Rational design and kinetics study of flexible sodium-ion full batteries based on binder-free composite film electrodes

Flexible sodium-ion full batteries were rationally designed by using hard carbon fibers from carbonized filter paper as a conductive supporting framework.


Introduction
Developing new and low-cost technologies in environmentally friendly energy storage systems is a life-time goal for researchers. [1][2][3][4][5] With the rapidly increasing demand for versatile energy storage devices, great interest has been aroused in exible/bendable electronic equipment, such as rollup displays, wearable and portable electronic devices and implantable biomedical products. [6][7][8] Nevertheless, exible rechargeable batteries still suffer from the lack of advanced electrodes with high energy density, high reversible capacities, fast chargedischarge rates and a long lifespan. The design of a exible battery usually requires light, exible, and small units with shape-conformability, aesthetic diversity, and excellent mechanical properties. 9 However, traditional exible electrode materials oen suffer from low specic power density and other poor performances due to a certain amount of binder being added to improve their exibility. Therefore, numerous research efforts have been directed to the design of exible, binder-free, and thin-lm electrodes. For instance, CNTs, graphene paper, carbon cloth or textiles, and composite materials have been used as exible binder-free electrodes. [10][11][12][13][14][15][16] Despite these advances, the rational design of cheap exible binder-free electrodes with high capacity and high energy density, fast charge-discharge rates and a long cycling lifetime remains a long-standing challenge.
Recently, sodium ion batteries (SIBs) for large-scale energy storage have been rapidly developed due to the abundance and low-cost of sodium resources, and have become the most promising alternative to lithium ion batteries (LIBs). [17][18][19] In particular, the investigation of cheap electrodes (such as TiO 2 nanotubes, hard carbon materials, electroactive organics/ graphene composites, and so on) and safe polymeric electrolytes for SIBs has recently become a hot topic within the scientic community. [20][21][22] Bella et al. reported some polymer electrolytes for SIBs, showing a wide electrochemical stability window versus Na/Na + and stable long-term constant-current charge/discharge cycling. 23,24 However, the energy density, charge-discharge rate and cycling lifetime of the electrode materials are extremely important for SIBs, which have been seriously limited by the intrinsic high potential of Na, large ionic size of Na ions and high polarization of electrodes. 25 Thus, the rational design and fabrication of high-voltage cathodes with suppressed polarization and well-matched anodes are key for the development of high-performance sodium-ion full batteries (SIFBs). 26 In addition, the research studies on exible SIFBs are in the beginning stage, and the electrochemical performances remain unsatisfactory due to the low chemical reaction kinetics for Na ion insertion. Therefore, the process control of well-matched SIFBs is also important and needs to be investigated.
A polyanion-type compound with a highly open 3D framework structure and high Na-transport/reaction kinetics, such as Na 3 V 2 (PO 4 ) 3 (NVP), can supply large and interconnected vacant sites, and build suitable paths for the diffusion of Na ions. [27][28][29][30][31][32] In particular, NVP has high potential plateaus at 3.4 V, and it can be used as an ideal cathode material of SIFBs. Yu et al. reported that interconnected 3D NVP/C composites delivered superior rate capability and excellent cycling stability, but the exploration of a suitable counter electrode vs. NVP to fabricate high-performance SIFBs still remains unsatisfactory. 33 Xia et al. reported an interesting exible SIFB using NVP/C@rGO composites as both the cathode and anode. 27 The reported cell exhibited good electrochemical performance, with 1.7 V as the output voltage plateau and a capacity of 74.1 mA h g À1 at 0.5C. However, its lower voltage plateau results in lower energy density. Among anode materials for SIBs, such as carbonaceous materials, 34,35 metal oxides/suldes, 36 etc., hard carbon (HC) has a favorable Na cation storage capacity (250-300 mA h g À1 ), good rate capability (up to 10C) and a median voltage of 0.1 V. [37][38][39][40][41][42][43] In particular, the NVP/HC electrode system possesses a high theoretical operating voltage at 3.3 V, which further endows it with great potential to be used as a cathode for high-energy and low-cost SIFBs. 44,45 Liqiang Mai et al. 46 reported a SIFB based on a NASICON structured NVP cathode and poorly graphitized hard carbon anode, which exhibited a theoretical average voltage of 3.3 V and a substantial increase in the energy density (>20%) compared to bulk and bare NVP based full cells.
Here, we report a high-performance exible sodium-ion full battery (FSIFB). This FSIFB is assembled with binder-free composite lm (BFCF) electrodes prepared at 800 C without using conductive carbon and current collectors. Carbonized lter paper bers decorated with different electrochemical active materials are used as hard carbon bers, a exible supporting framework and a 3D conductive network of the composite lm electrodes. The different pre-sodiated anodes and the electrolyte additives are designed for well-matched FSIFBs. The challenge of this design is to retain efficient Na ion diffusion in cathode and anode electrodes simultaneously and thus, achieving ultralong cycle ability at a fast charging/ discharging rate. Several merits of this FSIFB design are as follows: (1) compared with other exible supporting framework materials, such as carbonized cellulose and polyvinylidene uoride, reduced graphene oxide (rGO), graphene foam (GF), carbon ber cloth (CFC), carbon cloth (CC), and stainless steel cloth (ESI Tables S1 and S2 †), the hard carbon bers (HCFs) from carbonized lter paper as a supporting framework material of FSIFBs show unique advantages, such as low cost, simple and scalable preparation method, high carbon content and surface area, chemical functionalization, well exibility and conductivity, shape diversity, light weight, non-toxicity, unique morphology, good coordination between the cathode and anode and recyclability; (2) the HCF increases the active constituent part, charge reaction and Na + storage sites of NVP, directly resulting in a signicant improvement of the Na + transportation and the conductivity of the composite cathode; (3) the exible cross-linked porous framework of HCF and the porous structure of NVP in the BFCF-NVP/HCF not only are favourable for Na + insertion/desertion during the charging/ discharging processes, but also offer an elastic buffer to accommodate the volume change of NVP, resulting to an excellent cycle performance; (4) being free of an insulating binder and other additives, avoiding "dead volume" within the electrode; (5) porous NVP coated highly conductive HCFs for improving transport of Na + and electrons; (6) a HCF core/NVP shell structure for helping electron transport and Na + migration in BFCF; (7) the pre-sodiated anodes and the electrolyte additives designed for improving electrical transport behaviours and the dynamics of FSIFBs; and (8)  Ltd.) were added into another beaker and stirred for 0.5 h. Lastly, the above solutions were mixed together and the mixed solution was heated and evaporated at 70 C. The resulting gel was dried at 120 C. The obtained dark green precursor was sintered in two steps at 350 C for 4 h and then at 800 C for 8 h under a N 2 atmosphere.
2.1.2 Synthesis of BFCF-NVP/HCF cathodes. A lter paper was used as a support material. Firstly, the lter paper was spread on a glass plate and an appropriate amount of hydrazine hydrate was dripped onto the lter paper, then it was covered with another glass plate. Subsequently, it was dried at 120 C for 12 h. Second, an appropriate amount of NVP precursor was dispersed in N-methylpyrrolidone (NMP) to form a slurry. Then the slurry was coated on the lter paper aer processing. The coating thickness is 100, 150 and 200 mm, respectively. Owing to the 3D porous structure of lter paper, the slurry easily penetrated into it. Then, the lter paper coated with the slurry was dried at 60 C. The nal samples were punched into discs with a diameter of 14.0 mm and were sintered at different temperatures (700, 750 and 800 C) for 6 h, 8 h and 10 h in a N 2 atmosphere to form BFCF-NVP/HCF cathodes.
2.1.3 Synthesis of different anodes. The graphene/SiC nanocomposite (GN/SiC) sample was prepared following our previously reported method. 47 The treatment method of lter paper was the same as in the rst step for the synthesis of the BFCF-NVP/HCF cathodes. The preparation method of GN/SiC/ HCF and the PGN/SiC/HCF anodes can be seen in ESI Fig. S1. † The NaVOPO 4 anode was synthesized by using adenosine triphosphate (ATP) templates. First, 1.2 mmol ATP was added to 50 ml distilled water in a 70 C water-bath, which formed solution A. Then, 2.4 mmol NH 4 VO 3 and 0.9 mmol ascorbic acid were added to 50 ml distilled water, which was stirred for 20 minutes to form solution B. Finally, solutions A and B were mixed together, which was transferred to a 100 ml Teon-lined autoclave and kept at 100 C for 21 h. Subsequently, the brown mixture from hydrothermal treatment was dried at 80 C for 12 h to form a xerogel. The xerogel was sintered at 350 C for 4 h and then at 800 C for 12 h under a N 2 atmosphere.

Characterization
The characterization methods of samples can be seen in ESI S4. †

Electrochemical evaluation
The electrochemical properties of the BFCF electrodes were tested aer assembling coin-type cells (CR2032) in a glove box lled with pure argon. For the half-cell test, sodium metal was used as the counter and the reference electrode, a solution of 1 M NaClO 4 in EC : PC (1 : 1, v/v) or 1 M NaClO 4 in EC : PC (1 : 1, v/v) + 5% FEC as the electrolyte, and a Whatman glass microber lter (Grade GF/F) as the separator. For pouch-type FSIFBs, BFCF-NVP/HCF was used as the cathode and different electrodes as anodes, and a exible water-proof case made of aluminum-plastic lm (DNP, Japan) was used. The battery was aged for 12 h before testing to ensure full absorption of the electrolyte into the electrodes. Galvanostatic charge/discharge measurements were performed with a Channels battery analyzer (CT3008W). Electrochemical impedance spectroscopy (EIS) and cyclic voltammetry (CV) measurements were performed on a PARSTAT 2263 electrochemical workstation. EIS were recorded with frequencies ranging from 100 kHz to 10 MHz with an AC signal of 5 mV amplitude as the perturbation. The voltage range of CV measurements was 2.0-4.3 V and the scan rate was from 0.1 to 0.6 mV s À1 . All the tests were performed at room temperature.
We also provide the videos of the fabrication process for the pouch-type FSIFBs with a superior water-proof case to demonstrate the simple operability and potential applications of FSIFBs (vitro S1, see ESI S5 †).

Electrochemical performances of the pouch-type FSIFBs
Using the binder-free composite lm (BFCF) electrodes without using conductive carbon and current collectors, pouch-type FSIFBs were assembled and tested with a mass ratio of cathode/anode of about 2.56. To demonstrate the application of FSIFBs assembled with the BFCF-NVP/HCF cathode and the PGN/SiC/HCF anode, they were used to power a commercial red light-emitting diode (LED) (2.4 V, 0.3 W). The schematic illustration for their fabrication and microstructure is shown in Fig. 1a, showing electron transport and Na ion diffusion in the HCF core/NVP shell structure. Fig. 1b shows the schematic diagram of the FSIFB, showing that it lit up 7 LED lamps. To prove that it is a "exible" battery, the exibility of the cell was tested. The lit LED bulb driven by the FSIFB aer different bending cycles at a bending angle of 30-90 demonstrates different luminosities (ESI Fig. S2 †). As demonstrated in Fig. 1c, d and Video S2 of ESI S5, † a LED bulb can also be powered even when the battery was bent aer 1600 cycles. No electrical failure was observed during the bending process of the cell. Fig. 1c shows that the luminosity of the LED lamp is still present even aer the cell had been severely bent. Fig. 1e shows that there was no leakage when the cell was severely bent in water, see Video S2 of ESI S5. † What's more, when the pouch-type FSIFB aer 1600 bending cycles was disassembled, its BFCF-NVP/HCF cathode at different bending angles was still intact (ESI Fig. S3 and Video S2, ESI S5 †). The results show that the FSIFB has good exibility, similar to studies on exible batteries. 48,49 Fig . 2 shows the sodium storage performances of the pouchtype FSIFBs assembled with the BFCF-NVP/HCF cathode and the different anodes at different current rates of the cathode (Table S3 †). The charge/discharge curves of the FSIFBs are illustrated in Fig. 2a. Compared with the pre-sodiated HCF (PHCF) and NaVOPO 4 anodes, the FSIFB assembled with the PGN/SiC/HCF anode not only exhibits the highest output voltage of 3.34 V and lowest polarization, but the highest specic energy density, at 0.5 A g À1 reaching up to 234.1 W h kg À1 (Fig. 2b), much better than that of other SIBs reported in the literature (Table S2 †). Fig. 2c shows the charge/ discharge curves of the pouch-type FSIFB assembled with the BFCF-NVP/HCF cathode and the PGN/SiC/HCF anode at different current rates from 0.05 A g À1 to 20 A g À1 , exhibiting a small degree of polarization and the small decay of capacity at low current rates 0.05-0.5 A g À1 . In particular at ultrahigh current rates of 15 and 20 A g À1 , the discharge capacities still maintained at 51.7 and 27.7 mA h g À1 , respectively. Based on the above analysis, the electrochemical properties of the pouchtype FSIFBs, especially the rate capability and cycling stability, are signicantly affected by the pre-sodiated anode, which can be facilely controlled via the fabrication process. The results show that the BFCF-NVP/HCF cathode is well matched with the PGN/SiC/HCF anode in this FSIFB. More importantly, this pouch-type FSIFB not only exhibits a high output voltage of 3.34 V, high energy density (234.1 W h kg À1 at 0.05 A g À1 ) and high coulombic efficiency (approaching 100%), but also ultralong cyclability. Fig. 2d and e show the long-term cycling performances and coulombic efficiencies of the different FSIFBs (FSIFB-1 and FSIFB-2 for the repeated data that are further optimized) assembled with the BFCF-NVP/HCF cathode and the PGN/SiC/HCF anode, respectively. The initial specic capacities of FSIFB-1 and FSIFB-2 for repeated data are 81.87 and 88.93 mA h g À1 at 10 mA g À1 , respectively. Fig. 2d shows the long-term cycling stability (over 2905 cycles at 0.5 A g À1 ) of the FSIFB-1, which corresponds to 0.42% capacity decay per cycle. Even aer 1000 cycles at a high current rate of 5 A g À1 , the FSIFB-2 for repeated data could still display a specic discharge capacity of 30 mA h g À1 (Fig. 2e), but its cycle stability decreases due to its inherent low electrical conductivity of NVP, volumetric expansion/shrinkage during charge and discharge, and the solubility of the electrolyte. 50 These show unprecedented improvement in deformability and internal short-circuit prevention of cells, which offers great promise for nextgeneration versatile exible electronics. The remarkably enhanced cycling stability and rate capability of this FSIFB are ascribed to the synergistic effects between the BFCF-NVP/HCF cathode and the PGN/SiC/HCF anode. The highly conductive HCF can act as the conductive core to provide efficient electron transport. The 3D macroporous architectures and the hierarchical nanostructures in BFCF can signicantly facilitate the Na ion diffusion and enhance the contact area.

Na-migration kinetics study of the pouch-type FSIFBs
To explore the electrochemical performance and Na-migration kinetics of the FSIFBs assembled with the BFCF-NVP/HCF cathode and the different anodes, CV and EIS were performed. The CV curves of the FSIFBs assembled with the different anodes show signicant differences in the electrochemical reactions (Fig. 3a). It is obvious that the FSIFBs assembled with the pre-sodiated HCF (PHCF) and the PGN/SiC/ HCF anodes can exhibit an evident redox couple, which is associated with the reversible transformation of V 3+ /V 4+ accompanied by the insertion and extraction reaction of Naions from the NVP lattice matrix. 29 The oxidation peak and the corresponding reduction peak for the FSIFB assembled with the PGN/SiC/HCF anode are located at around 3.39 V and 3.12 V, respectively, showing stronger current intensity and smaller polarization than those of the FSIFBs assembled with other anodes. Fig. 3b shows the Nyquist plots of fresh FSIFBs assembled with the different anodes from 100 kHz to 0.01 Hz. They are composed of a semicircle at high-frequency and a long oblique line at low-frequency. According to a simple adsorption model, 51 the semicircle is related to the adsorption of Na ions from solvent on the particle surface of the electrode and charge balance, while the oblique line is related to the solid state diffusion of Na ions in the electrode. The insertion process of Na ions in a NVP/HCF single particle for the BFCF-NVP/HCF cathode is shown in Fig. 5b. The Na + insertion reaction contains a three-step process: (1) Na ions from the solvent are adsorbed on the NVP/HCF particle surface; (2) electrons in HCF enter the valence bands of NVP and diffuse into the surrounding Na sites to make charges to balance; (3) nally, both the Na ions enter the lattice of NVP and the balancing electrons co-diffuse into the inside of NVP. The calculated value (219 U) of R ct (charge transfer resistance) of the FSIFB assembled with the PGN/SiC/HCF anode is much smaller than that (1296 U) of the FSIFB assembled with the NaVOPO 4 anode, showing that the PGN/SiC/HCF anode plays an important role in making charge transfer easy.
The CV curves of the FSIFB assembled with the PGN/SiC/HCF anode at various scan rates are presented in Fig. 3c. With increasing scan rate, the oxidation and reduction peaks slightly move in positive and negative directions, respectively, revealing the good position repeatability of CV peaks and better electrochemical reversibility of the electrode reaction. 33 This phenomenon means larger polarization at high scan rates, which can be explained by the classical Randles-Sevcik method (eqn (1)). 52,53 Moreover, the diffusion coefficient (D, cm 2 s À1 ) of sodium ions in different electrodes can also be calculated from eqn (1).
where I p is the peak current (A), n is the number of electrons in the reaction (n ¼ 2 for NVP), A is the active surface area of the electrode (here 4.00 cm 2 for NVP), n is the scan rate (V s À1 ), and C Na is the concentration of Na ions in NVP (1.392 Â 10 À2 mol cm À3 ). Fig. 3d shows the linear tting proles between the peak current density (I p ) and the square root of scan rate (v 1/2 ) from CV proles (Fig. 3c). The oxidation and reduction currents exhibit a good linear relationship with v 1/2 , indicating a diffusion controlled process during the sodium storage in electrodes. Through the calculation, the values of D Na for the oxidation and reduction of the FSIFB assembled with the PGN/ SiC/HCF anode are 8.046 Â 10 À13 and 1.3102 Â 10 À12 , respectively, indicating a faster reduction reaction. Fig. 3e shows the EIS curves of the FSIFB assembled with the BFCF-NVP/HCF cathode and the PGN/SiC/HCF anode aer 10 cycles at different potentials at a current rate of 0.2 A g À1 . According to the surface layer model, 54 two depressed semicircles in the high-to-medium frequency region can be assigned to the migration of Na + through the solid electrolyte interphase (SEI) lm (4 in Fig. 5c) and the charge transfer (2 in Fig. 5c), respectively; and the sloping lines in the low frequency region are attributed to the impedance of Na-ion diffusion in the solid phase (3 in Fig. 5c). The rst semicircle (R SEI , resistance of Na-ion diffusion via SEI lm) in the high frequency region and a dot in the ultrahigh frequency region (ohmic resistance R e , electron resistance of the active material) are almost not changed with the electrode potential, while the second semicircle (R ct , resistance of charge transfer) in the medium frequency region varies with the potential signicantly. The calculated values of R ct and R p (polarization resistance) are plotted with the charge capacity in Fig. 3f. It can be seen that the change of R ct and R p is small with charge capacity or potential (charging state), revealing excellent stability. Fig. 3g and 4a illustrate the charging/discharging curves of the pouch-type FSIFB assembled with the PGN/SiC/HCF anode at different bending angles and a current rate of 0.5 A g À1 . It can be seen that the discharge capacity of the FSIFB bent from 180 to 30 remains almost constant, revealing that the electrical stability of the fabricated FSIFB is hardly affected by external bending stress. Fig. 4b shows the charge-discharge curves of this FSIFB at 0.5 A g À1 before and aer different bending cycles at a bending angle of 30-90 , respectively. The discharge capacity of the FSIFB is 52.6 mA h g À1 before bending cycles, is 35.8 mA h g À1 aer 1600 bending cycles (Fig. 4b), and its capacity retention is 67% (ESI Fig. S4 †). The aforementioned results clearly uncover the kinetics superiority of the FSIFB assembled with the BFCF-NVP/ HCF cathode and the PGN/SiC/HCF anode. Fig. 5a shows the Nyquist plots of the fresh FSIFB and the FSIFB aer 12 cycles at different potentials from 100 kHz to 0.01 Hz. The Nyquist plot of the fresh FSIFB at 2.5 V is composed of a semicircle at high-frequency and a long oblique line at low-frequency, which can be explained using a simple adsorption model (Fig. 5b). The Nyquist plot of the FSIFB aer 12 cycles at 2.9 V is composed of two semicircles and a long oblique line, which can be explained by the surface layer model (Fig. 5c). Fig. 5d shows the Nyquist plots of the FSIFB assembled with the BFCF-NVP/HCF cathode and the PGN/SiC/HCF anode aer different cycles at 0.2 A g À1 and 3.17 V. All of these Nyquist plots consist of two medium-to-high frequency depressed semicircles and a low-frequency linear part. According to the SEI model, 55 the resistance (R SEI ) and capacitance (C SEI ) of the SEI lm can be calculated using the following equations: where r, 3 and l are the conductivity, dielectric constant and thickness of the SEI lm, respectively. S is the supercial area of the electrode. If r, 3 and S are not changed much, the increase of R SEI and the decrease of C SEI mean the increase of thickness (l) of the SEI lm. For the completely uniform SEI lm, the current density (i) is given by where D e is the diffusion coefficient of electrons in the SEI lm. t is the time and when t ¼ 0, l ¼ l 0 . C 0 is the electron concentration in the SEI lm. F is the Faraday constant, and K is a constant. Aer integration, the following formula is obtained.
Eqn (6) is the parabola theorem of SEI lm growth. By this theory, the diffusion coefficient of electrons (D e ) and the electron concentration (C 0 ) in the SEI lm increase with the increase of the thickness (l) of SEI lm growth. In Fig. 5d the rst semicircle diameter (R SEI , from 83.8 to 86.4 U) in the high frequency region increases with the increase of the cycle number from the 2nd cycle to the 27th cycle, which means the progressive growth of the SEI lm and this increased thickness is caused by the continuous deposition of Na ions. However R SEI (from 86.4 to 86.6 U) is almost not changed with increasing the cycle number from the 27th cycle to the 36th cycle, indicating the stop of SEI lm growth and the formation of an SEI lm on the cycled electrode surface. The straight lines in the low frequency region of Fig. 5d represent the Warburg impedance (Z w ), which can be used to calculate the Na ion diffusion coef-cient (D Na ) of the FSIFBs aer different cycles (ESI Table S4 †). The result demonstrates that the D Na increases with the increase of the cycle number because of the increase of the diffusion coefficient of electrons (D e ) and the electron concentration (C 0 ) in the SEI lm. The formation of a stable and uniform SEI lm can effectively inhibit the self-discharge and the volume change of the cycled electrode, leading to a superior cycling performance (Fig. 2d and e). 56 The insertion/desertion process of Na ions in NVP may be written as where x is the degree of embedded sodium. Because Na 3 V 2 (PO 4 ) 3 only has about two Na extraction/insertion from/ into the unit structure, the maximum of x is 0.67.
The resistance of charge transfer (R ct ) may be written in the general form where x is the degree of embedded sodium. a is the symmetry factor of the electrochemical reaction. n is the number of electrons transferred in the electrochemical reaction. R is the molar gas constant. T is the thermodynamic temperature. k o is the rate constant of the standard reaction. c T is the maximum embedded concentration of Na + in the electrode. M + is the Na + concentration in solution. If the insertion/ desertion process of Na ions in the BFCF-NVP/HCF cathode is reversible, a ¼ 0.5, eqn (7) can be transformed as: According to eqn (9), when x ¼ 0.5, R ct has a minimal value (82 U at 3.19 V in Fig. 3f); when x < 0.5, R ct increases with the decrease of x; when x > 0.5, R ct increases with the increase of x. That is to say, R ct presents an increase tendency aer decrease with the increase of polarization potential of the electrode from 3.19 V to 3.52 V (Fig. 3f). Fig. 5d also shows that the second semicircle diameter (R ct ) in the medium frequency region at 2.9 V increases with the increase of the cycle number from the 2nd cycle to the 36th cycle signicantly. These results show that the FSIFB can maintain a high degree (x > 0.5) of embedded sodium in the insertion/desertion cycling process of Na ions. Fig. 5e shows the schematic of Na ion transport across the interphases and resistance contributions in the FSIFB. Fig. 5f shows the Thevenin equivalent circuit model 57 of this FSIFB. This model is comprised of an ideal voltage source, ohmic resistance (R s ) of whole reaction system and a series of branches C n (n ¼ 1, 2, 3, 4, 5, 6). V oc represents the open-circuit-voltage of the cell at partial equilibrium as a function of state-of-charge (SOC). According to previously published work, 58 W is the Warburg impedance which is related to the diffusion of Na ions in the solid matrix. R ct corresponds to the charge-transfer resistance. R s includes the interparticle contact resistance, electrolyte resistance and other physical resistances between the electrolyte and electrodes. V k is the cell's terminal voltage and i k is the throughput current. C n is the double layer capacitance on the electrode surface. They represent the ion transport across the six interphases, such as (1) the interphase between HCF and NVP, R ct1 through HCF and insertion capacity (C 1 ), (2) the interphase between NVP and the solid electrolyte interphase (SEI), R ct2 through NVP and insertion capacity (C 2 ), (3) the interphase between the electrolyte and SEI, R ct3 through SEI and insertion capacity (C 3 ), (4) the interphase between the electrolyte and SEI, R ct4 through SEI and insertion capacity (C 4 ), (5) the interphase between the SEI and GN/SiC, R ct5 through GN/SiC and insertion capacity (C 5 ), and (6) the interphase between GN/SiC and HCF, R ct6 through HCF and insertion capacity (C 6 ). According to the Nyquist plots in Fig. 5g and h, the folded FSIFB shows a semicircle with a smaller diameter (27 U) than that (96 U) of the lm FSIFB in the high-medium frequency regions. This indicates that the FSIFB exed to desirable tension in one direction during operation has improvement in the chargetransfer characteristics due to better particle-to-particle contact in the folded electrodes at a bending angle of 120 . 59 In addition, the distance of anode/cathode electrodes in the full cell has an important inuence on the resistance and the folded FSIFB may have a closer distance in the middle bending position, leading to the smaller resistance for the full cell.
To further investigate the structure change, the XRD patterns and SEM images of the BFCF-NVP/HCF cathode and the PGN/ SiC/HCF anode before and aer different cycles and charging at 0.5 A g À1 are shown in Fig. 6. The reversible insertion/ desertion process of Na ions in the NVP crystal structure causes a phase transition of NVP (eqn (7)) and the formation of an SEI lm. Aer charging, when two Na ions can desert from the Na 3 V 2 (PO 4 ) 3 crystal structure, rhombohedral Na 3 V 2 (PO 4 ) 3 is transformed into its sodium extracted phase of NaV 2 (PO 4 ) 3 . Aer discharging, when two Na ions can insert into the extracted phase, it becomes Na 3 V 2 (PO 4 ) 3 . Therefore, in the reversible phase transition process these extracted phases all have electrochemical activity. However, some inactive transformation products and the SEI lm were also formed with the increase of the cycle number because of the volume change and collapse of some Na sites caused by a phase change, which leads to capacity decay. As seen in Fig. 6a and b, there is signicant difference in the diffraction peaks of the BFCF-NVP/ HCF cathode (Fig. 6a) and the PGN/SiC/HCF anode (Fig. 6b) before and aer cycles and charging. The XRD patterns of the BFCF-NVP/HCF cathode aer different cycles can be well indexed to the new phase of C 10 H 16 O 4 , which has a similar SEI composition to those that have been reported. 60 This could be ascribed to the formation of an SEI lm on the cathode surface aer cycling, and the extracted phase of NVP was covered with the SEI lm. Compared with the XRD pattern aer 27 cycles, the diffraction peaks in the XRD pattern aer 3000 cycles have only minor changes, which shows that the structure of the SEI lm formed on the surface of the BFCF-NVP/HCF cathode is stable in the charge/discharge cycles, preventing the NVP particles from peeling off. In the pre-sodiated BFCF-GN/SiC/HCF anode aer 2905 cycles and charging, the strong diffraction peaks of graphene and SiC disappear, and the new phases of sodium oxalate Na 2 C 2 O 4 (JCPDS no. 49-1816) and methyl acrylate C 4 H 6 O 2 (JCPDS no. 36-1685) are formed. Furthermore, comparing the SEM images of the BFCF-NVP/HCF cathode in Fig. 6c and d with those in ESI Fig. S11, † the electrode aer 2905 cycles and charging shows that the NaVP 2 O 7 particles still tightly adhere to the HCF substrate and are connected closely with each other by conductive carbon (Fig. 6d), but obvious cracks appear in the electrode (Fig. 6c). The NaVP 2 O 7 particles have a smaller particle size (Fig. 6d), which facilitates shortening of Na + -ion diffusion paths and accelerates Na + intercalation/deintercalation. Fig. 6e shows that the presodiated BFCF-GN/SiC/HCF anode aer 2905 cycles and charging still maintains the morphology of HCF, and the Na 2 C 2 O 4 and C 4 H 6 O 2 nanoparticles also tightly adhere to the HCF substrate (Fig. 6f). Therefore, the HCF membrane electrode integrated with the active material and current collector is tolerant to the mechanical stress during cycling, which can keep the stable structure, and hence lead to high rate capability and cycling stability.

Electrochemical performance characterization of the sodium ion half-cells
We have successfully developed high-performance pouch-type FSIFB based on the binder-free composite lm (BFCF) electrodes. The electrochemical performance of BFCF electrodes was examined in a sodium ion half-cell (SIHC) form. ESI Fig. S5 † shows the electrochemical performances of the BFCF-NVP/HCF cathodes synthesized with different temperatures in the SIHC and 1 M NaClO 4 electrolyte (EC : PC (1 : 1, v/v) + 0% FEC). The rst discharge capacities of the BFCF-NVP/HCF cathodes synthesized at 700, 750 and 800 C at 0.1C were 74.24, 98.59, and 94.94 mA h g À1 , respectively. As shown in Fig. S5a-c, † the decay degree (about 18 mA h g À1 ) of discharge capacity for the BFCF-NVP/HCF synthesized at 750 C at current rates from 0.1C (1C ¼ 118 mA g À1 ) to 10C was signicantly less than that (about 33 and 29 mA h g À1 ) synthesized at 700 and 800 C, which might have resulted from the fast electrochemical activation process in BFCF-NVP/HCF. The BFCF-NVP/HCF cathode synthesized at 750 C not only has a at potential plateau of 3.4 V at 0.1C (ESI Fig. S5b †), corresponding to the redox couple of V 4+ /V 3+ , 61,62 but also showed much better rate performance during the whole cycling process, especially at high current rates (ESI Fig. S5d †). For instance, it maintained a discharge capacity of 70 mA h g À1 at 20C. But the BFCF-NVP/HCF cathode synthesized at 700 C just kept a discharge capacity of 35 mA h g À1 at 20C (ESI Fig.-S5a †) and there's no signal for the BFCF-NVP/HCF cathode synthesized at 850 C at 20C (ESI Fig. S5c †). ESI Fig. S6 † shows the charge-discharge curves of the BFCF-NVP/HCF cathodes synthesized with different sintering times at 750 C, showing that the BFCF-NVP/HCF cathode synthesized with a sintering time of 8 h has a better rate capability. So the sintering time and temperature are important to determine the performance of the nal electrodes.
The electrolyte additive such as uoroethylene carbonate (FEC) also has an important inuence on the electrochemical performance of SIBs. 63 Fig. 7 shows the effects of two different NaClO 4 electrolytes on the electrochemical performances of the BFCF-NVP/HCF cathode synthesized at 750 C in the SIHC. The results show that the FEC electrolyte additive obviously improved the high-rate capability and long-term cycling stability of the SIHC. As shown in Fig. 7a, the BFCF-NVP/HCF cathode in the electrolyte with 5% FEC additive can deliver a super high-rate capability, showing the discharge capacities of 98.66 and 88.30 mA h g À1 at 20 and 50C, respectively. Even at 100 and 150C, it can also deliver the discharge capacities of 70.16 and 60.40 mA h g À1 , respectively, while the BFCF-NVP/ HCF cathode in the electrolyte without additive (0% FEC) has only a discharge capacity of 70.0 mA h g À1 at 20C and almost no capacity above 20C (Fig. 7b). By comparing the CV curves of the BFCF-NVP/HCF cathode in different electrolytes (Fig. 7c), it is found that the FEC electrolyte additive can efficiently restrain the decomposition of the electrolyte component (a small reduction current peak appears near 3.3 V in the curve without FEC). 64 Through the calculation, the values of D Na for oxidation and reduction in the EC : PC + 5% FEC electrolyte are 1.096 Â 10 À11 and 8.03 Â 10 À12 , respectively, while the values of D Na for oxidation and reduction in the EC : PC + 0% FEC electrolyte are 7.331 Â 10 À12 and 2.42 Â 10 À12 , respectively. In addition, the BFCF-NVP/HCF cathode in the electrolyte with 5% FEC additive has better cycling stability than that in the electrolyte without additive (0% FEC) as shown in Fig. 7d. The BFCF-NVP/HCF cathode in the electrolyte with 5% FEC additive retains the capacity of 78.30 mAh g À1 at 20C aer 150 cycles with a high capacity retention of 88.67%. Fig. 7f shows the long-term cycling stability and the coulombic efficiency of the BFCF-NVP/HCF cathode in the electrolyte with 5% FEC additive, which retains a capacity of 49.43 mA h g À1 aer 1250 cycles at 150C. Fig. S5h † shows the cell with 5% FEC retains a capacity of 30.78 mA h g À1 aer 2905 cycles at 150C, indicative of a very low capacity fading of 0.0098% per cycle. However, aer 1500 cycles at 150C, its coulombic efficiency becomes unstable, due to the polarization, the decomposition of electrolyte and sodium metal, the formation of side products, and so on. 65 Fig. 7e shows the EIS curves of the fresh cathodes in different electrolytes, showing the smaller R ct of the BFCF-NVP/HCF cathode in the EC : PC + 5% FEC electrolyte. ESI Fig. S7a † shows the rate capability of the BFCF-NVP/HCF cathodes synthesized at 750 C with different coating thicknesses in SIHC and 1 M NaClO 4 electrolyte (EC : PC (1 : 1, v/v) + 5% FEC). The results show that the BFCF-NVP/HCF cathode with a coating thickness of 150 mm possesses the best rate capability. To understand the obtained superior electrochemical performances, more analyses of CV and EIS for the BFCF-NVP/HCF cathodes synthesized at 750 C with a thickness of 150 mm in the EC : PC + 5% FEC electrolyte were performed (ESI Fig. S7b-d †).
The structural compositions of the hard carbon ber (HCF) sample (ESI Fig. S8a and b †) synthesized by pyrolysis of lter paper at 750 C for 8 h and the graphene/SiC (GN/SiC) sample (ESI Fig. S8d †) are characterized by X-ray diffraction patterns in our previous report. 47 The graphene/SiC (GN/SiC) composite nanosheets were synthesized through an in situ thermochemical method at 800 C by using soda papermaking black liquor (SPBL) as a raw material. The electrochemical performance characterization of different anodes in the sodium ion half-cell (SIHC) form is shown in ESI Fig. S8c, e and S9. † The results in ESI Fig. S9a and b † show that the GN/SiC anode has poor electrochemical performances due to the formation of a solid electrolyte interface (SEI) and irreversible Na insertion into the SEI. So we used carbonized lter paper bers decorated with GN/SiC composite nanosheets (GN/SiC/HCF) as a exible supporting framework to prepare a BFCF anode, and the presodiation of the BFCF anode was performed prior to cell fabrication to provide rich Na ions for its depassivation. The results show that the PGN/SiC/HCF anode delivers a reversible capacity of 501 mA h g À1 at a current rate of 10 mA g À1 , which is higher than that of the GN/SiC (Al) with a binder and Al current collector and the GN/SiC/HCF without pre-sodiation (ESI Fig. S9a-c †). In particular, its long cycling performance was greatly improved at a high current rate of 1 A g À1 due to the depassivation of the GN/SiC/HCF, showing a capacity of 234.33 mA h g À1 aer 791 cycles with a high capacity retention of 91%, exhibiting a high coulombic efficiency (ESI Fig. S9d †).

Formation mechanism and characterization of BFCF electrodes
ESI Fig. S10 † schematically illustrates the preparation processes of the NVP precursor and BFCF-NVP/HCF cathode. First, NVP powders were prepared by a sol-gel method and dispersed in Nmethylpyrrolidone to form a slurry. Second, the slurry was coated on a lter paper spread over a glass plate, and then it was dried and sintered to form the BFCF-NVP/HCF cathode. The unique cellulose structure of lter paper was turned into a 3D conductive network framework of HCF and porous NVP was evenly coated on the HCF framework via the synthesis.
X-ray diffraction (XRD), Raman spectroscopy, N 2 adsorption and desorption isotherm measurements, scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS) of the BFCF-NVP/HCF cathodes synthesized at different temperatures were performed to investigate their composition and structure (Fig. 8). As shown in Fig. S10, † the XRD patterns of the BFCF-NVP/HCF synthesized at different temperatures all exhibit the same diffraction peaks as the NVP/C blank sample (Fig. 8a), corresponding to a rhombohedral NASICON structure of NVP with JCPDS card no. 53-0018. 46 The Raman spectrum (Fig. 8b) and the deconvoluted Raman spectrum (Fig. 8c) of the BFCF-NVP/HCF cathode synthesized at 750 C reveal the D band (1347 cm À1 ) and G band (1590 cm À1 ) with a ratio of I D /I G ¼ 1.19, indicating that the carbon in the BFCF-NVP/HCF is disordered hard carbon. 66 The pore structure of the BFCF-NVP/HCF synthesized at 750 C was elucidated by nitrogen adsorptiondesorption isotherms. Fig. 8d shows the type-IV adsorptiondesorption isotherm and distinct H3-type hysteresis, indicating the existence of uneven slit-shaped holes. Fig. 8e shows that the pore-size distribution of the BFCF-NVP/HCF is in the range of mesopores (5-30 nm). The mesoporous structure of the BFCF-NVP/HCF can also be observed from the SEM image in Fig. S12f. † The morphology of the BFCF-NVP/HCF cathode synthesized at 750 C is shown in Fig. S12, † displaying the core/shell structure of porous NVP coated highly conductive hard carbon bers. The accurate carbon content in the BFCF-NVP/HCF synthesized at 750 C was determined using a Vario EL III CHN elemental analyzer (ESI Table S5 †). The results show that the mass ratio of NVP : HCF in the BFCF-NVP/HCF is 55.6 : 44.4. In this work, the total mass of the BFCF-NVP/HCF is 4.5 mg, so the actual mass loading of NVP active material is about 2.34 mg cm À2 , which is much higher than that in a traditional electrode supported on Al foil (NVP/C@Al, about 1.6 mg cm À2 ). 65 The high loading of NVP active material is benecial to obtain high volume specic capacity in the cell. The high resolution transmission electron microscopy (HRTEM) images (ESI Fig. S13 †) of the BFCF-NVP/HCF sample synthesized at 750 C show that the core diameter of single HCF is about 60 nm, and the thickness of the NVP shell is about 30 nm. Moreover, the selected area electron diffraction (SAED) patterns in ESI Fig. S13g and h † show that some NVP crystal particles have a super lattice structure with the different interplanar spacings, which indicates that HCF can induce the nucleation and growth of NVP crystal particles and form a super lattice structure in the synthesis. The super lattice structure has abundant reactive sites of electrons and Na + in the quantum wells due to quantum connement and size effects. 66

Conclusions
In summary, we have successfully prepared exible and binderfree composite lm (BFCF) electrodes without using conductive carbon and current collectors for cheap exible sodium-ion full batteries (FSIFBs). This BFCF is supported on a carbonized lter paper ber matrix with an effectively conductive 3D network. The 5% uoroethylene carbonate (FEC) electrolyte additive obviously improved the rate performance of the BFCF cathode based on porous Na 3 V 2 (PO 4 ) 3 (NVP) coated hard carbon bers (HCF). Even at a super high-rate of 150C (equivalent to discharge within 24 seconds), it can also deliver a discharge capacity of 60.40 mA h g À1 , which is maintained at 30.78 mA h g À1 aer 2903 cycles. Pre-sodiated BFCF anodes can signicantly increase its reversible capacity and rate capacity. The pre-sodiated graphene/SiC/HCF (PGN/SiC/HCF) anode gives a highly reversible capacity of 501 mA h g À1 at 10 mA g À1 and an excellent rate capacity of up to 100 mA h g À1 at 20 A g À1 . Aer 791 cycles, it can still maintain a discharge capacity of 234.33 mA h g À1 at a high current rate of 1 A g À1 . More importantly, compared with traditional electrodes supported on Al foil, the optimized FSIFB assembled with the BFCF-NVP/HCF cathode and the PGN/SiC/HCF anode delivers both high-output voltage (3.34 V) and high energy density (234.1 W h kg À1 at a high-rate of 0.5 A g À1 ), ultralong cyclability (over 2905 cycles at 0.5 A g À1 and 1000 cycles at 5 A g À1 ) and high coulombic efficiency (approaching 100%). Unexpectedly, the electrochemical performances of the FSIFB were not inuenced when the battery was under various bending and twisting conditions. A discharge capacity of 35.8 mA h g À1 was achieved for this FSIFB aer 1600 bending cycles at a bending angle of 30-90 at 0.5 A g À1 , and its capacity retention is 67%, which has not been reported. This work provides an effective way to develop exible sodium-ion batteries by using bendable, low-cost electrode materials with excellent electrochemical performances.

Conflicts of interest
There are no conicts to declare.