Mathematical model of current-voltage characteristic of steady-state aluminum anodization

Highlights: • Model enables calculating current-voltage characteristic of porous metal anodizing. • The model involves several parameters required for calculations. • For aluminum, these parameters are obtained from published experimental data. • Calculated current-voltage characteristics agree well with the experimental data. -- Abstract: The developed mathematical model satisfactorily describes the dependence of anodic potential on the current density of steady-state aluminum anodization in the region of average current densities where its main assumptions are fulfilled: the absence of merging of adjacent pores and the absence of overheating of oxide relative to the electrolyte. The model involves several parameters required for calculations. For anodization of aluminum, the values of these parameters are obtained by the analysis of experimental results published by various authors. Calculated current-voltage characteristics agree well with published experimental data. Using the model equations and appropriate parameters, one can calculate not only the dependence of anodic potential on the current density, but also main relationships between the characteristics of anodization: the barrier layer thickness, potential, porosity, spherical radius of pore bottom and spherical radius of cavity in the metal.