The corrosion of carbon steel in a chloride environment due to periodic voltage modulation: Part I

The corrosion of carbon steel in a chloride environment due to periodic voltage modulation: Part I

Corrosion Science, Vol. 37, No. 10, pp. 1567-1582, 1995 Copyright 0 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 001&938X/9...

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Corrosion Science, Vol. 37, No. 10, pp. 1567-1582, 1995 Copyright 0 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 001&938X/95 $9.50 + 0.00

0010-938X(95)00066-6

THE CORROSION OF CARBON STEEL IN A CHLORIDE ENVIRONMENT DUE TO PERIODIC VOLTAGE MODULATION: PART I S.B. LALVANI Mechanical

Engineering

and G. ZHANG

and Energy Processes, Southern Illinois University IL 62901-6603, U.S.A.

at Carbondale,

Carbondale,

Abstract-The influence of positive half-cycle rectified sinusoidal potentials superimposed at three DC levels on carbon steel (1018) in 3.33% NaCl solution under nitrogen purge on materials degradation behavior was investigated. The results obtained show that although the material degradation rate increases with the peak potential of the alternating voltage (AV) signals, the increase in corrosion rate is strongly influenced by the choice of the applied DC potential level: the more anodic the DC potential, the greater is the corrosion rate. The samples were found to undergo extreme pitting, exacerbated by chloride participation and absence of oxygen. The current was found to increase with time at higher potentials lending support to the idea that autocatalytic reactions such as pitting are primarily responsible for the degradation of carbon steel. The corrosion rate of the alloy was found to decrease with frequency of the AV signal. A close relationship between the average DC current and corrosion rate for various levels of AV severity was observed. The data do not support the commonly held belief in the literature that the imposition of AV signals results in a change of corrosion mechanism.

INTRODUCTION Corrosion caused by alternating current (AC) or alternating voltage (AV) can and does occur in marine environments and induces pitting and damage of offshore platforms due to incorrect welding operations, corrosion of boats during improper battery charge, and corrosion of steam generating plants using seawater for cooling systems. Earlier work’-” on periodic modulation of current and voltage suggests that application of alternating current or alternating voltage signals causes localized pit formation and a simultaneous increase in the corrosion rate in sulfate solutions. When AV signals were applied to carbon steel samples in a simulated seawater solution, the material degradation rate was found to increase with the peak voltage of the signal, while the specimen was found to be pitted heavily, especially at higher peak voltages” ( > 40 mV (SCE)). In the above experiments, sinusoidal AV signals were applied to carbon steel specimens, while the DC potential was held constant at the corrosion potential (DC) of the specimen. Most research performed previously examined the relationship between the current generated and applied AV signal. Very few data are available on the actual rates of material degradation. Contrary to the popular belief in the scientific literature that AV signals are more deleterious to materials than the corresponding DC voltages, a recent paper13 on the corrosion of Cu-Ni alloy in seawater seems to suggest that there is very little difference Manuscript

received 6 January

1995. 1567

1568

S.B. Lalvani

and G. Zhang

between the AV and DC signals in that the mechanism of corrosion of the alloy is not affected by the choice of applied signal. In this paper, the influence of positive half-cycle rectified AV signals on the corrosion behavior of carbon steel held constant at three different DC potentials in a chloride solution is described. The rationale for conducting these experiments is to be able to discern the inlluence of AV signals from DC signals. In another paper, the influence of negative half-cycle AV signals and full AV signals on materials degradation will be described.

EXPERIMENTAL

METHOD

All of the mild carbon steel (1018) alloy specimens used in the study were obtained from Metal Samples Corporation, Munford, Alabama. The machined shape is a I/2 in (I .27 cm) long cylinder with a diameter of 3/8 in (0.95 cm). All specimens were polished to a 600 grit finish. Each specimen had one tapped end so that it could be mounted on to a threaded specimen holder. The exposure surface area of each specimen was approximately 0.7 in2 (4.5 cm’). A three-electrode cell filled with approximately 900 ml of 3.33% NaCl solution prepared by dissolving the salt in de-ionized water was used for both potentiodynamic and immersion tests. The arrangement of the electrodes was as follows: (1) working electrode (WE) -specimen; (2) counter electrode (CE) -platinum mesh; and (3) reference electrode - saturated calomel electrode (SCE). Prior to each run, the solution was purged with nitrogen gas to remove dissolved oxygen. Nitrogen gas purging and magnetic-bar stirring were continued and kept consistent throughout each test. In the immersion experiments, the effects of AV on the corrosion rate and on corrosive morphology of specimens were studied as functions of exposure time, AV level and AV frequency, respectively. The positive half-cycle rectified sinusoidal AV signal was applied between the working electrode and reference electrode. A Leader (Model LFG-1300s) function generator was used to supply the required AV waveform to the modulation input of an EC0 (Model 550) potentiostat. An oscilloscope was used to adjust as well as to monitor the AV signal applied. Before and after each immersion experiment, individual specimens were cleaned with distilled water and acetone and then chemically cleaned in Clark’s solution, dried, and then weighed. DC potentiodynamic experiments were performed using a potentiostat (Model 273) supplied by EG and G. The potentiostat was controlled by a PC computer with the electrochemical software (SOFT CORR MODEL 342) provided by the same company. Procedures and parameters specified in ASTM standard G587 were followed for all the experiments, i.e., the testing solution was purged with dry nitrogen for 30 min before the test began, and no nitrogen purge was applied when the experiment started. In this paper, DC has been defined as the current that does not exhibit any periodicity. Scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS) were performed on several immersion test specimens before and after removal of corrosion products. EDS analyses and SEM micrographs were conducted or taken at various locations on the specimens or under different magnifications to characterize the morphology and composition of the corrosion products. All alloy samples used for EDS analyses of the corrosion products were first rinsed with de-ionized water and then by acetone. The samples were then dried in air. It is unlikely that the above procedure would alter the nature of the solid corrosion products. An automated imaging analysis system was used to characterize the surface of the specimen from which corrosion products were removed. Selected representative surface of the corroded material was used to characterize the pit number and pit dimensions.

EXPERIMENTAL

RESULTS

AND

DISCUSSION

Experiments were conducted at the following three different levels of DC potentials. The open circuit potential* which was determined to be - 580 mV(SCE)

*The definition of open-circuit potential is from the ASTM procedure G5-82 (p. 125, Section 4.6). According to this procedure, the open circuit potential is the potential measured after 55 min immersion.

Carbon

-1.4-l -2

-1

Fig. 1.

0

steel corrosion:

1 2 Log Current Density,

DC polarization

1569

Part I

3

4

5

@/cm?

curves of carbon

steel (1018).

was held constant in one set of experiments. The corrosion potential+ calculated from the data obtained using the potentiodynamic polarization technique was found to be equal to - 780 mV(SCE), while a corrosion rate of 0.072 g cm-*y-i was evaluated when the solution was stirred under nitrogen purge. The potentiodynamic polarization diagram (Fig. 1) shows that carbon steel has no active/passive transition when immersed in a chloride solution. The current vs potential plots show that the Tafel regions, both anodic and cathodic, are linear. The potentiodynamic polarization diagram for the experiment in which quiescent conditions were maintained was found to be similar in shape to that shown in Fig. 1, and the corrosion rate was evaluated to be 0.008 g cm-*y - ’ . A potential of 0 mV(SCE) that is much more active to the corrosion potential and the open circuit potential was also chosen to represent a more anodic level for carbon steel dissolution in the experiments described below. Corrosion at open circuit potential In the experiments described below, the DC potential of the carbon steel specimen was maintained at its open circuit potential (- 580 mV(SCE)) determined in the absence of any external voltages. A positive half-cycle rectified signal of desired peak potentials was superimposed and applied between the working electrode and the reference electrode. Unless otherwise noted, the frequency of AV modulation was held at 60 Hz. The influence of peak potential on the materials degradation rate is shown in Fig. 2. The curve drawn in Fig. 2 represents the best fit. The zero AV experiment was conducted in the absence of any applied periodic waveform; however, the DC potential was maintained at -580 mV(SCE). The corrosion rate was found to be ‘The corrosion potential is the potential calculated data obtained during the potentiodynamic polarization

by performing experiment.

the Tafel analysis

of the experimental

S.B. Lalvani 25

and G. Zhang

,,,,),,,,,,,/,,,,,,J,,,,/,,,,,,,,/,,

0

,1,/,,,,,,/,,,,/,,,/,,,,,,,,,,,,,,,,,,/, 100

0

200

Alternating

Peak

300 Voltage,

400

mV

Fig. 2. Corrosion rate vs peak alternating potential. The DC potential of the specimen was held at the open circuit potential of - 580 mV(SCE) while a positive half-cycle rectified sinusoidal AV signal at 60 Hz was superimposed. Experiments were conducted at room temperature under nitrogen purge for 4 h.

equal to 1.90 g cmP2y-‘, which is considerably lower than the corrosion rate found in the presence of AV signals. The corrosion rate was found to increase with the peak potential. The ratio of the corrosion rates of specimens subjected to AV signals to the corresponding rates in the absence of AV signal was found to be between 2.9 and 10.6, depending upon the magnitude of the peak potential. The average DC current was also found to increase with the peak voltage (Table 1). The ratio of the average current Table 1. Average of DC current and corrosion rate. Experimental conditions as in Fig. 2 AV level (mV) 0 70 100 120 130 160 180 200 220 250 300 350

I average (mA cm-*)

Corrosion rate (g cm-* yP ‘)

0.312 0.635 0.647 0.650 0.654 0.805 1.007 0.959 1.095

1X82 5.452 6.191 6.316 6.768 7.058 8.657 8.059 9.458 12.146 16.016 19.986

1.276 1.405 1.892

Carbon

steel corrosion:

1571

Part I

PAd’ u

0.0

,,(,,,,,,((,,

-;::-/0

1

2 Time,

Fig. 3.

DC current

i 4

3

5

h

vs time. Experimental

conditions

as in Fig. 2.

of the specimens subjected to AV signals to the corresponding current in the absence of AV signal was found to be between 2 and 6.1, depending upon the magnitude of the peak potential. The data showing that superimposition of AV signals results in an increase in material degradation rate and corrosion current are in accordance with the results reported in the literature.‘* Examination of the polarization curve (Fig. 1) also indicates that when anodic signals are imposed upon the specimen, the material degradation rate should increase with the magnitude of the AV modulation. The DC current density as a function of time at different peak voltages was also monitored. The results are shown in Fig. 3. In general, the current is observed to increase with time of reaction. It is noted that when a relatively high AV signal (300 mV peak potential) was applied, the current initially increased sharply, and then the increase in the current decreased slightly with time. However, for the experiment conducted at a peak potential of 100 mV(SCE), the current is observed to increase with time, whereas the current initially increased with time and then leveled off to a constant value when a peak voltage of 200 mV(SCE) was applied. The data on corrosion rate vs time for the experiment conducted at a peak potential of 180 mV(SCE) and shown in Fig. 4 indicate clearly that corrosion also increases although the increase in the rate of dissolution decreases with time. The observed increase in current with time suggests that the reaction mechanism may involve an autocatalytic pathway(s). A set of experiments was conducted in which AV signals of varying frequency (20-140 Hz) of peak voltage 180 mV(SCE) were applied for a period of 4 h. The material degradation rate vs frequency data are plotted in Fig. 5. The data show clearly that with an increase in AV modulation frequency from 20 to 140 Hz, the

1512

S.B. Lalvani

‘6

and G. Zhang

““““,“‘,“‘,,‘,,‘,,,,,:,,,,,,,,,,i,,,,,,,,,,

Time,

Fig. 4.

Corrosion

h

rate vs exposure time. Experiments were conducted at a peak potential 180 mV(SCE). Other experimental conditions as in Fig. 2.

of

o~,,,,,,,,,,,,,,,,,l,,,,,,,,,,,, 0

25

50

75

Frequency,

Fig. 5.

Corrosion

rate vs frequency. Experiments 180 mV(SCE). Other experimental

100

125

150

Hz

were conducted at a peak potential conditions as in Fig. 2

of

Carbon

steel corrosion:

Time, Fig. 6.

DC current

vs time as a function

1573

Part I

h

of frequency.

Experimental

conditions

as in Fig. 5

corrosion rate decreased significantly. When the frequency of the signal used was 140 Hz, the corrosion rate is observed to be equal to that for the experiment in which no AV signal was superimposed. The DC current density vs time behavior at various frequencies is shown in Fig. 6. The data show that in general, current increases with time, however, the observed current is lower at higher frequencies. The following explanation is offered for the observed corrosion behavior of carbon steel as a function of AV frequency in the chloride solution. The double-layer impedance decreases linearly with the frequency and, hence, only a small fraction of current flows through the faradaic impedance (polarization resistance) at high frequencies, resulting in a lower metal dissolution rate. At lower frequencies, the time needed for Fe2+ diffusion into the solution is greater than the time in which the polarity of the electrode is changed. At lower frequencies, relatively low concentrations of Fe2+ are available near the electrode for redeposition (see Appendix). Moreover, the rate of Fe2+ redeposition is negligible, even at the most cathodic potential (- 580 mV(SCE)). It is also observed by Kuo et a1.14 that the dissolution rate of FeC12 (a product of corrosion) is the limiting step in the dissolution of iron in chloride media. Thus, at high frequencies, the rate of carbon steel dissolution can be expected to be lower, since the diffusion of FeC12 away from the electrode would be hindered.4 The oxidation of hydrogen atoms to H + is not thought to greatly influence the material degradation rate, since H+ has a high diffusivity constant. The current density vs time behavior at various frequencies is shown in Fig. 6. The data also show that, in general, current increases with time, however, the observed current is lower at higher frequencies.

1574

S.B. Lalvani

and G. Zhang

Corrosion at the corrosion potential In the experiments described below, the potential of the carbon steel was held at its DC corrosion potential (- 780 mV(SCE)) determined in the absence of any external AV modulation. The corrosion rate is found to increase with the peak voltage (Fig. 7). The increase in corrosion rate with the peak potential is observed to be less steep than that observed for the experiments conducted when the DC potential was held at the open circuit potential (Fig. 2). This behavior can be attributed to the more anodic DC potential (- 580 mV(SCE)) used in later experiments. The corrosion rate vs time behavior for the experiment conducted at a peak voltage of 180 mV(SCE) is shown in Fig. 8. It is interesting to observe that the rate of corrosion decreases with time, unlike the results from experiments where the DC potential was held at a more anodic value of -580 mV(SCE) (Fig. 4). It is known that when mild steel is subjected to AV modulation, the corrosion products formed include hydrous oxide layer.17 It is possible that the corrosion products formed provide resistance to diffusion of metal ions, and thus the observed decrease in current (or dissolution rate) with time. Corrosion at a potential anodic to corrosion potential In the experiments described below, the DC potential of the carbon steel specimen was held much more anodic (0 V(SCE)) to its DC corrosion potential

1.6

1.4

0.6 Alternating Peak

Voltage.

mv

Fig. 7. Corrosion rate vs peak alternating potential. The DC potential of the specimen was held at the open circuit potential of ~ 780 mV(SCE) while a positive half-cycle rectified sinusoidal AV signal at 60 Hz was superimposed. Experiments were conducted at room temperature under nitrogen purge for 4 h.

Carbon

x I

“E 2

steel corrosion:

1575

Part I

1.5 -

1.3 -

d 2

l.O-

s .:: 0.8 k s

0

1

2

3

Time, Fig. 8.

Corrosion

4

5

6

h

rate vs exposure time experiments were conducted at a peak potential 180 mV(SCE). Other experimental conditions as in Fig. 7.

of

of - 780 mV(SCE). In this set of experiments, the reaction time was held to 30 min unlike the previous experiments that were carried out for a longer period of time (4 h), since the rate of dissolution was found to be much higher at more anodic DC potentials. The corrosion rate is observed to increase with peak voltage (Fig. 9) and is found to be orders of magnitude greater than the experiments conducted at the open circuit or corrosion potentials. The various data are replotted in Fig. 10 to reflect the influence of DC potential on the material degradation rate. For the experiments conducted at three AV peak potentials (50,100 and 180 mV(SCE)), the corrosion rate is observed to be a much stronger function of the DC potential level than the magnitude of AV modulation. The data also show that although the corrosion rates do increase with the peak potential, the corrosion rate is much more dependent upon the potential maintained at the working electrode. In order to further determine the influence of potentials on the material degradation rate, an experiment was conducted in which instead of AV modulation of peak potential 180 mV(SCE), the potential at the electrode was maintained at its root mean square value (which is one-half the peak potential of the positive half-cycle rectified AV modulation) plus the open circuit potential of -580 mV(SCE). Thus, the potential was set at 580 + 180 x (l/2) mV(SCE) in the absence of AV modulation. The data shown in Fig. 11 clearly show that anodic current increases rapidly with time with fluctuations in current, which is typical of the response observed for autocatalytic reactions involving pitting. 15

1576

S.B. Lalvani 600

,

,

,

,

,

,

,

,

,

,

,

and G. Zhang

,

,

,

,

,

,

,

,

I,,

,

,

,

,

,

,

0

580

-

560

-

;‘ “E s

5400-

z

520

-

s ‘Z 0 ,= 0

500-

460

-

460

, , , , , 0

,111

/,I

,I

/

50

,

(

I,,

,

,

(

,

,,I,,]

700

Alternating

Peak

,

150

Voltage,

,

,

,,

)

,,

,

,

200

mV

Fig. 9. Corrosion rate vs peak potential. The DC potential of the specimen was held at 0 mV(SCE), while a positive half-cycle rectified sinusoidal AV signal at 60 Hz was superimposed. Experiments were conducted at room temperature under nitrogen for 0.5 h.

600

500

?

400

DC

Potential,

mV

Fig. 10. Corrosion rate vs DC potential. Experiments were conducted at three different values of positive half-rectified signal superimposed upon DC potentials. Experiments were conducted under nitrogen purge for 4 h for DC potentials of ~ 780 and - 580 mV(SCE) and 0.5 h for 0 mV(SCE).

Carbon

steel corrosion:

1577

Part I

0.030

0.025-

0.020s

a G i

0.015-

a

0.01 o-

o.005- +--

o.ooof’

I

020405000

I

I

,

I

I

I

I

I

I

loo

120

140

160

180

200

2 3

Time, m Fig. 11. Current vs time in the absence of AV modulation. The DC potential of the specimen was set at -490 mV(SCE). Experiments were conducted for 4 h under nitrogen purge.

Sample characterization A scanning electron microscope (SEM) was used to observe the corrosion deposits and the steel surface after the corrosion deposits were removed. Energy dispersive spectroscopy was used to determine the composition of the corrosion deposits for several different potential levels. Micrographs of samples subjected to 1,2 and 4 h of positive half-cycle rectified AV modulation of peak potential 180 mV(SCE) superimposed upon a potential of -580 mV(SCE) are shown in Fig. 12. The specimens are observed to undergo extreme pitting and the severity of pitting is observed to enhance with time. The pits become numerous and grow bigger with time and then are observed to merge and overlap with one another. Elemental composition of the corrosion products (Table 2), as determined by energy dispersive X-ray spectroscopy, shows higher participation of chloride for experiments in which the DC potential was kept more anodic. An imaging analysis system was used to determine the average number of pits formed, pit diameter and pit depth. Data were obtained for experiments conducted at a potential corresponding to the open circuit potential (- 580 mV(SCE)) on which an AV positive half-cycle rectified signal of peak potential of 180 mV(SCE) was superimposed. The number of pits formed is initially observed to increase with time and reach a maximum for time corresponding to about 10 h (Fig. 13). With further increase in time, the number of pits is observed to decrease. The average pit diameter is

1578

S.B. Lalvani

and G. Zhang

Carbon

steel corrosion:

1579

Part I

Table 2. Composition of corrosion products as determined by EDS. A positive half-cycle rectified sinusoidal AV of peak potential 180 mV(SCE) was applied for a period of 4 h

wt%

Element

DC potential of - 580 mV(SCE)

DC potential of -780 mV(SCE)

0.15 1.23 98.62

0.07 0.11 99.81

Cl Mn Fe Na

found to increase with time of experiment conducted. Over a period of 23 h, the size of pits is observed to grow five-fold. These data are in agreement with those observed using SEM. The number of pits formed grows with time; however, as the size of pits grows, they overlap one another, thus resulting in a total decrease in the number of pits. The average pit depth was also measured (Fig. 14) and is observed to increase rapidly with time. The pit depth grew by a factor of 2.8 over a 23 h period. The total average surface area of pits was calculated assuming that pits are cylindrical in shape. The increase in total pit area over that of the bare carbon steel as a function of time is also plotted in Fig. 14. The increase in area is found to be about 50% when experiments were conducted for 24 h.

4oi50

10

10 15

20

25

Time, h Fig. 13.

Number

and diameter

of pits vs time. Experimental

conditions

as in Fig. 4.

S.B. Lalvani

and G. Zhang

8

6

5 i z

4

iz

z

2

d 0

3

lb

1;

2b

;

Time, h Fig. 14.

Length

and area of pits vs time. Experimental

conditions

as in Fig. 4

One possible reason for the increase in corrosion rate with time (Fig. 4) could be ascribed to the increase in surface area of the pits with time. The increase in corrosion rate is six-fold from time of experiment of 1 h to 24 h, whereas the increase in surface area due to pit formation over the same time period is only two-fifths-fold. The increase in corrosion rate with time can be explained due to the auto-catalytic nature of pitting. In a pit, there is an excess concentration of positive change due to iron dissolution, resulting in the migration of chloride ions to maintain electroneutrality.” Thus, in the pit, there is a high concentration of FeCl*, and, as a result of hydrolysis, a high concentration of hydrogen ions. Both hydrogen and chloride ions stimulate the dissolution of most metals and alloys, and the entire process accelerates with time. The following reaction chemistry is assumed to take place. Anode Fe -+ Fe2+ + 2e-, Fe2+ + 2C1- -+ FeC12, FeCl2 + 2H20

+

Fe(OH),

(1) (2)

+ 2HCl;

(3)

Cathode 2Hf + 2e- +

HZ.

(4)

In the experiments conducted for this research, an inert atmosphere of nitrogen was maintained. Had oxygen been present (as in air), lower corrosion rates would be expected, since oxygen reduction at the cathode according to reaction (5) would

Carbon

steel corrosion:

Part I

1581

compete for electrons with reaction (4). Thus, due to a relatively higher concentration of H+ (and hence HCl), the forward rate of reaction (3) and, subsequently, the forward rates of reactions (2) and (1) would be suppressed, resulting in a lower metal dissolution rate. EvidenceI of lower pitting with dissolved oxygen in chloride solutions is reported in the literature. O2 + 2H20 + 2e- -+ 40H-.

(5)

CONCLUSIONS (1) At the open circuit DC potential of mild steel in sodium chloride solution (- 580 mV(SCE)), the application of positive half-cycle rectified sinusoidal potential significantly accelerates the corrosion processes of 1018 carbon steel in NaCl medium. (2) The corrosion rate increases with the peak potential. (3) For the experiments conducted using positive half-cycle signals, the corrosion rate is a much stronger function of the DC potential than the peak potential of the alternating potential. The more anodic the DC potential, the greater is the corrosion rate. (4) At the DC potential of- 580 mV(SCE), the corrosion rate increases with time due to the autocatalytic pitting effect and in part due to the increase in area available for corrosion. (5) When the DC potential is set at - 780 mV(SCE), the dissolution rate decreases with time, which is attributed to the increase in thickness of the corrosion product(s) layer on the metal surface. (6) Increasing the signal frequency decreases the corrosion rate of mild steel in NaCl solution, which is due to the shorting of the double layer capacitance between the iron and the electrolyte (NaCl solution). (7) Severe pitting on the steel is observed, especially at higher anodic DC potentials.

REFERENCES 1. S.R. Pookote and D.-T. Chin, Mater. Perform. 3,9 (1978). 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

D.-T. Chin and S. Venkatesh, J. electrochem. Sot.: Electrochem. Sci. Technol. 126, 1909 (1979). D.-T. Chin and T.-W. Fu, Corrosion, 25, 515 (1979). S.Z. Fernandes, S.G. Mehendale and S. Venkatachalam, J. upp. Electrochem. 10, 649 (1980). S. Venkatesh and D.-T. Chin, J. electrochem. Sot.: Electrochem. Sci. Technol. 128, 11, 2588 (1981). D.-T. Chin and P. Sachdev, J. electrochem. Sot.: Electrochem. Sci. Technol. 130, 1714 (1983). T.-C. Tan and D.-T. Chin, J. app. Electrochem. 18, 831 (1988). T.-C. Tan and D.-T. Chin, Corrosion 10, 984 (1989). M.L. Mateo and T.F. Otero, J. upp. Electrochem. 29, 26 (1990). E. Sabeva and I. Dobrewsky, J. app. Electrochem. 20, 980 (1990). D.-T. Chin, 1989 AIChE Annual Meeting, San Francisco, CA (1989). M.A. Pagan0 and S.B. Lalvani, Corros. Sci. 36, 127 (1994). W.W. Qiu, M. Pagano, G. Zhang and S.B. Lalvani, Corros. Sci. (accepted). H.C. Kuo and D. Landout, Corros. Sci. 16, 915 (1976). M.G. Fontant and N.D. Greene, Corros. Eng., 2nd edn, McGraw-Hill, New York, NY (1978). J.C. Scully, Fundamentals of Corrosion, 3rd edn, Pergamon Press, New York, NY (1990). M.L. Mateo, T.F. Otero and D.S. Schiferin, J. app. Electrochem. 20, 26 (1990).

1582

S.B. Lalvani

and G. Zhang

APPENDIX If the overall rate of corrosion is limited current density, i/A will be given by

by the transport

i/A = nF (diffusion D = nF$c,

of Fe*+ ions, then the

rate),

- cb),

where n is the number of electrons transferred, F is Faraday’s constant, and D, c, and cb are, respectively, the diffusivity, surface concentration and bulk concentration; 6 is the diffusion length. Assuming reasonable values of 6 (50 pm), cb ( = 0), D ( lop5 cm’s_‘), i/A (40 ,uA cmp2) and n (2), we estimate the surface concentration to be of magnitude 0.01 mM.