Validation of corrosion rates measured
by the Tafel extrapolation method
E.McCafferty *
Professorial Lecturer Department of Mechanical and Aerospace Engineering,School of Engineering
and Applied Science,George Washington University,Washington,DC 20052,United States
Received 15March 2005;accepted 14May 2005
Available online 16September 2005
Abstract
This paper discusses the validity and limitations of the Tafel extrapolation method for the determination of corrosion rates for activation-controlled corrosion processes.Experimental corrosion rates determined by the Tafel method are compared with corrosion rates obtained by an independent chemical (i.e.,non-electrochemical)method for iron in hydrochloric acid,iron in 3.5%NaCl,and for titanium in boiling 1M sulfu
ric acid.The methods of confirmation of the corrosion rates involved colorimetric analysis of the dissolved cation or the use of an ion-implanted inert Xe marker.Additional examples taken from the literature involving other metals and other methods of validation are also discussed.
Ó2005Elsevier Ltd.All rights reserved.
Keywords:Tafel equation;Tafel extrapolation;Corrosion rates;Uniform corrosion;Iron;Titanium
1.Introduction
One of the major laws in electrochemistry is due to Tafel [1],who in 1905estab-lished what Bockris and Reddy [2]consider to be the most frequently used law in electrochemistry.According to Tafel Õs law,which was empirically observed,the 0010-938X/$-see front matter Ó2005Elsevier Ltd.All rights reserved.doi:10.sci.2005.05.046*
Address:Consultant,Chemistry Division,Code 6134,Naval Research Laboratory,Washington,DC 20375,United States.Fax:+1202767
4642.
Corrosion Science 47(2005)
reaction rate
3202–3215
logarithm of the current density in an electrochemical reaction varies linearly with the electrode potential(at potentials removed from the open-circuit rest potential).
An appreciation of TafelÕs law with regard to corrosion reactions,however,de-pended upon several subsequent developments.For electrode processes involving a slow reaction step at the electrode surface(activation polarization),application of the absolute reaction rate theory of Eyring et al.[3]resulted in the well-known But-ler–Volmer equation[4].This equation relates the net current density,i,for a single electrode process,such as
Fe!Fe2þ+2eÀð1Þto the electrode potential,E:
i¼i0½e a nFðEÀE0Þ=RTÀeÀð1ÀaÞnFðEÀE0Þ=RT ð2Þwhere i0is the exchange current density(rate of either the forward or reverse half-cell reaction)at the equilibrium potential E0,a is the transfer coefficient(usually0.5), and n is the number of electrons transferred.
It is well known that the electrochemistry of corroding metals involves two or more half-cell reactions.For example,for iron in acid solutions,in addition to Eq.(1),the following half-cell reaction also occurs:
2Hþ+2eÀ!H2ð3ÞIn their landmark paper on the mixed potential theory of corrosion published in 1938Wagner and Traud[5]gave a detailed account of uniform corrosion based on the principle of superposition of the partial current–voltage curves for each of the partial half-cell reactions.For the diss
olution of iron in acid solutions,at equi-librium the total cathodic rate is equal to the total anodic rate:
j i! H jþj i!
Fe
j¼i
H
þi
Fe
ð4Þ
where the forward arrow refers to the cathodic direction.Thus,j i!
H j refers to the rate
of the reduction reaction in Eq.(3).
The electrode potential of the steady-state freely corroding condition given by Eq.
(4)is called the corrosion potential E corr,which lies between the equilibrium poten-tials of the two individual half-cell reactions.At E corr,Eq.(4)gives:
i Fe Àj i!
Fe
j¼j i!
H
jÀi
H
¼i corrð5Þ
Thus,the net rate of either iron dissolution or hydrogen evolution can be measured at E corr to give the uniform corrosion rate i corr at the freely corroding condition. Moreover,for such a system the Butler–V
olmer equation is modified to give:
i¼i corr½e a nFðEÀE corrÞ=RTÀeÀð1ÀaÞnFðEÀE corrÞ=RT ð6Þ
When the rate of the back reaction is negligible,Eq.(6)gives:
E¼aþb log ið7Þwhere a and b are constants.Eq.(7)is TafelÕs law.Moreover,in Eq.(6),when E=E corr,then i=i corr.This is the basis for the Tafel extrapolation.
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3204  E.McCafferty/Corrosion Science47(2005)3202–3215
A series of contributions from Stern[6–9]placed this method on afirm theoretical and experimental basis.At the time of the publication of these papers,there was con-siderable uncertainty as to the interpretation of electrochemical polarization curves. Final acceptance of the use of polarization curves in the determination of corrosion rates depended upon the experimental(and non-electrochemical)independent valida-tion of corrosion rates determined by the Tafel extrapolation method.The purpose of this paper is to examine several corrosion systems in which non-electrochemical vali-dation has been provided for corrosion rates determined by the Tafel extrapolation
method.
2.Examples considered
Three examples are taken from the authorÕs previous work.These are the corro-sion of iron in acid solutions[10],the corrosion of iron in neutral3.5%NaCl[11], and the corrosion of titanium in boiling sulfuric acid[12].Additional examples for other metals in various aqueous solutions are also cited.
2.1.Iron in acid solutions
Various investigators have shown that iron[13–18],aluminum[19–21],zinc[22–24]and other metals[25–28]immersed in acid solutions display anodic and cathodic regions of Tafel behavior.In the case of iron,the anodic half-cell reaction is given by Eq.(1),and the cathodic half-cell reaction is given by Eq.(3).The overall chemical reaction is the sum of these two half-cell reactions:
Fe+2Hþ!Fe2þ+H2ð8ÞThe overall chemical reaction in Eq.(8)suggests four ways to determine the cor-rosion rate by chemical(non-electrochemical)means.These are:(1)to determine the quantity of solid iron lost due to corrosion by measuring the weight loss(or thick-ness lost)of the metallic iron specimen,(2)to measure the concentration of dissolved Fe2+ions which are produced in solution,(3)to determine
the quantity of hydrogen gas which is produced by the corrosion reaction,and(4)to determine pH changes in solution caused by the consumption of H+ions.
With regard to the last method listed immediately above,usually the volume of the aqueous solution involved is sufficiently large so that pH changes are too small to be measured.However,changes in pH can be important in thin-layer condensed electrolytes,such as in atmospheric corrosion,or for vigorous reactions in small vol-umes of electrolyte.For example,the dissolution of Al alloy7075in acid environ-ments was shown to cease in small volumes of electrolyte when the supply of available H+ions had been consumed[29].
Fig.1shows anodic and cathodic polarization curves for pure iron in1M HCl after24h immersion[10].These polarization curves were determined by the poten-tiostatic method using10–15mV increments of potential,and steady state currents were observed within20min at each applied potential.Both the anodic and cathodic
E.McCafferty/Corrosion Science47(2005)3202–32153205
branches of the polarization curve display Tafel behavior,and the Tafel slopes can be extrapolated back to the open-circuit corrosion potential to give a corrosion cur-rent rate of30l A/cm2.
The open-circuit free corrosion rate was also determined separately by the color-imetric analysis of dissolved Fe2+ions using the o-phenanthroline method.Known aliquots of the solution containing dissolved Fe2+ions were withdrawn as a function of time and were analyzed to produce the corrosion-t
ime curve shown in Fig.2.As shown in Fig.2,the corrosion rate determined in this manner was0.665l mol Fe2+/ cm2h.From FaradayÕs law,this rate corresponds to a corrosion current density of 36l A/cm2,in good agreement with the value determined by the Tafel extrapolation method.
2.2.Iron in
3.5%NaCl open to the air
In neutral solutions,such as3.5%NaCl open to the air,the predominant cathodic half-cell reaction is
O2+2H2O+4eÀ!4OHÀð9Þrather than the hydrogen evolution reaction which occurs in acid solutions.
Polarization curves for iron after24h immersion in3.5%NaCl solution(0.6M) are shown in Fig.3[11].The solution was open to the air and was unstirred(quies-cent).The chloride concentration is the same as in natural seawater(although the solution does not contain the various other anions,cations,or organic matter found in small concentrations in natural seawater).Polarization curves were determined by the potentiostatic method.
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