Surface oxide films are formed on metals such as aluminium and titanium during electrochemical oxidation (or "anodizing"). The oxides produced are porous when anodizing occurs in solutions in which the oxide is a little soluble. The films typically consist of highly regular arrangements of pores with submicron diameters and can be used to create a wide range of electronic devices.

Such devices exploit various unique features of the porous films. These include the fact that they can be easily produced; their high internal surface area; uniform pore size; and large length-to-diameter ratio. The ability to tune the pore dimensions for a specific application by modifying the electrochemical conditions required for anodizing is also a plus. A good example of a device that can be made from these films is the dye-sensitized solar cell based on porous semiconducting titanium dioxide.

Poor understanding
However, there is a problem in that these materials are poorly understood. Scientists still do not know, for example, why pores actually form in the films. "For example, we are unsure as to why porous, rather than planar, films are formed in certain solutions, or why the arrangement of pores under some conditions is disordered and in others displays a beautiful, almost crystalline pattern," said Kurt Hebert of Iowa State.

Until now, researchers mainly relied on intuition for finding the correct experimental conditions to make self-organized anodic oxides, adds Patrik Schmuki, leader of the Erlangen-Nürnberg group that did the experimental part of the work. "Thanks to our new work, we now have a quantitative tool that seems to point to a straightforward and universal design of the self-ordering conditions needed for the growth of such structures on a wide range of materials," he told nanotechweb.org.

Ordered porous films
According to the researchers, these conditions are determined by the value of two simple parameters – the first is a ratio involving oxide and metal densities (the so-called Pilling-Bedworth ratio) and the second, the oxide formation "efficiency", which is the fraction of oxidized metal atoms that remain in the oxide film as metal ions rather than dissolving into solution. For a given metal, the model predicts that ordered porous films will form within this narrow efficiency range.

This prediction has already been confirmed by the team for both Al and Ti oxides. "As Patrik points out, we now know precisely what conditions must be applied to create ordered films on a given metal or alloy," said Hebert, "that is, the solutions must be able to dissolve the oxide at a rate specified by the efficiency range." The model also predicts that ordered films should be possible only on oxides with a metal charge greater than two, he adds. This explains why attempts to form ordered porous films of ZnO (a promising material for solar technology) have not succeeded (zinc metal ions have a charge of two).

Predictions
The researchers have also shown that a constant ratio exists between pore spacing and applied electrochemical voltage during anodizing, and they have successfully predicted this ratio for Al oxide films.

However, it is not all plain sailing just yet: the new model does predict the ratio of pore spacing to voltage but not the pore spacing itself, explains Hebert. The latter is in fact determined by a critical oxide thickness at which the material becomes unstable. "For us to fully understand the relationship between chemistry and porous layer geometry, we need to investigate why the instability kicks in at this thickness," stated Hebert. "If we can figure out how to control this thickness, we then should be able to produce any desired pore diameter and spacing."

The results were detailed in Nature Materials.