PART C CORROSION KINETICS

I. Corrosion Rates

II. Corrosion Reactions Mechanism

III. Polarization in Corrosion Study

IV. Experimental Measurement of Corrosion

V. Passivity

1. Corrosion RatesThe rate of electron flow to or from a reacting interface is a measure of the reaction rate

nFItMm

m = mass reacted (g)I = current (amp)t = time (s)M = molar mass (g/mol)n = number of electrons in electrode reactionF = Faraday’s constant (96485 Coul /mole of electrons)

For a corrosion reaction:

I. Corrosion rate (based on metal loss):

nFiM

tAwr

r = corrosion rate of metal (mass/area/time)(mass/area/time) {usually mdd: mg/dm2/d}

w = mass loss or reacted (g) i = current density (amp/cm2) NOTE: i=iCORR

A = electrode surface area (cm2)

nFItMw

i = I/A

This rate expression is useful for uniform corrosion.

Corrosion Rate (mass/area/time) for an Alloy:

an equivalent weight (M/n) is used in calculating corrosion rate:

nFiM

tAwr

fi = mass fraction of ith elementni = electrons exchanged in the ith elementMi = Molar mass (= atomic weight) of ith element Neq = number of equivalents in unit mass of alloyEW = equivalent weight of alloyExample:

For 304 stainless steel (Cr 19%, n=3; Ni 9.25%, n=2; Fe 71.75%, n=2)

Neq 0.19 3 52.00

0.0925 2

58.71

0.7175 2 55.85

0.03981

M/n = EW =1/ Neq

i

i

Mnf

nM

fN i

i

i

ieq

EW =1/ 0.3981 = 25.12 r = i .EW/F (mdd)

II. Penetration Rate (Corrosion rate based on thickness):

rp = Penetration rate (length/time)(length/time) C = Conversion factor including Faraday’s constant.i = current density of corrosion reaction (μA/cm2)ρ = density of metal (g/cm3)

C = 0.129 C = 0.129 {r in mpy{r in mpy mpy : mils/year mpy : mils/year 1 mil = 0.001 inch}1 mil = 0.001 inch}

C =3.27 C =3.27 {r in mm/yr}{r in mm/yr}

niMCrp

Example: What is r (mpy) for iron (ρ=7.87 g/cm3) which is equivalent to a corrosion current density of

of 1 μA/cm2 ?

Solution: r = 0.129 [(55.84)(1) / ((2)(7.87)] = 0.46 mpy

For metals… and For alloys…][ iii

i fnMCirp

Explanation:

For single metal:rp =r / ρ

(length/time) = (mass/area/time) / (mass/volume) “volume = area x length”

rp = (i M/n F)/ρ = (i M/n ρ F)rp = (i/F)(C’) (M/n.ρ) = (C i) (M/n.ρ) C’ = unit conversion factorrp = 0.129 i (M/n.ρ) mpy

For alloys:

Replace (M/n.ρ) by Σ(fi.Mi/ni.ρi) in the last equation above:

rp = 0.129 i Σ(fi.Mi/ni.ρi)

2. Corrosion Reactions Mechanism

Graphical representation of the processes occurring at an electro-chemical interface.

The corrosion reaction consists of two types of processes:

1. Charge transfer reactions … e.g. anodic Mlattice M+

surface + eM+

surface M2+surface + e

---------------------------------Mlattice Mn+

surface + n e cathodicO2 surface + 2H+ + 2e H2O2 surface

H2O2 surface + 2H+ +2e 2H2Osurface

----------------------------------------------- O2 surface + 4H+ + 4e 2H2Osurface

2. Mass transport of ions or molecules involved in the reaction … e.g. anodic Mn+

surface Mn+solution

cathodic O2 solution O2 surface

H2Osurface H2Obulk solution

I. Activation Control:

The case when corrosion is controlled by charge transfer reactions.

Either the anodic charge transfer OR the cathodic charge can be the controlling (rate limiting) step.

The anodic reactions and the cathodic reactions in a system can be studied INDIVIDUALLY by electrochemical methods.

II. Mass Transfer Control: If the cathodic reagent at the corrosion site (e.g., dissolved

O2 in the O2 reduction reaction) is in short supply, mass transfer of the reagent can become rate limiting.

Then, the cathodic charge-transfer reaction is fast enough to reduce the concentration of the reagent at the surface corrosion site to a value less than that in the bulk solution.

Rate Limiting Step in Corrosion Reactions

Activation control Mass transfer control

Reagent: O2, H+, OH-, H2O, Fe2+,…

The rate of any electrochemical reaction (ECR) is limited by various physical and chemical factors.

Thus, the reaction is said to be polarized or retarded by these factors.

Polarization is also known as ”over-voltage” or ”over-potential”. ηA is anodic polarization and ηc is cathodic polarization.

3. Polarization in Corrosion Study

Components of PolarizationThere are three possible components:

1) Activation over-potential (ηact) : Commonly encountered in anodic charge transfer reactions (metal oxidation):

Msurface = M n+surface + n e -

2) Concentration polarization (ηconc): Commonly encountered in cathodic reactions, particularly oxygen and hydrogen reductions:

3) Resistance polarization (ηR) OR Potential drop. If there is a resistance between the anode and the cathode in a cell, then the current flowing through that resistance will cause a potential drop given by Ohm’s Law:

V = IR This is important for paint films and for high-resistance solutions.

2H 2e H2

2H2O 2e H2 2OH

Theoretically, total polarization at an electrode is the sum of the three components: activation, concentration and resistance polarizations:

ηTOTAL = ηact + ηconc + ηR

The actual polarization is normally limited to one or the sum of two components. This is based on the relative amounts of these components which makes an over-potential negligible at a given electrode.

In many cases, ηAct is the only significant polarization component at the anode while ηConc is the only significant polarization component at the cathode.

ηact occurs when some step in the half-cell reaction controls the rate of charge transfer.

ηact is commonly found in anodic (oxidation) reactions, e.g. metal dissolution. ηact is

positive (anodic) if net current is dissolution (oxidation):

negative (cathodic), if net current is deposition (reduction).

3.1 Activation Polarization

At each electrode of corrosion cell there is a partial current. The anodic current, ia, is given by:

)exp(

)exp(.*exp)}*{exp(

RTzFii

RTzF

RTGzFA

RTzFGzFAi

A

AAf

oa

fa

Similarly, the cathodic current, ic, is

))1(exp(RT

zFii C

oc

The net current of cell is the difference between the two partial currents:

)})1(exp({)}exp({

RTzFi

RTzFiiii CA

oocanet

This is the Butler-Volmer (B-V) equation

expressing the relation between the net anodic current flowing at the electrode, inet and the over-potential, η, at that electrode.

Reaction Progress Coordinate

MetalMetal IonIon

Energy Energy HumpHump

Energy profile for equilibrium at an electrode

ΔG*

ΔG* is the activation Gibbs free energy

Free

Ene

rgy

Coor

dina

te

M Mz+ + z e-

++ββ = 0.5 = 0.5

Io Io

NOTATION of B-V equation:

R = universal gas constant;T = absolute temperature;z = number of electron transferred in electrochemical

reaction (≡ valency) →

F = Faraday constant (96,485 Coul/mol)ηA = over-potential (polarization) at the anodeηC = over-potential (polarization) at the cathodeβ = symmetry factor representing energy peak, usually

taken as 0.5iio o = exchange current density ( = exchange current density (a constant for the

system).).

The first term in {brackets} in B-V equation, above, describes the forward (metal dissolution, anodic) reaction while the second term in {brackets} describes the reverse (metal deposition, cathodic) reaction.

NOTE: ” z” is used in place of “n” to avoid confusion with η

Tafel’s Equation (based on B-V equation) If the polarization is anodic, with ηwith ηAA > 0.1 V > 0.1 V, the value of ic is insignificant. Making the approximation inet ≈ ia, the equation becomes: ][exp

RTzFiii A

oanet

If the polarization is cathodic with η > -0.1 Vwith η > -0.1 V, ia is insignificant and with approximation inet ≈ ic , then

Since β and z are constants for a given electrode process at constant temperature (usually room temperature, e.g. 25oC), this equation can be re-arranged as

η = ηA + ηC = a + b log i

Combine both equations, total over-potential is:

These are forms of Tafel’s EquationTafel’s Equation

o

aa i

ibA log

o

cc i

ibC log

zFRTba

303.2

zFRTbc )1(

303.2

The relationship between over-potential and current density (reaction rate) for the two half-cell reactions: Tafel’s equation plot

a=anodic over-potentialc=cathodic over-potential

ba=anodic Tafel constantbc=cathodic Tafel constant(units of b: V/decade where decade is interval between two quantities having the ratioof 10 to 1)

ia=anodic current densityic= cathodic current density

io=exchange current density

o

aaa i

ib log

o

ccc i

ib log

(io depends on surface conditions and is a measured quantity)

Mixed Potentials Theory• Net current density on freely-corroding

electrode must be zero.

• Therefore potential (Ecorr) will be that at which anodic and cathodic current densities are equal (lines intersect) and opposite.

• Sometimes called a mixed equilibrium Potential because the system is not at true electro-chemical equilibrium.

1. Combined Electrodes

Zinc corrodes in an acid solution. Anodic and cathodic reactions take place simultaneously on the surface:

Zn Zn 2 2e

2H 2e H2

Anodic

Cathodic

The two half-cell potentials:

2

2

/

/

HH

ZnZn

E

E

cannot exist separatelycannot exist separately on a conductive surface ……

They must change to a common intermediateintermediate potential called:

the “mixed potential” or “corrosion potential” Ecorr

Anodic and cathodic half-cell reactions present simultaneously on a corroding zinc surface.

Polarization of anodic and cathodic half-cell reactions for zinc in acid solution to give a mixed potential, Ecorr, and a corrosion rate (current density), icorr.

Evans Diagrams

In the Evans diagram, the intersection of the two polarization curves occurs @ the corrosion current, icorr (as shown in the previous plot)..

The exchange currents, (io)a and (io)c, can be obtained by extrapolating

the Tafel lines back to the equilibrium potentials (Erev)a and (Erev)c …

The origin (i = 0) is not shown on a logarithmic plot.

The bigger the difference in equilibrium potentials (bigger ∆Erev),

the bigger the value of icorr (greater the corrosion rate)…

2. Prediction of Corrosion TendencyStandard potentials of Fe and Zn oxidation:

Fe Fe2 2e (-0.44V SHE)

Zn Zn2 2e (-0.76V SHE)Zn corrosion would be more prevalent than Fe corrosion based on thermodynamic considerations (emf series of potentials).

However, due to kineticskinetics considerations:

- low exchange current density for hydrogen reduction on zinc (10-9 A/cm2) compared to that of H2 reduction on iron (10-6

A/cm2), and - lower exchange current density for zinc dissolution (10-8

A/cm2) compared to iron dissolution (10-6 A/cm2), the corrosion rate of Fe is faster than that of zinc: i corr, Fe > i corr, Zn

Note: lower io means higher η (see Tafel’s equation) Conclusion: Iron is better a catalyst for H2 evolution from acid than Zn.

N.B. Currents must balance for the coupled reactions. Current densities are equivalent to currents when surface areas are accounted for.

Comparison of electrochemical parameters for iron and zinc in acid solution, demonstrating the importance of io on determination of corrosion rates.

3. Effect of an Oxidizer

What happens if we add an oxidizer with a half-cell electrode potential much more noblemore noble than any others present (e.g. adding ferric-ferrous salts to a metal M in an acid solution).

Experimental observations:1. Corrosion potential Ecorr shifts to more noble

(positive) values1. Corrosion rate increases2. Hydrogen evolution rate is reduced

Use charge conservation and find Ecorr as the point where the two oxidation and reduction current current densitiesdensities are equal.

Total rate of reduction is the sum of all threesum of all three reduction reactions at any given potential

Total rate of oxidation is the sum of all threesum of all three oxidation reactions at any given potential

Ecorr is defined by the intersection of the totaltotal oxidation and total total reduction lines

In this example, at Ecorr the metal oxidation is the only oxidation so the total oxidation current density is the corrosion rate

The total reduction current is the sum of the iron and hydrogen reduction

Determine the mixed potential Ecorr for a corroding metal M exposed to acid solution with a second oxidizer, Fe3+/Fe2+ , present.

Rates of reduction ( and ) and oxidation (icorr) from above.2HH

i 23 FeFe

i

What if the exchange current density from an oxidizer is very low?

In this case, there would be no measurable effect and the corrosion potential would not change. No effect on corrosion when oxidizer of low io is added to an acid.

NOTE: the thermodynamic driving force remains the same ; but the kinetics change !Exchange currents on Zn and Pt are different: 1. ECorr,couple > ECorr,Zn

2. H2 evolution on Zn decreases. 3. iCorr,couple >iCorr,Zn

22 //

)()(ZnZneHHetherm EEE

4. Effect of Coupling Active Metal to a Noble Metal

Isolated zinc corrodes in acid …Zn Zn2+ + 2e

2H+ +2e H2

Platinum is inert in acid. When Zn & Pt are coupled:

zinc corrosion increases H2 evolution occurs on platinum rather than on

zinc: Activation polarization of H2 reduction ηH2/Pt is less than

ηH2/Zn Pt is a good catalyst for H2 evolution; Zn is not.

• The more active metal corrodes faster when coupled, more noble metal corrodes slower;• The more active metal becomes anode, more noble becomes cathode.

N.B. Actual rates depend on Tafel slopes, exchange currents, etc. without detailed information we only predict trends.

5. Effect of Galvanic Coupling The more efficient the hydrogen evolution process (i.e., the higher the exchange current), the larger the effect of galvanic coupling …

Pt is more efficient a cathode for H2 evolution than AuComparison of zinc-platinum and zinc-gold couples (equal areas).

6.

7. Effect of Electrode Area Ratio

Galvanic corrosion of zinc-platinumzinc-platinum couples at different cathode (Pt) areas

CONCLUSIONS:

Increasing cathode area increases corrosion rate, or Increasing cathode area / anode area increases

corrosion rate To control corrosion, cathode area / anode ratio should

be low (ia = I/Aa; high corrosion current when low anode area).

REMINDER:

Corrosion [mixed] potential are determined by point where total oxidation rate equals total reduction rate.

Rates of individual processes are determined by mixed potential.