SIandAII Ch2 Reaction Kinetics in Corrosion
Transcript of 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