Multivariate Optimization of Self-doped TiO₂ Nanotube Synthesis for Enhanced Optical and Electronic Performance

This paper presents the cathodic polarization of anodic TiO₂ nanotube layers (TNT) on Ti to promote the electrochemical reduction of Ti⁴⁺ lattice into Ti³⁺, accompanied by oxygen-vacancy formation and proton intercalation, resulting in self-doped nanotubes (SD-TNT). Although this reduction route has been known since the early reports of TNT, the quantitative relationship between the polarization parameters and the resulting electronic response remains to be established. Hence, a full factorial design (FFD) coupled to response surface methodology (RSM) was employed to assess simultaneously the cathodic potential, the polarization (self-doping) time, and the calcination temperature, using the cathodic current density (j _c) associated with the Ti⁴⁺/Ti³⁺ reduction as the response. The optimum condition, obtained by FFD/RSM, was -1.5 V, applied for 480 min, to layers calcined at 450 °C, which delivered a j _c of -0.325 mA cm^-2. Under these conditions, SD-TNT were also investigated using electrochemical impedance spectroscopy (EIS), which revealed a decrease of the charge-transfer resistance from 831.9 to 92.35 Ω, together with a lower capacitance, constant phase element exponent, and a shorter time constant, consistent with a higher density of Ti³⁺ centers and oxygen vacancies distributed along the tube axis. Raman deconvolution of the anatase E_g mode confirmed the increase of the oxygen-vacancy contribution after cathodic polarization, whereas the calcination temperature controlled the anatase/rutile ratio and, therefore, the apparent band gap. The multivariate approach, thus, provides quantitative criteria to select the cathodic polarization parameters of TNT.