## 3 Results
It can be found that compared with the relative content of Ag\({}^{+}\) in Figure 8b,e, the increase in the proportion of Ag\({}^{+}\) is attributed to the fact that the Na\({}_{2}\)SO\({}_{4}\) presence accelerates the oxidation of Ag\({}^{0}\) in the MO-Na\({}_{2}\)SO\({}_{4}\) mixed solution, which is the reason for the decrease in photocatalytic degradation effect with the increase in degradation cycles. Figure 8f shows the XPS spectrum of the Ti 2p of the Ag/TiO\({}_{2}\)-5 W-50 s after photocatalytic degradation in the MO-Na\({}_{2}\)SO\({}_{4}\) mixed solution. The results are consistent with those in Figure 8c,f. The reaction rate was calculated via linear fitting according to the first-order kinetics equation of degradation. The formula for the first-order kinetic equation for degradation is [45]  
\[\ln\left(\frac{\text{C}_{0}}{\text{C}_{\text{t}}}\right)=\text{kt} \tag{3}\]  
where t is the irradiation time, C\({}_{0}\) (mg L\({}^{-1}\)) and C\({}_{\text{t}}\) (mg L\({}^{-1}\)) are the same as those in Equation (1), and k is the pseudo-first-order rate constant (min\({}^{-1}\)). In the experiments, the photocatalytic degradation efficiency for MO was represented by the initial k. The initial k was obtained using experimental data up to 40 min of the simulated irradiation because the subsequent data seemed to deviate from the linear plot of ln (C\({}_{0}\)/C\({}_{\text{t}}\)) vs. t, owing to the decreasing MO concentration in the bulk solution. The linear regression coefficient R\({}^{2}\) of Ag/TiO\({}_{2}\)-5 W-50 s and the initial rate constant k in the pure MO solution were 0.98634 and 0.04543 min\({}^{-1}\); meanwhile, in the MO-Na\({}_{2}\)SO\({}_{4}\) solution, the linear regression coefficient R\({}^{2}\) was 0.98954 and the initial rate constant k was 0.03609 min\({}^{-1}\), as shown in Figure 9. Apparently, the linear regression coefficients of both were close to 1, which suggested that the pseudo-first-order kinetic was suitable for describing the kinetics of MO photodegradation; the photocatalytic process was a concentration-controlled reaction rate. And, the k value in the MO solution is larger than that in MO-Na\({}_{2}\)SO\({}_{4}\), so the photocatalytic degradation efficiency of MO using Ag/TiO\({}_{2}\)-5 W-50 s in the pure MO solution is better than that in the MO-Na\({}_{2}\)SO\({}_{4}\) solution. The results are consistent with those in Figure 7b. Figure 10 shows the schematic diagram of the photocatalytic degradation mechanism of Ag/TiO\({}_{2}\). Under UV irradiation, the photogenerated electrons in the TiO\({}_{2}\) conduction band migrate to Ag, forming electron-hole pairs. Consequently, a Schottky barrier is formed at the Ag-TiO\({}_{2}\) interface, acting as an electron trap. As a result, the electron capture sites on Ag inhibit the recombination of e\({}^{-}\) and h\({}^{+}\), causing more residual h\({}^{+}\) in  
the TiO\({}_{2}\) valence band to oxidize H\({}_{2}\)O on the membrane surface, generating \(\cdot\)OH and increasing the \(\cdot\)OH concentration, thereby promoting the oxidative decomposition of MO. Simultaneously, the e\({}^{-}\) captured on Ag can independently transfer to the adsorbed oxygen on the membrane surface, producing O\({}_{2}\)\({}^{-}\), which also facilitates the degradation of MO [46]. While a large amount of SO\({}_{4}\)\({}^{2-}\) appeared in the solution after the addition of Na\({}_{2}\)SO\({}_{4}\), SO\({}_{4}\)\({}^{2-}\) was adsorbed on the surface of the photocatalyst, acting as a pore-trapping agent to increase the generated content of SO\({}_{4}\)\({}^{-}\); both \(\cdot\)OH and SO\({}_{4}\)\({}^{-}\) can make the Ag\({}^{0}\) on the surface of the catalyst oxidize to Ag\({}^{+}\), leading to the decrease in the degradation efficiency of the photocatalyst in the solution of MO-Na\({}_{2}\)SO\({}_{4}\)[34]. Figure 10: Schematic illustration of photocatalytic degradation mechanism of Ag/TiO\({}_{2}\) in MO-Na\({}_{2}\)SO\({}_{4}\) mixed solution.