## 3 Results and Discussion
### Electrochemical Measurement  
The poly(S-Sty-P) terpolymer @ GF and poly(S-Sty-P) terpolymer @ CCB were both successfully employed as cathode materials in Li-S battery. The first cycle of cyclic voltammetry (CV) curves of these two batteries were depicted in Figure 8. The CV curve of poly(S-Sty-P) terpolymer @ CCB resembled the curve of charge-discharge curves of poly(S-Sty-P) terpolymer @ GF. They both had two distinct reduction peaks at about 2.3 and 2.1 V, and one oxidation peak at 2.4 V. Both of the curves were characteristic of the CV curve of element sulfur [26]. With the open circuit voltage of 3 V and current of 0.2 C, the charge-discharge curve of poly(S-Sty-P) @ CCB battery showed two plateaus (Figure 9a) at 2.35 and 2.05 V; and the charge-discharge curve of poly(S-Sty-P) @ GF battery showed two plateaus (Figure 9b) at 2.33 and 2.03 V. Both of the charge-discharge curves were in accordance with the characteristic curve of Li-S battery. This fact demonstrated that S-S and organosulfur moieties in the terpolymers were electroactive. The reactions involved during the charge and discharge process were shown in Figure 10.  
Figure 8: (**a**) The first cycle of cyclic voltammetry (CV) curves of poly(S-Sty-P) terpolymer @ CCB battery; (**b**) the first cycle of CV curves of poly(S-Sty-P) terpolymer @ GF battery. Figure 7: (**a**) SEM of poly(S-Sty-P) terpolymer @ GF; (**b**) SEM of poly(S-Sty-P) terpolymer @ CCB. From Figure 11, it can be seen that the initial specific capacity of poly(S-Sty-P) terpolymer @ CCB battery was 935.88 mAh/g. After 60 cycles, the specific capacity gradually decreased to 542.71 mAh/g. After 100 cycles, the specific capacity stayed at 407 mAh/g, with the coulombic efficiency around 100% and the capacity retention rate about 43.5%. Comparatively, the initial specific capacity of poly(S-Sty-P) terpolymer @ GF battery was 1008.35 mAh/g, and the discharge specific capacity reduced to 639.03 mAh/g after 60 cycles, and maintained at 611 mAh/g after 100 cycles, with the capacity retention rate around 60.59%. Therefore, it had a better cycle stability. This was because the functional groups of poly(S-Sty-P) terpolymer can capture the intermediate polysulfides, and subsequently suppress polysulfide diffusion as a consequence of the embedment [5]. In addition, the S-S bonds in the terpolymer were involved with the \(\pi\)-\(\pi\) conjugation of graphene [27], expanding the conjugated system, which effectively enhanced the interaction on the positive electrode interface and limited the \"shuttle effect\" of polysulfides [28]. Therefore, the electrochemical performance of the Li-S battery was improved. Figure 10: The reactions involved during the charge and discharge process. Figure 9: **(a)** The charge-discharge curves of poly(S-Sty-P) terpolymer @ CCB battery; **(b)** the charge-discharge curves of poly(S-Sty-P) terpolymer @ GF battery. When the current densities were gradually increased from 0.2, 0.5, 1, 2, to 5 C, with 10 cycles at each current density, the rate performance of the batteries were obtained (Figure 12). At different current densities, the discharge specific capacities of poly(S-Sty-P) terpolymer @ CCB battery were 935.4, 580.04, 434.92, 286.32, and 277.68 mAh/g. When the current density was back to 0.2 C, the discharge specific capacity of this battery was about 431.12 mAh/g. Comparatively, the discharge specific capacities of poly(S-Sty-P) terpolymer @ GF battery were 1008, 688.68, 531.18, 435.42, and 302.90 mAh/g. When the current density was back to 0.2 C, the discharge specific capacity of this battery was about 515.52 mAh/g, suggesting better rate performance. Since, compared with the conductive carbon black particle's structure, the graphene sheet had a larger specific surface area, higher stratified porosity, and more contact sites which can touch more active substances [29, 30]. This structure was conducive to the infiltration of the electrolyte, resulting in the shorter diffusion path for lithium-ion.