Michael Pagitsas

Non-linear dynamics of the passivity breakdown of iron in acidic solutions

Abstract Breakdown of the iron passivity in acid solutions accompanied by current oscillations was investigated by using electrochemical techniques, which reveal the non-linear dynamical response of the system in the current–potential (I–E) and current–time (I–t) planes. Current oscillations of the Fe|electrolyte electrochemical system were studied in the (a) absence and (b) presence of chlorides. In case (a) two oscillatory regions were distinguished; one at low potentials associated with the formation–dissolution of a ferrous salt and another at higher potentials associated with the formation-breakdown of the oxide film. Chaotic oscillations appear in the former region whereas periodic oscillations of a relaxation type appear in the latter region. In case (b), complex periodic and aperiodic oscillations are induced by small amounts of chlorides due to pitting corrosion. Pitting corrosion is a multistage localized process of a great technological importance. It consists of a local breakdown of the passive oxide film and formation of individual areas of metal active dissolution. It was shown that oscillatory phenomena might be used for the characterization of pitting corrosion. Examples of the application of the non-linear dynamical response to pitting corrosion were discussed at early and late stages of the pit growth.

The improved Franck—FitzHugh model for the electrodissolution of iron in sulphuric acid solutions: linear stability and bifurcation analysis. Derivation of the kinetic equations for the forced Franck—FitzHugh model

Abstract A linear stability and bifurcation analysis is carried out on the improved mathematical model proposed by Franck and Fitzhugh for the oscillations observed during the electrodissolution of iron in sulphuric acid solutions. For the improved Franck—Fitzhugh model a logarithmic instead of a linear dependence of the Flade potential on H + concentration is considered. Also a correcting function, o, related to the transference number of the H + , is incorporated into the Nernst-Planck equation, which is applied between the bulk of the solution and the diffusion layer, to account for the effect of the charge transport by Fe 2+ and SO 2− 4 . This type of analysis together with the inherent physico-chemical constraints gives the conditions and the limits of the control parameters for stable, decaying or periodic solutions of the dynamical equations which describe the system. The transition to periodic solutions occurs through a Hopf bifurcation. The advantage provided by the improved model is that the control parameters which are involved in the bifurcation condition include the H + concentration of the solution, h 0 , the applied potential E p , and a function related to the transference number of the H + ions, o. Therefore, a direct comparison of the bifurcation results with the experimental data can be made to determine more explicitly the parameters for which the model provides not only qualitatively but also quantitatively reasonable predictions. The kinetics equations for the periodically forced improved and simplified Franck—FitzHugh model are derived.

A point defect model for the general and pitting corrosion on iron∣oxide∣electrolyte interface deduced from current oscillations

Abstract Analysis of the passive–active oscillatory region of the Fe∣0.75 M H2SO4 system, perturbed by adding small amounts of halide species, allow the distinction between pitting and general corrosion. Complex periodic and aperiodic current oscillations characterize pitting corrosion whereas monoperiodic oscillations of a relaxation type indicate general corrosion. A point defect model (PDM) is considered for the microscopic description of the growth and breakdown of the iron oxide film. The physicochemical processes leading to different types of corrosion can be clarified in terms of the PDM. Occupation of an anion vacancy by a halide ion results in the localized attack of the passive oxide and pitting corrosion. On the other hand, the formation of surface soluble iron complexes is related to the uniform dissolution of the passive oxide and general corrosion.

Distinction between general and pitting corrosion based on the nonlinear dynamical response of passive iron surfaces perturbed chemically by halides

We report on different types of current oscillations induced by fluoride and chloride species in the Fe|H2SO4 electrochemical system. On the basis of the nonlinear dynamical response of the system, certain criteria are deduced, which allow the distinction between general and pitting corrosion. We use a point defect model (PDM) for the description of the iron oxide film along with the formation of surface complexes between the oxide iron cations and halides in order to explain the difference between general and pitting corrosion.

The influence of chloride ions on the dynamic characteristics observed at the transition between corrosion and passivation states of an iron electrode in sulphuric acid solutions

Abstract The role of chloride ions on the current oscillations of relaxation type at the transition of iron between the active and passive states in sulphuric acid solutions is investigated. Pitting corrosion occurs in the presence of chloride ions. The periodic relaxation oscillations observed in the absence of chloride become aperiodic and finally disappear under stationary conditions of the Fe disc electrode in the presence of chloride. However, under rotational conditions, quasiperiodic and chaotic oscillations are observed upon gradually increasing the chloride additions. The rich dynamical response of the system Fe/2M H 2 SO 4 + x M Cl − , under various conditions of chloride concentrations, electrode rotation and potential has been characterized by using the current—time series and power spectra. Examples of quasiperiodicity and chaos are given.

GENERALIZED HOPF, SADDLE-NODE INFINITE PERIOD BIFURCATIONS AND EXCITABILITY DURING THE ELECTRODISSOLUTION AND PASSIVATION OF IRON IN A SULFURIC ACID SOLUTION

Periodic current oscillations of relaxation type are observed in a certain potential range during iron electrodissolution in sulfuric acid solutions when the iron electrode turns from the active to the passive state and vice versa. The system displays in the current-potential (I-E) plane a hysteresis loop consisting of the stable active and passive steady states and an unstable steady state which corresponds to an intermediate situation between active and passive states. In the present study, the dynamical characteristics of the I-E polarization curve were studied. It was shown that transition from the oscillatory to the active steady state goes via a generalized Hopf bifurcation, whereas transition from the oscillatory to the passive steady state goes via a saddle-node infinite-period (SNIPER) bifurcation. Single pulse and pulse series stimulation of the active and passive steady states proved that both steady states are excitable. The refractory periods and the thresholds of excitability were measured. Further perturbation experiments were carried out at the two steady states away from the bifurcation points, and it was shown that the active steady state is a stable focus and the passive one is a stable node.

Bursting and beating current oscillatory phenomena induced by chloride ions during corrosion/passivation of iron in sulphuric acid solutions

Abstract The current oscillations of the relaxation type, observed within the transition potential region of an iron electrode, from activity to passivity, in sulphuric acid solutions are studied in the presence of various concentrations of chloride ions. The presence of chloride ions initiates pitting corrosion phenomena resulting in a new kind of current oscillation in the transition region. Special attention is paid to current oscillations generated for 0.03 C Cl− 2 SO 4 + x M Cl − system, (0.03 x C Cl− ≥ 0.06 M. The dynamic behaviour of the Fe/2 M H 2 SO 4 + 0.1 M Cl − system is also studied. New kinds of oscillation are observed, delineating a significant change of the electrodissolution/passivation mechanism of the Fe within the transition region in 2 M H 2 SO 4 solution containing chlorides in concentrations higher than 0.06 M.

Polarization behaviour of a cobalt rotating disc electrode in sulphuric acid solutions in the absence and presence of chloride ions

Abstract The anodic polarization behaviour of a cobalt rotating disc electrode in sulphuric acid solutions in the absence and presence of chloride ions has been investigated. The current-potential polarization curves in sulphuric acid solutions exhibit a limiting current before the overpassivation region. In the presence of chloride ions, the plateau region is extended towards the oxygen evolution potential. Current oscillations appear within a potential range in the limiting current region beyond a threshold concentration of chloride ions under rotational conditions. The oscillatory potential region in the presence of chloride ions lies in the neighbourhood of the transition from the plateau region to the overpassivity which occurs in the absence of chloride ions. The conditions under which current oscillations appear were investigated by varying the concentration of chloride ions, the electrode rotation rate and the potential. On the basis of the results, a qualitative interpretation of the origin of the current oscillations observed during the electrodissolution of Co in 1.58 M H 2 SO 4 + x M Cl − is suggested, related to the “pitting” corrosion phenomenon.

Dynamical response of the sinusoidally perturbed electrodissolution/passivation of iron in sulfuric acid solutions: Entrainment, spike generation, and quasiperiodicity

The iron/sulfuric acid (Fe/2 M H(2)SO(4)) system exhibits periodic current oscillations of relaxation type within the potential transition region formed between the active and passive states of the iron electrode when it is polarized in the 2 M sulfuric acid solution. In the present work the dynamical response of the Fe/2 M H(2)SO(4) electrochemical oscillator is investigated when the applied potential at the iron electrode is sinusoidally perturbed. The behavior of the periodically perturbed Fe/2 M H(2)SO(4) oscillator differs significantly from the response of other forced oscillators, as the potential amplitude E(p) and the frequency ratio omega(p)/omega(0) vary. The omega(p) and omega(0) are the angular frequencies of the perturbed applied potential and the unperturbed oscillator, respectively. A special feature of its response is the appearance of a number of spikes, generated within the passive section of a periodic oscillatory cycle for omega(p)/omega(0)<2.9, for periods of the autonomous oscillator T(0) greater, similar 3 s. The number of the generated spikes depends on the amplitude and frequency of the perturbed applied potential as well as on the period of the autonomous oscillator. Spikes are not generated for omega(p)/omega(0)=1 and the system is harmonically entrained by the forcing frequency. However, when the system is subharmonically entrained for omega(p)/omega(0) close to 2, spike generation does occur. By increasing the perturbation frequency for omega(p)/omega(0) greater, similar 2.9 and T(0) greater, similar 3 s, or by decreasing the autonomous period for T(0)<3 s and all the omega(p)/omega(0)<2.9 ratios, the spike generation pattern, is replaced by a quasiperiodic pattern. The dynamical response of the perturbed Fe/2 M H(2)SO(4) electrochemical oscillator is characterized by using time-delay reconstructions of the attractors, Poincare maps, and Fourier power spectra.

Periodic and aperiodic current oscillations induced by the presence of chloride ions during electrodissolution of a cobalt electrode in sulphuric acid solutions

Abstract The current oscillations observed during the electrodissolution of a cobalt rotating disc electrode in 1.58 M H 2 SO 4 containing chloride ions are studied. The oscillatory behaviour appears in a certain potential range within the limiting current plateau region. The conditions under which periodic and aperiodic current oscillations occur are investigated. In general, the electrochemical behaviour exhibits different features at low (0.03–0.09 M) and high (0.09–0.7 M) chloride ion concentrations. Detailed experimental results are given in the presence of 0.07 and 0.2 M Cl − . The initiation of oscillations is connected with pitting corrosion phenomena and occurs when the chloride ion concentration is higher than 0.03 M under certain rotational conditions of the Co disc electrode. Sustained current oscillations occur when active and passive sections of the electrode surface are allowed to coexist on the electrode surface. For the range of low Cl − ion concentrations, the recorded current-time oscillations, at a fixed potential, exhibit a variety of waveforms (relaxation, mono periodic, mixed mode and aperiodic or chaotic). The nature of the current oscillations is strongly dependent on both the potential and the rotation rate of the Co disc electrode. The electrode potential and rotation rate are the factors affecting the formation, the dissolution rate of the film on the electrode surface and consequently its thickness. For the range of high Cl − ion concentrations the effect of the rotation rate is also significant, but that of the potential is weak. The potential oscillatory region is correlated with the region of negative resistance of the polarization curve which is defined in the transition from the partially passive to the overpassive state of the Co electrode.