REVIEW

Fundamental aspects of the polarization resistancetechniquethe early days

Florian Mansfeld

Received: 22 July 2008 /Revised: 11 August 2008 /Accepted: 12 August 2008 / Published online: 29 August 2008# Springer-Verlag 2008

Abstract The work of Oldham and Mansfeld dealing withthe concept of the polarization resistance technique that canbe used to determine corrosion rates from potential Ecurrent I curves measured in the vicinity of the corrosionpotential Ecorr has been summarized. In addressing theinterpretation of this technique as the linear polarization(resistance) technique, Oldham and Mansfeld pointed outthat curvature of polarization curves in the vicinity of Ecorrhas to occur in order for the ButlerVolmer equation, asmodified for corrosion reactions, to be valid. Theyproposed a modification of the SternGeary linear polari-zation equation and presented a new graphical method forthe calculation of corrosion rates from polarization curves.Some of the earliest computer programs for the determina-tion of corrosion current densities, and Tafel slopes frompolarization data collected in the vicinity of Ecorr andexamples of their application have been discussed.

Keywords Polarization resistance technique .

SternGeary linear polarization equation . Corrosion rates

Introduction

The year 1970 was the start of a series of papers by Oldhamand Mansfeld dealing with some fundamental aspects of thepolarization resistance technique and its application fordetermining corrosion rates [15]. In a review article

entitled The Polarization Resistance Technique for Mea-suring Corrosion Rates that was published in 1976 [6],Mansfeld pointed out that the theoretical and experimentalresults contained in the paper entitled Concerning theEvaluation of Corrosion Reactions by Superposition ofElectrochemical Partial Reactions and Concerning thePotential Formation on Mixed Electrodes [7] by Wagnerand Traud form the basis of the polarization resistancetechnique. An English translation of this classic paper thatdescribes the concept of mixed potential theory has beenpublished recently with comments on its significance forthe application of electrochemical techniques in corrosionresearch by Mansfeld [8]. It was pointed out that Wagnerand Trauds paper [7] is a milestone in the history ofcorrosionin fact it is the beginning of modern corrosionscience as we know it today.

In 1951, Bonhoeffer and Jena, studying the electrochem-ical behavior of iron samples with different carbon content,found that the slope of the polarization curve at thecorrosion potential Ecorr was correlated to the corrosionrate of these samples [9]. They defined this slope as thepolarization resistance Rp according to:

Rp dE=dIEcorr 1

In 1957, Stern and Geary [10] derived an equation (theSternGeary equation) that related quantitatively the slopeRp of a polarization curve in the vicinity of Ecorr to thecorrosion current density icorr:

Rp B=icorr 2where B=babc/2.303(ba+bc). In Eq. 2, ba and bc are theanodic and cathodic Tafel slopes, respectively. The dimen-sion of Rp is ohm.cm

2. Figure 1 illustrates the determinationof Rp as the slope of the experimental polarization curve atEcorr. ASTM G59 Standard Practice for Conducting

J Solid State Electrochem (2009) 13:515520DOI 10.1007/s10008-008-0652-x

Dedicated to the 80th birthday of Keith B. Oldham.

F. Mansfeld (*)The Mork Family Department of Chemical Engineering andMaterials Science, University of Southern California,Los Angeles, CA 90089-0241, USAe-mail: mansfeld@usc.edu

Potentiodynamic Polarization Resistance Measurementsdescribes the experimental procedure for determining Rpaccording to Eq. 1.

It will be noticed that for accurate determination of icorr,the value of the parameter B has to be known for the systemat the time of the measurement of Rp (Eq. 2). As discussedby Mansfeld [6], numerical values of the parameter B inEq. 2 have usually been determined by one of the followingmethods:

1. The Tafel slopes ba and bc are calculated from the Tafellines obtained in separate experiments for the samematerial and under identical test conditions.

2. Tafel slopes are taken from literature values for thesame or similar corrosion systems.

3. Theoretical values of Tafel slopes are assumed.4. Tafel slopes are obtained from the same polarization

curve that was used to determine Rp.5. The parameter B is determined by calibration using

weight loss data.

The work of Oldham and Mansfeld

In addressing the concept of the polarization resistancetechnique, Oldham and Mansfeld noticed a shift from theoriginal concept of the technique as discussed by Wagnerand Traud and others [7, 911] to the concept of the linearpolarization (resistance) technique and warned against the

expectations that straight-line relationships between poten-tial and current have to be found for all corroding systems[2]. In a discussion of the data presented by Indig and Groot[12], Mansfeld and Oldham [1] used a modification of theSternGeary equation [3] to include more than oneoxidation and reduction reactions as was assumed in theoriginal treatment. Indig and Groot [12] had determinedcorrosion rates of stainless steel in an alkaline solution at288 C by a weight loss technique and by use of the SternGeary linear polarization method. The rates measured bythe two techniques differed by almost a factor of 10, icorrcalculated from the weight loss data being much less thanthat calculated from the SternGeary Eq. (2). Indig andGroot suggested that the SternGeary formula by neglect-ing the reverse of the cathodic reaction, i.e.

1=2H2 OH $ H2O e 3would overestimate icorr. Based on a modified value of icorrcalculated from the exact polarization resistance theory andthat obtained from the SternGeary Eq. (2), it was shownby Mansfeld and Oldham [1] that the approximationinherent in the SternGeary treatment leads to an overes-timate in icorr of about 45% which goes a small way toexplain the tenfold discrepancy with the icorr valuesobtained from weight loss data [12].

In addressing the question of the linearity of polarizationcurves in the vicinity of Ecorr, Oldham and Mansfeld [2]demonstrated that not only is there no theoretical reason forpolarization curves to be linear at Ecorr, the non-linearitypossibly being severe, but that the polarization curves mustdisplay curvature in the vicinity of Ecorr for the SternGearytreatment to be valid. Figure 2ad shows polarizationcurves that have been calculated for a variety of Tafelslopes in a plot of the dimensionless parameter I/Icorr vs.polarization EEcorr [6]. These plots have been calculatedbased on the ButlerVolmer equation modified for corrod-ing electrodes:

I=Icorr exp 2:3 E Ecorr =ba exp 2:3 E Ecorr =bc4

Also included is the tangent of a polarization curve atEcorr from which Rp can be determined using Eq. 1. It isapparent from these curves that the curvature of thepolarization curve is determined by the ratio of the Tafelslopes ba/bc as can be seen by going from Fig. 2a to d. Forequal Tafel slopes, a straight-line relationship is observedover a wider range of EEcorr. (Fig. 2c). Figure 2a refers toneutral, aerated solutions, while Fig. 2b is characteristic foriron in deaerated acids. Figure 2c describes the systemstainless steel 430/1 N H2SO4, and Fig. 2d refers to apassive metal on which reduction of H+ (acid media) oroxygen (neutral media) occurs. These examples show that

Fig. 1 Linear plot of current as a function of polarization showingsuperposition of partial anodic and cathodic currents to measuredpolarization curves and determination of polarization resistance Rp [6]

516 J Solid State Electrochem (2009) 13:515520

the experimenter has to expect a wide variety of polariza-tion curves of different shape even in close vicinity of Ecorr.The shape of a polarization curve might change with timeas Tafel slopes change due to changes of the corrodingelectrode surface and/or the corrosive environment [6].

Oldham and Mansfelds conclusions were as follows [2]:

1) Only exceptionally will the polarization curve of acorroding metal be linear at Ecorr.

2) Whether or not the polarization curve is linear at Ecorr, itsgradient there may be employed to determine icorr byapplication of the SternGeary method or its extension[3].

3) The gradient of the polarization curve should varysignificantly over a range of about 26 mV from Ecorr,and perceptible non-linearity should be apparentlyclose to Ecorr. The absence of such non-linearity shouldbe treated with suspicion, since it probably reflects thepresence of ohmic control and invalidates the measure-ment of corrosion currents by the SternGeary method.

As will be discussed below, development of appropriatesoftware programs allows determination of the experimental

ba, bc and icorr values based on a fit of the measuredpolarization curve to Eq. 3 without the need for calculationof Rp according to Eq. 1 unless the Rp values are to becompared with values obtained from others techniques suchas electrochemical impedance spectroscopy (EIS) [13, 14] orthe noise resistance Rn obtained from electrochemical noisedata [14].

In a paper entitled Corrosion Rates from PolarizationCurves, [5] Oldham and Mansfeld pointed out thatmethods such as the Tafel extrapolation or intercept methodsuffer from the drawback of requiring data obtained fromregions far from Ecorr. In such regions, the net current flowis large, as a result of which ohmic voltage drops andconcentration polarization might distort the polarizationcurve which leads to erroneous values of icorr. In addition,large changes in the surface structure might result especial-ly from anodic polarization. In order to complement thepolarization resistance technique and the Tafel extrapolationtechnique, Oldham and Mansfeld [5] suggested a thirdmethod which had the advantage of not requiring a prioriknowledge or estimation of the Tafel slopes ba and bc.Because this new method did not involve taking data far

Fig. 2 Currentpolarization plots for various combinations of Tafel slopes [6]

J Solid State Electrochem (2009) 13:515520 517

from Ecorr, it ran less danger than does the intercept methodof problems occurring due to ohmic drop and concentrationpolarization, changes of surface activity, or the influence ofsecondary electrochemical reactions. The new methodproposed by Oldham and Mansfeld [5] enables thoseregions of the polarization curve that are useless for eitherthe SternGeary or the intercept method to be used todetermine icorr.

Reference to Fig. 3 illustrates the different stages of themethod that are described in more detail in the originalpaper [5]. First, points A and C are selected, and thecurrents ia and ic are determined. By drawing tangents atpoints A and C, the potential differences |a| and |c| aredetermined. Based on this set of experimental data, icorr canbe determined [5]. Experimental results obtained with thenew graphical method were presented for the system Fe/1 NH2SO4 [5]. Figure 4 shows good agreement between theicorr data obtained with the new graphical method over a24-h period and the average corrosion current densitycalculated from the amount of iron found in the testsolution after the 24-h test (analysis by atomic absorption).

Data obtained with the polarization resistance technique arealso shown in Fig. 4 for comparison.

Further developmentsanalysis of polarization curvesby computer programs

As discussed by Mansfeld in a paper entitled Tafel Slopesand Corrosion Rates Obtained in the Pre-Tafel Region ofPolarization Curves [15], a more accurate determination ofRp and Tafel slopes can be performed by computer analysisof polarization curves obtained in the vicinity of Ecorr. Theanalysis based on the computer program CORFIT [16] hasthe advantage that Tafel slopes can be determined in thepre-Tafel region and that ba and bc can be calculated even ifonly a cathodic or anodic polarization curve has beenobtained. The calculated errors of ba, bc Rp, and icorrindicate how much experimental scatter is involved. IfCORFIT cannot find a solution of an experimentalpolarization curve, the scatter of the data is too large, orthe basic equation that relates I to E=EEcorr (Eq. 4) isnot obeyed due to excessive IR-drop or other complicationsdiscussed by Oldham and Mansfeld [15]. The method hasbeen used to explain the observed changes of corrosionrates with exposure time based on the relative changes ofthe rates of the anodic and cathodic reactions occurring oniron in 1 N H2SO4 [16]. Contrary to the usual procedure,Tafel lines were constructed from the calculated values ofba, bc, and icorr that were obtained using CORFIT near Ecorr.The calculated Tafel lines illustrated these changes [16].

In 1992, Shih and Mansfeld [17] published a paperdealing with the software program POLFIT for quantitativeanalysis of polarization curves. This program provides fullgraphics functions and has both simulation and fittingprocedures based on Eq. 2. Electrochemical parameterssuch as ba, bc, icorr, Rp, and Ecorr, the errors for each of theseparameters and the results of the statistical analysis aredisplayed in tabular form. A unique feature of POLFIT is

Fig. 3 Illustration of graphical method. The polarization curve hasbeen drawn for ba=30 mV, bc=120 mV, and icorr=1.00 A; =10 mV [5]

Fig. 4 Corrosion c.d. Icorr as a function of time for Fe/1 N H2SO4obtained with the graphical method determination of Rp and fromchemical analysis of the test solution [5]

518 J Solid State Electrochem (2009) 13:515520

the possibility of eliminating the uncompensated resistanceRu in the data analysis based on the modified Eq. 4:

i icorr exp 2:3 E iRu =ba exp 2:3 E iRu =bc gf5

Inspection of the deviation between the experimental andfitted current data points at each potential allows elimination ofdata points with excessive scatter and detection of systematicerrors such as those arising from the neglect of Ru in the dataanalysis. The performance of POLFIT has been evaluated fortheoretical data with various random noise levels [17].

Figure 5 shows a potentiodynamic polarization curverecorded in the vicinity of Ecorr for Cu exposed to 0.5 NNaCl and the results of the analysis using POLFIT [17].The table in Fig. 5 lists the fit parameters ba, bc, and Icorrand their errors as well as the calculated values of B and Rp.Also displayed are Ecorr and the normalized values icorr andRop. Additional statistical data are included in the table.

Figure 6 gives another example for the application ofPOLFIT for electroplated ZnNi exposed to 0.5 N NaCl.These data were obtained as part of a larger effort todevelop chromate-free conversion coatings for galvanizedsteels [18]. The deviation between the measured and fitteddata is very small except in the vicinity of Ecorr which is

due to the difficulty of an accurate determination of Ecorr asE at i=0 using POLFIT (Fig. 6b).

Since the development of the CORFIT and POLFITprograms, many other computer programs that can be usedfor the determination of corrosion current densities andTafel slopes from polarization data obtained in the pre-Tafelregion have been discussed. Some of these programs areavailable as part of commercial instrumentation for thecollection of electrochemical data. It has to be noted thatsome of these computer programs are based on the linearpolarization concept, i.e., the polarization data determinedin the vicinity of Ecorr are fit to a straight line, the slope ofwhich is assumed to be equal to Rp.

Summary

The papers by Oldham and Mansfeld [15] have provided athorough discussion of the background of the polarizationresistance technique and the experimental conditions thathave to be met for the correct application of the technique.

Fig. 6 Potentiodynamic polarization curve for Zn-Ni exposed to0.5 N NaCl (a), deviation between experimental and fit data (b), andresults of data analysis using POLFIT [15]

Fig. 5 Potentiodynamic polarization curve for Cu exposed to 0.5 NNaCl and results of data analysis using POLFIT [15]

J Solid State Electrochem (2009) 13:515520 519

Curvature of a polarization curve in the vicinity of Ecorr hasto be expected. The degree of curvature depends on theratio of the Tafel slopes ba/bc. Absence of curvature mightbe due to excessive ohmic drop and/or concentrationpolarization. The graphic method proposed by Oldhamand Mansfeld [5] has the advantage that it doe not require apriori knowledge or estimation of ba and bc to calculate icorrfrom Rp values (Eq. 2). Computer programs such asCORFIT [16] and POLFIT [17] or more recent versioncan be used to determine icorr and the Tafel slopes in thepre-Tafel region of a polarization curve.

Acknowledgment The author gratefully acknowledges the guidanceand friendship provided by Keith Oldham when he joined the NorthAmerican Rockwell Science Center as a junior colleague in 1969. KeithOldham shared his vast knowledge of many areas of electrochemistryfreely and with patience with the author to discuss various aspects of therole of electrochemistry in corrosion processes. The work cited here isonly a very small indication of the influence Keith Oldham played in theauthors future work in corrosion science and engineering.

References

1. Mansfeld F, Oldham KB (1970) Corrosion 26:2072. Oldham KB, Mansfeld F (1971) Corrosion 27:4343. Mansfeld F, Oldham KB (1971) Corros Sci 11:7874. Oldham KB, Mansfeld F (1972) Corrosion 28:1805. Oldham KB, Mansfeld F (1973) Corros Sci 13:8136. Mansfeld F (1976) Adv Corros Sci Technol 6:1637. Wagner C, Traud W (1938) Z Elektrochem 44:3918. Wagner C, Traud W (2006) With a perspective by F. Mansfeld.

Corrosion 62:8439. Bonhoeffer KF, Jena W (1951) Z Elektrochem 55:15110. Stern M, Geary AL (1957) J Electrochem Soc 104:5611. Kaesche H (1959) Z Elektrochem 63:49212. Indig ME, Groot C (1969) Corrosion 25:45513. Mansfeld F, Shih H, Greene H, Tsai CH (1993) ASTM STP

1188:3714. Cottis R, Turgoose S (1999) In: Syrett BC (ed) NACE15. Mansfeld F (2005) Corros Sci 47:317816. Mansfeld F (1992) Corrosion 29:39717. Shih H, Mansfeld F (1992) ASTM STP 1154:17418. Song YK, Mansfeld F (2005) Mater Corros 56:229

520 J Solid State Electrochem (2009) 13:515520

Fundamental aspects of the polarization resistance techniquethe early daysAbstractIntroductionThe work of Oldham and MansfeldFurther developmentsanalysis of polarization curves by computer programsSummaryReferences

/ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 150 /GrayImageDepth -1 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 600 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputCondition () /PDFXRegistryName (http://www.color.org?) /PDFXTrapped /False

/SyntheticBoldness 1.000000 /Description >>> setdistillerparams> setpagedevice