## 4 Conclusions  
In conclusion, we successfully designed a cross-linked polymeric binder through esterification reaction of CMC and FA and used it in Sb\({}_{2}\)O\({}_{3}\) for LIBs. It was found that CMC-FA@Sb\({}_{2}\)O\({}_{3}\) electrodes exhibited good cycling stability and rate capability, better than the electrodes with conventional binder. The results are ascribed to that the novel binder could improve the connection between active materials, conductive agent, and current collector, and also could accommodate the volume expansion of the Sb\({}_{2}\)O\({}_{3}\) anode in the cycles. Further studies will probably focus on preventing side reactions, improving the cycling stability of initial cycles and solving the aggregation of Sb\({}_{2}\)O\({}_{3}\) by decorating with functional materials, which may reduce the activation time and improve the early cycling performance of the CMC-FA@Sb\({}_{2}\)O\({}_{3}\) electrode. Furthermore, this low-cost cross-linked binder may be generalized to other electrode materials for lithium ion batteries, which suffer from large volume-changes during cycling.  
[PERSON], [PERSON] and [PERSON] conceived and designed the experiments; [PERSON], [PERSON] and [PERSON] performed the experiments; [PERSON], [PERSON] and [PERSON] analyzed the data; [PERSON] wrote the paper, [PERSON] and [PERSON] revised the paper. All the authors have discussed the results and commented on the manuscript.  
This work was supported by Program for Changjiang Scholars and Innovative Research Team in University (IRT_16R21), the Chinese 02 Special Fund (2017 ZX02408003), the Key Research Projects of Colleges and Universities in the Henan Province (15A430023), the Scientific and Technological Project of Henan Province (182102210297), Open Fund of National Joint Engineering Research Center for abrasion control and molding of metal materials (HKDNM201802, HKDNM201807), Scientific Research Starting Foundation for Ph.D. of Henan University of Science and Technology (13480065), Science Foundation for Youths of Henan University of Science and Technology (2013 QN006) and the Student Research Training Plan of Henan University of Science and Technology (2018029).  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Materials**} & **Current Density** & \multirow{2}{*}{**Cycle Number**} & **Specific Capacity** & \multirow{2}{*}{**Ref**} \\  & **(mA/g)** & & **(mA/g)** & \\ \hline octahedral Sb\({}_{2}\)O\({}_{3}\) & 200 & 50 & 640.8 & [30] \\ carbon-coated Sb/Sb\({}_{2}\)O\({}_{3}\) & 100 & 100 & 686 & [51] \\ hollow Sb\({}_{2}\)O\({}_{3}\)/BiTiO\({}_{2}\) & 100 & 100 & 593 & [52] \\ bundle shaped Sb\({}_{2}\)O\({}_{3}\) & 20 & 100 & 594.1 & [25] \\
3D nest-shaped Sb\({}_{2}\)O\({}_{3}\)/RGO composites & 50 & 100 & 562 & [53] \\ CMC-FA@Sb\({}_{2}\)O\({}_{3}\) & 200 & 200 & 611.4 & This work \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of the electrochemical performances of CMC-FA@Sb\({}_{2}\)O\({}_{3}\) with previously reported Sb\({}_{2}\)O\({}_{3}\)-based composites as anode materials for lithium ion batteries.  
Figure 6: Schematic illustration of the proposed mechanism of cross-linked CMC-FA binder and PVDF/CMC binder in Sb\({}_{2}\)O\({}_{3}\) electrodes.