## 3 Results
### Catalysis Process Characterization  
Figure 7a shows the percentage rate of degradation of methylene blue over a period of eight hours. After eight hours of reaction, TiO\({}_{2}\)-nt achieved the greatest degradation (75.01%), slightly higher than that of TiO\({}_{2}\)-ns/TiO\({}_{2}\)-nc (72.68%), we will call final degradation to the percentage of conversion achieved after 8 h of reaction. From 1 to 4.5 h, the percentage of catalytic degradation had a linear behavior, that is, a constant reaction rate. Then, the degradation rate decreased smoothly until the final concentration was reached. The lowest final degradation was achieved by TiO\({}_{2}\)-nc, with only 43.01% while TiO  
Figure 6: (**a**) Raman spectra of TiO\({}_{2}\) nanostructures; and (**b**) E\({}_{\text{g(1)}}\) mode displacement, thickness and oxygen vacancies for each nanostructure. -nb/TiO\({}_{2}\)-nc obtained 60.8%. In fact, a similar catalytic activity from 1 h to 4 h was observed for TiO\({}_{2}\)-nt and TiO\({}_{2}\)-ns/TiO\({}_{2}\)-nc, nevertheless, after 5 h their rate of degradation changes. PL studies showed that TiO\({}_{2}\)-ns/TiO\({}_{2}\)-nc had a higher amount of single-ionized oxygen vacancies than the other three catalytic materials. Oxygen vacancies have been related in sensors as active sites that increase reactivity on the surface of oxides [26; 35]. In catalysis, single-ionized oxygen vacancies have similar behavior. In this case, oxygen vacancies react with O\({}_{2}\) and electrons producing superoxide radical anion (O\({}_{2}^{-}\)) which help to degradation of pollutants [22; 24; 27; 36; 37]. A relationship between the number of single-ionized oxygen vacancies and degradation percentage for TiO\({}_{2}\) films with thickness less than 500 nm is shown in Figure 7b. The degradation percentage increases as the number of single-ionized oxygen vacancies increases. As shown in Table 1, the thickness of TiO\({}_{2}\)-nt was 4.2 times higher than the thickness of TiO\({}_{2}\)-ns/TiO\({}_{2}\)-nc, however, the number of single-ionized oxygen vacancies in TiO\({}_{2}\)-nt was 2.64 times less than in TiO\({}_{2}\)-ns/TiO\({}_{2}\)-nc. Therefore, TiO\({}_{2}\)-ns/TiO\({}_{2}\)-nc dramatically increased the degradation considering that it is a smaller amount of catalyst [38]. So, the single-ionized oxygen vacancies help to enhance the catalytic activity because they increase the active sites for adsorption [23; 39; 40]. Our results show that the band gap was narrowed in TiO\({}_{2}\) samples with thickness less than 0.5 \(\upmu\)m and with a higher number of single-ionized oxygen vacancies. Therefore, a relationship between the band gap, single-ionized oxygen vacancies with catalytic activity is shown in Figure 7b. The band gap energy is reduced with increasing oxygen vacancies in TiO\({}_{2}\) films because the oxygen vacancies create donor states under the conduction band. The band gap narrowing helps to generate a greater amount of photocharge carriers which causes an increase in the rate of the catalysis process [15; 24; 26; 36; 40]. In contrast, TiO\({}_{2}\)-nt was made with a longer synthesis process than hybrid nanostructures, which can increase the manufacturing costs of catalysts. Additionally, we found that S\({}_{\text{a}}\) of TiO\({}_{2}\)-ns/TiO\({}_{2}\)-nc was higher compared to TiO\({}_{2}\)-nb/TiO\({}_{2}\)-nc, however, the highest S\({}_{\text{a}}\) was for TiO\({}_{2}\)-nt. We suggest that S\({}_{\text{a}}\) can affect the photocatalytic activity because the films with a thickness less to 500 nm show a significant roughness effect on the degradation, as shown in Figure 7b [41]. On the other hand, Figure 7c shows a comparison between the geometric parameters, final degradation, and oxygen vacancies of TiO\({}_{2}\) nanomaterials. Note that the geometric parameters play an important role in the catalytic, crystal structure, and optical properties, this is because geometric parameters such as the thickness of the film, inner and outer diameters are associated with the surface area of nanomaterial [42; 43].