## 3 Results and Discussion
After the first cycle, there was no significant change. The cycling performance of SP/C was obtained by charging/discharging at various current densities. Figure 4c shows the charge/discharge profile at a current density of 1A g\({}^{-1}\). SP/C exhibited a reversible capacity of approximately 220 mAh g\({}^{-1}\) or higher. Initially, a reversible capacity of approximately 260 mAh g\({}^{-1}\) was observed. However, the discharge capacity decreased with an increasing number of cycles, and it was stable from the \(\sim\)30 th cycle. The charge/discharge profile at a higher current density of 10 Ag\({}^{-1}\) is shown in Figure 4d. Starting with a discharge capacity of approximately 220 mAh g\({}^{-1}\), it decreased to approximately 125 mAh g\({}^{-1}\) at the 3000 th cycle. However, it exhibited an excellent cycling life. A rate capability test was performed to determine the stability of SP/C (Figure 5a). The current density was increased from 1 to 100 A g\({}^{-1}\), and further decreased to 1 A g\({}^{-1}\). Discharge capacities of approximately 271, 242, 211, 189, 170, 157, 146, 138, 132, 125, 120, 116, and 112 mAh g\({}^{-1}\) were observed at the current densities of 1, 2, 5, 10, 20, 30, 50, 50, 60, 70, 80, 80, 90, and 100 A g\({}^{-1}\), respectively. The stability was confirmed by almost recovering the original reversible capacity at 1 A g\({}^{-1}\). The excellent rate performance of SP/C could be attributed to the presence of numerous macropores, owing to the co-doping of S and P [24]. This could be further explained by the charge/discharge profiles at each current density (Figure 5b). As the current density increased, the flat section sharply decreased, indicating that the adsorption of Na ions at the active site was much faster than the intercalation between the graphene layers. In other words, the macropores narrowed  
Figure 4: (a) Charge/discharge curves of SP/C during the first cycle; (b) CV curves of SP/C at a scan rate of 0.2 mV s\({}^{-1}\); (c) cycling performance of SP/C in SIB at current densities of 1 A g\({}^{-1}\) and (d) 10 A g\({}^{-1}\). the diffusion distance of Na ions and increased the diffusion rate. The abundant active sites increased the Na storage capacity by the adsorption of numerous Na ions. To further analyze the excellent rate performance of SP/C, CV was conducted at various scan rates, from 0.2 mV s\({}^{-1}\) to 2.0 mV s\({}^{-1}\), for investigating the reaction kinetics (Figure 6a). As the scan rate increased, the peak current also increased, but the shape of the CV curve remained similar. Therefore, the capacitive behavior was analyzed for the scan rate and peak current, as shown in Equation (1) [25,26]. \[i(V)=a\
u^{b}, \tag{1}\]  
where \(a\) and \(b\) are the correlation coefficients, \(v\) is the scan rate, and \(i\) is the current. When \(a\) value \(b\) approaches 0.5, it indicates a diffusion-controlled process; whereas, when \(a\) value \(b\) approaches 1.0, it indicates a surface-controlled process. Figure 6b represents the slope corresponding to Equation (1) at 0.1 V, and the \(b\) values of the cathodic and anodic peak in this potential are 0.9038 and 0.9010, respectively. Both values are close to 1.0, indicating that the kinetics mainly correspond to the surface-controlled process. Figure 5: (**a**) Rate capability at various current densities ranging from 1 to 100 A g\({}^{-1}\); (**b**) charge/discharge profiles at different rates. Figure 6: (**a**) CV curves of SP/C at various scan rates from 0.2 to 2.0 mV s\({}^{-1}\); (**b**) linear relationship between the logarithms of the current and scan rates of the cathodic and anodic peaks at 0.1 \(V\); (**c**) CV curve and capacitive contribution of SP/C at a scan rate of 2.0 mV s\({}^{-1}\); (**d**) corresponding capacitive contribution to the total capacity at different scan rates. The relative contributions of the intercalation and capacitive processes at a specific scan rate can be calculated using Equation (2) [27; 28].