Mathematical modeling studies of electrochemical growth of oxide films on metals
This dissertation consists of two parts. First, a mathematical model was formulated to investigate the structural change of the oxide film on aluminum due to cathodic charging. The model assumed a duplex film structure composed of a barrier layer on the metal side and a porous layer on the solution side. The processes formulated in the model include all relevant capacitive processes, conduction in both layers of the oxide film, and interfacial reactions, such as pore filling by oxide growth at potentials higher than the open circuit potential. The model was fit with the anodic current transients during subsequent anodic polarization to determine the structural parameters in the model. As a result, the structural changes caused by cathodic charging were found to be described by the growth of pores in the outer portion of the initial film. The pores may be produced by the non-uniform electrochemical dissolution of the oxide during cathodic current flow;Secondly, a defect cluster model has been developed for ionic conduction in amorphous anodic oxide films. The physical processes in the model include the hopping of oxygen vacancies, as the rate limiting step, and metal ion transport within each vacancy-centered cluster. A mathematical model was formulated for the overall ionic conduction across an oxide. Based on the steady-state solution of the modeling equations, the transference number tM and the field coefficient B in the current-field relation i = Aexp(BE) were derived for A12O3, Ta2O5, Nb2O5 and WO3. The model predicts comparable transference numbers for both metal and oxygen ions and the calculated values of tM are very close to the experimental values. Also with the consideration that the hopping of an oxygen vacancy involves the rotation of a stoichiometric unit OMp, the model predicts the values of B to be about 5 x 10-6 cm/V for the oxides, which is close to most experimental values.