SIandAII Ch2 Reaction Kinetics in Corrosion

8/22/2019 SIandAII Ch2 Reaction Kinetics in Corrosion

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Surfaces, Interfaces, and their Applications II Reaction kinetics

Dr. Patrik Schmutz, Laboratory for Joining Technologies and Corrosion, EMPA Dbendorf, 2013 1

2 Reaction Kinetics in corrosion

2.1 Introduction

In an electrochemical process, different steps are necessary for a reaction to be completed and

occur. Figure 2.1 presents the case of the hydrogen reduction reaction which is one of the

most important cathodic reactions controlling corrosion rates. The particularity of this

reaction is also that it contains all the possible phenomena taking place during an

electrochemical process.

Figure 2.1: Reduction of hydrogen on a metallic surface reaction steps

The proton has to diffuse towards the interface (a), adsorb on the surface and exchange an

electron (b), recombine (c) or diffuse into the metal (c) and finally leave the surface as a gas

molecule (d):

Transport reaction in the double layer (diffusion)

Exchange of charges charge transfer reaction

Recombination of the adsorbed species

Diffusion in the metal hydrogen embrittlement

Creation of a gas phase


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During the contact of a metallic material with an aqueous environment (immersed or as a

liquid film through condensation of moisture), a potential difference is established overthe electric double layer (see chapter 9.3.2 of Surface, Interfaces, and their Applications I).

Formere adsorption of solvent molecules and ions, this potential difference is determined by

the condition that the charge has to be identical on both sides of the double layer. Such

adsorption phenomena can be observed for mercury, for example.

- The very high electronic conductivity of the metals results in very narrow chargeseparation on this side of the interface of the double layer.

- In the electrolyte, the charge distribution extends far inside the liquid phase. There is adistinction between the well-defined Helmoltz plane and the diffuse part (Gouy-

Chapman).

- In semiconductors, a diffuse layer can also develop on the solid side of the interface.Summary: The electrical double layer induces potential differences at the solid/liquid

interface determining the kinetic evolution of an electrochemical reaction.

2.2 Charge transfer reaction

Considering in more detail the limiting steps (as listed above) of an electrochemical process,

the fastest reaction is certainly the transfer of an electrical charge through the metal-liquid

interface. This process is however still much slower than the electrical conductivity in the

metal itself.

Initial stage of metal dissolution (and redeposition) as well as hydrogen reduction are

classical examples of charge transfer controlled reactions. Considering now separately eachof the components of the overall reaction mentioned below, the reaction kinetics can be

derived

The electrochemical reaction is following, like for a chemical reaction, an exponential

Arrhenius law relating the reaction rate to the chemical activation energy barrier.

With the following parameters

: Reaction rate

: Maximal rate

: Chemical activation energy

: Temperature: Universal gas constant


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The important difference between the chemical and electrochemical processes is the presence

of the potential drop through the metal-liquid interface modifying the activation energy. In an

electrochemical process, the reaction kinetic can be varied at room temperature whereas

chemical reaction acceleration relies on temperature increase. Increasing the potential of the

metal (anodic polarization), decreases the energy barrier and facilitates the conversion of

metal atoms in ions, Fig. 2.2. Inversely, decreasing the potential on the metal will favourreduction of the dissolved metal ions.

Figure 2.2: Schematic description of the influence of an applied potential on the activation

energy

The forward reaction rate (metallic dissolution in this case) can be formulated as a current

density iM (per cm2) flowing through the interface with a first constant chemical term and apotential drop dependent term containing the reaction valence n and a charge transfer

coefficient :

RT

nF

RT

Gckconsti

MM

*

0

exp


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At the equilibrium (Er= reversible potential), dissolution and deposition currents are

equal and corresponds to the exchange current density (i0) which is materials specific.Besides the reaction specific parameters, the concentrations cx of the oxidized and reduced

species also influence the reversible potential and exchange current density.

Note: The exchange current density is not a measure of a corrosion rate, but it has its

importance in defining the polarizability of a reaction and indirectly influences the kinetics of

individual reactions.

2.2.1 Volmer- Butler equation

Polarized away from the electrochemical equilibrium (Reversible potential), the reaction

current is given by the exponential Volmer Butler expression.

When a single reaction is considered, the applied potential versus the reversible potential is

calledoverpotential

The metal dissolution (anodic reaction) current is defined as positive and inversely the metal

deposition (reduction reaction) is negative.

2.3 Electrochemical measurements

In order to measure precisely electrochemical reaction kinetics, a three electrodes cell is

necessary, Fig. 2.3. To understand the working principle and necessity to use a potentiostat

and three electrodes, it is important to consider the signification of the Volmer Butler

relationship. Electrode potential is fully determined by the current density flowing through

the interface, meaning that it is only possible to set a precise potential on the working

electrode, by regulating and flowing a current through the counter electrode with the help of a

potentiostat (using a simple voltage source will not do the job !).

nM

rMM

rMMM c

RT

EnFkc

RT

EnFkiii

)1(expexp0

RT

nF

RT

nFiiM

)1(expexp0

rE


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The Working electrode (grey electrode on Fig. 2.3) consists of the material that is to be

investigated. The reaction of interest is going to happen on its surface.

The Counter electrode (green electrode on Fig. 2.3) is necessary for the current flow

regulated by the potentiostat. This electrode has to be inert and is usually made out of

platinum.

The potential of the working electrode needs to be controlled with respect to a stable surface,the Reference electrode (orange electrode on Fig. 2.3):

One of the most used/stable one is the Calomel electrode consisting of a chemically stable

mercury chloride in contact with a saturated KCl solution:

Hg / Hg2Cl2 // Hg2Cl2 (solid) / KCl (saturated solution)

Hg + Cl- Hg2Cl2 + 2e-

ESCE = +240 V SHE (standard hydrogen electrode)

Figure 2.3: Schematic description of the electrochemical cell and potentiostatic control for

anodic dissolution investigation.

With such a setup, electrochemical reaction kinetics can be characterized precisely. The

surface is polarized away from the reversible potential by flowing the necessary currentthrough the counter to the working electrode. This electrochemical potentiodynamic

measurement is one of the most used characterization method and can be compared to the

tensile tests used in mechanical testing. The system is brought more and more out of

equilibrium and the current necessary to reach a given potential is recorded.

Why is a potentiostat and electrochemical polarization necessary in order to

characterize electrochemical reaction kinetics?

Because at equilibrium, the total current on the considered surface is always zero ( i tot = 0 )

and obviously not measurable.


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Foruniform dissolution of a homogeneous alloy, anodic and cathodic partial reactions are

statistically distributed over the whole metal surface. Thus, for the whole metal, the same

potential is measured independently of the position of the reference electrode.

For such homogeneous surfaces and considering the Volmer-Butler expression, there are two

ways of measuring reaction rates:

1) With the polarization resistance method, Fig. 2.4, very small polarization voltages(10-20 mV around the reversible potential) are considered. For this potential range,

the exponential term can be developed in a series of exponents where only the first

term is significant.

exp x (x0) = x

This way, a linear relation applies between overpotential and measured current, the

exchange current density (i0) can then be determined.

Figure 2.4: Linear evolution of the current density around the reversible potential

MiiFn

RT

0


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2) With the Evans Diagram method, the sample surface is brought completely out ofequilibrium in the anodic and the cathodic domain. This procedure requires the

presence of oxidized and reduced species for a given reaction: for example a metal

and dissolved metallic ions. The potentialcurrent relationship is analysed far away

from equilibrium (> 200 mV) and with the current plotted in a logarithmic scale, a

linear relationship is obtained. It is possible to extract the anodic (a) and cathodic(c) Tafel slopes.

Note: Using this procedure, one can study the kinetics of the anodic and cathodic

partial reactions. The Tafel coefficients ba,c can be formulated for the naturallogarithm, which is directly related to the Arrhenius law. In the practice, it is more

convenient to extract the coefficient from the common base 10 logarithm and a

multiplication factor of 2.3 is arising.

( - Er) = a + b * ln i natural logarithm( - Er) = a + * log i common logarithm

with a,c = 2.3ba,c

Each of the slopes contains the information about the reaction valence n and charge

transfer coefficient , the important parameters for the mechanisms of theelectrochemical reaction. The intersection of the two slopes at the Reversible

potential further allows the determination of the exchange current density

i0. This

way, all the parameter of an electrochemical reaction can be assessed graphically.

Figure 2.5: Schematic description of electrochemical potentiodynamic measurements plotted

in the Evans Diagram form. The current is displayed as absolute value on a logarithmic scale


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2.4 Corrosion processes and Mixed electrodes

All the reaction kinetics and electrochemical characterization concepts presented until now,

obviously apply to corrosion rate determination, but with the difference that in the case of a

corrosion process, the cathodic and anodic reactions are related and involving species fromdifferent reactions.

We are in presence of a so-calledMixed Electrode situation:

Metal is dissolving: M Mz+

+ ze-

In presence of oxidizing species: Oxz+

+ ze-

Ox

Additivity of the partial reactions

According to Wagner and Traud, anodic and cathodic partial reactions proceed independently

of each other at the metal surface. The corresponding partial current densities ia andiccan be

algebraically added up to the total current density i tot .

This results in the total potentiodynamic polarization curve, which can be measured

experimentally. The current density is in this case a function of the Polarization potential which is measured from the corrosion potential Ecor. The expression is similar to the Volmer

Butler expression, but the Tafel coefficients are related to different reactions for the anodic

and cathodic part:

With the polarization potential formulated as function of the relative overpotentials and

reversible potentials.

.

Figure 2.6 shows schematically in the Evans diagram form, all the parameters involved in a

corrosion reaction. Corrosion current density (icor) can be determined from the intersectionof the cathodic Tafel slope of the oxidant and the anodic Tafel slope of the metal dissolution.

It has to be mentioned that the two exchange current densities (

i0,Mand

i0,Ox) cannot be

measured but can still influence individual reaction kinetics.

OxcOxaMcMatot iiiii ,,,,

OxcMa

cortot ii,,

expexp

)( ,MrcorM EE )( .OxrcorOx EE


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Figure 2.6: Evans diagram in the case of a corrosion process. Only the red curves can be

effectively measured

In the practice, the exponential evolution of the current will be measured like for a single

reaction (Fig. 2.7), the reaction involved should however always be clearly identified.

Figure 2.7: Total potentiodynamic polarization curve of a metal electrode corroding with H2

formation. ( ----- partial current density ___ total current density)

Note: Also the potential is usually expressed simply as E independently if a simple or a

mixed electrode is concerned. It is however necessary to always clarify which kind of system

is considered.


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2.5 Mass charge relationship (Faradays law)

Another method to characterize the uniform corrosion rate of a metal/alloy surface corroding

actively is to determine the mass loss after a given immersion time. This value can further be

compared to electrochemical measurements. The corrosion current flowing is proportional to

the amount of metal dissolved, i.e. the corrosion rate as given by Faradays law:

G = M

z F I t

Meaning of the symbolsG: transferred mass g

M: atomic mass g/mol

z: valence of the metal ion

F: Faradays constant A.s/mol

I: electric current A

t: time s

With Faradays law, the units used to express corrosion rates can be converted to each other

by consideration of metal density:

vcor weight loss per time and area g/m2day

dcor thickness decrease per time mm/year

icor current density of metal dissolution A/cm2

vR crack propagation rate m/s

These rates are listed in the following table for various frequently used metals.

Reaction i

(mA/cm2)

vcor

(g/m2day)

dcor

(mm/year)

vR

(m/s)

Cu --> Cu2+ 0.001 0.285 0.012 3.7 . 10-13

0.01 2.845 0.116 3.7 . 10-12

M = 63.57 0.1 28.454 1.164 3.7 . 10-11

= 8,92 1.0 284.54 11.64 3.7 . 10-10z = 2 10.0 2845.4 116.4 3.7 . 10-9

Fe --> Fe2+ 0.001 0.250 0.012 3.7 . 10-13

0.01 2.500 0.116 3.7 . 10-12

M = 55.85 0.1 24.998 1.160 3.7 . 10-11

= 7.86 1.0 249.98 11.60 3.7 . 10-10z = 2 10.0 2499.8 116.0 3.7 . 10-9

Zn --> Zn2+ 0.001 0.293 0.015 4.76 . 10-13

0.01 2.926 0.150 4.76 . 10-12

M = 65.38 0.1 29.264 1.498 4.75 . 10-11

= 7.13 1.0 292.64 14.98 4.75 . 10-10z = 2 10.0 2926.4 149.8 4.75 . 10-9

Al --> Al3+ 0.001 0.081 0.011 3.48 . 10-13

0.01 0.805 0.109 3.46 . 10-12

M = 26.97 0.1 8.048 1.088 3.45 . 10-11

= 2.70 1.0 80.48 10.88 3.45 . 10-10z = 3 10.0 804.8 108.8 3.45 . 10-9


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2.6 Diffusion controlled reactions

For corrosion reactions in which oxygen gas is the most important oxidizing agent (see

overall reaction below occurring in all natural environments with neutral to alkaline pHs),

the oxygen reduction rate is only charge-transfer controlled close to the equilibrium reversible

potential. Oxygen molecules are larger than the protons considered previously and arediffusing slower.

For larger polarization potentials (i.e. around the corrosion potential), the reaction rate is

limited by the transport of O2 to the electrode. A concentration gradient is therefore formed at

the interface (oxygen depletion at the metal surface). This gradient leads to an O 2 diffusion

process towards the electrode surface.

The diffusion current density i in the diffusion layer can be approximated with the help ofFicks first law:

In this one-dimensional equation valid for homogeneous system, n stands for the number of

transferred electrons, F for the Faraday constant, D for the diffusion constant and c for theconcentration of the diffusing gas. When observing corrosion processes it is usually

sufficient to assume a linear concentration gradient (Fig. 2.8) in the diffusion layer. Ficks

law becomes:

i = - nFD c0 - c

with c0 as the concentration in the bulk of the electrolyte, c as the concentration at the metal

surface andas the thickness of the diffusion layer.

If at the metal surface, the solution is fully depleted (c = 0 when fast charge transfer occur), a

potential independent limiting current is present, which can be calculated with the following

equation:

The maximal current that can evolve is then only determined by the diffusion layer parameter(thickness and Diffusion rate) and the concentration of the diffusing species in solution.


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The diffusion layer thickness d depends on the hydrodynamic conditions:

d: 0.001 cm forced convection (stirring)

d: 0.05 cm natural convection

Figure 2.8: Concentration profile in the diffusion interface according to Nernst. The diffusionlayer depends on the hydrodynamic conditions (flow rate).

Figure 2.9: Current density evolution for a corroding system with the metal dissolution under

charge-transfer control and the diffusion limited O2 reduction


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On figure 2.9, the current evolution and equilibrium conditions at the corrosion potential Ecor

is presented for the situation of a metallic anodic iA dissolution reaction controlled by the

charge transfer and the oxygen reaction iC far away from its reversible potential and underdiffusing limiting conditions. In such a case, it is obvious that the corrosion process and rate

is completely and only controlled by the oxygen reaction. The diffusion limiting current being

the maximal corrosion rate that can be obtained.

This example is very important in the sense that it shows that it is not sufficient to know

precisely the kinetics of the anodic metal dissolution. In corrosion process, the cathodic

reaction rate is often the controlling factor

2.6 Migration diffusion controlled reactions

Diffusion processes can also be accompanied by migration phenomena. When charged

particles (ions) are moving in the diffusion layer and are subsequently reduced on the surface,

the effect of an additional electrical field is to be considered.

The deposition of Ag is here considered as an example. When charge transfer occurs at the

electrode surface, excess negative charges from the nitrite anions are generated. Because the

electro-neutrality has to be maintained at any time, both species concentration ca = cb should

be constantly equal in the diffusion layer. This means that additional Ag+

cations will migrateto the surface increasing the cathodic reduction reaction, Fig. 2.10.

Figure 2.10: Schematic description of diffusion and migration process in the case of

deposition of one species involved in the electrochemical process


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The limiting current density increase is then function of the relative charges of the cations and

anions involved. In the case of silver nitrate, it is for example a factor of 2:

With

Za: valence of species A

Zb: valence of species B

D: diffusion constant

d: thickness of diffusion layer

Ca: concentration of species A at the surfaceC

0a: concentration of species A in the bulk solution

Note: this migration-diffusion effect can be relevant to the corrosion rates when the cathodic

reaction kinetics is including strong oxidizing agent depositing on the surface (like Fe cations

for an aluminium surface).

2.6 In summary

It is possible to distinguish 2 main types of corrosion processes and it is important to

point out that they are controlled by the cathodic reaction taking place

H - type: fast charge transfer limited cathodic reaction

Example: hydrogen in acidic solution

O - type: slower diffusion limited cathodic reaction

Example: oxygen in neutral/ alkaline solution

This means that the corrosion potential cor unlike the thermodynamic reversible potentialEMe/Mez+ is always a mixed potential, which is determined by the kinetics of the anodic

and cathodic partial reaction(s). Typical examples of this influence are the change of

corrosion potential (corrosion rates) of zinc as a function of the pH-value of the solution

(Fig. 2.11a) or the influence of the oxygen content on the corrosion potential of iron (Figure

2.11b).


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Figure 2.11: a) Influence of the solutions pH-value on the corrosion potential of zinc

(schematically). pH 3 < 2 < 1. b) Influence of the oxygen content on the corrosion potential of

iron (schematically). O2 content 1 < 2

SIandAII Ch2 Reaction Kinetics in Corrosion

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