## 2 Materials and Methods  
TiO\({}_{2}\) nanostructures were synthesized by electrochemical anodization using platinum mesh as a counter electrode and titanium foil as the anode. Titanium foils with an area of 1.5 cm\({}^{2}\) and a thickness of 100 \(\upmu\)m (American Elements, 99.95% purity) were first cleaned with trichloroethylene, acetone, and deionized H\({}_{2}\)O before the electrochemical process.  
The nanostructures were grown using a procedure described in our previous work [16]. The electrolyte solution was prepared with 0.255 wt% NH\({}_{4}\)F and 1 wt% of deionized water in ethylene glycol. A voltage of 30 V and Inter-Electrode Spacing of 1 cm were used for the anodization process. TiO\({}_{2}\)-nt were grown through a three-step anodization process of 1, 4 and 20 h. After the first and second anodization steps, a detachment process of the nanotubes was realized in order to obtain a template of dimples (Ti nanobowls) on Ti foil. For TiO\({}_{2}\)-nc, a two-step anodization process was done, the first one lasting 1 h and the second one 10 min. Whereas the self-assembled nanostructures were synthesized by a two-step anodization process, the first one lasting 1 h and the second one: 15 min for TiO\({}_{2}\)-ns/TiO\({}_{2}\)-nc and 40 min for TiO\({}_{2}\)-nb/TiO\({}_{2}\)-nc. Afterwards, a thermal treatment at 450 \({}^{\circ}\)C was carried out for 1.5 h to pass from the amorphous phase to the anatase phase for each nanostructure.  
In order to understand the morphological, optical, chemical, structural and catalytic properties of these nanomaterials, several characterization techniques were used: the morphology was studied by SEM (FEI, model SCIOS) and the topography by AFM (Nanosurf Easy Scan 2.3). The elemental composition of TiO\({}_{2}\) nanostructures was determined by EDS at 10 keV (EDAX, model APOLLO). The reflectance spectrum was determined by a Semicon-soft MProbe UVVis SR thin film measurement system. To validate the transformation from the amorphous phase to the anatase phase of our TiO\({}_{2}\) nanostructures, the vibration modes related to anatase crystal structure were calculated by Raman Microscopy (Witec, model alpha 300 R, Ulm, Germany) with a green laser excitation of 532 nm. The phase identification of TiO\({}_{2}\) nanomaterials was determined by XRD (D8 Discover Bruker diffractometer).  
Also, to determine the main defect states that increase the emission and its relationship with the morphology, photoluminescence spectra were determined by fluorescence spectroscopy (Fluoromax-3, Jobin Yvon, Paris, France); and TRPL data were recorded in a nanosecond time-resolved photoluminescence spectrometer (NanoLog FR3, Horiba Jobin Yvon). The samples were excited with a 330 nm diode laser and the emissions were monitored at 418 nm, 448 nm, and 532 nm.  
The photocatalytic activity was evaluated by the discoloration technique of the dye solution using a 254 nm UV lamp (model UVG54 from Mineralight brand, Houston, TX, USA). The dyed solution was prepared with 10 mg of methylene blue in 1 L of deionized water. The distance between the UV lamp and dyed solution was about 15 cm. A sample of each nanomaterial was immersed in 0.1 L of dyed solution with an effective area of 1 cm\({}^{2}\) at room temperature. The concentration of the dye was monitored using the absorbance spectrum of each solution at certain time intervals by spectrophotometry (Perkin Elmer, model Lambda 3B, Waltham, MA, USA). To determine the active species, scavenging experiments were carried out using methanol, 2-propanol, and superoxide dismutase (SOD) to scavenge \(\text{h}^{+}\), OH\({}^{-}\), and O\({}_{2}^{-}\), correspondingly.  
The percentage of degradation was calculated using Equation (1) [11].  
\[Degradation(\%)=\frac{A_{0}-A_{t}}{A_{0}}\times 100 \tag{1}\]  
where \(A_{0}\) is the absorbance of methylene blue before irradiation, and \(A_{t}\) is the absorbance after irradiation.