Transcript Document

§2.11 interaction between adsorbate and metal
(1) Hydrophobic interaction (intermolecular reaction—
non-covalent interaction , surface activity);
(2) Electrostatic and chemical interaction (coordination);
(3) Interaction between adsorbate molecules; (aggregate,
island, crystallization)
(4) replacement of adsorbed water molecules
R H sl  n H 2 O ad  R H ad  n H 2 O sl
 G ad   H ad  T  S ad
Different from gaseous
adsorption
1) Difference between adsorption on
gas/solid interface and solution/electrode interface
Nearly all dissoluble organic compounds has more or less
surface activity at the solution/electrode interface, i.e., can
adsorb on the interface. At solution/electrode interface,
adsorbed species have to replace the formerly adsorbed
water molecules and become contact physically or
chemically with the electrode surface.
RHslon + nH2Oad
RHad + nH2Osoln
2) Adsorption isotherms:
Isotherm describes the relationship between the activity
(ai) of a species in solution and the amount of material
adsorbed per unit area on electrode surface (i).
The isotherms are developed from the condition that the
electrochemical potential for the adsorbed and solution
species are equal:
i

ads
 i
0 , ads
i
so ln
 RT ln a
ads
i

0 , so ln
i
 RT ln a
so ln
i
G
a
ads
i
a
ads
i
0

a
0 , ads
i
so ln
i
a

0 , so ln
i
  G i0
exp  
RT

so ln
i




i
The general form of an isotherm.
3) Langmuir isotherm
Assumptions:
1) no interaction between species; i.e., Gad is not a function
of coverage.
2) No heterogeneity of surface, all surface sites are equal.
3) there is a maximum coverage,  (monolayer)
sl
 
B 
bc i
1  bc
k ad
k des
sl
i
Bc 

1
 Surface concentration

B 
k ad
k des
Langmuir isotherm: plot of fractional coverage versus
concentration
4) adsorption in solution
R H sl  n H 2 O ad ===R H ad  n H 2 O sl
n
K ad 
X R H ,ad X H 2 O ,sl
X R H ,sl X
B c R H ,sl 
X R H ,ad 
n
H 2 O ,ad

(1   )
  n (1   )
n
n
n 1

  (1   ) n
X H 2 O ,ad 
(1   ) n
  (1   ) n

n
1
Bockris-Swinkels
adsorption isotherm
When n = 1  
bc
1  bc
c sl
RHslon + nH2Oad
K R H ,ad 
( X R H ,ad )( X H 2 O ,slon )
RHad + nH2Osoln
n
( X R H ,soln )( X H 2 O ,ads )
n
n 1
 
  [  n (1   )] 
K ad
0


c


R H ,slon

n 
n
n
 (1   )  
 55.4
Frumkin adsorption isotherm
Bc 

1
exp(  2 a )
Bockris-Swinkels
adsorption isotherm
Water concentration
Adsorption isotherms 1) Langmuir, 2) Temkin, 3)
Frumkin
5) Factors on adsorption
1) Effect of potential
Adsorbate desorbs at higher polarization.
Why?
Z 
N  N 
N  N 
Frumkin
Bockris



B  B 0 exp 




 

 q  0 d   C  1    0  2  
0


RT  



  E  Z 
K ( )  K ( 0 ) exp   nZ 

kT



-dipole moment of water molecule, E-electric field strength in
compact layer,  factor of intermolecular interaction, n- number
of water molecule replaced by organic adsorbant. Z-orientation
coefficient
Z 
N  N 
N  N 
2) Nature of metal
Desorption
capacitance peak
of n-pentanol in
0.1 M electrolyte
on different metal.
n-pentanol leaves metal’s surface when q = -13.10.6 C/cm2.
Attention:
Because surfactant can affect the surface state of electrode
significantly, therefore, the purification of solution used for
electrochemical study is very important.
Deionized water  triple distilled water
Homework
1. The PZC measured in NaF and NaCl are different, try to
make explanation to this difference and make comparison
between their values.
2. Describe the variation of surface excess of cation and
anion in KBr solution with respect to rational potential and
give explanation.
3. Why PZC can be only measured on metals with high
hydrogen overpotential?
4. Adsorbates with aromatic rings can adsorbed on
electrode surface with different configuration, explain the
effect of potential on their configuration.
Chapter 3
transport phenomena in electrolytic systems
and concentration overpotential
§3.1 significance of mass transport
Interfacial reaction
Mechanism of electrode process
Heterogeneous reaction
Surface region
electrode
Preceding
Chem. rxn
O*
Mass
transfer
Os
Ob
Desorption/adsorption
*
O
Bulk solution
EC rxn
R*
Desorption/ adsorption
R*
Chem. rxn
succeeding
Rs
Mass
transfer
Rb
Why do we need to concern mass transport?
e
Limiting
current
Limiting
current
A typical polarization curve for a irreversible electrode reaction
§3.2 fundamentals of transport phenomena
In any electrolysis, the species consumed (or generated) at
the electrode must be transported toward it (or carried away).
Cu2+ + 2e¯  Cu
The copper ions migrate toward
the cathode under the electric field.
Electrorefining of Cu
The transference number of Cu2+
is ca. 0.4, this means for 10 Cu
atoms deposited only 4 are
transported by electric migration,
the remaining 6 must reach the
cathode by other transport
mechanism.
1 Flux density and velocity
Driving force:
gradients of the
electrochemical potential

 i  z i e 0


 i
  i    i  zi F 
i
a physical parameter with dimension of Newton
per mole is a force.
For a certain species j, consider two points in the solution,
r and s (an infinitesimal distance form one another ) and:
This difference of
over a distance can arise because of
differences of concentration (or activity) of species j at r and
s (a concentration gradient) or because of difference of  at
r and s (an electric field or potential gradient). In general, a
flux of species j will occur to alleviate this difference of
.
The flux, J (mol s-1 cm-2), is proportional to the gradient,
grad or  of
.
J i  grad  i
or
J i  i
2 Basic concepts
transport modes:
1) electric migration
2) diffusion
3) convection
1) Electric migration
B
A
C
movement of charged species
under electric field due to
electrostatic
interaction
(potential gradient)
species move with respect
to liquid.
C－, Z－, U－; C＋, Z＋, U＋;
flux

  Exu c
0
x ,m
Ex strength of electric field, u0 ionic mobility,
(3.1)
2) Convection
Turbulent flow
Mechanical and magnetic stirring
Hydrodynamic movement
due to displacement of
solution planes
include: natural convection
and forced convection
Laminar flow
Nernst diffusion layer of
stagnant solution
Convection:
species move with liquid due to density different (density
gradient) caused by either concentration or temperature
difference.

x ,c
 xc
(3.2)
3) Diffusion:
A molecular mode of transport which tends to equalize
concentrations and which is set up only if concentration
difference / gradient exist.
species move with respect to liquid
Fick’s first law for stationary state

x ,d
 c 
 

 x 

x ,d
 c 
 D 

 x 
D diffusion coefficient, (c/ x) concentration gradient.
Influential factors for diffusion coefficient
Ions
105 D / cm2s-1
Ions
105  D / cm2s-1
9.34
OH
5.23
Li+
1.04
Cl
2.03
Na+
1.35
NO3
1.92
K+
1.98
Ac
1.09
Pb2+
0.98
SO42
1.08
Cd2+
0.72
CrO42
1.07
Zn2+
0.72
Fe(CN)63
0.76
Cu2+
0.72
Fe(CN)63
0.64
H+
Crystalloid
Colloid
Radius of
solvated ions,
temperature,
viscosity,
concentration
Di 
RT
z i Fi
U0
Theoretical calculation of diffusion co-efficient
Di 
kT
6  ri
Leveling effect




G
dif
2 kT
Di  
exp  


h
RT 


ci d  i 
D i   Li R T  1 

 i dc i 

Diffusion coefficient is a function of concentration.
Extension of diffusion layer
c0
After
the
electrolysis
current
is
switched on, the diffusion layer is set
up and extends progressively toward
the interior of the solution; i.e., its
thickness of diffusion layer grows
with time.
depleted layer –
diffusion layer
diffusion
Microscopic, molecule by molecule transport mechanism.
Brownian motion, no directionality except that resulting form a
concentration gradient.
Movement of a species under the influence of a gradient of
chemical potential (i.e., a concentration gradient)
migration
Microscopic, molecule by molecule transport mechanism,
driven by electric field. Has directionality governed by field.
Movement of a charged body under the influence of an electric
field (a gradient of electrical potential)
convection
Macroscopic (segmented by solution element) transport
mechanism, directional, based on external forces. Stirring or
hydrodynamic transport, but also natural convection
(convection caused by density gradients) and forced convection.
transport modes:
1) electric migration

2) diffusion

x ,m
x ,c
3) convection

  Exu c
0
x ,d
 xc
 c 
 D 

 x 
3 simplification of mass transport
The general equation for mass transport
J  J d ,i  J c ,i  J m ,i
 c 
0
  Di 
   x ci  E x u ci
 x 
It is rather complicated.
No
convection
in
the
immediate vicinity of the
electrode.
At
increasing
distance from the electrode,
mass transport by convection
becomes more and more
important.
No diffusion exists beyond diffusion layer because there is no
concentration gradients.
electric migration takes place both inside and outside the
diffusion layer.
Elimination of electric migration:
When supporting electrolyte of high concentration (nonelectroactive species) was added (10 times more than
electroactive species), the mass transport due to electric
migration of electroactive species can be neglected.
Elimination of convection:
At immediate vicinity to electrode within stationary
liquid layer or make mass transport occur in stationary
medis, no convection occurs.
§3.4 Diffusion in absence of convection:
steady state and nonsteady state
1) Fick’s first law
unidirectional diffusion within a isotropic medium, can be
generalized to a three-dimentional diffusional flux
J x ,d
 c 
 D 


x


  i ( / x )
J x ,d   D  c
Where grad or  is a vector operator, i is the unit vector along
the axis and x is distance.
For 3D mass transfer
 i

x
 j

y
k

z
 depends on the choice of a suitable coordinate system for
each particular case.
2) Fick’s second law
Generally, most diffusional processes of electrochemical
interest involve time-dependent concentration characteristics.
The amount of species accumulated
within the volume element due to the
x-directional flux is
A
B
Jx=x
Jx=x+dx
D
C
dx
The change of the concentration
in the reference volume can be
expressed as
 dc 
J x x   Di  i 
 dx  x  x
J x  x  dx
 ci
t
  dc i 
d  dc i
  Di 
  
  dx  x  x dx  dx

J x  x  J x  x  dx
dx
 
 dx 
 
 d 2 ci 
 Di 
2 
dx


For Cartesian coordinates:
   ci     ci     ci 

D

D

D

t
x 
x  y 
y  z 
z 
 ci
 ci
t
 div ( D grad c i )
 ci
t
Fick’s second
law
 D i  ci
2
The unidirectional diffusion for a real solution
 ci
d  dc i 
 Di


t
dx  dx 
For stationary state
 ci
t
0
J x x
 dc i 
  Di 

dx

 x x
3) Stationary state diffusion
c0
 ci
t
0
Transition state (nonsteady state):
the thickness of diffusion layer
() grows with time. The
stationary state under pure
diffusion
is
only
an
approximation.
At the initiation of diffusion, large variations of either the
flux toward the interface or the local concentration are
produced. At long times, either the increase or the depletion
of the reacting species at the interface causes density
gradients, which generate the bulk fluid motions of natural
convection.
c
Diffusion
layer
 cease to grow when diffusion
c0
layer reaches the region with
strong mechanical stirring, and
the diffusion become steady.
cs
0
y
The stationary state is achieved
by complex transport mechanism
(convective diffusion) rather than
by diffusion alone.
2
At infinite-plane interface D  2 c  0
i
i
d ci
dx
2
0
d ci
 K
dx
ci  K 0  K 1 x
The concentration profile is represented by a straight line.
4) Apparatus for achieving stationary diffusion
anode
stirrer
cathode
capillary
Bulk solution

c0
C
C0
Cs
electrode
x
Diffusion at steady conditions
0
s



C
C

C




  const .  

x





Therefore:
ci, 0
J x ,d
ci, 1
Membrane with micropores
C0 Cs 
 c 
 D 

  D 

 x 


The current corresponding to
diffusion:
i   nF J x , d
C0 Cs 
 nF D 




C0 Cs 
i  nF D 




When the surface concentration becomes 0 (complete
concentration polarization), the current reaches maximum –
limiting current density
id  nFD
c
0

i
id
c c
0

c
0
s
 1
c
s
c
0
The plane-interface diffusion equation can be applied to real
systems as long as the diffusion distance is much larger than
the microscopic unevenness of the plane.
Question: using limiting diffusion current, how to determine D
and c0?
5) Helmholtz plane, diffused layer and diffusion layer
Double layer region,
diffusion region,
convection region
Surface concentration:
cs = c– = c+
When the electrolyte is not very dilute, the thickness of the double layer
is 10-9 – 10-8 m (i.e.,1-10 nm ). x1 is usually taken as x0 = 0. the
thickness of diffusion region is ca. 10-5 – 10-4 m (i.e., 10 –100 m)
3.5 Diffusion with convection and RDE
1 Diffusion with convection
Ideal / nonideal stationary state
Difference between stationary and non-stationary states:
1) ci = f(x); ci = f(x, t);
2) the thickness of diffusion layer
3) relativity
y
The velocity at different
distance from the impact
point can be expressed as
x
y 
u0
y
 


Impact point
In boundary layer, there is gradient of flux.
 y  0.33
u0
y
x
 B  5.2
y
u0
The thickness of the boundary layer usually defined as the
distance at which vy = 0.99 u0.
Relationship between the thickness of boundary layer
and diffusion layer

B

3
 B  5.2
= 10-2 cm2 s-1,
Di

Di = 10-5 cm2 s-1
y
u0
  Di 
1/ 3
1/ 6
y
1/ 2
1 / 2
u0
 contains the effect of convection on
diffusion
 depends not only on Di but also on the hydrodynamic factor (, u0)
and the shape of electrode (y)
The effective thickness of the diffusion layer
ci  ci
 dc i 

 const


E
 dx  x  0
0
ci  ci
0
E 
s
s
( dc i / dx ) x  0
To extrapolate the tangent line
at cs to AL, the distance E is
the effective length of diffusion
layer.
When x > , mass transport mainly rely on convection, while x < , it
mainly depends on diffusion. In fact, diffusion and convection co-exists.
ci  ci
0
j  nFD i
s
E
 nFD i
2/3
0 
1/ 2
1 / 6
y
1 / 2
(ci  ci )
0
s
0
j d  nFD i
ci
E
 nFD i
2/3
0 
1/ 2
1 / 6
y
1 / 2
0
ci
Discussion:
jd  Di3/2, there exists convection
j = jd + jc
jd depends on stirring, viscosity, and position
3.3.2 Rotating disc electrode
Diffusion under convection:
ci  ci
0
j  nF D i
s
E
 nF D i
2/3
0 
1/ 2
1 / 6
y
1 / 2
(ci  ci )
0
s
This formula demonstrates that the current density of
plane electrode depends significantly on the shape /
dimension of the electrode.
If this kind of electrode is used to study the kinetics of
electrode process, only the statistic/averaged results
over the total electrode surface can be obtained.
In 1942, an electrochemist in the former Soviet Union named
Levich solved the problem by using rotating disc electrode
(RDE) method.
PTFE sheathing
Embedded metal disc electrode
High-speed electric motor
The impact point is the
center of the disc.
Rotating ring disk electrode
(RRDE)
IL = (0.620)∙z∙F∙A∙D2/3∙1/2∙–1/6∙c
Levich Equation
 speed of rotation (rad∙s-1),
 kinematic viscosity of the solution (cm2∙s-1),
kinematic viscosity is the ratio between solution
viscosity and its specific weight.
For pure water:  = 0,0100 cm2∙s-1, For 1.0 mol∙dm-3
KNO3 is  = 0,00916 cm2∙s-1
(at 20°C).
c concentration of electroactive species (in mol.cm-3, note
unusual unit)
D diffúsion coefficient (cm2∙s-1), A electrode area in cm2
j d  nF D
2/3
i


1/ 2
0
1 / 6
y
1 / 2
   r  G ( )
r
Impact point
As distance from the center increases,
thickness
of
diffusion
layer
()
increases while the u0 increase which
cause decrease of .
s
i
 r  r  F ( )

y
(c  c )
0
i
 y   H ( )
 
  
 
1/ 2
y
 is a dimensionless
parameter related to
distance.

r
y
   r  G ( )
Impact
point
 y   H ( )
 r  r  F ( )
At y = 0,  = 0, G(0) = 1, F(0) = H(0) = 0,  = r, r = y = 0
As the distance away from the impact point (y) increases, G()
decreases together with , while –H() increases with increase of y,
and F() first increases and then decreases with r changing with the
same tendency.
When   3.6, both F() and G() become smaller enough to be
neglected. The range within 0 <  < 3.6 is the hydrodynamic boundary
region.
s
0
ci / ci
1.0
 y   0 .5 1
 ci
3/2
1 / 2
v
2
Di
y
2
  0.51
3/2
v
1 / 2
y
2
0.8
0.6
  ci 
y 


y


2
0.4
0.2
Integration at y = 0, ci= cis,
y, ci= ci0
ci  ci
0
ci ( y )  ci 
s
B
Di
A

s
0.8934(3 B )
D i
3 / 2
v
0.51
1/ 2
1/ 3

0
1
2
y / 1.61 D 
1/ 3
i
y
0
exp ( 
y
3
3B
) dy
1 / 2 1 / 6
v
3
ci  ci
0
i 
s
1/ 3
  ci 


 y  y 0
I  0.62
nF
vi
D
 1.61 D i 
2/3
i

Levich equation
1/ 2
v
1 / 6
1 / 2
v
1/ 6
(c  c )
0
i
s
i
I 
so we can vary δ by
changing ω
I d  0.62
nF
vi
Di 
2/3
1/ 2
v
1 / 6
1/ 2
The way to increase
current density and
eliminate diffusion
polarization
0
ci
I  0.62
nF
vi
I d  0.62
nF
vi
Di 
2/3
1/ 2
Di 
1/ 2
Validity:
1) laminar fluid
2) diffusion control
2/3
v
v
1 / 6
1 / 6
( ci  ci )
0
s
0
ci
Valid when concentrated
supporting electrolyte presents
to eliminate electric migration.
Application:
1) measurement of D: from the slope of Id~ 1/2
2) on knowing of D, measure n and c0
3) determine whether or not diffusion is r.d.s.
Normalization of the current to the rate of rotation: to plot
i/1/2 as a function of potential and compare the response
for different values of .
Using RDE, the limiting
diffusion current can be raised to
10-100 Acm-2, three-order times
that of common electrode.
I
600 rpm
300 rpm
100 rpm
Id

S  0.62
nF
vi
2/3
Di
v
1 / 6
0
ci
1/2
Catalytic voltammograms for film of NiFe hydrogenase
adsorbed at a rotating disc PGE electrode under 0.1 atm H2.
(Pershad et al Biochemistry 38, 8992 (1999)
Based on detectable coverage limit, kcat >> 1500 sec-1 at 30 oC
2x
[4Fe-4S]2+/+
+/0
[3Fe-4S]
3800 rpm
15.0
3000 rpm
Current / A
2000 rpm
1000 rpm
5.0
E (H+/H2)
i
-0.4
-0.2
keeps increasin
as rotation rate
increased.
lim
Buffer
-5.0
-0.6
H2 oxidation ra
0
Potential vs SHE
0.2
Scan rate 0.2 V