1. §2.11 interaction between adsorbate and metal
Hydrophobic interaction (intermolecular reaction—non-covalent interaction , surface activity);
Electrostatic and chemical interaction (coordination);
Interaction between adsorbate molecules; (aggregate, island, crystallization)
replacement of adsorbed water molecules
Different from gaseous adsorption

2. RHslon + nH2Oad RHad + nH2Osoln
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

3. 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:

4. The general form of an isotherm.

5. 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)
 Surface concentration

6. 
Langmuir isotherm: plot of fractional coverage versus concentration

7. 4) adsorption in solution 1
Bockris-Swinkels adsorption isotherm
When n = 1

8. RHslon + nH2Oad RHad + nH2Osoln
Bockris-Swinkels adsorption isotherm
Water concentration
Frumkin adsorption isotherm

9. Adsorption isotherms 1) Langmuir, 2) Temkin, 3) Frumkin

10. 5) Factors on adsorption
1) Effect of potential
Adsorbate desorbs at higher polarization.
Why?

11. Frumkin
Bockris
-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

12. 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.

13. Deionized water  triple distilled water
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

14. 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.

15. Chapter 3
transport phenomena in electrolytic systems　and concentration overpotential

16. §3.1 significance of mass transport
Interfacial reaction
Heterogeneous reaction
Mechanism of electrode process Ob
Surface region
Bulk solution Os
Mass transfer O*
Chem. rxn
Desorption/adsorption R*
EC rxn
Desorption/ adsorption Rb Rs
Preceding
succeeding
electrode

17. Why do we need to concern mass transport?
Limiting current e
A typical polarization curve for a irreversible electrode reaction

18. §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.
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.
Electrorefining of Cu

19. 1 Flux density and velocity
Driving force:
gradients of the electrochemical potential
a physical parameter with dimension of Newton per mole is a force.

20. 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 or

21. 2 Basic concepts transport modes: 1) electric migration 2) diffusion
3) convection

22. 1) Electric migration flux 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＋;
(3.1)
flux
Ex strength of electric field, u0 ionic mobility,

23. 2) Convection Mechanical and magnetic stirring Turbulent flow
Hydrodynamic movement due to displacement of solution planes
include: natural convection and forced convection
Laminar flow
Nernst diffusion layer of stagnant  solution

24. Convection:
species move with liquid due to density different (density gradient) caused by either concentration or temperature difference.
(3.2)

25. 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
D diffusion coefficient, (c/ x) concentration gradient.

26. Influential factors for diffusion coefficient
Ions
105 D / cm2s-1
105  D / cm2s-1 H+
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+
Fe(CN)63
0.76
Cu2+
0.64
Crystalloid
Colloid
Radius of solvated ions, temperature, viscosity, concentration

27. Theoretical calculation of diffusion co-efficient
Leveling effect
Diffusion coefficient is a function of concentration.

28. Extension of diffusion layerc0
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

29. 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.

30. transport modes:
1) electric migration
2) diffusion
3) convection

31. 3 simplification of mass transport
The general equation for mass transport
It is rather complicated.

32. No convection in the immediate vicinity of the electrode
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.

33. Elimination of electric migration:
When supporting electrolyte of high concentration (non-electroactive 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.

34. §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
Where grad or  is a vector operator, i is the unit vector along the axis and x is distance.
For 3D mass transfer
 depends on the choice of a suitable coordinate system for each particular case.

35. 2) Fick’s second law
Generally, most diffusional processes of electrochemical interest involve time-dependent concentration characteristics. A B C D
Jx=x dx
Jx=x+dx
The amount of species accumulated within the volume element due to the x-directional flux is
The change of the concentration in the reference volume can be expressed as

36. For stationary state For Cartesian coordinates: Fick’s second law
The unidirectional diffusion for a real solution
For stationary state

37. 3) Stationary state diffusionc0
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.

38. At infinite-plane interfacecs y
Diffusion layer
 cease to grow when diffusion layer reaches the region with strong mechanical stirring, and the diffusion become steady.
The stationary state is achieved by complex transport mechanism (convective diffusion) rather than by diffusion alone.
At infinite-plane interface
The concentration profile is represented by a straight line.

39. x 4) Apparatus for achieving stationary diffusion anode stirrerCs C
electrode 
capillary
cathode
anode
stirrer
Bulk solution c0

40. Diffusion at steady conditions
Membrane with micropores
ci, 0
ci, 1
Therefore:
The current corresponding to diffusion:

41. When the surface concentration becomes 0 (complete concentration polarization), the current reaches maximum – limiting current density
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?

42. cs = c– = c+ 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 – 10-4 m (i.e., 10 –100 m)

43. 3.5 Diffusion with convection and RDE
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

44. In boundary layer, there is gradient of flux.
Impact point
The velocity at different distance from the impact point can be expressed as
In boundary layer, there is gradient of flux.
The thickness of the boundary layer usually defined as the distance at which vy = 0.99 u0.

45. Relationship between the thickness of boundary layer and diffusion layer
= 10-2 cm2 s-1,
Di = 10-5 cm2 s-1
 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)

46. The effective thickness of the diffusion layer
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.

47. Discussion:
jd  Di3/2, there exists convection
j = jd + jc
jd depends on stirring, viscosity, and position

48. 3.3.2 Rotating disc electrode
Diffusion under convection:
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.

49. 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.

50. Rotating ring disk electrode
(RRDE)

51. 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

52.  is a dimensionless parameter related to distance.y r 
Impact point
As distance from the center increases, thickness of diffusion layer () increases while the u0 increase which cause decrease of .
 is a dimensionless parameter related to distance.

53. y r 
Impact point
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.

54. Integration at y = 0, ci= cis, y, ci= ci01 2 3
0.2
0.4
0.6
0.8
1.0
Integration at y = 0, ci= cis, y, ci= ci0

55. so we can vary δ by changing ω
Levich equation
The way to increase current density and eliminate diffusion polarization

56. Validity:
1) laminar fluid
2) diffusion control
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.

57. 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 .  I
100 rpm
300 rpm
600 rpm
Using RDE, the limiting diffusion current can be raised to Acm-2, three-order times that of common electrode.
1/2 Id

58. Based on detectable coverage limit, kcat >> 1500 sec-1 at 30 oC
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
[3Fe-4S]+/0
2 x [4Fe-4S]2+/+ -
3800 rpm
15.0
3000 rpm
H2 oxidation rate
keeps increasing
as rotation rate is
increased.
Scan rate 0.2 V/s
2000 rpm A m
1000 rpm
Current /
E (H+/H2)
5.0 i
lim
Buffer -
5.0 -
0.6 -
0.4 -
0.2
0.2
Potential vs SHE