Low‐Temperature Carbonized Nitrogen‐Doped Hard Carbon Nanofiber Toward High‐Performance Sodium‐Ion Capacitors

Carbon nanofiber (CNF) was widely utilized in the field of electrochemical energy storage due to its superiority of conductivity and mechanics. However, CNF was generally prepared at relatively high temperature. Herein, nitrogen‐doped hard carbon nanofibers (NHCNFs) were prepared by a low‐temperature carbonization treatment assisted with electrospinning technology. Density functional theory analysis elucidates the incorporation of nitrogen heteroatoms with various chemical states into carbon matrix would significantly alter the total electronic configurations, leading to the robust adsorption and efficient diffusion of Na atoms on electrode interface. The obtained material carbonized at 600 °C (NHCNF‐600) presented a reversible specific capacity of 191.0 mAh g−1 and no capacity decay after 200 cycles at 1 A g−1. It was found that the sodium‐intercalated degree had a correlation with the electrochemical impedance. A sodium‐intercalated potential of 0.2 V was adopted to lower the electrochemical impedance. The constructed sodium‐ion capacitor with activated carbon cathode and presodiated NHCNF‐600 anode can present an energy power density of 82.1 Wh kg−1 and a power density of 7.0 kW kg−1.


Introduction
In the past decades, lithium-ion batteries have received considerable attention due to the superiority in operating voltage, specific energy, self-discharge, and the safety. Nevertheless, elemental scarcity of lithium in the earth's crust (20 ppm) as well as the high price (US$5000 per ton) are the major concerns for its future sustainability, which makes researchers focus on cheap and available substitutes. [1,2] As the fourth most abundant metal element in the earth, the ubiquity of sodium in vast oceans and salt lakes also provides a high crustal content of 23 600 ppm and a price of US$135-165 per ton. [3][4][5] The redox potential of sodium is −2.7 V, which is similar to that of lithium, so the construction of sodium-based devices can be learnt from the fabrication experience of lithium-ion batteries. [6][7][8][9][10][11][12][13][14][15] In addition, unlike lithium, aluminum does not react with sodium to form alloys at low potentials, so inexpensive aluminum current collectors with lightweight can be used for sodium-ion batteries and sodium-ion capacitors (SICs). Compared with sodium-ion batteries, SICs have superior power density and outstanding cyclic life. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] Nevertheless, there exists a mismatch issue in kinetics between the cathode and anode, and it is crucial to enhance the rate property of the anode. Although graphite was widely utilized as intercalation anode in lithium-ion systems, it is not suitable to serve as active material in sodium-ion systems because the thermodynamical instability of sodium intercalation compound leads to a low specific capacity. Alternatively, amorphous carbon was chosen in sodium-ion systems. Extensive attention was paid to carbon nanofiber (CNF) due to its unique one-dimensional structure, good electrical conductivity, and self-supporting characteristics. [33] CNF not only immobilizes active materials but also compensates for the poor electrical conductivity of active materials, thereby improving the electrochemical performance.
Electrospinning, a typical method for preparing CNF, has attracted much attention due to its advantages of easy operation and high throughput. [34] Previous research found that the carbonization temperature in the range of 800-1500°C had a significant impact on the morphology, chemical composition, interlayer spacing, and electrochemical performance of CNF and demonstrated CNF with a diameter of 200-300 nm could provide a lithium-ion storage capacity of 350 mAh g −1 at 0.1 A g −1 . [35,36] These results suggest CNF is a versatile matrix for accommodating alkaline metal ions in the interlayer to harvest energy. Carbon nanofiber (CNF) was widely utilized in the field of electrochemical energy storage due to its superiority of conductivity and mechanics. However, CNF was generally prepared at relatively high temperature. Herein, nitrogen-doped hard carbon nanofibers (NHCNFs) were prepared by a lowtemperature carbonization treatment assisted with electrospinning technology. Density functional theory analysis elucidates the incorporation of nitrogen heteroatoms with various chemical states into carbon matrix would significantly alter the total electronic configurations, leading to the robust adsorption and efficient diffusion of Na atoms on electrode interface. The obtained material carbonized at 600°C (NHCNF-600) presented a reversible specific capacity of 191.0 mAh g −1 and no capacity decay after 200 cycles at 1 A g −1 . It was found that the sodium-intercalated degree had a correlation with the electrochemical impedance. A sodium-intercalated potential of 0.2 V was adopted to lower the electrochemical impedance. The constructed sodium-ion capacitor with activated carbon cathode and presodiated NHCNF-600 anode can present an energy power density of 82.1 Wh kg −1 and a power density of 7.0 kW kg −1 .
For this purpose, recently people explored CNF preparation via electrospinning and used them as active material of anode in sodium-ion systems. Jin et al. [37] investigated the effect of different carbonization temperatures on the performance of sodium-ion storage and concluded that 1250°C was the optimal between 800 and 1500°C. The CNF prepared by Chen et al. [38] had a sodium-ion storage capacity of 233 mAh g −1 at 0.05 A g −1 , and the retention was 97.7% after 200 cycles. Zhu et al. fabricated CNF with a nitrogen doping content of 11.21% at the carbonization temperature of 800°C and achieved a sodium-ion storage capacity of 293 mAh g −1 at 0.05 A g −1 , which still remained at 150 mAh g −1 after 200 cycles at 1 A g −1 . [39] Above results proved the validity of CNF by electrospinning protocol as robust sodium storage materials; however, the following issues involving CNFs prepared by electrospinning still need to be solved. First, the carbonization temperature is generally above 800°C. High carbonization temperature makes CNFs have a high degree of graphitization and low defect content, which is conducive to the improvement of Coulombic efficiency during the initial cycle. However, few contents of heteroatoms decrease the additional active sites and the sodium storage capacity accordingly. Second, the prepared CNFs lack several types of heteroatoms, especially pyridine nitrogen and pyrrole nitrogen. Nitrogen-doped carbon materials usually have different doping concentrations of pyridine nitrogen, pyrrole nitrogen, and graphitic nitrogen. Adjusting these nitrogen-doped structures can control the electrochemical performance of the material. Unfortunately, few works have been devoted to the elemental engineering of CNF and the intercalation chemistry of sodium ion in CNF-based electrodes.
Herein, nitrogen-doped hard carbon nanofibers (NHCNF) were prepared by adopting electrospinning technology and low-temperature carbonization process as shown in Figure 1. Different from the conventional high-temperature carbonization, low-temperature carbonization is adopted in this work. The advantages of low-temperature carbonization are listed below. First, the increased interlayer spacing is in favor of the improvement of sodium-ion reaction kinetics. Second, more heteroatoms are doped in the carbon matrix with various chemical states to change total electronic configurations. Furthermore, sloping capacity increases to facilitate the transport of sodium ions. Therefore, robust adsorption and efficient diffusion of Na atoms on electrode interface can be achieved. With high pyridine and pyrrole nitrogen doping content, NHCNF had excellent electrochemical performances. Subsequently, NHCNF was presodiated to 0.2 V to balance the energy output and electrochemical impedance before full cells were constructed. Finally, SICs constructed with presodiated NHCNF anode and AC cathode delivered good electrochemical performance.  Figure S1, Supporting Information. The difference of diameter derives from the carbonization temperature. Specifically, the diameter decreases with the enlargement of carbonization temperature, which can be visually observed from TEM images ( Figure S2, Supporting Information). The distribution of C, N, and O elements in NHCNFs is uniform from the mapping analysis of energy dispersive spectrometer ( Figure S3, Supporting Information). Besides, augmenting the carbonization temperature is beneficial to increase the content of C atoms in the material (Table S1, Supporting Information). The prepared NHCNFs possess highly short-range disordered microstructures with amorphous nature (Figure 1d-f). The interlayer spacing of NHCNF-400, NHCNF-600, and NHCNF-800 is 0.49, 0.47, and 0.42 nm, respectively, which shrinks as the carbonization temperature increases. Obviously, large interlayer spacing is beneficial to sodium-ion intercalation. Figure 3a shows the XRD patterns of NHCNF-400, NHCNF-600, and NHCNF-800. There are two broad characteristic peaks located at 25°and 43°, corresponding to the (002) and (100) planes of carbon materials, respectively. Figure 3b shows the Raman spectra of the prepared NHCNFs. Two characteristic bands, the D band and the G band, appearing at the wavenumber of 1350 and 1580 cm −1 , are related with the defects of the material and graphitized carbon. [40] The intensity ratio of D band to G band can quantitatively represent the disorder degree of NHCNFs. The I D /I G of NHCNF-400, NHCNF-600, and NHCNF-800 are 1.25, 0.84, and 0.58, respectively, indicating graphitization degree has a positive correlation with carbonization temperature. The prepared NHCNFs were also characterized by XPS to evaluate the chemical composition. Characteristic peaks located at binding energies of 285, 399, and 532 eV represent C 1 s, N 1 s, and O 1 s ( Figure S4, Supporting Information). The nitrogen content decreases as the carbonization temperature increases (Table S2, Supporting Information). Deconvolution of C 1 s and N 1 s is further shown in Figure 3c,d. C 1 s spectra can be deconvoluted into five sub-peaks, in which the main peak of C-C is located at 284.8 eV and peaks of C=N, C=O, C-N, and O-C=O are located at 285.4, 286.2, 287.1, and 288.1 eV, respectively. [41] The content of C-C, C=O, and O-C=O changes little, while there is a large fluctuation for the content of C=N and C-N, indicating that the carbonization temperature has a significant influence on the content of nitrogen atom as shown in Table S3, Supporting Information. Among them, NHCNF-600 possesses the highest C=N content and the lowest C-N content, suggesting that the bonding of nitrogen atoms in NHCNF-600 is mainly pyridine nitrogen. The results are consistent with N 1 s high-resolution XPS spectra, which can be deconvoluted into pyridinic nitrogen (398.7 eV), pyrrolic nitrogen (399.9 eV), and graphitic nitrogen (401.1 eV). [42] Previous report have validated that pyridinic and pyrrolic nitrogen located at the defects and edges of carbon materials help to increase the active sites and improve sodium storage capacity, while graphitic nitrogen located on the basal plane is harmful to the electrochemical stability during sodium storage. [43][44][45][46] Therefore, high content of pyridinic and pyrrolic nitrogen and low content of graphitic nitrogen contribute to the improvement of the electrochemical properties of sodium storage. As shown in Table S4, Supporting Information, the content of pyridinic nitrogen decreases with the rise of carbonization temperature, and the content of pyrrolic and graphitic nitrogen increases, demonstrating that graphitic nitrogen is more stable at high carbonization temperature. When considering the total content of nitrogen in NHCNFs, the amount of pyridinic nitrogen, pyrrolic nitrogen, and graphitic nitrogen in NHCNFs all decreases. Pyridinic nitrogen, pyrrolic nitrogen, and graphitic nitrogen content of NHCNF-600 are 54.3%, 30.3%, 15.4% (in nitrogen element) and 6.74%, 3.76%, 1.91% (in the material), respectively. This doping level is superior to other nitrogen-doped carbon materials reported in related literatures, as shown in Table S5, Supporting Information. Figure 4a-c exhibits the charge-discharge profiles of the first three cycles for NHCNF electrodes. Initial discharge capacities are all close to 400 mAh g −1 and the initial charge capacities are 60. 5,191.0, and 133.1 mAh g −1 for NHCNF-400, NHCNF-600, and NHCNF-800, respectively. Capacity decay during the initial cycle is principally derived from the generation of solid electrolyte interface (SEI) layer that consumes sodium ions irreversibly. The capacities can be retained in subsequent several cycles. The initial Coulombic efficiencies (ICEs) of NHCNF-400, NHCNF-600, and NHCNF-800 are 15.5%, 46.9%, and 32.3%, respectively. It should be noted that low ICEs induce low-capacity output after full cells are constructed in systems of lithium-ion or sodium-ion batteries. [47] Nevertheless, this issue can be circumvented by presodiation due to the compensation of the lost sodium ions. Capacity contribution above and below 0.1 V is shown in Figure 4d. As other literatures indicate, the region above and below 0.1 V corresponds to the adsorption/desorption and insertion/extraction of sodium-ion, respectively. NHCNF-600 possesses the highest adsorption/desorption capacity due to its appropriate interlayer space and active sites. Although the measurement is performed in the voltage range of 0.01-2.5 V, the charge capacity below 1 V is employed considering the practical application of NHCNF when full cells are assembled. [48] Therefore, the charge capacity below 1 V is also provided. The values for NHCNF-400, NHCNF-600, and NHCNF-800 are 15.4, 79.2, and 87.1 mAh g −1 , respectively. Figure 4e shows the rate performance of various NHCNF electrodes. NHCNF-600 possesses the highest specific capacity at any current density. Especially, the specific capacity remains 84.4 mAh g −1 when the current density reaches 2 A g −1 . Cyclic performance of NHCNFs at 1 A g −1 is shown in Figure 4f. Considering the low capacity at this current density, cyclic performance of NHCNF-400 was not evaluated. Although no capacity decay is observed for both NHCNF-600 and NHCNF-800, NHCNF-600 delivers about a 50% higher specific capacity than NHCNF-800, demonstrating NHCNF-600 possesses excellent reversibility of sodium-ion storage.

Results and Discussion
To gain a deeper insight into the Na adsorption and diffusion behavior on NHCNF materials, we carried out ab-initio calculations based on density functional theory (DFT). In Figure S5a, Supporting Information, the fully optimized configurations of samples with graphitic, pyridinic, and pyrrolic nitrogen represent the different chemical states of nitrogen in NHCNFs. Furthermore, we used the electron localization function (ELF) to comprehend the charge distribution on the carbon plane  Figure S5b, Supporting Information). Here, the high charge density of C-N represents the strong covalent bonding with local bosonic character. A closer observation at these ELFs reveals that pyrrolic nitrogen tends to generate a larger defective area because it substitutes two carbon atoms.
Based on these findings, we further computed the differential charge density to explore the interaction between Na and nitrogen with different chemical states in NHCNFs ( Figure  5a). The electrons tend to accumulate around pyridinic and pyrrolic N, and an obvious charge transfer appears between Na atom and its most adjacent N atom. In comparison, the charge transfer between Na and graphitic N is obviously scarce. The distance of Na to the carbon plane is 1.83 and 2.19Å for pyrrolic and pyridinic N-doped carbon materials, which also indicates the strong adsorption of Na induced by pyrrolic nitrogen. However, for graphitic N-doped carbon, this distance is 2.38Å, even higher than pristine carbon (2.23Å). Bader charge analysis quantitatively confirms the significant electron transfer from Na to pyrrolic (0.92 e − ) and pyridinic nitrogen (0.91 e − ). In contrast, the graphitic nitrogen only attracts a charge of 0.72 e − from a single Na, suggesting its relatively weak adsorption to Na atoms.
The climbing-image nudged elastic band (CI-NEB) technique is employed to explore the minimum energy paths (MEPs) for the diffusion of Na (Figure 5b). For pristine carbon, the path is from the carbon ring center to its most adjacent counterpart. When graphitic nitrogen is introduced, the path seems to change little due to the weak interaction between graphitic nitrogen and Na. For both pyridinic and pyrrolic nitrogen, the migration path of Na shifts to a curved line with inclination toward nitrogen. This  phenomenon can be easily understood from the above electronic analysis that pyrrolic and pyridinic nitrogen generate a large charge transfer from Na atoms. According to our calculations, the energy barrier of Na on N-doped carbon is within a minimum range of 0.13-0.16 eV (Figure 5c), suggesting a rather smooth migration of Na on carbon without hindrance. The above DFT calculations validate that the chemical state of nitrogen can significantly affect the adsorption and diffusion of Na, in which pyrrolic nitrogen exhibits the highest adsorption ability and graphitic nitrogen offers a lower diffusion barrier. As to NHCNF-600 sample with both high pyrrolic and graphitic nitrogen content, it naturally displays the highest Na storage capacity and best rate capability among various NHCNF samples.
To show the merits of NHCNF-600, SICs were constructed using NHCNF anode and activated carbon (AC) cathode (Figure 6a). Presodiation is vital for sodium-ion capacitor to avoid the possibility of sodium depletion during the generation of SEI layer at initial charge/ discharge cycles. [49,50] The active material of the cathode is activated carbon, which does not contain any sodium resources. If presodiation is not carried out, sodium-ion stored in the anode is all originated from the electrolyte, which causes a large concentration fluctuation for the electrolyte. Presodiation process can decrease the consumption of the electrolyte. A well-established strategy is to electrochemically intercalate Na ions into the target electrode. Herein, the correlation between presodiation potential and electrochemical impedance spectroscopy is exhibited in Figure 6b,c. The curve consists of two semicircles and an oblique line, in which the intersection with the horizontal axis represents the ohmic impedance, the first semicircle is the impedance generated by the SEI layer, the second semicircle arises from the charge transfer impedance, and the oblique line stands for the ion transfer impedance. The concentration of sodium-ion in the electrode bulk becomes higher as the anode potential steadily lowers during discharge process meaning an increasingly sluggish sodium-ion diffusion kinetics and higher impedance. The sharply rising impedance during the potential drop from 0.2 to 0.1 V is ascribed to the changing sodium intercalation mechanism of NHCNF-600. [51] When the electrode is charged, the descending impedance corresponds to the process of sodium-ion deintercalated from the bulk phase of the electrode, which is beneficial to sodium-ion diffusion kinetics. The impedance drops sharply as the potential rises from 0.1 to 0.2 V. Sodium-ion deintercalation occurs when the potential is below 0.1 V, and the sodium-ion desoption occurs when the potential is above 0.1 V. [51] Although the reduction of presodiation voltage will increase the voltage window of SIC, which is beneficial to the improvement of energy density, too low presodiation voltage leads to a sharp increase in SIC impedance, which is not conducive to the performance of rate and cycle characteristics. Consequently, considering the aforementioned factors, presodiation voltage was chosen to be 0.2 V. SIC full cells were assembled using AC cathode and presodiated NHCNF-600 (pre-NHCNF-600) anode. Figure 6d shows the cyclic voltammetry (CV) profiles of SIC with different cathode/anode mass ratios of 1:1, 2:1, and 3:1 at 0.1 mV s −1 , respectively (denoted as SIC-1, SIC-2, and SIC-3). A quasi-rectangular shape is observed in reduction process, corresponding to the linearity between capacitance and time. However, SICs exhibit an irregular CV profile during oxidation process, possibly because of the excessive sodium intercalation reaction into the anode. It can be found that the resistance of NHCNF during sodium intercalation is higher than deintercalation (Figure 6b,c). Therefore, this deviation from rectangular characteristic is caused by higher impedance. Since the specific capacitance can be represented by the area enclosed in CV curve, we found that SIC-2 has the highest specific capacitance. The rate performance of SICs is shown in Figure 6e. It can be seen that specific capacitances of SIC-1, SIC-2, and SIC-3 are 31.7, 41.8, and 37.7 F g −1 at 0.05 A g −1 based on the total mass of cathode and anode active materials, respectively, and decrease with the amplification of current density. SICs exhibit specific capacitances of 22.9, 32.8, and 29.1 F g −1 at 0.4 A g −1 , and 12.8, 21.6, and 16.8 F g −1 at 4 A g −1 , respectively. It is well acknowledged that the mass ratio of cathode to anode has great influence on the electrochemical performance. A low ratio brings about an inadequate utilization of cathode capacitance and anode capacity, which is not beneficial for the improvement of energy density. In contrast, when a high ratio is adopted, although an enhanced energy density can be obtained, the much lower potential (<0 V vs Li + /Li) of the anode induced by excessive capacity utilization may generate sodium dendrite which challenges the safety and cyclic performance of devices. Figure 6f shows the Ragone diagram of SIC-2. The maximum energy density is 82.1 Wh kg −1 at 39.9 W kg −1 , and the power density can reach 7.0 kW kg −1 at 23.4 Wh kg −1 . The performance is outstanding compared with other SICs in the literature, such as graphitic carbon nanofibers (GCNF)//AC, [52] mesoporous single-crystal-like TiO 2graphene (MWTOG)//AC, [53] carbon microsphere (CM)//activated CM, [54] and mesoporous Nb 2 O 5 /graphene/ mesoporous Nb 2 O 5 nanosheets (G@mNb 2 O 5 )//AC, [55] indicating the pre-eminence of the as-constructed NHCNF-600//AC SIC. Cyclic performance was evaluated at 1 A g −1 in a voltage window of 1-4 V as shown in Figure 6g. SIC-1, SIC-2, and SIC-3 present similar capacitance retentions of about 70% for 4000 cycles. Nevertheless, SIC-2 exhibits the highest specific capacitance.

Conclusion
In summary, we prepared nitrogen-doped hard carbon nanofibers by the electrospinning technology and low-temperature carbonization process. The material carbonized at 600°C (NHCNF-600) had a diameter of 300-400 nm with uniform morphology and a high nitrogen-doped content, which was derived from the low carbonization temperature. DFT analysis expounds the incorporation of nitrogen heteroatoms with various chemical states into carbon matrix would bring about the robust adsorption and efficient diffusion of Na atoms on electrode interface by altering the total electronic configurations. NHCNF-600 possessed a reversible specific capacity of 191.0 mAh g −1 at 0.05 A g −1 and had almost no decay after 200 cycles. Moreover, it was found that there was a sensitive correlation between the EIS and electrochemically sodium-intercalated potential for NHCNF-600. A presodiation potential of 0.2 V was chosen to lower the impedance. SIC constructed with presodiated NHCNF-600 anode could exhibit good electrochemical performance: a maximum energy density of 82.1 Wh kg −1 and a maximum power density of 7.0 kW kg −1 .

Experimental Section
Materials and reagents: Polyacrylonitrile (PAN) and N,N-dimethylformamide (DMF) were all obtained from Sigma-Aldrich. The commercial activated carbon (AC, YP80F) was purchased from Kuraray Chemicals. They were used directly without any additional treatment.
Preparation of NHCNF: 1 g of polyacrylonitrile was added to 9 mL of DMF and stirred at 60°C for 12 h to obtain an electrospinning solution. The spinning voltage, receiving distance, and flow rate were 18 kV, 16 cm, and 1 mL h −1 , respectively. The obtained precursor was first pre-oxidized in air at 280°C, followed by a carbonization process for 2 h in N 2 . The heating rate was 5°C min −1 . The carbonization temperatures were 400, 600, and 800°C, respectively, and the as-prepared NHCNFs were marked as NHCNF-400, NHCNF-600, and NHCNF-800, respectively.
Physicochemical characterization: The morphology of the samples was analyzed by scanning electron microscopy (SEM; Zeiss SIGMA) and transmission electron microscopy (TEM; JEOL JEM-2100F). The crystal structure data were obtained by X-ray powder diffraction (XRD) and Raman spectra, which were performed on Bruker D8 X-ray diffractometer and LabRam HR-800, Horiba Jobin Yvon, respectively. The chemical composition analyses of the elements were probed by X-ray photoelectron spectroscopy (XPS; Thermo 250XI).
Preparation of electrodes: The prepared NHCNFs were uniformly dispersed into N-methylpyrrolidone (NMP) with the binder (PVdF) and conductive agent (Super C45) in a mass ratio of 8:1:1 to form the slurry. The slurry was coated on the surface of the current collector of carbon-coated copper foil by the doctorblade method, dried at 80°C for 1 h in air, and vacuum dried for 12 h at 80°C. NHCNF electrode had a diameter of 11 mm. AC electrode was carried out with a similar process. The difference was that the current collector was changed to carbon-coated aluminum foil. The loadings of active materials in anode are about 1 mg cm −2 . For the cathode, the loading is the same, or double and triple the values above-mentioned.
Electrochemical measurements: Half cells were assembled to assess the electrochemical property of NHCNFs using Na foil anode and NHCNFs cathode. 1 M NaClO 4 solution dissolved in ethylene carbonate (EC) and propylene carbonate (PC) (1:1 by volume) containing 5% fluoroethylene carbonate (FEC) was utilized as the electrolyte. Glass fiber (Whatman) was employed as the separator. Galvanostatic charge-discharge measurement was performed with a voltage range of 0.01-2.5 V. EIS was carried out by discharging half cells to a specific voltage. SICs were assembled with presodiated NHCNF anode and AC cathode, and the same separator and electrolyte were completed in a glove box filled with argon gas with H 2 O and O 2 contents below 0.1 ppm. Presodiation was achieved by several galvanostatic charge-discharge cycles at 0.05 A g −1 to stabilize the capacity and a final discharge to 0.2 V. Current density and the specific capacity were calculated based on the mass of NHCNF. The specific capacitance, energy density, and power density were calculated based on the active materials of both cathode and anode. The energy density was calculated by the following formula: and the power density was achieved on the basis of the formula: where I, C, m, U, and U m , respectively, represent the current, the specific capacity, the mass of active materials of both cathode and anode, the voltage, and the average discharge voltage. Computational details: All the calculations are based on density functional theory (DFT) with the projector augmented wave (PAW) method using the Vienna ab initio Simulation Package (VASP). [56] The exchange-correlation energy is described in the frame of generalized gradient approximation (GGA) proposed by Perdew-Burke-Ernzerhof (PBE). [57] The cutoff energy is set as 500 eV for the plane wave expansion. A 3 × 3 supercell is adopted for N-doped graphene and pristine graphene to explore the adsorption and diffusion of Na. Bader charge analysis is performed to investigate the amount of charge transferred from Na atom to graphene matrix. To evaluate the k-points in the Brillion zone, the Monkhorst-Pack grid of 11 × 11 × 1 is introduced. [58] The climbing-image nudged elastic band (CI-NEB) technique is utilized to understand the energy barrier and diffusion paths with minimum energy for Na ions on the surface of carbon materials. [59] Each ionic step ends when the energy and lattice force were <1 × 10 −6 eV per atom and 0.03 eVÅ −1 , respectively. The energy threshold of electronic self-convergence was 1 × 10 −8 eV per atom.