## 3 Results
Compared with the UV-Vis DRS of TiO\({}_{2}\) in Figure 4a, the UV-Vis DRS of Ag/TiO\({}_{2}\) exhibits a redshift in Figure 4b. It can be discovered that when the deposition time of Ag is 100 s, the larger the deposition power of Ag, the greater the redshift of the absorption edge, and the degree of redshift increases with the increases in the sputtering power of Ag, as shown in Figure 4b. And, in Figure 4c, it is shown that when the deposition power of Ag is 5 W, as the deposition time of Ag is prolonged, the absorption edge first blueshifted and then redshifted. Compared with TiO\({}_{2}\), Ag/TiO\({}_{2}\) films show different degrees of redshift. The findings revealed that the surface modification of small Ag particles has a considerable impact on optical properties. The reason for this phenomenon may be that the decrease in the particle size leads to the increase in the internal stress P (P = 2\(\gamma\)/r, where \(\gamma\) is the surface energy and r is the particle radius), and the overlap of electron wave functions results in a redshift in the absorption limit [20]. The absorption displays the localized surface plasmon resonance of Ag nanoparticles centered at around 520 nm for the Ag/TiO\({}_{2}\) films [25]. The band gaps (E\({}_{\text{g}}\)) of Ag/TiO\({}_{2}\) and TiO\({}_{2}\) are determined through the Tauc graphical method to analyze the optical characteristics of the films, as shown in Figure 4d-f using Equation (2) [26]:  
\[\alpha\text{h}\
u=\text{C}\big{(}\text{h}\
u-\text{E}_{\text{g}}\big{)}^{1/2} \tag{2}\]  
where \(\alpha\) is the absorption coefficient, C is constant, h is the photon energy, and E\({}_{\text{g}}\) is the band gap. The E\({}_{\text{g}}\) of the samples are estimated from the Tauc plots, via the extrapolation of the linear part of the Tauc plot at zero F(R) [27; 28], as shown in Figure 4d-f. The E\({}_{\text{g}}\) of pure TiO\({}_{2}\) is 3.28 eV in Figure 4d. The E\({}_{\text{g}}\) of Ag/TiO\({}_{2}\)-5 W-100 s, Ag/TiO\({}_{2}\)-10 W-100 s, and Ag/TiO\({}_{2}\)-15 W-100 s are 2.43 eV, 2.5 eV, and 2.64 eV in Figure 4e, respectively. The E\({}_{\text{g}}\) of Ag/TiO\({}_{2}\)-5 W-50 s, Ag/TiO\({}_{2}\)-5 W-100 s, and Ag/TiO\({}_{2}\)-5 W-150 s are 2.66 eV, 2.7 eV, and 2.59 eV in Figure 4f, respectively. When the Ag deposition power is 5 W and the deposition time is 100 s, the corresponding band gap of 2.43 eV is the minimum. These results indicate that Ag modification can change the band gap of TiO\({}_{2}\). Compared with pure TiO\({}_{2}\), if the amount of silver modification is appropriate, the photocatalyst can expand its light response range and produce a certain redshift. The luminous group of MO is a nitrogen-conjugated double bond. In the experiment, the value of the characteristic peak decreased over time, indicating that the concentration of MO gradually decreased. After the photocatalytic reaction reached equilibrium, the recycled photocatalyst was immersed in water and no dye color was found. This indicates that the degradation reaction is mainly photocatalytic degradation, and the dye molecules are degraded through photocatalysis rather than adsorption. \begin{table}
\begin{tabular}{c c} \hline
**Sample** & **Ra (nm)** \\ \hline TiO\({}_{2}\) & 2.025 \\ Ag/TiO\({}_{2}\)-5 W-50 s & 2.203 \\ Ag/TiO\({}_{2}\)-5 W-100 s & 7.534 \\ Ag/TiO\({}_{2}\)-5 W-150 s & 3.118 \\ Ag/TiO\({}_{2}\)-10 W-100 s & 4.723 \\ Ag/TiO\({}_{2}\)-15 W-100 s & 7.082 \\ \hline \end{tabular}
\end{table} 
Table 1: Surface roughness of TiO\({}_{2}\) and Ag/TiO\({}_{2}\). The photocatalytic activity of Ag/TiO\({}_{2}\) and TiO\({}_{2}\) was investigated by measuring the UV-Vis spectra of MO solution after the photocatalytic degradation reaction under the same conditions. Figure 5a shows the UV-Vis absorption spectra of MO before (Co) and after photocatalytic degradation through Ag/TiO\({}_{2}\) and TiO\({}_{2}\) in pure MO solution.