) for species i in equilibrium between  and .



0,
i


i  i
i  
i  i
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
x


   Fdx    dx
F  e
 - strength of electric field
(2) Potential of solid phase
Electrochemical reaction can be simplified
as the transfer of electron from species in
solution to inner part of an electrode.
e
e
e
++
+
+

Vacuum, infinite
charged sphere
This process can be divided into two separated steps.
10-6 ~ 10-7 m
W2 + 
W1

(3) Inner, outer and surface
potential
W2 + 
10-6 ~ 10-7 m

W1
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.
Moving unit charge from
vicinity (10 –6 ~10-7 m) into inner
of the sphere overcomes surface
potential (). Short-distance
force takes effect .
For hollow ball, 
can be excluded.
W2
Outer potential also termed as
Volta Potential () is the potential
measured just outside a phase.
 arises due to the change in
environment experienced by the
charge (redistribution of charges
and dipoles at the interface)
10-6 ~ 10-7 m
W2

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:
W1  W2    
    ze0    ze0 (   )
distance
infinite
i , i ,   0

zi e0 
10-6~10-7
hollow
zi e0 

zi e0 


i
a
i
inner
workfunction
We
(4) Work function and surface potential
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.
We  i  zi e0 

3) Measurability of inner potential
(1) potential difference
For two conductors contacting with each
other at equilibrium, their electrochemical
potential is equal.






e  e
e  e  e0  = e  e  e0 





Δ e  0


Δ 

e  e


e0
e  e  e0 (   )


e  e0   e0    e  e0   e0  


e0    e0 (    )  (e  e0   )  (e  e0   )
We  e  e0 


  
 We
e0
We
different metal with different


 We  0
Therefore


Δ  0


 Δ  0

No potential difference between well contacting
metals can be detected


Conclusion
V

0

Δ e  0

V ~ Δe , not Δ nor Δ


Δ  0


Δ  0





e0 V  e  e
Galvanic and voltaic potential can not be measured
using voltmeter.
(2) Measurement of inner potential difference
n
If electrons can not exchange freely
among the pile, i.e., poor electrical
conducting between phases.
n 1
1
1
Δ V  Δ
n
i



i 1

e0
1
Fermi level
 en
n
e
n 1
  i Δ i 1  n Δ1
1’
1
n
n
1
Δ V  Δ
n
i



i 1
1
n
  i Δ i 1
1
1
Fermi level
1'
e
 e1
e0

(3) Correct connection
n 1
1
Δ V  Δ 
n
i
i 1
n
n



 e e
1
n 1





V   
e0
  i Δ i 1  n Δ1






e  e


e0

V         
1

1’
n
1
Fermi level

Δ  0
Knowing V,  can
be only measured when

Δ   0
(4) Analysis of real system
Cu|Cu2+||Zn2+|Zn/Cu’
Consider the cell:
I
I
S2
S1
I’
II
V II  I V I '   I   I '
 ( I   S1 )  ( S1   S2 )  ( S 2   II )  ( II   I ' )
          
I
S1
S1
S2
S2
II
II
I'
II
I
For homogeneous solution without liquid junction potential
V II  I Δ S  S Δ II  const.
I
the potential between I and II depends on outer potential
difference between metal and solution.
V II  I Δ S  S Δ II  const.
I
Using reference with the same
V  Δ   const.
I
II
I
S
the exact value  of unknown electrode can not be detected.
I
I S
V

V1   1  const. 2  2  const.
II
I
I
S
II
( V )  (   )
I
II
I
S
The value of IS is unmeasurable but the change of is [
(IS )] can be measured.
I

S
absolute potential
Chapter 2
Electrode/electrolyte interface: structure and
properties
2.4 origination of surface potential
1) Transfer of electrons
Zn
Zn2+ Zn2+ Zn2+ Zn2+ Zn2+
e- e - e- e- e- e- e- e-
Cu
2) Transfer of charged species
eCu2+
e- Cu2+
Cu2+(aq)
e-
e-
Cu
Cu
Cu2+
ee-
Cu2+
ee-
Cu2+
3) Unequal dissolution / ionization
AgI
I¯
+
I¯
I¯
AgI
AgI
I¯
I¯
I¯
I¯
+
+
+
+
+
+
+
4) specific adsorption of ions
I¯
I¯
I¯
I¯
I¯
I¯
I¯
+
+
+
+
+
+
+
5) orientation of dipole molecules

–
–
–
–
+
+
– +
+ –
+
+ –
– +
+ –
– +
+ –
– +
+ –
–
–
–
–
–
Electron atmosphere
6) Liquid-liquid interfacial charge
KCl
HCl
K+
H+
+
H
Cl
HCl
KCl
H+ Cl-
H+ Cl-
H+ ClDifferent transference number
1) Transfer of electron
2) Transfer of charged species
3) Unequal dissolution
4) specific adsorption of ions
5) orientation of dipole molecules
6) liquid-liquid interfacial charge
1), 2), 3) and 6): interphase potential
4), 5) surface potential.
Electric double layer
e-
–
–
–
–
–
–
–
e- Cu2+
ee-
Cu
Cu2+
capacitor
ee-
Cu2+
Electroneutrality: qm = -qs
ee-
+
+
+
+
+
+
+
Cu2+
Holmholtz double layer (1853)
2.5 Ideal polarizable electrode and Ideal nonpolarizable electrode
iec
equivalent circuit
icharge
i = ich + iec
Charge of electric double layer
Electrochemical rxn
Faradaic process and non-Faradaic process
ideal polarizable electrode
an electrode at which no charge
transfer across the metal-solution
interface occur regardless of the
potential imposed by an outside
source of voltage.
I
0
E
no electrochemical current:
i = ich
Virtual ideal polarizable electrode
Electrode
Solution
K+ + 1e = K
Hg
-1.6 V
2Hg + 2Cl- - 2e- = Hg2Cl2
+0.1 V
Hg electrode in KCl aqueous solution: no reaction takes
place between +0.1 ~ -1.6 V
ideal non-polarizable electrode
an electrode whose potential does
not change upon passage of current
(electrode with fixed potential)
I
no charge current:
0
i = iec
E
Virtual nonpolarizable electrode
Ag(s)|AgCl(s)|Cl (aq.)
Ag(s) + Cl  AgCl(s) + 1e
For
measuring
the
electrode/electrolyte
interface, which kind of electrode is preferred,
ideal polarizable electrode or ideal nonpolarizable electrode?
2.6
interfacial structure
Experimental methods:
1) electrocapillary curve measurement
2) differential capacitance measurement
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?
The Gibbs adsorption isotherm





ni  ni  ni  ni

S

a’
a
S’
b
b’

ni  ni  ni  ni
ni
 
A
dG  SdT  dA   i dni
i
interface
Interphase
Interfacial
region
When T is fixed
dG  dA   i dni
i
dG  dA   i dni
i
Integration gives
G  A   i ni
dG  dA Ad   i dni   ni d
Ad   i ni d  0 d  Σ i d i
d  Σ i d i   e d e
de  Fd
e 

q
F
Gibbs
adsorption
isotherm
d  Σ i d i  qd
Lippman equation
d  i di  qd
When the composition of
solution keeps constant
d   qd
  

q  
   1 ,  2 ,1 ,
Electrocapillary curve
measurement
Electrocapillary curve
  

q  
   1 ,  2 ,1 ,
Zero charge potential: 0
q0
(pzc: potential at which
the electrode has zero
charge)
Electrocapillary curves for mercury
and different electrolytes at 18 oC.
C 2
 m  
2
C 2
Theoretical deduction of    m  
2
d  qd;
q  C;
d  C d
m
0


  d  C  d

C 2
  m      0   2
2

Differential capacitance
Cdl
Rs
Rct
2
q   c( )  d
1
Differential capacitance
Measurement of interfacial capacitance
– +
– +
– +
– +
– +
capacitor
The double layer capacitance
can be measured with ease
using
electrochemical
impedance spectroscopy (EIS)
through data fitting process.
Differential capacitance curves
Cd = C()
Integration of capacitance for charge density
Cd / F·cm-2
Differential capacitance curves
KI
60
KBr
40
KCl
K2SO4
20
0.0
KF
0.4
0.8
1.2
1.6
/V
Dependence of differential
capacitance on potential of
different electrolytes.
q / C·cm-2
Charge density on potential
-12
-8
-4
0
NaF
4
KI
8
12
0.4
Na2SO4
0.0
-0.4
-0.8
-1.2
/V
Dependence of differential capacitance on concentration
Potential-dependent
Concentration-dependent
Minimum capacitance at
potential of zero charge (Epzc)
36 F cm-2;
18 F cm-2;
differential capacitance curves for an
Hg electrode in NaF aqueous solution
Surface excess
q








q   
qs
+
z F    z F    qs  q
c0

Mv Av
v Mz+  v Az-
v z  v z
d MA  v d   v d 
d    i d i  0
d  dW .E.  dR.E.
d  qd    i d i
 qd    d     d 
For R.E. in equilibrium with cation
d   z FdR.E. d MA  v d   v d 
For any electrolyte
  
   v 



 MA R.E.
  
   v 



 MA R.E.
q / C·cm-2
Surface excess curves
KBr
6
cation
excess
KCl
4
2
KAc
0
KF
Anion
excess
-2
KF
-4
-6
0.4
KCl
KAc
0.0
-0.4
KBr
-0.8
-1.2
/V
2.7 Models for electric double layer
E
1) Helmholtz model (1853)
0
d
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)
C  0 r

A
d
q  0 rV

A
d
q charge on electrode (in
Coulomb)
2) Gouy-Chappman layer (1910, 1913)
E
Plane of shear
0
d
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.
Gouy and Chapman quantitatively described the
charge stored in the diffuse layer, qd (per unit area of
electrode:)
Boltzmann distribution
 x F 
C ( x)  C exp 

 RT 
0
 x F 
C ( x)  C exp

 RT 
0
Poisson equation
4x

E


2
x
x

2
 x  F C ( x)  C ( x)
  x F 
  x F 
 x  C F exp 
  exp

 RT 
  RT 
0
 2 x
4C 0 F    x F 
  x F 

exp 
  exp


2
x
   RT 
 RT 
  x 1    x 
 


2
x
2  x  x 
2
2
   x 
8C 0 F

 
 x  x 

2
  x F 
  x F 
exp  RT   exp RT 



 
Integrate from x = d to x = 
For 1:1 electrolyte
RTc0   1F 
 1 F 
q
exp
  exp 


2   2 RT 
 2 RT 
For Z:Z electrolyte
 z 1 F 
RTc0   z 1 F 
  exp 

q
exp
 2 RT 
2   2 RT 


qd  8RTC

1
* 2
zF0
sinh
2 RT
Experimentally, it is easier to measure the differential
capacitance:
1
* 2
zF0
zF (2C )
Cd 
cosh
RT
2 RT
e x  e x
sinh x 
2
Hyperbolic functions
2) Gouy-Chappman layer (1910, 1913)
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
3) Stern double layer (1924)
Combination of Helmholtz and Guoy-Chapman Models
The potential drop may be broken into 2:
m  s  (m  2 )  (2  s )
m  s  (m  2 )  (2  s )
Inner layer + diffuse layer
This may be seen as 2 capacitors in series:
Ci
M
Cd
S
1
1
1
 
Ct Ci Cd
Ci: inner layer capacitance
Cd: diffuse layer capacitance-given by Gouy-Chapman
Ci
Cd
M
S
1
1
1
 
Ct Ci Cd
Total capacitance (Ct) dominated by the smaller of the two.
At low c0
At high c0
Cd dominant
Ci dominant
Cd  Ct
Ci  Ct
Stern equation for double layer
q
Ci 
  1
1
  1 
Ci
RTc0   1F 
 1F 
exp
  exp 


2   2 RT 
 2 RT 
Discussion:
When c0 and are very small
1
  1 
Ci
RT  1F  0

 c
2  2RT 
Discussion:
When c0 and are very large
1
  1 
Ci
1

Ci
RT
 1 F  0
exp
 c
2
 2 RT 
RT
 1 F  0
exp
 c
2
 2 RT 
dq
F
RTc0   1F 
 1F 
Cd 

exp
  exp 


d1 2 RT
2   2 RT 
 2 RT 
Cd plays a role at low potential near to the p. z. c.
Fitting of Gouy-Chapman
model to the experimental
results
Fitting result of
Stern Model.
4) Gramham Model-specific adsorption
E
Triple layer
0
d
Specifically adsorbed anions
Helmholtz (inner / outer) plane
5) BDM fine model
Bockris-Devanathan-Muller, 1963
1
1
1 4 di 4 d0
 i 0 

Cd C C
i
0
i
Cd  C 
4 di
i
di i =5-6
do i =40
If rH2O = 2.7 10-10 m, i=6
Cd  20 F  cm-2  18 F  cm-2
Cd  36 F  cm-2
The progress of Model for electric double layer
1) Helmholtz model
2) Gouy-Chappman model
3) Stern model
4) Graham model
5) BDM model
What experimental phenomenon can they explain?
2.8 Fine structure
of the electric double layer
Without specific adsorption
– BDM model
With specific adsorption
– Graham model
Models of electric double layer
Who can satisfactorily explain all
the experimental phenomena in
differential capacitance curve?
Stern model: what have solved, what not?
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.
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.
i = 5-6
i = 40
Capacitance of compact
layer mainly depends on
inner layer of water
molecules.
1
1
1 4di 4d o
 


Cc Ci Co
i
o
di
do
i
Cc  Ci 
4di
If the diameter of adsorbed water molecules was
assumed as 2.7 10-10 m, i = 6, then
i
Cc 
4d i
1
6
2


 20Fcm
11
8
9 10
4  3.1416 2.7 10
The theoretical estimation is close to the experimental
results, 18-20 F cm-2, which suggests the reasonability of
the BDM model.
Inner Helmholtz Outer Helmholtz
plane 1
plane 2
Specially adsorbed anion
Solvated cation
Primary
Secondary
water layer water layer
Weak
Solvation
and
strong interaction let anions
approach electrode and
become
specifically
adsorbed.
4. BDM model
– Bockris, Devanathan
and Muller, 1963
Summary:
For electric double layer without specific adsorption
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