1. Electrochemistry for Engineers
Electrochemistry for Engineers
LECTURE 5
Lecturer: Dr. Brian Rosen
Office: 128 Wolfson
Office Hours: Sun 16:00

2. Forced Convection

3. Ideally polarizable electrodes
Double layer charging (if R ≠ infinity)

4. Kinetically controlled current flow
- Reaction rate constant, k
- Reaction rate law, (ex. r = kCO)
- Exchange current (iO)
- symmetry factor, α

5. Mass transport controlled
- 1D diffusion model
- Cottrell experiment
- Mass transport limiting current

6. Mass transport + kinetic control

7. Separate Contributions
When in the “mixed control” regime, it is sometimes possible to separate the “activation” parameters from the “transport” parameters by operating with a system with well defined transport properties = Rotating electrodes

8. Rotating Disc Electrodes
insulator

9. Laminar Flow at Electrode
Velocity
(cm/s)
Rotation
Rate
(s-1)
Kinematic viscosity (cm2/s)

10. Diffusion-Convection Layer
Systems with convection form diffusion-convection layers of constant thickness adjacent to the electrode surface. This is due to the drag created at the interface. The thickness is function of convection rate and form.
Coexistence of diffusion
and convection when x < δO

11. How to model Steady State Mass-Transport Limiting Current Density
At the limiting current, the concentration of “O” at the electrode surface is zero (in a reduction) and the rate of convection and rate of diffusion are equal.

13. separate and integrate
Recall..
Levich Equation

14. PEM Fuel Cells

15. Oxygen Reduction in Acid
Mass transport limiting current density at 3000 rpm

16. Linear Sweep Under Rotation
Kinetic current >> mass transport limit
MASS TRANSPORT LIMITED
Current estimated by Levich Equation
Dependence on ω
Kinetic current << mass transport limit
KINETIC LIMIT
Current estimated by BUTLER-VOLMER
No dependence on ω

17. Levich Plots
Mixed control
as kinetic limitations
set in at high ω
Limiting current
(plateau)
Mass transport control
At exceptionally high speeds (generally >2500 rpm), reactions with slow kinetics
cannot keep up with the increasing speed of mass transport. These kinetic limitations
cause the limiting current to fall BELOW the current predicted by the Levich equation

18. Modeling Mixed Control
Measured current under mixed control
Mass transport limited current
Kinetically limiting current in the absence of mass transfer limitations

19. Kouteckỳ-Levich Equation

20. Kouteckỳ-Levich Equation
Where E2 < E1 (reduction)
E2>E1 (oxidation)
As expected, iK grows larger (1/iK grows smaller) as the overpotentials is increased.

21. Plotting Mixed Control – f(E) Oxygen Reduction
1/iK
(-)

22. Mixed Control Visualized Pt 1
Kinetic Control
Mixed Control
Mass transport controlled

23. Mixed Control Visualized Pt 2iK
ilim i

24. Mechanistic Data on O2 Reduction

25. Mechanistic Information▪ ● ▲
Data from Eliran Hamo (EML-TAU)

26. Rotating Ring-Disc Electrodes (RRDE)
Recall convection pattern v(x,r)
Ring and disc are both WORKING ELECTRODES and
are INDEPENDENTLY CONTROLLED

27. Operation RO OR O Scanning E  (-) Constant E (+)
DISC
RING r
OR
RO O
One can measure the extent a specific product is
made at the disc by
reversing the reaction at the ring

28. Recall…
To what extent does the 2e- reaction occur at various potentials?

29. Example Operation or RRDE
Scanning E  (-)
Constant E (+)
DISC
RING r
O2 + 2H+ + 2e- H2O2
H2O2  O2 + 2H+ + 2e-
O2 + 4H+ + 2e- H2O O2
What is the practical limit for selecting the potential of
the ring in this case?

30. Ficks 2nd Law - RRDE RDE: (from before) RRDE:
Concentration is a function
of radius due to depletion!
RRDE:
DISC
RING r

31. Solving as before we get:……

32. RRDE Collection Efficiency
x = fraction of R that makes it to the ring electrode
y = fraction of R that is flung back into solution
1-x-y = fraction of R that is subjected to other processes (decomposition, conversion to non-
electroactive species.