Precise electrochemical prediction of short tantalum oxide nanotube length

While the thickness of compact oxide films formed on valve metals can be easily predicted from the anodization constant and applied voltage, a similar predictive method is not available for oxide nanotubes (NTs) formed on these substrates. This is due to the unknown anodization charge efficiency, oxide flow from pore base to walls during anodization, and the unknown characteristics of the oxide, such as density and porosity. Here, we report a simple and precise method to predict the length of short (50 to 1000 nm), adherent Ta oxide NTs, formed by the anodization of polycrystalline Ta in sulfuric acid solutions containing HF at concentrations significantly lower than normally used for long NT growth. It is shown that the NT length can be calculated from the total anodic charge passed during anodization, demonstrating that factors such as anodization charge efficiency and oxide density are independent of the HF concentration and anodization time. The very useful and versatile correlation of anodization charge density and Ta oxide NT length allows for the calculation of NT length using only charge measurements and eliminates the need for electron microscopy examination of each sample. This work also opens the door to many new applications for which short metal oxide NTs, having lengths accurately but simply gauged just from the anodization charge density passed, are of great interest.