1

Corrosion Rate, R

Corrosion rate can have different units.

Units

R = x/t, thickness loss per unit time mils per year (mpy)

mm per year (mm/y)

R = m/At, weight loss per unit area per unit time mg/dm2/day (mdd)

i = I/A = Q/At, current density Amperes/cm2 (A/cm2)

= nFm/MAt

Note:

• Values can be converted back and forth with appropriate constants.

• Weight loss and current have to be normalized by exposed area.

• Electrochemical measurement of corrosion rate (current) can be converted to other

units (next slide)

• These approaches assume uniform corrosion - valid for localized corrosion?

2

Faraday's Law

Needed to convert electrochemical measurement to other units.

’

equivalent = mole of charge

n (eq/mol) =

= charge on ion

mol charge mol matter

3

Thermodynamics vs. Kinetics

Corrosion resistance depends on both thermodynamics and kinetics.

From a corrosion standpoint, thermodynamics is the study of

materials’ tendency to corrode, while kinetics is the study of the

rate of corrosion.

Thermodynamics answers the question “can a metal corrode?” and

kinetics answers the question “how fast will it corrode?”

Remember that we have seen how Faraday’s constant relates current

to flux or rate:

J = i/nF

4

Kinetics at Equilibrium • Consider the electrochemical half-cell reaction at

equilibrium:

M Mz+ + ze-

• At equilibrium no net current flows to or from the

surface of the electrode. This, however, does not

mean that nothing is happening on the surface of the

electrode. A “dynamic equilibrium” condition exists

at the surface of the electrode where the rate in the

forward direction, rf, is equal to the rate in the reverse

direction, rr.

• When the reaction is at equilibrium, the electrode potential is equal to the

reversible potential, Erev.

E

Erev

log i io

rf

rr

inet = iox - ired = 0

M M+z

This is another form

of Faraday’s Law rf = rr = ioM/nF (g/cm2s)

where io is the exchange current density, which is

equivalent to the reversible rate at equilibrium, and M is

molecular weight.

5

Electrochemical Polarization

Erev

• At Erev, the electrochemical half-cell

reaction is at equilibrium and the rate in

both directions is io:

M Mz+ + ze-

What happens as you move away from

equilibrium?

• At potentials different from Erev, the

reaction will proceed predominantly in

one direction. At higher potentials it

will go in the oxidizing (anodic)

direction:

M Mz+ + ze-

• At lower potentials it will go in the

reducing (cathodic) direction:

Mz+ + ze- M

log i

E

io

(Ecorr)

(icorr)

O2 + 4H+ + 4e- → 2H2O

6

Electrochemical Polarization

Polarization, h = E - Erev, is a change in

potential from the reversible

(equilibrium) half-cell potential. h is also

called the overpotential or overvoltage.

Electrochemical kinetics describe the

relationship of current and overpotential.

As shown in the figure, there tends to be

an exponential dependence of current on

potential.

log i

E

io

Erev

h > 0

In electrochemistry, potential and current

are inter-dependent. You can control

either one and measure the other.

7

Substituting:

RT

nF)1(expi

RT

nFexpii 00net

hh

For an applied cathodic overpotential (potential less noble than

the reversible potential):

Development of Butler-Volmer Equation

Some references don’t have n in the Butler-Volmer equation. It is

really only valid for a simple one electron reaction anyway.

RT

nF)1(expi

RT

nFexpiiii c

0c

0acnet

hh

8

Tafel Equation

For a sufficiently large value of anodic polarization from the reversible

potential (overpotential h > 50 mV), the Butler-Volmer equation

simplifies to:

rearranging, one gets the Tafel equation:

where ba = 2.3RT/nF is the anodic Tafel slope. For = 0.5 and n = 1,

ba = 0.12 V (or V/decade). This calculation is only for a single

electron reaction. Most reactions are very complicated and b 0.12 V,

but b 0.12 V (often 0.04 – 0.15 V).

A similar equation is found for cathodic polarization:

RT

nFexpii a

0

h

ha = ba log (i/io) or i = i0 10h/b

hc = bc log (i/io)

9

Plots

ba

ha

hc

bc

ErevM/M+

log i

E

ioM/M+

The Tafel Equations describe the

polarization kinetics under

activation control and are straight

lines in a plot of E-log i. Such a

plot is called an Evans Diagram:

The Butler-Volmer Equation is

sometimes plotted in linear coordinates.

The symmetry of the curve will depend

on the symmetry factor, b. When b =

0.5, the curve is symmetrical:

Bockris and Reddy, Modern Electrochemistry

10

Measurement of Polarization Curves

In order to obtain the potential-current relationship, the potential can be stepped

incrementally or scanned at a fixed rate (potentiodynamic polarization). Alternatively, i

can be controlled at different values and E measured.

Potentiodynamic polarization - Typically start at a potential of about E = Eoc - 250 mV

and scan potential in the positive direction at 0.1 to 1 mV/s to a value about E = Eoc +

250 mV. (May want to go higher to look for other behavior such as passivation or

pitting.) Net current is measured at various intervals as a function of potential and

plotted as E vs. log |i|. Remember that the current density below the corrosion potential

is negative. Since log 0 = -, on log scale the curve points to left at Ecorr.

Jones

11

Determination of Corrosion Rate from

Measured Polarization Curves Corrosion rate can be determined from mass loss, which is time consuming and

has limited sensitivity.

Corrosion rate can be determined electrochemically from measured polarization

curves using our understanding of polarization behavior by:

1. Tafel extrapolation

2. Non linear least squares fit to ideal equation, which is similar in form to

the Butler-Volmer equation

3. Linear polarization resistance (discussed later)

Other electrochemical techniques will also be discussed later.

12

Determination of Corrosion Rate from

Polarization Curves 1. Tafel Extrapolation

Extrapolate Tafel behavior (straight line in semi-log plot) to Ecorr (zero-

current potential) to get icorr. Also get Tafel slopes from this analysis.

If anodic and cathodic extrapolations do not intersect at the zero-current

potential, typically consider cathodic extrapolation to be less in error.

Jones

13

Polarization Curves

The anodic portion of the polarization curve often does not exhibit Tafel

kinetics for a variety of reasons (surface roughens, films form, concentration

in solution changes).

Knowing that the net current near Ecorr is a sum of the anodic and cathodic

currents, one can determine the anodic Tafel slope from the net current and

the cathodic kinetics.

c

corr

a

corrcorrnet

b

)E2.3(Eexp

b

)E2.3(Eexpii

Jones

14

Determination of Corrosion Rate from

Polarization Curves Can get corrosion rate very accurately in minutes!

From Faraday’s Law: r = CMicorr/rnF

where:

C - constant to alter units of thickness and time icorr - corrosion current density (A/cm2)

M - molecular weight of metal (g/mol) r - density of metal (g/cm3)

Limitations:

• Lab environment may not be identical to

service environment.

• icorr could change with time, measurement is

representative of point in time.

• Polarization far from Ecorr will change electrode

surface – destructive test.

• Extrapolations are sometimes difficult because

of limited or no linear region, need 1 order of

magnitude current for Tafel slope.

• Anodic and cathodic lines might not

extrapolate to the same current density,

probably best to use extrapolation of

cathodic current.