## 3 Results and Discussion
The photocatalytic effect of the recycled photocatalyst is shown in \[\mathrm{D}=\frac{\mathrm{K}\lambda}{\beta\cos\theta} \tag{2}\]0 The abscissae 0-24 min, 24-42 min, 42-60 min, 60-78 min, 78-96 min and 96-114 min correspond to the first, second, third, fourth, fifth and sixth photocatalytic reactions, respectively. The result indicates that the rate of photocatalytic degradation of AR73 by the photocatalyst recycled for the fifth time is lower than those of the previous four times, but it can still reach 77.05%, as shown in \[\mathrm{D}=\frac{\mathrm{K}\lambda}{\beta\cos\theta} \tag{2}\]1 This phenomenon may be caused by the adsorption of some insoluble or insoluble intermediates on the catalyst surface, which occupies the activity of the photocatalyst, affects the absorbance of the catalyst and reduces the yield of photogenerated electron-hole pairs. Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) in water was irradiated with a high-pressure mercury lamp for 40 min to achieve self-cleaning, and the conditions for self-cleaning were the same as those for photocatalytic degradation of AR73. In the sixth photocatalytic degradation experiment of AR73, the concentration of AR73 was 0.91 mg L\({}^{-1}\) and the degradation rate was 95.45% after irradiation for 18 min. This indicated that through self-cleaning, the precipitation on the surface was further degraded by the photocatalyst to soluble small molecules, restoring the photocatalytic activity of Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\). Figure 8 shows the linear fitting of first-order kinetics of photocatalytic degradation of AR73 by Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) and TiO\({}_{2}\). The degradation reaction rate constant K can be acquired with the following equation [23]:  
\[\mathrm{D}=\frac{\mathrm{K}\lambda}{\beta\cos\theta} \tag{2}\]2  
where C\({}_{0}\) (mg L\({}^{-1}\)) and C\({}_{\text{t}}\) (mg L\({}^{-1}\)) have the same meaning as in formula (1). The fitting results are shown in \[\mathrm{D}=\frac{\mathrm{K}\lambda}{\beta\cos\theta} \tag{2}\]3 It shows that the photocatalytic process has a concentration-controlled reaction rate. The degradation reaction rate constant of Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) was better than that of TiO\({}_{2}\). This result is consistent with Figure 6c. \[\mathrm{D}=\frac{\mathrm{K}\lambda}{\beta\cos\theta} \tag{2}\]4 The rate of AR73 degradation by Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) for six cycles. When the ultraviolet light irradiates on the surface of the sample, the electrons in the conduction band come from electrons of Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) in the valence band absorbing the energy of photons. Photogenerated electrons are formed in the conduction band, photogenerated holes are formed in the valence band, and highly active hole-electron pairs are formed, forming a redox system. Under the action of an electric field, photogenerated electrons and holes are separated and transferred to Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) (001) and (101) crystal planes, respectively [24]. Photogenerated holes (h\({}^{+}\)) can oxidize OH\({}^{-}\) and H\({}_{2}\)O molecules absorbed on the surface of TiO\({}_{2}\) to generate \(\cdot\)OH and \(\cdot\)O\({}_{2}\)\({}^{-}\). Photogenerated electrons (e\({}^{-}\)) can also react with dissolved oxygen (O\({}_{2}\)) in water to form superoxide radicals (\(\cdot\)O\({}_{2}\)\({}^{-}\)), and \(\cdot\)O\({}_{2}\)\({}^{-}\) further reacts with H\({}_{2}\)O to form OH\({}^{-}\)[25].