Chaotic dynamics in a model of metal passivation

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Punit Parmananda and Roger W. Rollins Department of Physics and Astronomy, Condensed Matter and Surface Science Program, Ohio University, Athens, Ohio 45701-2979

Alan J. Markworth Engineering Mechanics Department, Battelle Memorial Institute, Columbus, Ohio 43201-2693 (Received 23 October 1992; accepted 25 March 1993)

The dynamic behavior of a model for the passivation of a metal surface in contact with an aqueous solution is investigated. The model, which is characterized by a three-dimensional state space and five-dimensional parameter space, is obtained by combining elements from passivation models developed by Talbot and Oriani and by Sato. A three-dimensional subspace of parameter space has been studied; the remaining two dimensions are not thought to provide any additional interesting dynamics. The model exhibits remarkably rich dynamics, including the period-doubling, intermittency, and crisis routes to chaos, folds and bubbles in periodic portions of the attractor, and multiple attractors with complex, intertwined basins of attraction.

I. INTRODUCTION Passivity of a metal or alloy has been defined as "a loss of chemical reactivity under certain environmental conditions".1 The phenomenon is of immense technological importance because loss of passivity can result in corrosion processes that may lead to failure. The coupled chemical rate equations that describe the kinetics of passivation, as well as other types of heterogeneous electrochemical processes, are generally nonlinear and may give rise to very complex dynamics. Such behavior has long been known to exist; for example, oscillations in the oxidation kinetics of phosphorus were reported in 1898.2 Within the past few years, many electrochemical reactions have been found to exhibit behavior that is typical of nonlinear deterministic systems.3"7 Behaviors observed experimentally include spontaneous oscillations, period doubling, quasiperiodic and mixed-mode oscillations, deterministic chaos, multistability, and hysteresis. Yet there are very few models8 that are based on realistic chemical reactions and give the rich behavior observed experimentally. However, several theoretical models for metal passivation have been interpreted using linear stability theory and methods of nonlinear analysis such as bifurcation analysis.9'10 The passivation models considered to date have, for the most part, involved only two independent state variables. Nevertheless, their dynamics can be quite com-

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J. Mater. Res., Vol. 8, No. 8, Aug 1993

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plex, including multiple steady states and periodic oscillations. However, these models cannot exhibit chaos, for which at least three independent state variables are required. One model with three state variables was presented by Talbot and Oriani,11 although their development actually resulted in only two of the three variables being independent. [See their Eqs. (43) t

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