## 3 Results
### Catalytic Activity of CoSN@C  
To test the catalytic activity of the synthesized catalyst, RhB was chosen as a model pollutant, and the comparative performance of SN@C, CoN@C, and CoSN@C for the degradation of RhB by PMS was examined. Figure 3a shows the degradation of RhB by several catalytic systems. In the experiment, the initial concentration of RhB was 20 mg L\({}^{-1}\), the concentration of PMS was 1 mM, the initial pH of the reaction system was 5 after adding PMS, and the reaction temperature was approximately 20 \({}^{\circ}\)C. RhB concentration decreased minimally when only PMS was employed, showing that PMS self-activation's effect on creating reactive radicals was minimal [34; 35]. With SN@C + PMS, CoN@C + PMS, and CoSN@C + PMS, the RhB degradation rates reached 34.0%, 66.0%, and 99.5% in 3 min 44.5%, 92.3%, and 100% in 4 min, respectively. Both the introduction of sulfur modification and Co loading on MOFs-derived carbon exhibited strong activation properties for PMS, with Co loading on sulfur carbide-modified MOFs achieving the best RhB degradation with CoSN@C. Meanwhile, Figure 3b showed the adsorption equilibrium of CoSN@C for RhB was reached within 30 min. Moreover, \(\sim\)40% of TOC was removed after 10 min reaction (Figure 3d). To further study the kinetic characteristics of SN@C, CoN@C, and CoSN@C on the RhB degradation reaction, a fit was performed using Equation (1) for the primary reaction kinetic model:  
\[ln\bigg{(}\frac{C_{a}}{C_{0}}\bigg{)}=-kt \tag{1}\] \begin{table}
\begin{tabular}{c c c c} \hline
**Catalysts** & \
\begin{tabular}{c} **Surface Area** \\ **(m\({}^{2}\) g\({}^{-1}\))** \\ \end{tabular} & **Pore Size (nm)** &
\begin{tabular}{c} **Pore Volume** \\ **(cm\({}^{3}\) g\({}^{-1}\))** \\ \end{tabular} \\ \hline CoSN@C & 293.30 & 3.26 & 0.24 \\ CoN@C & 876.66 & 4.76 & 1.04 \\ SN@C & 185.02 & 5.23 & 0.24 \\ \hline \end{tabular}
\end{table} 
Table 1: Surface area, pore size, and pore volume parameters of SN@C, CoN@C and CoSN@C.  
Figure 2: XRD patterns of ZIF-67 and ZIF-67-S precursors (**a**); CoN@C and CoSN@C (**b**); nitrogen adsorption and desorption isotherms for SN@C, CoN@C, and CoSN@C (**c**). where \(C_{0}\) (mg L\({}^{-1}\)) and \(C_{a}\) (mg L\({}^{-1}\)) are the initial RhB concentration and RhB concentration at moment \(a\) (min), \(k\) is the primary reaction rate constant (min\({}^{-1}\)), and \(t\) is the reaction time (min). According to Table 2, the apparent reaction rate constants (\(k\)) for RhB degradation by SN@C, CoN@C, and CoSN@C as catalysts for activated PMS were 0.122 min\({}^{-1}\), 0.442 min\({}^{-1}\), and 1.852 min\({}^{-1}\), respectively. CoSN@C activated PMS was the most rapid of the materials, with an apparent reaction rate constant (\(k_{app}\)) 4.2 times greater than CoN@C and 15.2 times greater than SN@C. The N site, C site, and S site performances alone have limited ability to activate PMS. In contrast, the active site containing Co is the key that can efficiently activate PMS and generate reactive oxygen species to degrade RhB. The Co-containing active sites synergistic with S-doping can activate PMS to degrade organic matter more efficiently [36]. Figure 4a exhibits the RhB degradation efficiency at various PMS molar concentrations. The RhB degradation rates at 4 min were 95.52%, 100%, and 97.76% when the PMS molar concentrations were 0.5 mM, 1 mM, and 2 mM, respectively. When the PMS molar concentration was above 1 mM, the growing trend of the RhB degradation rate slowed, which shows that there is also an optimum value for PMS concentration. The addition of excess PMS may produce excess sulfate radicals, not only leading to react with itself, but also be consumed by excessive PMS to ROS with lower oxidation capacity [37]. For future studies, a 1 mM PMS molar concentration was selected. The effect of the change in catalyst dosage on the RhB degradation rate was evaluated, and the results are depicted in Figure 4b. When the catalyst dosage of CoSN@C was 0 mg L\({}^{-1}\), 0.025 mg L\({}^{-1}\), 0.05 mg L\({}^{-1}\), and 0.1 mg