evan diagram

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Evans Diagrams MEHRAN UNIVERSITY OF MEHRAN UNIVERSITY OF ENGINEERING AND TECHNOLOGY, ENGINEERING AND TECHNOLOGY, JAMSHORO, SINDH, PAKISTAN JAMSHORO, SINDH, PAKISTAN DEPARTMENT OF METALLURGY AND DEPARTMENT OF METALLURGY AND MATERIALS ENGINEEING MATERIALS ENGINEEING

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Page 1: Evan diagram

Evans DiagramsMEHRAN UNIVERSITY OF MEHRAN UNIVERSITY OF

ENGINEERING AND ENGINEERING AND TECHNOLOGY, JAMSHORO, TECHNOLOGY, JAMSHORO,

SINDH, PAKISTANSINDH, PAKISTANDEPARTMENT OF METALLURGY DEPARTMENT OF METALLURGY AND MATERIALS ENGINEEINGAND MATERIALS ENGINEEING

Page 2: Evan diagram

Where we left off

Page 3: Evan diagram

Tafel Equation

Page 4: Evan diagram

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

Page 5: Evan diagram

Butler-Volmer Equation – High Field Strength

ialoverpotent cathodichigh at

exp

ialoverpotent anodichigh at

1exp

0`

0`

RTnFii

RTnFii

cc

aa

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

Page 6: Evan diagram

Butler Volmer Equation - Tafel Equation

nnb

in

ain

a

iba

in

in

in

in

inFRT

inFRT

oo

acc

a

ccc

c

ccc

c

10590

or 0590

10590 or 0590

equation Tafel known wellthe is equation The

reactionanodic C25 at 1

05901

0590

reactioncathodic C25 at 05900590

00

00

0

..

ln.ln.

log

log.log.

log.log.

lnln

Page 7: Evan diagram

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.

Page 8: Evan diagram

Current Voltage Curves for Single Electrode Reactions

CurrentV

olta

ge

Electrochemical reactions of different i0 or degrees of reversibility

The iE curves from the previous slide have been rotated.

Page 9: Evan diagram

Single Chemical ReactionOnly at appreciable over-potentials does the reverse reaction become negligible

At Ee the forward and reverse currents are equal

Page 10: Evan diagram

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

Page 11: Evan diagram

11

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

Page 12: Evan diagram

12

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

RTnFii o

Page 13: Evan diagram

So far we have looked mainly at single electrochemical reactions

Page 14: Evan diagram

KINETICS OF AQUEOUS CORROSIONAnodic and cathodic reactions are coupled at a corroding metal surface

14

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.

Page 15: Evan diagram

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

Butler Volmer graphs for two electrochemical reactions

Page 16: Evan diagram

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.

Page 17: Evan diagram

Evans DiagramsIt 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.

Page 18: Evan diagram

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

Page 19: Evan diagram

Evans Diagrams

In this case the cathodic reaction with the higher oxidation potential is controlling the reaction

Page 20: Evan diagram

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,

Page 21: Evan diagram

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.

Page 22: Evan diagram

Evans Diagrams• 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 – 10-12 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

Page 23: Evan diagram

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

Page 24: Evan diagram

α Values for Some ReactionsMetal System α

Pt Fe3+ + e ↔ Fe2+ 0.58Pt Ce4+ + e ↔ Ce3+ 0.75Hg Ti4+ + e ↔ Ti3+ 0.42Hg 2H+ + 2e ↔ H2 0.50Ni 2H+ + 2e ↔ H2 0.58Ag Ag+ + e ↔ Ag 0.55

Page 25: Evan diagram

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

Page 26: Evan diagram

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.

maxLim corrb

c

sbc

iCnFD

i

CCnFDi

Page 27: Evan diagram

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

layer diffusion Nernst the ionconcentrat surface the

ionconcentrat bulk the constantFaraday the

electrons of number the currentcathodic the

:WheremaxLim

s

b

c

corrb

c

sbc

CCFni

iCnFD

i

CCnFDi

Page 28: Evan diagram

Mass Transfer Control

Diffusion or Mass Transfer Controlled

Activation Controlled

Page 29: Evan diagram

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

Page 30: Evan diagram

Mixed Transfer Control

Polarization curve for the cathodic process showing: 1.Activation polarization2.Joint activation-concentration polarization3.Mass transport-limited corrosion control

The cathodic Tafel plot often shows deviation from ideal Tafel behavior

Page 31: Evan diagram

Evans Diagrams

Anodic Control

Mixed Control

Cathodic Control

Page 32: Evan diagram

Galvanic Corrosion – Influence of i0

Page 33: Evan diagram

Cyclic Voltammetry at a Pt Electrode in Sulphuric Acid Solution

Oxygen Adsorption Pt-O

Oxygen Evolution O2

Reduction of adsorbed oxide film (Pt-O)Hydrogen

Evolution H2 ↑

Reduction of adsorbed H (Pt-H)

Formation of adsorbed H (Pt-H)

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.