## 3 Results and Discussion
### Performance of CeO\({}_{2}\) in the Photocatalytic Degradation of Citric Acid  
To verify the feasibility of CeO\({}_{2}\) in degrading citric acid under ultraviolet light exposure, photocatalytic tests were conducted. The UV spectrum peak of citric acid is primarily concentrated around 430 nm [30]. Therefore, we used a visible spectrophotometer to measure the UV spectrum of citric acid at 430 nm and calculated the concentration of citric acid using the Beer-Lambert law (Equation (4)). The Beer-Lambert law has certain limitations,  
Figure 3: (a) PL spectra of CeO\({}_{2}\) and H-CeO\({}_{2}\), (b) Fluorescence lifetimes of CeO\({}_{2}\) and H-CeO\({}_{2}\). and the calculated error is relatively accurate only in dilute solutions [31]. Thus, a dilute solution of citric acid was used to simulate the residual citric acid after polishing. \[log\frac{I_{0}}{I}-A=\varepsilon cl \tag{4}\]  
\(I_{0}\) and \(I\) represent the intensities of the incident light and the transmitted light, respectively. \(l\) is the path length of the absorbing solution and \(c\) is the concentration. \(log_{10}(I_{0}/I)\) is the absorbance or optical density and \(\varepsilon\) is known as the molar extinction coefficient. As shown in Figure 4a,b, after 30 min in a dark environment, the concentration of citric acid decreased due to physical adsorption by the cerium oxide material; however, the reduction was minimal. Various concentrations of CeO\({}_{2}\) (0.1 g/L, 0.15 g/L, 0.2 g/L, 0.25 g/L, and 0.3 g/L) were added under UV irradiation to degrade a 0.2 g/L citric acid solution. The degradation efficiency of citric acid is shown in Figure 4a,b. The degradation rate \(D\) of citric acid was obtained using Equation (5), where \(c\) is the concentration of citric acid at the current time and \(c_{-30}\) represents the concentration of citric acid 30 min before the start of irradiation. \[D=\left(1-\frac{c}{c_{-30}}\right)\times 100\% \tag{5}\]  
It can be observed that without the addition of H\({}_{2}\)O\({}_{2}\), the removal rate of citric acid shows a parabolic distribution as the concentration of CeO\({}_{2}\) increases. At a CeO  
Figure 4: (**a**) Degradation capability of citric acid solution at different CeO\({}_{2}\) concentrations, (**b**) Photocatalytic degradation curve of citric acid, (**c**) Linear relationship between \(ln(c_{0}/c)\) and time (\(t\)), (**d**) Rate constant \(k\) at different CeO\({}_{2}\) concentrations. concentration of 0.2 g/L, the degradation rate reaches its maximum of 33.58% after 60 min. The kinetic curves of citric acid are shown in Figure 4c, presenting a linear relationship between \(ln(c_{0}/c)\) and time (\(t\)), where \(c_{0}\) represents the concentration of citric acid just before the start of irradiation. These curves indicate that the degradation of citric acid follows the Langmuir-Hinshelwood pseudo-first-order kinetics (as shown in Equation (6)). \[ln(c_{0}/c)=kt \tag{6}\]  
\(k\) is the reaction rate constant obtained from the slope of the \(ln(c_{0}/c)=kt\) curve. As shown in Figure 4d, the \(k\) value is highest at a CeO\({}_{2}\) concentration of 0.2 g/L, reaching 0.00609, which is twice the \(k\) value at a CeO\({}_{2}\) concentration of 0.1 g/L. From the experimental results mentioned above, it can be seen that the adsorption of citric acid by cerium oxide is relatively weak. To rigorously verify the photocatalytic role of CeO\({}_{2}\), we also conducted adsorption and degradation experiments of citric acid with CeO\({}_{2}\) in the dark. The results, shown in Figure 5a,b, indicate that CeO\({}_{2}\) does not degrade citric acid in the dark. The observed reduction in citric acid concentration is attributed to the adsorption of citric acid onto CeO\({}_{2}\). However, since the adsorption is weak, it does not significantly affect the degradation process. Therefore, the adsorption of citric acid by CeO\({}_{2}\) can be considered negligible. Thus, in subsequent experiments, the impact of adsorption was no longer considered.