1. Evans Diagrams

2. Where we left off

3. Tafel Equation
The Tafel slope is an intensive parameter and does not depend on the electrode surface area.
i0 is and extensive parameter and is influenced by the electrode surface area and the kinetics or speed of the reaction.
Notice that the Tafel slope is restricted to the number of electrons, n, involved in the charge transfer controlled reaction and the so called symmetry factor, .
n is often = 1 and although the symmetry factor can vary between 0 and 1 it is normally close to 0.5.
This means that the Tafel slope should be close to 120 mV if n = 1 and 60 mV if n = 2. (The latter is normally not the case)

4. Butler-Volmer Equation
where:
I = electrode current, Amps
Io= exchange current density, Amp/m2
E = electrode potential, V
Eeq= equilibrium potential, V
A = electrode active surface area, m2
T = absolute temperature, K
n = number of electrons involved in the electrode reaction
F = Faraday constant
R = universal gas constant
α = so-called symmetry factor or charge transfer coefficient dimensionless
The equation is named after chemists John Alfred Valentine Butler and Max Volmer

5. Butler-Volmer Equation – High Field Strength
ia and ic are the exhange current densities for the anodic and cathodic reactions
These equations can be rearranged to give the Tafel equation which was obtained experimentally

6. Butler Volmer Equation - Tafel Equation

7. Current Voltage Curves for Electrode Reactions
Without concentration and therefore mass transport effects to complicate the electrolysis it is possible to establish the effects of voltage on the current flowing. In this situation the quantity E - Ee reflects the activation energy required to force current i to flow. Plotted below are three curves for differing values of io with α = 0.5.

8. Current Voltage Curves for Single Electrode Reactions
Electrochemical reactions of different i0 or degrees of reversibility
The iE curves from the previous slide have been rotated.
Voltage
Current

9. Single Chemical Reaction
Only at appreciable over-potentials does the reverse reaction become negligible
At Ee the forward and reverse currents are equal

10. Electrochemical reaction which has a large exchange current density, i0, This means that a small applied voltage results in an appreciable increase in current.
Electrode reactions which have a high exchange current density are not easily polarised. Examples are the hydrogen evolution reaction on Pt and AgCl + e ↔ Ag + Cl-
The H+/H2(Pt) and Ag/AgCl make good reference electrodes because they are not easily polarised

11. Electrochemical reaction in which the i0 value is very low
Electrochemical reaction in which the i0 value is very low. This means that it takes an appreciable over-potential to produce a significant current.
This electrode is easily polarisable since a small current would result in a significant change in voltage 11

12. At low overpotential the Butler Volmer equation is linear (Stern Geary equation)12

13. So far we have looked mainly at single electrochemical reactions

14. Anodic and cathodic reactions are coupled at a corroding metal surface
KINETICS OF AQUEOUS CORROSION
Anodic and cathodic reactions are coupled at a corroding metal surface
Schematics of two distinct corrosion processes.
(a) The corrosion process M + O  Mn+ + R showing the separation of anodic and cathodic sites. (b) The corrosion process involving two cathodic reactions.

15. Butler Volmer graphs for two electrochemical reactions
Wagner Traud Method
The cathodic and anodic reactions are drawn together on the same graph to show how the currents are equal at the corrosion potential

16. Note in the previous diagram that:
ia = ic = icorr at the corrosion potential Ecorr
Ecorr is a mixed potential which lies between (Ee)c and (Ee)a. In this case it is closer to (Ee)a because the i0 and the kinetics of the anodic reaction is faster.
The metal dissolution is driven by the anodic activation overpotential ηa = Ecorr - (Ee)a
The cathodic reaction is driven by the cathodic activation overpotential ηc = Ecorr - (Ee)c
The thermodynamic driving force
ΔE = (Ee)c - (Ee)a
ΔE is usually large enough to put Ecorr in the Tafel region for both reactions, i.e. the reverse reaction is negligible.

17. Evans Diagrams
It is convenient to represent the linear plots of i and E as log i/E plots with the negative cathodic current plotted positively, i.e. both the anodic and cathodic current appear in the positive quadrant.
The linear region gives us the Tafel slopes
The i0 for the individual reactions can be obtained by extrapolating back to (Ee)a and (Ee)c if these values are known.

18. Evans Diagrams
The intersection of the two curves at Ecorr gives us icorr
Of course you do not see the portion of the E/logic and E/logia at potentials more positive and more negative of Ecorr respectively.
However, it is important to realise that they exist.
I believe it is worthwhile to look at your Tafel type measurements as a linear representation of current and voltage.
The logarithmic plots involve a mathematical manipulation of data and errors can be introduced.
Nevertheless Evans Diagrams are a convenient way of viewing electrochemical reactions

19. Evans Diagrams
In this case the cathodic reaction with the higher oxidation potential is controlling the reaction

20. Evans Diagrams
In this example because of the faster kinetics. the cathodic reaction taking place at the lower oxidation (+ve)
Potential is influencing the corrosion rate more,

21. Evans Diagrams
The situation in the previous example often occurs for a metal corroding in acid, compared with the metal corroding in dissolved oxygen.
Despite the thermodynamic driving force, Ee, being greater for oxygen than H2/H+, the acid corrosion is faster.
In some cases the oxygen and acid have a synergistic effect. For example in the case of Ni corrosion. The reaction is quite slow in sulphuric acid (0.5 M) and it is also slow in water saturated with air at pH 7. In the latter case a passive protective oxide film is formed. However, in the presence of sulphuric acid and air. The corrosion rate is relatively rapid. The acid dissolves the protective oxide film allowing oxygen to corrode the metal.

22. Evans Diagrams i0 can vary from 10-3 – 10-12 A cm-2
The relative corrosion rates of metals depends on the i0 and mass transfer.
With acid corrosion: 2H+ + e → H2
i0 can vary from 10-3 – A cm-2
The Tafel slope  120 mV/decade
For oxygen corrosion O2 + H2 O + 4e → 4OH-
I0 is difficult to difficult to determine because it is very low, but it is of the order of <10-10 A cm-2
The Tafel slope >120 mV/decade

23. Exchange Current Densities in 1 Molal H2SO4
Electrode Material
-log10(A/cm2
Palladium
3.0
Platinum
3.1
Rhodium
3.6
Nickel
5.2
Gold
5.4
Tungsten
5.9
Niobium
6.8
Titantium
8.2
Cadmium
10.8
Manganese
10.9
Lead 12
Mercury
12.3
The exchange current density for the hydrogen reduction reaction on metals is useful because it give an indication of the speed of this reaction on various metals.

24. α Values for Some Reactions
Metal
System α Pt
Fe e ↔ Fe2+
0.58
Ce e ↔ Ce3+
0.75 Hg
Ti e ↔ Ti3+
0.42
2H e ↔ H2
0.50 Ni Ag
Ag+ + e ↔ Ag
0.55

25. Evans Diagrams The slowest reaction controls the rate of corrosion.
Normally this is the cathodic reaction.
In this example:
A small changes in kinetics of cathode have a large effect on corrosion rate.
A small changes in kinetics of anode have small effect on corrosion

26. Mass Transfer Control
If the cathodic reagent at the corrosion site (e.g., dissolved O2 in the O2 reduction) is in short supply, mass transfer of the reagent can become rate limiting.
The cathodic charge-transfer reaction at the metal/solution interface is fast enough to reduce the concentration of the reagent at interface (cathodic sites) to a value less than that in the bulk solution.
This sets up a concentration gradient and the reaction becomes diffusion controlled.

27. Mass Transfer Control
When the corrosion rate is limited by mass transfer it can be increased by:
By altering the bulk concentration
By stirring and reducing the thickness of the Nernst diffusion layer

28. Mass Transfer Control Diffusion or Mass Transfer Controlled
Activation Controlled

29. Mass Transfer Control
Increase in corrosion potential, Ecorr, and the corrosion current, icorr, due to an increase in mass transfer caused by stirring.

30. Mixed Transfer Control
The cathodic Tafel plot often shows deviation from ideal Tafel behavior
Polarization curve for the cathodic process showing:
Activation polarization
Joint activation-concentration polarization
Mass transport-limited corrosion control

31. Evans Diagrams
Cathodic Control
Anodic Control
Mixed Control

32. Galvanic Corrosion – Influence of i0

33. Cyclic Voltammetry at a Pt Electrode in Sulphuric Acid Solution
The peak height of the adsorption/desorption processes is directly proportional to scan, i.e., the charge iE or area under the curve. This contrasts with a diffusion process where the peak height is proportional to the square root of the scan rate.
Oxygen Adsorption Pt-O
Formation of adsorbed H (Pt-H)
Oxygen Evolution O2 ↑
Reduction of adsorbed H (Pt-H)
Reduction of adsorbed oxide film (Pt-O)
Hydrogen Evolution H2 ↑