Application of the transmission line model for porous electrodes to analyse the impedance response of TiO₂ nanotubes in physiological environment

TiO₂ nanotubes constitute a relevant surface modification technique to improve the surface properties of orthopedic implants. However, the interpretation of their electrochemical characterization by impedance spectroscopy in physiological environments remains unclear. The present study proposes a “Two-channel transmission line model” based on the de Levie's theory for porous electrodes. This approach considers cylindrical pores of finite length where the electrical signal is distributed in various directions along the pores walls. Transport phenomena occur mostly in the nanotubes' solid channels and are considered as “anomalous”, i.e., frequency-dependent due to the semi-conductive properties of TiO₂. In these conditions, the interface cannot be modeled by usual parallel or series arrangements of R-L-C elements. The impedance of the almost non-reactive interface is regarded as purely pseudo-capacitive and modeled by a distributed Constant-Phase-Element (CPE). It is shown that such transmission line model applies to the nanotubes system since it permits to fit successfully (with significant fitting parameters values) EIS data measurements of two very different morphologies of nanotubes in a physiological environment. From a practical point of view, results indicate that the huge increase in the effective surface thanks to the self-structured nanotube layer might improve the biocompatibility without any concomitant decrease of the corrosion resistance.