On the Nature of Self-Organization of Porosity During Aluminum Anodization

Porous aluminum oxide (PAOX) is one of the most studied examples of spontaneous self-organization in electrochemistry. Despite the intense research efforts over more then 50 years, there is still no overarching theory that is able to explain and predict the electrolyte-specific self-assembly potentials. Therefore, in this paper, we present the derivation and application of a consistent theoretical framework that allows us to determine this potentials for all employed electrolytes at which the highest proportion of hexagonally arranged pores can be expected. The model is based on the idea that the pores can be regarded as invariant physical objects during a stationary electrochemical process. This makes it possible to use a multinomial coefficient to determine an extreme point at which entropy production becomes minimal when a hexagonal pore arrangement is present. Therefore, the self-arrangement potentials can be identified as the argument of the extreme point.