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Oscillation and Chaos in Pitting Corrosion of Steel E. García,* M.A. Hernández, F.J. Rodríguez, J. Genescá,** and F.J. Boerio***

ABSTRACT The potential and current oscillations during pitting corrosion of steel in sodium chloride (NaCl) solution were studied. Detailed analyses using numerical diagnostics developed to characterize complex time series clearly showed that the irregularity in these time series corresponds to deterministic chaos rather than to random noise. The chaotic oscillations were characterized by power spectral densities, phase space, and Lyapunov exponents. KEY WORDS: chaos, electrochemical noise, pitting corrosion, steel

INTRODUCTION Potential and current fluctuations spontaneously generated by corrosion reactions are known as electrochemical noise (EN). These potential and current fluctuations (oscillations) are commonly observed in many electrochemical processes, such as electropolishing,1-2 passivation,3-4 and localized corrosion,5-6 which are strongly influenced by the growth and dynamic breakdown of the anodic film. The most important difficulty in the use of electrochemical noise measurements (ENM) resides in the interpretation of the experimental data. In the Submitted for publication January 2002; in revised form, July 2002. This paper was presented as paper no. 197 at CORROSION/99, April 1999, San Antonio, TX. * Programa de Ingeniería Molecular, Instituto Mexicano del Petróleo (IMP), Eje Central, Lázaro Cárdenas #152, 07730 México, DF, México. ** Dpto. Ingeniería Metalúrgica, Facultad Química, UNAM, Ciudad Universitaria, 04510 México, DF, México. *** Department of Materials Science and Engineering, University of Cincinnati, Cincinnati, OH 45221-0012.

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literature, four different approaches have been proposed for processing the experimental records: the statistical, the spectral, the chaos-theory, and the wavelet transform-based methods. Cottis, in his excellent review of the interpretation of electrochemical noise data, has designated chaos analysis as a new and somewhat more speculative method to interpret measurements of the electrochemical noise (potential and current noise) associated with corroding metals.7 Legat, et al., carrying out an interesting study related to the detection of various types of corrosion processes by means of the chaotic analysis of electrochemical noise, concluded that the chaotic analysis of measured electrochemical noise can help to determine the type of corrosion and provide some data concerning the physical picture of the different types of corrosion.8 In recent years, interest in the behavior of nonlinear dynamic systems has considerably increased. Under some circumstances, these systems exhibit a behavior that has been termed “deterministic chaos.” This means that the system always behaves in a deterministic way (i.e., nonrandom); however, the detailed behavior is extremely sensitive to the initial conditions, thus being in the long range and completely unpredictable.9-10 García, et al., having applied the nonlinear dynamic analysis to study the pitting corrosion process of nickel in seawater, obtained experimental evidence that seems to demonstrate that the oscillatory dynamics of the noise signal is of deterministic chaotic nature.11 The possibility that some corrosion processes may exhibit chaotic behavior has been examined by Stringer, et al.,12 and all that such behavior implies.

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Over the last 30 years, chaos theory has been developed to characterize nonperiodic and chaotic systems. The theory of chaos has been applied in the characterization of various systems, including electrochemical processes.13 A review showing the application of deterministic chaos theory to materials science14 reveals the prevalence of nonlinear dynamic effects on the behavior of materials. Pitting may exhibit either random or deterministic (sometimes chaotic) behaviors (features) following the composition of the corrosive electrolyte with respect to the pitting resistance of the material under consideration.15 It has been shown that transitions from randomness to chaos depend on the corrosive solution composition.16 Chaos during the growth of an artificial pit has been proven by Corcoran and Seiradzki for a silver electrode in 1 M perchloric acid (HClO4).17 Baroux, et al., analyzed random and deterministic behaviors in pitting corrosion phenomena using signal analysis techniques and the theory of deterministic chaos.18 They propose that chaos analsis should be used as a modeling tool in the study of the pitting mechanism. The pitting corrosion of copper in artificial seawater19 is also chaotic in nature as well as the pitting process of aluminum at its free corrosion potential in the presence of chloride.20-21 From the pioneering work of Li, et al., it is clearly shown that the electrodissolution of iron in aqueous sodium chloride (NaCl) solutions exhibit current oscillations under potentiostatic conditions.22 The potential oscillations observed under galvanostatic conditions were all aperiodic and the irregularity in these time series corresponded to deterministic chaos rather than to random noise. Some work has also been carried out to apply chaos theory to study the corrosion process of steel in NaCl or seawater. Sazou, et al., having investigated the role of chloride in the current oscillations of relaxation type at the transition of Fe between the active and passive states in sulfuric acid (H2SO4) solutions, demonstrate that under rotational conditions quasiperiodic and chaotic oscillations are observed as chloride additions gradually increase.23 Actually, EN is today a useful and powerful tool both for the fundamental understanding of various aspects of corrosion and for the solution of practical problems of corrosion protection, in particular in the area of corrosion monitoring.24 A characteristic feature of ENM in comparison with other electrochemical methods for investigating corrosion is that the information is obtained without perturbing the system to be measured. The high sen(1)

(2)

†

ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428. UNS numbers are listed in Metals and Alloys in the Unified Numbering System, published by the Society of Automotive Engineers (SAE) and cosponsored by ASTM. Trade name.

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FIGURE 1. Flat electrochemical cell.

sitivity of the technique also permits detection of the initiation of localized corrosion on passive metal surfaces. The goal of the present study was to analyze the EN measured on steel in NaCl solution by the use of various mathematical tools from the chaos theory in order to characterize the mechanism of different types of corrosion.

EXPERIMENTAL PROCEDURES Cold-rolled steel (CRS), ASTM 1010(1) (UNS G10100)(2) sheets of 2 cm by 2 cm were ground with silicon carbide (SiC) paper up to 1200 grit, washed with distilled water, degreased with acetone (CH3COCH3), dried under an air stream, and kept in a desiccator until test time. These samples were used as a working electrode in a flat cell (PAR† model K0235) leaving an area of 1 cm2 exposed on only one face. The electrochemical cell was a three-electrode setup including the working electrode, a saturated calomel reference electrode (SCE), and a platinum wire mesh auxiliary electrode. The experimental arrangement is shown in Figure 1. The electrolyte was a 3 wt% NaCl solution at atmospheric temperature. EN consists of spontaneously generated potential and current fluctuations, which can be measured in freely corroding systems. For the application of this electrochemical technique, it is necessary to have equipment capable of acquiring potential and/or current data in time periods between 0.25 s and 1.5 s.25 The collected data obtained during a time interval is called a time series. The ENM were carried out using a Solartron 1286† electrochemical interface coupled to a personal computer (PC), which could store the data for further analysis. The method consisted of measuring, as a function of time, the electrochemical potential noise (EPN) between the working electrode

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(a)

(a)

(b)

(b)

(c)

(c)

FIGURE 2. Time series of EPN: (a) Type 1, (b) Type 2, and (c) Type 3.

FIGURE 3. Time series of ECN: (a) Type 1, (b) Type 2, and (c) Type 3.

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and a SCE and the electrochemical current noise (ECN) between the counter and working electrode. In the EPN measurements, the specimen was left at the open-circuit potential (free corrosion potential). For the ECN, this was obtained by maintaining the sample to the corrosion potential in the three-electrode cell. This was achieved by using the electrochemical interface, which also acted as data logger/ analyzer at a sampling rate of one reading every 0.7 s controlled by a PC. No significant noise contribution to the EN was observed for the experimental set-up. After gathering the data as a potential/current time record of sufficient length, 2,048, the direct current (DC) drift was removed. The logarithmic spectral density vs frequency plots was obtained by using an algorithm based on fast Fourier transform (FFT) of spectral analysis. The resolved frequency bandwidth of interest lies between 1 mHz and 700 mHz.

FIGURE 4. A view of the sample surface showing pitting corrosion corresponding to signal noise Type 1.

RESULTS AND DISCUSSION To obtain information regarding the corrosion process, EPN and ECN were measured in a freely corroding system (Figures 2 and 3). The carbon steel in the chosen electrolyte corroded uniformly or locally. Three typical forms of EN generated by different types of corrosion were seen: —Type 1 (Figures 2[a] and 3[a]): the EN generated consisted of fluctuations of high amplitude with a high repetition rate. —Type 2 (Figures 2[b] and 3[b]): oscillations of Type 1 and transients of small amplitude were combined. —Type 3 (Figures 2[c] and 3[c]): the time series was formed by small oscillations. This behavior, with time series of different shapes, seems to indicate that the corrosion products formed on the metal surface have a different grade of stability, thus producing a corrosive attack whose morphology is different. The EN of Type 1 is associated with pitting corrosion (Figure 4), whereas EN Type 3 signals seem to correspond to uniform corrosion or achievement of a passivation state (Figure 5). This fact is also reflected in the changing corrosion potential values as a function of time (Figure 6). The power spectrum, which is a graph of power spectral density against frequency of voltage and current noise corresponding to EN Types 1 and 3, are shown in Figures 7 and 8. Detailed analysis shows the presence of a characteristic frequency at ~22 mHz and a first harmonic at approximately 44 mHz for EN Type 1. A 1/f function can be observed for EN Type 3, with no characteristic frequency. When the film rupture and repassivation (breakdown and film repair) are the dominant mechanisms in the pitting corrosion process, the EN signal time series presents high-frequency transients of increas-

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FIGURE 5. A view of the sample surface showing uniform corrosion corresponding to signal noise Type 3.

FIGURE 6. Corrosion potential of CRS as a function of time.

ing amplitude according to Searson and Dawson.26 Localized corrosion of carbon steel was observed in 3 wt% NaCl (Figure 4). The EN generated by localized corrosion, being of Type 1, can be presumed to have been generated by the initiation of pits. In this case, the power spectrum of voltage and current noise

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(a)

(b) FIGURE 7. Spectral analysis of EPN: (a) Type 1 and (b) Type 3.

show that the high-frequency components increase from 10–11 V2/Hz to 10–9 V2/Hz (Figure 7) for voltage and 10–19 A2/Hz to 10–16 A2/Hz (Figure 8) for current noise. The power values, ~700 mHz, increase from 10–11 V2/Hz to 10–9 V2/Hz (Figures 7[a] and [b]) for voltage. This change could be associated with the change from Type 3 to Type 1 signals. Analogously, the current noise increase from 10–19 A2/Hz to 10–16 A2/Hz (Figure 8) for the same reasons. All phenomena of high-amplitude oscillations can be associated with the formation of unstable films, which are formed by ferrous chloride (FeCl2).27 The stabilization of these layers can take place through the formation of complex species of Fe(III) and chloride, as indicated by Li, et al.28 The presence of this complex species, which may change the stability of corrosion films, could be an explanation for the different signal noises obtained during experimentation.

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This type of spectrum has been attributed to chaotic signals.13 Assuming this to apply here, chaotic analysis, therefore, has been applied to characterize the processes generating the different types of EN. The behavior of a dynamic system is best described in its phase space.29 Each possible state of the system corresponds to a point in the phase system, whereas the evolution of states is represented by a trajectory. A graph describing the evolution of the system from different initial conditions is called an attractor.30-31 It is evident that different types of EN form different types of attractors. A graphic presentation of attractors for the different potential and current signal noises obtained are shown in Figures 9 and 10. During localized corrosion of steel (EN Type 1), the attractor of voltage noise consisted of multiple loops (Figures 9[a] and 10[a]). The attractors of EN gener-

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(a)

(b) FIGURE 8. Spectral analysis of ECN: (a) Type 1 and (b) Type 3.

ated by uniform and mixed corrosion (EN Type 2) indicated a transition state from high to low periodicity, clearly shown in the current signal (Figures 9[b] and 10[b]). During the passivation, the attractor of voltage and current noise (Figures 9[c] and [10c]) presents only a low periodicity. The attractors of different types of EN form different structures; however, to quantify the geometry of an attractor, its static characteristics and its dynamic characteristics (Lyapunov exponents) must be estimated. Lyapunov exponents are the most important parameters characterizing the properties of an attractor of a dynamical system. The Lyapunov exponents measure the average rates of divergence of nearby trajectories in phase space, thus quantifying how unpredictable the system is, depending on initial conditions. When at least one Lyapunov exponent is

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positive, then the system is chaotic. On the other hand, when no positive Lyapunov exponent exists, the long-term predictability of the system is guaranteed. In order to characterize the unpredictability of processes that generate different types of EN, the maximum Lyapunov exponent has to be estimated. To do this, the method proposed by Rosenstein, et al., was used.32 The maximum Lyapunov exponent, λ1, quantifies the greatest rate at which the distance between two nearby trajectories increases exponentially in time. If λ1 > 0, there is at least one direction in the phase space along which an attractor exhibits chaotic (unstable) behavior. The values of the λ1 estimated for the attractors of electrochemical voltage and current noise in the different types of corrosion were calculated over a period of 30 days (Figure 11). It can be seen that the

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(a)

(a)

(b)

(b)

(c)

(c)

FIGURE 9. Attractor representation in a bidimensional space phase for the three types of EPN obtained: (a) Type 1, (b) Type 2, and (c) Type 3.

FIGURE 10. Attractor representation in a bidimensional space phase for the three types of ECN obtained: (a) Type 1, (b) Type 2, and (c) Type 3.

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values of λ1 are lower than 0.2 for EN Type 1, whereas the values of λ1 are higher than 0.2 for EN Type 3. The evaluation of the maximum Lyapunov exponent of ECN, Figure 11(b), is clearer than EPN. Three regions can be distinguished in this plot: —from 0 to 14 days, with alternation between EN Type 1 and 3 —from 15 to 25 days, with values of λ1 lower than 0.2, corresponding to EN Type 1 —from 26 to 30 days, with values of λ1 higher than 0.2 (EN Type 3), which is in accordance with Figure 5 corresponding to uniform corrosion It can be noted that during pitting corrosion (EN Type 1), the λ1 is positive, which is in accordance with the results previously published by Corcoran and Sieradzky,17 demonstrating that the fluctuations that occur during this process are chaotic in nature.

(a)

CONCLUSIONS ❖ EN can provide valuable information in corrosion studies. The ENM technique has been used to monitor the corrosion of carbon steel in NaCl solution. ❖ Information has been obtained that supports the presence of a characteristic frequency at 22 mHz and a first harmonic at ~44 mHz, for both the EPN and ECN, during the pitting corrosion process of carbon steel in NaCl solution. ❖ Pitting corrosion can be understood as a mechanism of film breakdown and repair, the passive film being formed by FeCl2. This layer can be stabilized by the formation of complex species such as Fe(III) and chlorides, which produce different noise signals. ❖ The analysis of EN by mathematical tools known from the theory of chaos has been confirmed as a rich source. Chaotic analysis provides more data concerning the type of corrosion. It has been demonstrated that the EN signal measured during pitting corrosion of 1010 steel in NaCl solutions is chaotic in nature.

ACKNOWLEDGMENTS This research was supported by a grant from Consejo Nacional de Ciencia y Tecnología, CONACYT, México (Project no. 400313-5-CO68A) and Instituto Mexicano del Petroleo (IMP) (Project no. FIES 1998VI-1). REFERENCES 1. D.T. Chin, A.J. Wallance, Jr., J. Electrochem. Soc. 120 (1973): p. 1,487. 2. M. Datta, D. Landolt, Electrochim. Acta 25 (1980): p. 1,255. 3. M.E. Orazem, M.E. Miller, J. Electrochem. Soc 143, 2 (1987): p. 392. 4. P. Russell, J. Newman, J. Electrochem. Soc. 133, 1 (1986): p. 59. 5. H.H. Strehblow, J. Wenners, Phys. Chem. 98 (1975): p. 199.

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(b) FIGURE 11. Lyapunov exponent of the EN signals as a function of time: (a) EPN and (b) ECN.

6. M. Keddam, M. Krarti, C. Pallotta, Corrosion 43 (1987): p. 454. 7. R.A. Cottis, Corrosion 57, 3 (2001): p. 265. 8. A. Legat, J. Osredkar, V. Kuhar, M. Leban, Mater. Sci. Forum 289-292 (1998): p. 807. 9. E. Rietman, Exploring the Geometry of Nature (New York, NY: Windcrest, 1988), p. 21. 10. J.T. Sandefur, Discrete Dynamical Systems (Oxford, U.K.: Clarendon Press, 1990), p. 208. 11. E. García, J. Genescá, J. Uruchurtu, Afinidad 55, 473 (1998): p. 26. 12. J. Stringer, A.J. Markworth, Corros. Sci. 35, 1-4 (1993): p. 751. 13. A. Legat, V. Dolec˘ ek, J. Electrochem. Soc. 142, 6 (1995): p. 1,851. 14. A.J. Markworth, J. Stringer, R.W. Rollins, MRS Bull. 20, 7 (1995): p. 20. 15. S. Hoerle, T. Sourisseau, B. Baroux, Critical Factors in Localized Corrosion III, Proc. The Electrochemical Society 98-17 (Pennington, NJ: The Electrochemical Society, 1999), p. 437. 16. S. Hoerle, B. Baroux, Passivity and its Breakdown, Proc. The Electrochemical Society 97-26 (Pennington, NJ: The Electrochemical Society, 1998), p. 57. 17. S.G. Corcoran, K. Sieradzki, J. Electrochem. Soc. 139, 6 (1992): p. 1,568. 18. B. Baroux, H. Mayet, D. Gorse, Pits and Pores: Formation, Properties, and Significance for Advanced Luminescent Materials, Proc. The Electrochemical Society 97-7 (Pennington, NJ: The Electrochemical Society, 1997), p. 461. 19. E. García, J. Uruchurtu, J. Genescá, Afinidad 53, 464 (1996): p. 215. 20. U. Cano, J. Malo, J. Uruchurtu, Corros. Prot. Mater. 13, 1 (1994): p. 6.

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21. P.R. Roberge, Light Met. Process. Appl., Proc. Int. Symp. (Quebec City, Quebec: Canadian Institute of Mining, Metallurgy, and Petroleum, 1993), p. 753. 22. W. Li, K. Nobe, A.J. Pearlstein, J. Electrochem. Soc. 140, 3 (1993): p. 721. 23. D. Sazou, M. Pagitsas, G. Christos, Electrochim. Acta 37, 11 (1992): p. 2,067. 24. J.L. Dawson, “Electrochemical Noise Measurement: Definitive In-Situ Technique for Corrosion Applications in Electrochemical Noise Measurement for Corrosion Applications,” eds. J.R. Kearns, J.R. Scully, P.R. Roberge, D.L. Reichert, J.L. Dawson, ASTM STP 1277 (West Conshohocken, PA: ASTM International, 1996), p. 24.

25. K. Hladky, J.L. Dawson, Corros. Sci. 22 (1982): p. 231. 26. P.C. Searson, J.L. Dawson, J. Electrochem. Soc. 135 (1988): p. 1,908. 27. H.C. Kuo, D. Landolt, Corros. Sci. 16 (1972): p. 915. 28. W. Li, X. Wang, K. Nobe, J. Electrochem. Soc. 139 (1990): p. 1,184. 29. T. Mulling, The Nature of Chaos (Oxford, U.K.: Clarendon Press, 1993), p. 27. 30. M.H. Packard, J.P. Crutchfield, J.D. Farmer, R.S. Shaw, Phys. Rev. Lett. 45 (1980): p. 712. 31. H.L. Swinney, Physica D 7 (1983): p. 3. 32. M.T. Rosenstein, J.J. Collins, C.J. De Luca, Physica D 65 (1993): p. 117.

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