| Passivation of metals is characterized by the unique shape of the anodic polarization curve, which shows a maximum current at the transition potential followed by a rapid decrease of several orders of magnitude to the passivation potential. Electrochemical oscillations have been observed in the active-passive region of potential. The objective of this thesis was to select or propose mechanisms of passive film formation and to build mathematical models which would simulate electrochemical oscillations observed experimentally near the active-passive transition. Feinberg's linear algebraic method, linear stability and bifurcation analysis, and orthogonal collocation were used to study passive film mechanisms and models. By utilizing these mathematical methods the criteria needed to obtain steady state multiplicities or current oscillations were determined for models in the literature and for several models proposed by the author. The two simple adsorption-type models, which were developed considering only the effects of reaction kinetics, can give multiple steady states and the oscillatory behavior related to the active-passive transition. The minimum requirements of both models are anodic dissolution to produce a metallic ion and either subsequent homogeneous reactions or a surface reaction to form a single adsorbate. The steady state behavior of these two models was examined by varying the functional forms of adsorption, desorption, and surface reaction rates, as appropriate. Multiple steady states and oscillations can occur when a factor of exp(-(beta)(THETA)) is in either the adsorption, desorption, or surface reaction rate. Neither a coupling between chemical reactions and transport processes nor spatial inhomogeneity is essential to produce periodic solutions. However, the effect of coupling of kinetics and mass transport of species in the electrolyte was investigated and can alter the parameter regions where oscillations occur when only reaction kinetics are considered. |
