Determination of Electrochemical Parameters

Corrosion Science 49 (2007) 3168–3184

www.elsevier.com/locate/corsci

Determination of electrochemical parametersand corrosion rate for carbon steel inun-buffered sodium chloride solutions

using a superposition model

Luis Caceres a,*, Tomas Vargas b, Leandro Herrera b

a Chemical Engineering Department, Universidad de Antofagasta, Av. Angamos 601 Antofagasta, Chileb Chemical Engineering Department, Universidad de Chile, Beauchef 861, Santiago, Chile

Received 3 October 2005; accepted 27 March 2007Available online 19 April 2007

Abstract

Corrosion of carbon steel in un-buffered NaCl solutions was studied applying linear potentialsweep technique to a rotating disk electrode. Current–potential curves were obtained from linearpotential sweep at a rate of 1 mV s�1 in solution with concentrations in the range 0.02–1 M NaCland rotation rates in the range 170–370 rad s�1, at 22 �C. Potential sweeps, which were conductedin the potential range �700 to �100 mV/SHE, were started from the cathodic limit in order toapproach the measurement of corrosion under rust-free conditions. Polarization curves were analyzedwith a superimposition model developed ad hoc and implemented in a computer program, whichenabled determining the corrosion rate and kinetics parameters of the underlying anodic and cathodicsub-processes. The anodic sub-process, dissolution of iron, was well described in terms of a purecharge transfer controlled reaction, while the cathodic sub-process, oxygen reduction on iron, waswell described in terms of mixed mass transfer and charge transfer control. Increase of electrode rota-tion rate increases the limiting current of oxygen reduction, which results in an enhanced corrosionrate of carbon steel. Increase of NaCl concentration has a dual effect: the limiting current of oxygenreduction decreases as a result of the influence of NaCl concentration on solution viscosity and theanodic dissolution of iron increases due to the influence of NaCl on pitting formation. However, thislast mechanism predominates and a net increase in carbon steel corrosion rate is observed in this case.� 2007 Elsevier Ltd. All rights reserved.

0010-938X/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.corsci.2007.03.003

* Corresponding author. Tel.: +56 55 637342; fax: +56 55 240152.E-mail address: [email protected] (L. Caceres).

mailto:[email protected]

L. Caceres et al. / Corrosion Science 49 (2007) 3168–3184 3169

Keywords: A. Mild steel; B. Modelling studies; B. Polarization; C. Kinetic parameters

1. Introduction

Studying corrosion of iron or carbon steels in NaCl containing solutions is relevant forunderstanding the behaviour of these materials in marine conditions [1] and other indus-trial conditions where normally chloride ions are present [2,3]. Oxidation of carbon steelsin NaCl solutions is also the base of galvanocoagulation methods aimed at producingreagents such as ferrous and ferric ions intended for industrial treatment of wastes [4].

Linear potential sweep technique is one of the various methods that can be used fordetermining corrosion rates of these materials. However, the advantage of the linearpotential technique is that the analysis of the obtained current–potential curves alsoenables the determination of the kinetics parameters of the anodic and cathodic sub-processes. This information is very relevant in the present case if one wants to understandin depth the mechanism of corrosion of iron and carbon steels in NaCl containing solutions.

For instance, the linear potential sweep technique has been used to determine thekinetic parameters for oxygen reduction on iron in un-buffered chloride solutions assum-ing mixed charge transfer and mass transfer control [5,6]. Similarly, the kinetic parametersfor iron oxidation under pure charge transfer control in acid electrolytes have been alsocalculated [7]. The approach used in those cases has been based on the analysis of therespective single branch of the polarization curve, either anodic or cathodic. However,it has been recognized that the determination of the kinetics parameters with this simpli-fied approach are subject to some uncertainty. In fact, for the experimental current to beassociated only to one single sub-process, either anodic or cathodic, current needs to bemeasured at potentials sufficiently distant from the corrosion potential, where undesirablereactions which interfere with the determinations can be activated [8,9]. As an alternativemethod several superimposition models have been proposed to determine kinetic param-eters by deconvoluting the polarization curve in potential ranges closer to the corrosionpotential [10–14]. This approach enables more accurate determinations of corrosion ratesand kinetic parameters from linear potential sweep data.

In the present study, the kinetics parameters for carbon steel corrosion in aerated NaClsolutions were determined from experimental polarization curves by developing a super-position model for oxygen reduction and iron oxidation which was implemented in a com-puter program. The application of this model permitted a more accurate characterizationof the kinetic parameters of oxygen reduction and iron oxidation than the one obtained bythe single analysis of the cathodic and anodic branches. It also enabled to explicitly under-stand how these sub-processes affect the rate of corrosion of carbon steel in the chloridesolutions.

2. Experimental

A BAS/100 electrochemical interface with a BAS/RDE-1 rotating electrode system wasemployed for voltammetry measurements. A conventional three electrode cell was used:a rotating working electrode made of carbon steel (WE), a platinum wire as a counterelectrode and an Ag/AgCl 1 M KCl cell as a reference electrode. The WE was a 4 mm

3170 L. Caceres et al. / Corrosion Science 49 (2007) 3168–3184

diameter · 5 mm cylinder made of carbon steel SAE 1010 with chemical content wt% 98.5Fe, 0.2 C, 0.6 Mn and traces of P, S, Si, Sn, Cu, Ni, Cr and Mo. An 8 mm diame-ter · 20 mm polyamide plastic rod was drilled along its axis to insert the specimen inone end and adapt a rotating shaft in the other. The specimen was inserted in the plasticrod applying resin adhesive in order to minimize a crevice formation between the exposedcircular surface of the steel and the plastic rod. The cell was immersed in a thermostaticbath operating at 22 �C.

Measurements were conducted in electrolytes prepared by dissolving laboratory gradeNaCl in distilled water. In each run, once the cell was filled with electrolyte, air was bub-bled for about 15 min until a saturated concentration of oxygen was reached. Oxygen con-centration in the electrolyte was measured using a WTW model 340 oxygen meter. Justbefore each measurement, the WE was abraded in a rotating plate with wet SiC paper (ini-tially with 400 grade and thereafter with 1200 grade), then degreased by immersion in ace-tone, cleaned in an ultrasound bath for 2 min rinsed with distilled water and immediatelyinserted in the cell.

Current–potential polarization curves were obtained from linear potential sweep at arate of 1 mV s�1, a sweep rate reported to guarantee obtaining steady-state current–poten-tial curves [5]. Potential sweeps were conducted in the potential range �700 to �100 mV/SHE and started from the cathodic limit, �700 mV/SHE, in order to minimize the influ-ence of surface rust formation on the measurements. Measurements were conducted inelectrolytes with 0.02, 0.1, 0.5 and 1 M NaCl with the working electrode rotating in therange 10–370 rad s�1. Several measurements were conducted at each experimental condi-tion after successive polishing of the carbon steel electrode, until reproducible polarizationcurves were obtained. However, reproducible polarization curves could only be obtainedat rotation rates of 170 rad s�1 or larger. At rotation rates below 170 rad s�1 there waspresence of air bubbles which remained attached on the electrode surface and could notbe removed at these low rotation rates, which interfered with the measurements.

3. Results and discussion

3.1. Polarization curves

Curves obtained at various rotation rates at the lowest and highest NaCl concentrationsused, 0.02 and 1 M, are shown in Figs. 1 and 2. An interesting feature in those results isthat the currents in the anodic branch of the curve decrease with an increase in the rotationrate of the electrode. This clearly shows that the anodic branch, which in neutral solutionsis known to be solely related to charge transfer controlled iron dissolution [15] is distortedby the influence of the mass transfer controlled cathodic process. From this observation itis evident that in this system it is not correct to determine the iron dissolution kineticparameters directly from a single analysis of the experimentally obtained anodic branch,even though at potential ranges where a ‘‘pseudo’’ Tafel region is achieved. With a sym-metric reasoning, one can also assume that the cathodic curves are correspondingly dis-torted by the influence of the anodic process. Therefore, it does not seem accurate todetermine oxygen reduction parameters directly from a single analysis of the respectivecathodic curve branch. This is why in the present system to determine the kinetic para-meters of the anodic and cathodic sub-processes and the corrosion rate it is necessary

-30.0

-20.0

-10.0

0.0

10.0

20.0

-700-500-300E (mV/SHE)I (

A/m

2 )

170 rad s-1210 260

310

370

Fig. 1. Experimental current–potential curves for different electrode rotation rates in 1 M NaCl solution.

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

-700-500-300-100E (mV/SHE)

I (A

/m2 )

170 rad s-1

210260

310370

Fig. 2. Experimental current–potential curves for different electrode rotation rates in 0.02 M NaCl solution.


to analyze the complete polarization curves with a superposition model which considerssimultaneously both sub-processes.

3.2. The model and kinetic parameters determination

Several models have been proposed as a basis for analysing linear potential sweep databy a curve fitting procedure. Some authors have applied a model which is restricted to sys-tems which are completely under charge transfer control which are not adequate for the


present case [9]. A modified model based on a cathodic process with mixed charge trans-fer–mass transfer controlled and an anodic process with charge transfer control has beenlater proposed [12]. This equation could be applied to obtain electrochemical parametersfor steel corrosion in near neutral solutions. Later a more complex model which includescathodic and anodic processes with combined diffusion, pitting and passivation pheno-mena have been presented and implemented as a computer program [13]. In this modeloxygen reduction on metal surfaces is assumed to be a first order reaction with respectto oxygen concentration in the electrolyte. This approximation is not directly applicableto the present system, where a 0.5 order dependence on oxygen concentration has beenreported [5].

The model developed in the present work assumes that the anodic reaction is underpure charge transfer controlled and the cathodic reaction is under mixed charge trans-fer–mass transfer control [15]. As a different feature, the order of the reaction with respectto oxygen concentration was left as another parameter to be determined during the fittingprocess. The expression for the total current is:

i ¼ iO2þ iFe ð1Þ

where iO2is the current associated to oxygen reduction, the predominant cathodic reac-

tion, and iFe is the current associated to iron oxidation. The kinetic expression for oxygenreduction was assumed to be [5,6]:

iO2¼ i0O2

1� iO2

ilO2

� �m

fc exp 2:3gO2

tc

� �ð2Þ

The kinetic expression for iFe is [5,6]:

iFe ¼ i0Fefa exp 2:3gFe

ta

� �ð3Þ

The dimensionless f factors [5] for sodium chloride solution are expressed as

fa ¼ asCl�

� �j1 asOH�

� �j2 ð4Þfc ¼ as

Cl�� j3 as

OH�� j4 ð5Þ

where asCl� , as

OH� are the activity values of Cl and OH� ions on the electrode surface,respectively, j1, j2, j3, j4 are dimensionless parameters, iO2

(A m�2) and iFe (A m�2) the par-tial current densities for oxygen reduction and iron oxidation, respectively, ilO2

(A m�2)the limiting current density for oxygen reduction, i0O2

(A m�2) and i0Fe (A m�2) the ex-change current densities for oxygen reduction and iron oxidation, respectively,gO2¼ E � EeqO2

ðmVÞ, gFe = E � EeqFe (mV), the oxygen reduction and iron oxidationoverpotential, respectively, E (mV) applied potential, EeqO2

; EeqFe ðmVÞ the equilibriumpotential for oxygen reduction and iron oxidation and ta, tc the anodic and cathodic Tafelslope expressed as mV dec�1, respectively.

In order to facilitate manipulation Eqs. (2) and (3) were expressed as follows:

iO2¼ a 1� iO2

c

� �m

expðbEÞ ð6Þ

iFe ¼ d expðeEÞ ð7Þ


where a ¼ fci0O2ðA m�2Þ; b = 2.3/tc (mV�1); c ¼ ilO2

ðA m�2Þ; d = fai0Fe (A m�2);e = 2.3/ta (mV�1).

From the fitted parameters the values of exchange current densities, limiting current,and Tafel slopes, were calculated as follows:

i0O2¼ a exp bEeq

O2

� �ð8Þ

i0Fe ¼ d exp eEeqFeð Þ ð9Þ

il ¼ c ð10Þ

tc ¼2:3

bð11Þ

ta ¼2:3

dð12Þ

A conventional software routine based in the simplex method [16,17] was used to findparameters a, b, c, d and e using experimental polarization data. A maximum of 600 cur-rent–potential values were available from each polarization experiment. The calculatingprocedure is further explained in Appendix A.

A ferrous iron concentration value of 1 · 10�6 M was arbitrarily assumed for EeqFe cal-

culation following the suggestion given by Bockris et al. [18]. The corrosion potential Ecorr

and current icorr were calculated from the zero total current density value of the theoreticalexpressions (1) and (9).

3.3. Fitted parameters and model application

Values of parameters a, b, c, d and e obtained using the model from experimental polar-ization curves obtained at each NaCl concentration and electrode rotation rate, are givenin Table A1, Appendix A. Electrochemical kinetic parameters calculated from parametersin Table A1 according to Eqs. (8)–(12) are listed in Table 1.

With the determined kinetic parameters it is now possible to represent and analyze thecurrent–voltage curves simulated by the model for the global current and for each of theassociated anodic and cathodic sub-processes involved in carbon steel corrosion in NaClsolutions. Fig. 3 shows a comparison of the experimental polarization curve (continuousline) obtained for the case of corrosion of a carbon steel electrode in 0.5 M NaCl solutionsat 260 rad s�1 with the curve calculated with the model using the respective fitted param-eters (dotted line). The degree of adjustment observed between the calculated curve andthe experimental one for this particular case is representative of those obtained in allthe other experimental cases.

Curves in Fig. 3 show that there is a wide potential range, between point A (�550 mV/SHE) and point C (�180 mV/SHE), where the theoretical curve coincides perfectly withthe experimental one. It is then possible to say that in this potential range carbon steel cor-rosion in NaCl solutions is well described simply in terms of one anodic sub-process, theanodic dissolution of iron under charge transfer control, and a single cathodic reaction,oxygen reduction under with mixed charge transfer–mass transfer control.

At potentials more cathodic than point A, the experimental cathodic current becomeslarger than the theoretical current. This deviation, which increases with the increase ofpotential, indicates the onset of the reduction of protons involving formation of gaseous

Table 1Kinetics parameters calculated from the model

NaCl(M)

X(rad s�1)

i0Fe

(A m�2)ta

(mV dec�1)i0O2� 104

(A m�2)tc

(mV dec�1)il(A m�2)

Ecorr

(mV)icorr

(A m�2)

002 170 0.07 245 1.9 228 10.9 �234 2.6210 0.11 291 1.4 215 12.2 �214 2.5260 0.08 267 1.6 207 13.3 �221 2.5310 0.09 274 0.8 205 14.4 �216 2.5370 0.10 291 1.0 200 15.1 �206 2.5Average 0.09 274 1.3 211

0.1 170 0.06 215 2.4 237 8.9 �242 3.2210 0.07 228 2.2 232 10.5 �234 3.4260 0.12 247 3.2 235 11.3 �234 4.3310 0.06 211 1.3 221 12.7 �236 3.6370 0.11 245 1.6 217 12.9 �223 4.5Average 0.08 229 2.1 228

0.5 170 0.20 202 0.8 200 8.5 �303 6.9210 0.11 184 1.9 225 9.3 �295 5.6260 0.12 192 3.3 237 10.2 �291 5.8310 0.08 185 1.6 225 10.3 �286 5370 0.16 200 6.7 247 10.6 �289 6.9Average 0.13 193 2.9 227

1 170 0.02 123 0.2 204 7.7 �332 3.7210 0.06 149 6.1 261 8.8 �328 5.3260 0.13 163 1.6 207 10.5 �323 8.3310 0.05 142 1.9 237 10.7 �326 5.3370 0.08 158 1.1 223 12.2 �323 5.7Average 0.07 147 2.2 226


hydrogen on the carbon steel [15]. This result shows that this reaction is only relevant atthis high cathodic potential range and should have little importance in the vicinity of thecorrosion potential. Therefore, it should not have major influence on the corrosion rate ofcarbon steel and it does not need to be considered in the model.

At potentials more anodic than point C the experimental anodic current becomes largerthan the theoretical current. The potential at point C, 180 mV/SHE, is in the potentialrange where pitting formation has been observed in corrosion of iron in NaCl solutions[19]. Therefore, one can assume that the observed increase in anodic current with respectto the simple charge transfer mechanism can be related here to the distorting effect intro-duced by pitting formation. From this deviation it becomes clear that an attempt to draw aTafel line based on the anodic branch in a log(i)–E plot will give an underestimated Tafelslope (calculated as mV dec�1) with respect to that obtained from Eq. (1). For instance,using methods such as graphical extrapolation in a log (i)–E plot or numerical calculationbased on mixed charge transfer reaction (i.e. four-point method [20]) will produce under-estimated absolute anodic Tafel values. For various polarization curves this underestima-tion were found to be between 5% and 40% with respect to fitted values using Eq. (1). It isvery interesting to note that the lowest underestimations were observed at 1 M NaCl.Probably at this concentration a faster pit development will generate faster inhibitionthrough rust coverage giving rise to an apparent Tafel-like behaviour. The evidence of

-2

-1

0

1

2

-700-600-500-400-300-200-100

E (mV/SHE)

AB

C

O

Lo

g (

i/(A

/m2 ))

Fitted total current curve

Experimental curve

C'

Fig. 3. Experimental polarization curve (continuous line) for carbon steel electrode rotating at 260 rad/s�1 inaerated 0.5 M NaCl solution. Fitted curve (dotted line) and Tafel slope, both calculated from the model, aresuperimposed.


the pit activity comes from the proximity between corrosion and pitting potentials. In fact,based on experimental data reported in a former investigation [19], pitting potentials val-ues are between 37 and 66 mV more positive than corrosion potentials (Table 1) for iron inNaCl concentrations from 0.02 to 1 M. However, experimental density current deviationsfrom Tafel behaviour are significant only at potentials 100 mV more positive than corro-sion potential. This can be interpreted as evidence of a previous metastable stage in theonset of the pitting process [21].

Fig. 4 shows the same polarization curve shown in Fig. 3, but now in E–i coordinates andtogether with the respective calculated curves for the anodic and cathodic sub-processes. Asexpected from corrosion theory, the experimental curve approaches the currents of the sin-gle the sub-processes only at potentials far from the corrosion potential. For instance, theexperimental curve represents well the intrinsic cathodic current reaction only at potentialcathodic to �500 mV/SHE. This is clear evidence that in this system the experimentalcathodic current cannot be directly used to obtain the kinetic parameters associated tothe single cathodic sub-process. In fact, values of tc and i0O2

calculated from directly fittingthe experimental cathodic current to the equation log(i(1 � i/il)

�0.5) vs. E following the pro-cedure used in [5], differ up to 60% with respect to values calculated here with the superim-position model. This broad variation is a the result of combined uncertainty in thedetermination of the limiting current and the slope of the curve log(i(1 � i/il)

�0.5) vs. E.

3.4. Cathodic limiting current

As the potential sweep started from the cathodic side an important part of the cathodiccurve was obtained before the onset of surface iron oxide formation, and correspondsto oxygen reduction on a practically rust-free carbon steel surface. A high correlation

Fig. 4. Total and partial current densities fitted using the model from experimental data in Fig. 3.


coefficient value between il and X0.5 was obtained at every NaCl concentration, as can beseen in Fig. 5. These results confirm validity of the Levich relationship [22]:

il ¼ 0:62nFD2=3O2

m�1=6CO2X1=2 ð13Þ

where CO2ðmol m�3Þ is the oxygen concentration of the bulk in, DO2

ðm s�2Þ the oxygendiffusion coefficient, F (96,485 coulomb mol�1) the Faraday constant, n the number ofelectrons transferred, m (m s�2) the kinematic viscosity and X (rad s�1) the rotation rateof the iron steel electrode. The Levich slope values indicated as S in Fig. 5 are in agreement

0.1 M S = 0.70 R2 = 0.99

0.02 M S = 0.82 R2 = 0.99

1 M S = 0.60R2 = 0.98

0.5 M S = 0.7R2 = 0.96

5

9

13

17

12 14 16 18 20

(rad/s)Ω 0.5

i l A

/m2

1 M

0.5 M

0.1 M

0.02 M

Fig. 5. Linear dependency of the limiting current density from X0.5 at different NaCl solution concentrations.


with those reported in other investigations [23]. Assuming that S is solely dependent onNaCl concentration at a fixed temperature, an overall analytical expression for il datashown in Fig. 5 is as follows:

il ¼ ð0:6144þ 0:2261eð�9:7942CNaClÞÞX0:5

for 0:02 < CNaCl < 1M

and 170 < X < 370 rad s�1

ð14Þ

The n values associated with the reduction of dissolved oxygen were calculated by usingEq. (13) using physical data from different sources [24–26]. These values are between2.4 and 4. Possibly, oxygen reduction on carbon steel could take place simultaneouslyby both, a 2 and 4 electron transfer process as reported for bare and passive iron, respec-tively [5,23].

3.5. Influence of electrode rotation rate on anodic and cathodic sub-processes

Fig. 6 shows current–potential curves calculated with the model for the anodic andcathodic sub-processes at two extreme NaCl concentrations, 0.02 M and 1 M NaCl, ateight different electrode rotating rates. The trend observed in the cathodic current curvesin that figure shows that the electrode rotation rate has a clear influence on the kinetics ofoxygen reduction on carbon steel. This reaction, therefore, is clearly influenced by masstransfer phenomena which is itself dependent on fluidodynamic conditions at the electrodesurface. As values of tC and i0O2

seem to vary randomly with variations of electrode rota-tion rate (see Table 1) one can conclude that the increase in the cathodic currents withrotation rate is due to variations in the limiting current, il, which consistently increaseswith the increase of rotating rate (see previous section).

On the other hand, Fig. 6 shows that anodic current curves vary randomly with theincrease of rotation rate. This behaviour confirms that the anodic parameters ta and i0Fe

calculated with the model are in fact independent of mass transfer influence and truly rep-resent the intrinsic kinetic parameters associated to a pure charge transfer control. Ran-dom variation of anodic parameters is related to the statistical nature of the pittingprocess mainly originated from its early metastable stage. This effect has been reportedas current fluctuations in corrosion of mild steel in NaNO2–NaCl solutions using a sta-tionary electrode [21].

3.6. Effect of NaCl concentration on anodic and cathodic sub-processes

Fig. 7 shows i–E curves for the anodic and cathodic sub-processes at two rotation rates,310 and 370 rad s�1, for each of the four NaCl concentrations used, 0.02, 0.1, 0.5 and 1 M.Results in that figure show that the anodic current curves clearly rises with an increase inNaCl either at low or high rotation rates. As data in Table 1 shows that i0Fe varies ran-domly with variations of NaCl concentration, variations in the anodic current curvescan be mainly attributed to variations of ta, which systematically decreases as NaCl con-centration increases (see Table 1). This tendency shows that the increase in NaCl concen-tration enhances the rate of pitting formation occurring on the surface of carbon steel.

The trend observed in the cathodic curves in this Fig. 7 shows that the concentration ofNaCl has also an influence on the kinetics of oxygen reduction on carbon iron oxidation.

0.0

5.0

10.0

15.0

-700-500-300-100

E (mV/SHE)

I (A

/m2 )

I (A

/m2 )

170 rad/s

210260310

370

0.0

5.0

10.0

15.0

-700-500-300

E (mV/SHE)

170 rad/s

210

310

370

260

Fig. 6. Partial anodic and cathodic curves for carbon steel disk rotating at different angular velocities: (a) 0.02 MNaCl solutions; (b) 1 M NaCl solutions. Corrosion currents at each curves interception are highlighted with adot.


The cathodic current decreases with a NaCl concentration increase, behaviour which isdetermined by the decrease in the cathodic limiting current. This tendency can be relatedto the increase in solution viscosity which accompanies the increase of NaCl concentrationwhich, subsequently, reduces the cathodic limiting current as shown by the Levich rela-tionship [22]. The effect of NaCl concentration increase is more marked at high rotationrates. On the other hand, variations of kinetics parameters associated to the mechanismof charge transfer control in oxygen reduction, i0O2

and tc, showed only a random varia-tion with the increase in NaCl concentration.

0.0

5.0

10.0

15.0

-700-500-300-100

E (mV/EHE)

E (mV/EHE)

I (A

/m2)

I (A

/m2)

1 M

1 M

0.5 M

0.5 M0.1 M0.1 M

0.02 M

0.02 M

0.0

5.0

10.0

15.0

-700-500-300-100

1 M

0.5 M

0.1 M

0.02 M

0.02 M

0.1 M

0.5 M

1 M

Fig. 7. Partial anodic and cathodic curves for carbon steel disk at different NaCl concentrations: (a) 310 rad/s;(b) 170 rad/s. Corrosion currents at each curves interception are highlighted with a dot.


3.7. Kinetics expressions

After analyzing the influence of electrode rotation rate and NaCl concentration on theanodic and cathodic sub-processes it is possible to write explicit expressions for the kinet-ics of each of these sub-processes. In the case of the anodic sub-process as i0Fe and ta variedrandomly with rotation rates average values of these parameters were calculated for each


NaCl concentration, which are shown in Table 1. Then, the dependence of these averagevalues on NaCl concentration was analyzed and found to be:

i0Fe ¼ 0:096� 0:008CNaCl ð15Þta ¼ 257� 115CNaCl ð16Þ

From these results the rate of the anodic dissolution of carbon steel could be finally ex-pressed as:

iFe ¼ ð0:096� 0:008CNaClÞ expE

591� 265CNaCl

� �ð17Þ

In the case of the cathodic sub-process the influence of rotation rate and NaCl concentra-tion is summarized in its effect on mass transfer, which influences the limiting current,which are summarized in Eq. (14). On the other hand, as i0O2

and tc varied randomly withrotation rates average values of these parameters were calculated at each NaCl concentra-tion, which are presented in Table 1. From these results the rate of the cathodic oxygenreduction on carbon steel can be finally expressed as:

iO2¼ 2:1� 10�4 1� iO2

ð0:6144þ 0:2261eð�9:7942CNaClÞÞX0:5

� �0:5

expð0:0103EÞ ð18Þ

3.8. Corrosion rate

Fig. 8 summarizes the dependence of corrosion current on the electrode rotating rateand NaCl concentrations. The trends observed in that figure can be now well understoodin terms of the behaviour of the cathodic and anodic sub-processes described in Figs. 6 and 7.

0

2

4

6

8

10

150 250 350 450

rad s-1

I (A

/m-2

)

1 M 0.5 M0.1 M0.02 M

Fig. 8. Corrosion current density vs. electrode rotation rate.


In those figures values of corrosion currents are defined at the crossing of the respectiveanodic and anodic curves and are graphically represented as filled circles.

Fig. 8 shows that in solutions with 0.02, 0.1 and 0.5 M NaCl, the influence of rotationrate on the corrosion current does not show a clear trend, but at 1.0 M NaCl corrosionrate, on average, increases with rotation rate increase. The behaviour observed at 0.02,0.1 and 0.5 M can be explained in terms of the trend observed in anodic and cathodiccurves in Fig. 6a, drawn for 0.02 M NaCl. At this low NaCl concentration the anodiccurve crosses the respective cathodic curve in a potential region where the cathodic processis mainly controlled by charge transfer and is, therefore, independent of mass transfer. Onthe other hand, the behaviour observed at 1.0 M can be explained with respect to Fig. 6b,which shows that the situation changes at 1 M NaCl: at this high NaCl concentration thekinetics of the anodic process is much faster and the anodic curve now crosses the cathodiccurve at a much higher potential, where the cathodic process is strongly influenced by masstransfer.

Fig. 8 shows that the corrosion current increases with an increase in NaCl concentra-tion. This behaviour can be explained in terms of Fig. 7 which shows that even thoughthe cathodic limiting current decreases with a NaCl concentration increase, the stronginfluence of NaCl concentration on the anodic current predominates and the result in anet increase of the corrosion current.

4. Conclusions

Current–potential curves for carbon steel corrosion in NaCl solutions were obtainedfrom linear potential sweep at a rate of 1 mV s�1 in solution with concentrations in therange 0.02–1 M NaCl and rotation rates in the range 170–370 rad s�1.

The observed influence of rotation rate on the obtained polarization curves gave evi-dence that the cathodic and anodic current branches are interdependent on both the ano-dic and cathodic sub-processes and can not be independently used to characterize carbonsteel corrosion.

Application of a superimposition model developed ad hoc and implemented in a com-puter program enabled determining the corrosion rate of carbon steel and the kineticsparameters of the underlying anodic and cathodic sub-processes.

The anodic sub-process, dissolution of iron, is well described in terms of a pure chargetransfer controlled kinetics in which the Tafel slope decreases with a NaCl concentrationincrease.

The cathodic sub-process, oxygen reduction on iron, is well described in terms of amixed mass transfer and charge transfer controlled kinetics where the limiting currentincreases with the rotation rate increases but decreases with NaCl concentration increase.

The influence of NaCl concentration and electrode rotation rate on carbon steel corro-sion rate can be well explained in terms of their specific influence on the anodic and catho-dic sub-processes.

Acknowledgments

The financial support from projects MECESUP ANTO102 and MEL 2004 developedin the Faculty of Engineering at the Universidad de Antofagasta, Antofagasta, Chile, isgreatly appreciated.


Appendix A. Unconstrained optimization method for parameter determination

The unknowns’ parameters a, b, c, d, e were determined by minimization of the totalsum of the squared values as follows:

SSV ¼Xn

1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðiexp

j � ijÞ2q

ð20Þ

where n is the number of current, potential data, iexpj is a steady-state current density mea-

surement taken at a given applied potential Ej in the iron steel/NaCl solution cell, and ijthe theoretical expression for current density at the same potential

Table A1Fitted parameters for experimental current–potential values according to Eq. (18)

NaCl conc. X(rad s�1)

a

(A m�2)b

(m V�1)c

(A m�2)d

(A m�2)e

(mV�1)Ecorr (mVSHE)

icorr

(A m�2)

1 M NaCl 10 0.047 �0.014 3.7 �935.4 0.016 �369 3.042 0.277 �0.009 4.0 �1315.5 0.017 �357 3.184 0.281 �0.011 5.2 �999.0 0.016 �348 4.4

168 0.121 �0.011 7.7 �1823.8 0.019 �332 3.7209 0.498 �0.009 8.8 �808.3 0.015 �328 5.3262 0.763 �0.011 10.5 �776.1 0.014 �323 8.3314 0.310 �0.010 10.7 �1047.7 0.016 �326 5.3367 0.276 �0.010 12.2 �618.2 0.015 �323 5.7Av. 0.322 �0.011 �935.4 0.016

0.5 M NaCl 10 0.005 �0.021 2.4 �329.3 0.015 �341 2.242 0.046 �0.016 4.7 �301.9 0.014 �321 3.684 0.079 �0.016 6.7 �239.6 0.013 �307 4.8

168 0.489 �0.012 8.5 �217.8 0.011 �303 6.9209 0.451 �0.010 9.3 �226.8 0.013 �295 5.6262 0.540 �0.010 10.2 �190.8 0.012 �291 5.8314 0.385 �0.010 10.3 �170.9 0.012 �286 5.0367 0.797 �0.009 10.6 �189.9 0.012 �289 6.9Av. 0.349 �0.013 �233.4 0.013

0.1 M NaCl 10 0.062 �0.014 2.7 �55.2 0.017 �232 1.142 0.220 �0.012 5.0 �43.8 0.011 �253 3.084 0.213 �0.011 6.2 �34.8 0.012 �233 2.3

168 0.383 �0.010 8.9 �42.0 0.011 �242 3.2209 0.410 �0.010 10.5 �35.8 0.010 �234 3.4262 0.555 �0.010 11.3 �38.3 0.009 �234 4.3314 0.360 �0.010 12.7 �47.9 0.011 �236 3.6367 0.527 �0.011 12.9 �36.6 0.009 �223 4.5Av. 0.341 �0.011 �41.8 0.011

0.02 MNaCl

10 0.020 �0.008 2.7 �23.0 0.010 �306 1.342 0.128 �0.009 5.0 �23.1 0.010 �257 1.684 0.156 �0.010 7.4 �16.4 0.009 �243 1.7

168 0.416 �0.010 10.9 �22.7 0.009 �234 2.6209 0.485 �0.011 12.2 �13.6 0.008 �214 2.5262 0.729 �0.011 13.3 �16.5 0.009 �221 2.5314 0.426 �0.011 14.4 �14.9 0.008 �216 2.5367 0.636 �0.012 15.1 �13.1 0.008 �206 2.5Av. 0.374 �0.010 �17.9 0.009

Av., Average value.


ij ¼ a 1� iO2

c

� �m

exp bEj

� �þ d expðeEjÞ ð21Þ

To ensure convergence in the optimization process the procedure to handle expression (21)was as follows:

(a) The independent variable E was normalized in terms of its median and standarddeviation values.

E0 ¼ E � Em

Edð22Þ

where Em and Ed are the arithmetic average and the standard deviation of potentialvalues considered for minimization, respectively.

(b) Due to difficulties experienced with the implicit iO2variable of Eq. (6), the corre-

sponding m value was previously estimated by linear regression from a ln(i) vs.ln(1 � i/il) plot at different X values and �500 mV [5].Thus using m = 0.5, Eq. (1) is expressed as

ij ¼a2c

expðbEjÞ½�a expðbEjÞ þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2 expð2bEjÞ þ 4c2

q� þ d expðeEjÞ ð23Þ

For this equation, the first term of the right hand side is the explicit form of thecathodic partial current density and the second term the anodic partial currentdensity.

(c) The quality of the fit for a given potential interval was evaluated using the root meansquared error defined as

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPnj¼1 iexp

j � ij

� �2

ðn� rÞ

sð24Þ

where, r is the number of independent variables.
(d) Initial estimates of a, b, c, d, e parameters for optimization was done in a sequential
order. First, c equals to the experimental current value at �500 mV (EHE), b equalto the minimum-squared slope of the experimental values log (i(1 � i/c)�0.5) vs. E, ina selected potential cathodic range, a equals to i exp(�bE)(1 � i/c)�0,5, e equals tothe minimum-squared slope of the experimental values log (i) vs. E, in a selectedpotential anodic range, and d equals to i exp(�eE).

References

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Determination of Electrochemical Parameters

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