## 4 Conclusions  
In this research work, two tubular and two hybrid nanostructures were studied for catalytic applications. TiO\({}_{2}\) nanosheets assembled on TiO\({}_{2}\) nanocavities, TiO\({}_{2}\) nanobowls assembled on TiO\({}_{2}\) nanocavities, and TiO\({}_{2}\) nanocavities were prepared by a two-step anodization process, while TiO\({}_{2}\) nanotubes were prepared in a three-step process. SEM results showed that the length of the nanotubes was 6.68 times larger than nanocavities and their inner diameter was 2.24 times greater, however, the wall thickness of nanocavities was wider than nanotubes. Besides, TiO\({}_{2}\) nanosheets had greater inner diameter and thinner thickness than TiO\({}_{2}\) nanobowls. Concerning their nanocavities of self-assembled nanostructures, the nanocavities in TiO\({}_{2}\)-ns/TiO\({}_{2}\)-nc had a larger length than the nanocavities in TiO\({}_{2}\)-nb/TiO\({}_{2}\)-nc. Another important factor is average surface roughness: for tubular nanostructures, the highest roughness was obtained by nanotubes, while, for self-assembled nanostructures, TiO\({}_{2}\)-ns/TiO\({}_{2}\)-nc had a higher roughness. The results of the PL study showed that TiO\({}_{2}\)-ns/TiO\({}_{2}\)-nc had a higher emission than the other three TiO\({}_{2}\) films. The defect states related to geometric parameters of these TiO\({}_{2}\) films were single-ionized oxygen vacancies. Hence, an important relationship between these nanostructures and single-ionized oxygen vacancies was observed. The number of single-ionized oxygen vacancies increases as the length of tubular nanostructure decreases, and the thickness of the self-assembled nanostructures decreases. As a consequence of the higher number of single-ionized oxygen vacancies, the band gap of self-assembled nanostructures and nanocavities is narrowed because the localized states are overlapped into the conduction band. By the homogeneous organization of nanotubes and larger thickness of the film, the intensity of phase anatase of TiO\({}_{2}\) nanotubes was higher than in other samples. Nevertheless, this film had more displacement of the E\({}_{\text{g(I)}}\) mode. This work demonstrated that the hybrid structure of TiO\({}_{2}\)-ns/TiO\({}_{2}\)-nc had the highest number of single-ionized oxygen vacancies that help to increase the chemisorption of the oxygen molecular and photogenerated charge carriers which in turn increase the superoxide radical anions. The phenomenon of catalysis is efficient mainly because oxygen vacancies operate as active sites in the catalysts. Therefore, active sites increase the rate of redox reaction leading to the breakdown of methylene blue molecules. Due to the higher amount of single-ionized oxygen vacancies of TiO\({}_{2}\)-ns/TiO\({}_{2}\)-nc, the degradation of methylene blue was similar to that of nanotubes, however, nanotubes had a thickness about 4.7 times larger than TiO\({}_{2}\)-ns/TiO\({}_{2}\)-nc. In this way, single-ionized oxygen vacancies are a vital characteristic of the catalyst because they promote the generation of the reactive species. Additionally, the shape of the nanosheets is a key geometric parameter that helps to speed up the catalysis process because highly active sites carry out higher reduction processes if the nanostructure has a higher surface area. These novel materials could be used to inactivate bacteria and viruses, water splitting, and water decontamination.