## 1 Introduction  
Nowadays, advanced energy conversion and storage devices, such as supercapacitor, lithium-ion batteries (LIBs) and solar cells, have gradually become research hotspots to manage the energy supply for future sustainable resources [1; 2; 3; 4]. Among them, LIBs have been widely used in almost all aspects of our lives for their high energy density, long life span, and environmental friendliness [5; 6; 7; 8; 9; 10; 11]. Although the energy density of LIBs grew very quickly in recent years, it still could not meet people's growing demand. For graphite, the anode material of a commercial lithium battery, the theoretical specific capacity of which is only about 372 mAh g\({}^{-1}\), and this poses a great obstacle to the increase of lithium ion battery capacity [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22]. Nevertheless, the post-transition metal oxides (PTMOs) have attracted much attention because of their high theoretical capacity (>600 mAh g\({}^{-1}\)) [23], such as SnO\({}_{2}\)[24], Sb\({}_{2}\)O\({}_{3}\)[25; 26; 27], Sb\({}_{2}\)O\({}_{4}\)[28] and Sb\({}_{6}\)O\({}_{13}\)[29]. Among these PTMOs, Sb\({}_{2}\)O\({}_{3}\) has advantages of low cost, simple synthesis process, and easily availability of raw materials, making it a promising electrode material for rechargeable lithium-ion batteries [30]. However, the lithium storage mechanism of Sb\({}_{2}\)O\({}_{3}\) is found to be phase conversion and alloying, which could cause great volume increases or shrinksduring cycling [23]. Thus, Solid Electrolyte Interphases (SEI), on Sb\({}_{2}\)O\({}_{3}\) electrode during initial cycle, would be disrupted, exposing new active site and forming new SEI during cycling, resulting in a decrease in capacity [31]. To stabilize an Sb\({}_{2}\)O\({}_{3}\) electrode, many researchers have been working on controlling the morphology of Sb\({}_{2}\)O\({}_{3}\), such as synthesizing porous Sb\({}_{2}\)O\({}_{3}\)[32] and Sb\({}_{2}\)O\({}_{3}\) nanowires [33], and decorating Sb\({}_{2}\)O\({}_{3}\) with different carbon materials; for instance, carbon cloth [34], reduced graphene oxide [35] and so on. Even though these methods can improve the electrochemical performance of Sb\({}_{2}\)O\({}_{3}\) electrodes, the synthesis processes are complex and of high cost, which limits their wide application. Moreover, the addition of carbon material will reduce the specific capacity of the electrode. A binder plays a crucial role in affecting the performance of LIBs. Compared to traditional linear binder, cross-linked binder not only could improve the binding between active material and conductive agent, but also can accommodate volume expansion of the electrode during cycling [36; 37; 38]. The construction of three-dimensional crosslinking structure can improve the cycling stability of the battery, which has been described in many studies [38; 39]. For example, [PERSON] and his colleagues obtained enhanced electrochemical performance of Si anode for lithium-ion batteries by using a PAA-PVA polymeric binder [39]. Recently, [PERSON] et al. synthesized a stable cross-linking polymeric network of CMC and citric acid (CA) and used it in silicon-based anodes of LIBs, in which an enhanced cycling stability was obtained comparing to linear polymeric PVDF and CMC binders [36]. Moreover, a more stable silicon electrode was also obtained by designing corn starch-maleic anhydride cross-linked binder [40]. In these studies, various novel binder systems for stabilizing the silicon anode for LIBs were fabricated, enhancing their cycling stability. It is known that Si and Sb\({}_{2}\)O\({}_{3}\) are similar alloying mechanism in degradation of capacity during repeated lithium ion insertion/extraction [38; 41]. In this work, we designed a cross-linked polymeric binder with esterification reaction of CMC and Fumaric Acid (FA), and successfully applied it in Sb\({}_{2}\)O\({}_{3}\) anode for LIBs.