Sustainable Lignin-Derived Carbon as Capacity-Kinetics Matched Cathode and Anode towards 4.5 V High-Performance Lithium-Ion Capacitors

The Li-ion capacitors (LICs) develop rapidly due to their double-high features of high-energy density and high-power density. However, the relative low capacity of cathode and sluggish kinetics of anode seriously impede the development of LICs. Herein, the precisely pore-engineered and heteroatom-tailored defective hierarchical porous carbons (DHPCs) as large-capacity cathode and high-rate anode to construct high-performance dual-carbon LICs have been developed. The DHPCs are prepared based on triple-activation mechanisms by direct pyrolysis of sustainable lignin with

The Li-ion capacitors (LICs) develop rapidly due to their double-high features of high-energy density and high-power density. However, the relative low capacity of cathode and sluggish kinetics of anode seriously impede the development of LICs. Herein, the precisely pore-engineered and heteroatomtailored defective hierarchical porous carbons (DHPCs) as large-capacity cathode and high-rate anode to construct high-performance dual-carbon LICs have been developed. The DHPCs are prepared based on triple-activation mechanisms by direct pyrolysis of sustainable lignin with urea to generate the interconnected hierarchical porous structure and plentiful heteroatominduced defects. Benefiting from these advanced merits, DHPCs show the well-matched high capacity and fast kinetics of both cathode and anode, exhibiting large capacities, superior rate capability and long-term lifespan. Both experimental and computational results demonstrate the strong synergistic effect of pore and dopants for Li storage. Consequently, the assembled dual-carbon LIC exhibits high voltage of 4.5 V, high-energy density of 208 Wh kg −1 , ultrahigh power density of 53.4 kW kg −1 and almost zerodecrement cycling lifetime. Impressively, the full device with high mass loading of 9.4 mg cm −2 on cathode still outputs high-energy density of 187 Wh kg −1 , demonstrative of their potential as electrode materials for high-performance electrochemical devices. materials as both cathode and anode have been proposed. [10][11][12][13][14] Carbon materials with tailored microstructure and heteroatoms would allow for significant contribution from fast surface-controlled kinetics in anode and also facilitate ion capacitive adsorption on cathode surface, boosting their charge storage capacity, rate-capability and cycling lifetime simultaneously. The pore-structure and defects are two critical factors effecting the charge storage ability and electrochemical behaviour of carbon materials. [12,[15][16][17][18] The porous structure with intrinsic vacancy and edges defects provides sufficient locations for lithium ion intercalation and adsorption while the pores not only buffer the diffusivity constraints but also facilitate the ion transport, resulting in excellent rate capability. [19,20] The external defects of heteroatoms such as nitrogen element can introduce extra lithium storage capacitance via pseudocapacitance. [11,16] Especially, their synergistic effect of pore-structure and defects in carbon materials are of great importance for the highperformance charge storage with ultrafast and long-cycling capabilities. [15,19,20] Biomass is one of the promising carbon sources for charge storage electrodes by virtue of its abundance and sustainability to meet the cost-effective and environmental requests for the commercialization of LICs. Whereas, the synthetic process of tailored biomass-derived porous carbon with engineered defects generally includes additional poreintroducing agents (KOH, [21,22] ZnCl 2 , [23] etc) or templates (NaCl, [24] KCl, [16] MgO, [25] etc), leading to the increased complexity and expense of process. Besides, the geographical restrictions and inhomogeneity of natural biomass become the severe challenge impeding their mass application. Therefore, it is highly desirable to construct highperformance 'double-carbon' LICs from biomass-derived electrode materials with balanced capacity and fast kinetics by a low-cost and scalable strategy.
Herein, we develop the lignin-derived dual-carbon LICs with ultrahigh power density and energy density, based on the precisely poreengineered and heteroatom-tailored defective hierarchical porous carbons (DHPCs) as large-capacity cathode and high-rate anode in an optimal capacity-kinetics matching fashion. The DHPCs are synthesized based on a triple-activated mechanism via a rather straightforward and low-cost pyrolysis of sustainable lignin and urea. Consequently, the lignin-derived carbons with hierarchical porous structure and abundant defects with high heteroatoms (predominant N) contents were achieved, endowing the DHPCs with numerous active sites and enhanced kinetics for PF 6 − adsorption cathode and Li + storage anode. The resulting synergism guarantees DHPCs as both cathode and anode possessing large specific capacities, superior rate performance as well as excellent cycling stability. Using identical DHPCs as cathode and anode, the fabricated dual-carbon LIC can achieve a large energy density of 208 Wh kg −1 at 450 W kg −1 and an ultrahigh power density of 53.4 kW kg −1 at the energy density of 79 Wh kg −1 , and outstanding cycling life without capacity decay after 4000 cycles at 5 A g −1 .
Particularly, increasing the mass loading on cathode to 9.4 mg cm −2 , the LIC can still output a large energy density of 187 Wh kg −1 at 222 W kg −1 and stable cycling ability.  Figure S1, Supporting Information), a rational synthetic strategy was employed to simultaneously realize the carbonization, activation and heteroatoms doping of the resultant carbon materials, which involves a pretreatment followed by direct pyrolysis. In this route, three poreforming mechanisms are considered to create the hierarchical porosity, which is different from the reported porous carbons. [26,27] First, the inorganic impurities including NaCl, KCl and Na 4 CO 3 SO 4 in this industrial lignin ( Figure S1b, Supporting Information) that work as hard templates and chemical activation agents play a vital role in generating the hierarchical porosity. [17,24,28] Second, the urea is adopted to act as nitrogen source and also enrich the porosity of carbon. [29] The industrial lignin assisted with ethanol and water is controlled to turn into viscous liquid state at setting temperature of 70°C. As the temperature rising up, the urea decomposes mainly in the range of 120-255°C ( Figure S2, Supporting Information), but the decomposition gases (e.g. NH 3 , CO 2 ) are trapped by the viscous fluid-like lignin and meanwhile forced to react with lignin-derived quasi-biochar, resulting in etched carbon fragments with increased porosity. The last poreforming mechanism is related to the pyrolysis and self-activation of lignin. The pyrolysis gases of lignin generated under high-temperature release and leave pores in the carbon skeleton [30,31] and the generated gases such as CO 2 and H 2 O can etch the carbonaceous materials in turn.

Results and Discussion
In the case of heteroatoms doping, the urea-derived ammonia and free radicals arising from its decomposition will attack the carbon and replace oxygen-containing groups (e.g. ether-like oxygen, carboxylic acid) on the carbon to form nitrogen-containing functional species. [29] Moreover, the industrial lignin itself contains the N and S elements ( Figure S1c To further elaborate their microstructure, X-ray diffraction (XRD) patterns together with Raman spectroscopy were performed. The XRD  Figure 2g). Notably, the (002) peak gradually shifts towards a lower angle with preparation temperature increasing. Correspondingly, the average interlayer spacings (d 002 ) of DHPCs-700, DHPCs-800 and DHPCs-900 are, respectively, calculated to be 0.357, 0.392 and 0.419 nm, which increase with temperature increasing. Their larger d 002 than 0.335 nm of graphite facilitates Li + intercalation/de-intercalation. Despite of the lowest N-doping (Table S1, Supporting Information), the d 002 of DHPCs-900 is the largest among DHPCs samples, which is presumably attributed to the intrusion of molten salt between the forming graphene sheets at higher temperature. [32] For comparison, the diffraction peak (002) of DHPCs-800 shifts slightly towards lower position than PHPCs-800, manifesting the larger d 002 of DHPCs-800. As shown in Figure 2h, two characteristic Raman peaks around 1338 and 1580 cm −1 are belonged to D band (structural disorders) and G band (graphitic feature) of carbon materials, respectively. The half width at half maximum of these two bands and the I D /I G value (DHPCs-700: 1.08; DHPCs-800: 1.02; DHPCs-900: 1.0) become gradually narrower and lower with the temperature increasing, which illustrates the development of local shortrange ordering structure and decrement of disorder. [33] The high ratio of I D /I G for DHPCs, which is higher than 0.99 of PHPCs-800, confirms their highly disordered structure with abundant defects, [22] induced by the addition of urea in preparation process.
The pore structures were characterized by N 2 adsorption-desorption isotherms. All the isotherms in Figure 2i belong to the typical IV (H 4 ) type, featuring with steep rise of N 2 uptake at P/P 0 < 0.1, obvious hysteresis loop at P/P 0 > 0.47 and sudden increasement at P/P 0 > 0.92, indicating their hierarchical porous structure with coexistence of micropore, mesopore and macropore. The pore size distributions (PSD) of DHPCs calculated by density functional theory (DFT) method further clarify their hierarchical porous structure with both mesopores mainly distributed at 2.5 and 4.0 nm and micropores around 0.7, 1.1 and 1.4 nm ( Figure 2j). Especially, DHPCs-800 and DHPCs-900 possess higher pore volume (PV) than those of DHPCs-700 and PHPCs-800 (Table S2, Supporting Information). The specific surface areas (SSA) are 1638, 1834, 2111 and 1598 m 2 g −1 for DHPCs-700, DHPCs-800, DHPCs-900 and PHPCs-800, respectively. Compared with PHPCs-800, the wider PSD, higher SSA and PV of DHPCs could be more favourable for the ionic accessibility and rapid migration within the porous framework. A detailed comparison of physical parameters of DHPCs with previously reported porous carbons for LICs is provided in Table S2, Supporting Information.
The elemental mapping images of DHPCs-800 demonstrate O, N and S heteroatoms uniformly distributed in this material skeleton ( Figure S5, Supporting Information), and the four characteristic peaks of C, O, N and S elements are clearly observed in XPS spectra ( Figure S6a, Supporting Information). High-resolution C 1 s spectrum of DHPCs-800 confirms the presence of C-S (283.6 eV) and C-N (285.8 eV) bonds [34] (Figure S6b [35][36][37] Notably, the predominant N-5 and N-6 could produce pseudocapacitive charge storage capacity, [37] while N-Q could increase electronic conductivity via carbon plane. [16,36] Moreover, the oxygen-contained groups of C=O ( Figure S6c, Supporting Information) could provide some additional lithium-ion storage sites. [38] Besides N and O, the S element originating from industrial lignin has been successfully in-situ implanted into DHPCs, as demonstrated by S 2p XPS spectrum ( Figure S6d, Supporting Information). Impressively, high nitrogen contents of 13.7, 11.7 and 6.7 at.% are achieved for DHPCs-700, DHPCs-800 and DHPCs-900, respectively, much higher than that of PHPCs-800 (Table S1, Supporting Information). It is expected that the synergy of the different heteroatoms would play a significant role in boosting both cathodic and anodic capacitive electrochemical performance of DHPCs. [39,40] The electrochemical performances of the as-prepared DHPCs as both cathode and anode of LICs were firstly tested in half-cell configurations. Figure 3a presents the cyclic voltammetry (CV) curves of DHPCs-700, DHPCs-800 and DHPCs-900 as cathodes at 10 mV s −1 within 2-4.5 V. All the CV curves clearly display quasi-rectangular shape, manifesting the predominant capacitive charge storage mechanism. It is revealed that the DHPCs-800 shows the largest integration area, indicative of the highest capacity at this rate. Even increasing the sweeping rate to 200 mV s −1 , the CV curve maintains similar rectangular shapes for DHPCs-800 but occurs obvious distortion for DHPCs-700 and DHPCs-900, implying better electrode kinetics of DHPCs-800 (Figure 3b and Figure S7, Supporting Information). The discharge capacities and rate capability of DHPCs-700, DHPCs-800, DHPCs-900 and PHPCs-800 are compared at different discharge rates of 0.1-30 A g −1 (Figure 3c and Figure S8). The DHPCs-800 shows the discharge capacity of 115 mAh g −1 at 0.1 A g −1 , higher than 106 mAh g −1 of DHPCs-700 and 94 mAh g −1 of DHPCs-900. More importantly, DHPCs-800 can still output high specific capacities of 60 mAh g −1 and 49 mAh g −1 even at high discharge rates of 20 and 30 A g −1 , respectively. Such superior rate capability is among the best results of the reported porous carbons, including N-doped porous carbon (86 mAh g −1 at 0.1 A g −1 and 46 mAh g −1 at 20 A g −1 ), [17] nitrogen-doped AC (127 mAh g −1 at 0.4 A g −1 and 73.7 mAh g −1 at 12.8 A g −1 ), [41] N-doped hierarchical carbon (125 mAh g −1 at 0.1 A g −1 and 98 mAh g −1 at 15 A g −1 ), [19] B/N dual-doped CNFs (113 mAh g −1 at 0.1 A g −1 and 63 mAh g −1 at 10 A g −1 ) [10] and graphene@hierarchical meso−/microporous carbon (112 mAh g −1 at 0.2 A g −1 and 73.3 mAh g −1 at 8 A g −1 ). [42] In addition, PHPCs-800 at 0.1 A g −1 initially reaches the capacity up to 158 mAh g −1 , quickly reduces to 113 mAh g −1 ( Figure S8, Supporting Information) and holds 43 and 29 mAh g −1 at 20 and 30 A g −1 respectively. The linear galvanostatic charge/discharge (GCD) profiles without obvious plateau of DHPCs at 0.1-30 A g −1 further demonstrate their capacitive storage behaviour (Figure 3d and Figure S9, Supporting Information). Apparently, the moderate porosity and defects with a trade-off among SSA, PV and heteroatoms content would synergistically contribute to the high capacitive capacity and excellent rate capability of DHPCs-800. Furthermore, DHPCs-800 cathode also presents stable cycling performance for 5000 cycles, maintaining a high capacity of 92 mAh g −1 at 2 A g −1 (Figure 3e). Therefore, it is verified that DHPCs-800 is a promising cathode candidate for LICs benefiting from the engineered pores and heteroatom-doping.
The anode performances of DHPCs-700, DHPCs-800, DHPCs-900 and PHPCs-800 were measured within 0.02-3.0 V. It is noted that the irreversible capacity observed from the first-cycle GCD and CV measurements (Figures S10a-c and S11, Supporting Information) is mainly ascribed to the solid electrolyte interface (SEI) formation and decomposition of electrolyte. [43,44] The subsequent nearly overlapped cycles verify the excellent stability of SEI layer. The DHPCs-800 shows the highest capacity either above 0.2 V (high-slope region) or below 0.2 V (low-slope region) ( Figure S10d, Supporting Information), as demonstrated by performance comparison at 0.1-20 A g −1 (Figure 4a,b and Figure S12, Supporting Information). Specifically, DHPCs-800 holds large specific capacities of 263 and 150 mAh g −1 even at 10 and 20 A g −1 , much higher than those of DHPCs-700 (179 and 104 mAh g −1 ), DHPCs-900 (161 and 120 mAh g −1 ) and PHPCs-800 (87 and 57 mAh g −1 ) (Figure 4a and Figure S13, Supporting Information). The lithium storage strongly depends on the type of defects, functional groups, spacing of graphitic interlayers and porosity. By comparison, DHPCs-900 shows the better rate capability but lower specific capacities from 0.1 to 10 A g −1 than those of DHPCs-700 and DHPCs-800, due to the larger interlayer spacing, SSA, PV and higher electrical conductivity (40.6 S m −1 ) but lower heteroatoms content of DHPCs-900 than those of DHPCs-700 and DHPCs-800 (Tables S1 and S2, Supporting Information), which also implies the strong impact of heteroatoms doping on charge storage especially at low current densities and pivotal role of interlayer spacing, SSA, PV and electrical conductivity in determining rate performance. Meanwhile, because DHPCs-800 has the higher heteroatoms content than that of DHPCs-900 and the larger interlayer spacing, SSA, PV and higher electrical conductivity (4.7 S m −1 ) than those of DHPCs-700, the synergistic effect of these factors brings the higher specific capacities of DHPCs-800 than those of DHPCs-700 and DHPCs-900. Compared with PHPCs-800, abundant heteroatoms endow DHPCs-800 numerous surface defects sites for Li + adsorption and extended interlayer distance reduces Li + diffusion barrier, while hierarchical porous structure with broad PSD shortens Li + transport path, thus improving lithium storage and transport performance. Furthermore, DHPCs-800 remains an impressive specific capacity of 481 mAh g −1 after 1000 cycles at 2 A g −1 (Figure 4c), demonstrative of superior cyclability. Importantly, it is revealed that the GCD profiles shape consisting of several lines with different slopes, DHPCs produce different charge storage mechanisms (Figure 4b and Figure S12, Supporting Information), which is significantly different from the energy storage behaviour of capacitive carbon materials (straight line) [19,41] and graphite (evident plateau around 0.2 V). [6,45] Specifically, the slope capacity stems from lithium adsorption to produce double-layer capacitance and pseudocapacitance, while the plateau capacity is from lowpotential lithium intercalation in the nanosized graphitized region (Figure 4d). [10,[46][47][48] These two charge storage processes co-exist in the overlapped region without clear potential boundary. To deeply understand the energy storage behaviour, the kinetic analysis of DHPCs-800 was conducted with CV curves measured from 1 to 20 mV s −1 (Figure 4e). The power law of i = av b is adopted to distinguish the predominant mechanism at a fixed potential, in which i means peak current, v is sweeping rate, while a and b are the constants, and b takes a value between 0.5 (diffusion controlled intercalation) and 1 (capacitive charge storage). [49] The kinetics b values are calculated to be 0.78, 0.76 and 0.59 at several fixed potentials of 1.97, 0.85 and 0.02 V (Figure 4f), respectively, representing its hybrid energy storage mechanism undergoing the transition from a capacitive behaviour to diffusion-dominated process along with the potential decreasing. Quantitatively, the ratios of capacitive contribution (k 1 v) and diffusioncontrolled intercalation (k 2 v 1/2 ) are calculated from the formula i(v) = k 1 v + k 2 v 1/2 . [50] Figure 4g shows the capacitive contribution of DHPCs-800 accounts for 46% of total capacity at 5 mV s −1 (orange region). Moreover, the proportion of capacitive contribution grows from 33% at 1.0 mV s −1 to 69% at 20 mV s −1 , suggesting a dominant role of capacitive behaviour with scan rate increasing (Figure 4h). Controlling pore structure and heteroatom-induced defects are the important strategies for carbon-based materials. [15,19,37] In this regard, DHPCs-800 with moderate dopants content, SSA and PV exhibits satisfactory electrochemical property. To further understand the synergistic effect of pore structure and heteroatomsinduced external defects on lithium ion storage, computational simulations were conducted. The model structures of different carbon frameworks are built and optimized, and the obtained adsorption energy (E ads ) are shown in Figure S14, Supporting Information. The E ads of graphene layer with sub-nanometer pore [51] is calculated to be −5.79 eV for Li, higher than −4.53 eV of flawless graphene, implying that the introduction of sub-nanometer pore is conducive to lithium adsorption in graphene. Further, introducing the C-N (N-5 and N-6) and C-S sites into the defective graphene, the adsorption energy is more negative of −6.53 eV, obviously higher than those of un-doped graphenes. Therefore, it is indicated that the synergistic effect of pore and dopants can significantly boost lithium adsorption and storage performance.
To demonstrate the applicability, DHPCs-800 was applied as both cathode and anode simultaneously to assemble dual-carbon LICs (denoted as DHPCs-800//DHPCs-800 LICs). Before assembling, DHPCs-800 anode was pre-lithiated for expanding voltage range of the device, and compensating the initial lithium loss from the formation of SEI film. [52,53] After pre-lithiation, it can be seen that, during the first charging process above open-circuit voltage (OCV), the PF 6 − and Li + ions from electrolyte move towards to reserve directions simultaneously until reaching the maximum voltage (Figure 5a). When the voltage discharges to OCV, the PF 6 − and Li + ions return to the electrolyte. With the voltage continuously decreases, the Li + ions supplied by the prelithiated anode are pulled towards cathode surface to form electric double layer until the minimum voltage (V min ). The next charge process starts from the V min to OCV, a reverse process from the OCV to V min happens, in which the Li + ions desorb from the cathode and go back to the anode. [52,54] For obtaining the maximum energy density and power density of full device, mass match of cathode and anode needs consideration especially the capacity and kinetics match at high current densities, thereby the mass ratio of cathode and anode is set as 1:1-3:1.
The DHPCs-800//DHPCs-800 LICs exhibit excellent electrochemical performances that could be ascribed to the following aspects. First, the large SAA and multi-scale porous architecture of DHPCs-800 cathode are conducive to electrolyte permeation and ions adsorption to obtain a mass of double layer and fast electrolyte transport, together with the additional pseudocapacitance provided by the heteroatoms, generating the large capacitive capacity and superior rate capability. Second, the synergistic effect of pore and abundant dopants defects greatly boosts the lithium adsorption and storage, guaranteeing the large capacity of DHPCs anode. Third, the distinctive structure of DHPCs-800 anode together with large interlayer spacing also provides a large amount of capacitive contribution and fast ion transport kinetics, endowing robust power density at high rates. Last but not least, the double balance of capacity and kinetics between cathode and anode contributes to achieve high-energy density and high-power density for full LICs. Therefore, it is demonstrated that the DHPCs material is an excellent candidate for both cathode and anode of LICs boosting the 'double high' feature with long-term cycle lifespan.

Conclusion
In summary, the sustainable lignin-derived DHPCs featured with designed porosity and heteroatoms were demonstrated as high-capacity cathode and power-support anode simultaneously for ultrahighperformance LICs. The DHPCs derived from industrial lignin allow precise control of defects types including pores and heteroatoms by carbonization temperature, featuring of interlinked hierarchical pores with appropriate SSA, abundant heteroatoms and enlarged interlayer spacing. After synergistic optimalization, DHPCs-800 presents a large specific capacity of 115 mAh g −1 at 0.1 A g −1 as cathode, and excellent rate capability with holding 263 mAh g −1 even at a high rate of 10 A g −1 as anode. It is theoretically revealed that synergistic effect of pore and dopants could ameliorate lithium adsorption and storage. The dualcarbon DHPCs-800//DHPCs-800 LIC delivers a large specific energy of 208 Wh kg −1 at 450 W kg −1 , and still offers 79 Wh kg −1 even at ultrahigh specific power of 53.4 kW kg −1 , together with no capacity fading measured at 5 A g −1 after 4000 cycles. Additionally, the LIC with high mass loading of 9.4 mg cm −2 also presents a competitive performance. Therefore, it is believed that our proposed porosityengineered and heteroatom-tailored strategy of fabricating sustainable lignin-derived DHPCs will open a new avenue to developing capacitykinetics matched carbon electrodes as anode and cathodes simultaneously of 'double-high' LICs for fast-charging energy-storage.

Experimental Section
Preparation of DHPCs: The industrial lignin was bought from Wuhan East China Chemical co. LTD. The industrial lignin and urea (m lignin: m urea = 1:1) were uniformly mixed in small amount of ethanol and water, and placed in oven at 70°C for 4 h. Subsequently, the mixture was directly pyrolyzed in tube furnace firstly at 400°C for 1 h, then treated at target temperature (700, 800 and 900°C) for 1 h in Ar atmosphere. The black products underwent grinding and were repeatlly rinsed by 1 M hydrochloric acid and deionized water until pH = 7. After drying at 120°C overnight, DHPCs carbonized at different temperatures of 700, 800 and 900°C were obtained, and correspondingly were denoted as DHPCs-700, DHPCs-800 and DHPCs-900, respectively. To verify the effect of urea, a contrast sample was synthesized under the similar procedure of DHPCs-800 without addition of urea, and denoted as PHPCs-800.
Electrochemical characterization: For the fabrication of cathode, the electrode was made by mixing 80 wt% of active materials, 10 wt% of conductive carbon black and 10 wt% of polytetrafluoroethylene (PTFE) to form a homogeneous mixture, which was pressed into a uniform film with the aid of roller press. Then, the film was dried at 100°C and cut into the circular electrodes with weight loadings of 1.5-1.9 mg cm −2 , which then were pressed onto the aluminiumbased current collector as cathode. The anode slurry was prepared by careful mixing the active materials, conductive carbon black and polyvinylidene fluoride (PVDF) with mass ratio of 8:1:1 in N-methyl-2-pyrroli-dinone (NMP) and coated on Cu foil. After drying in vacuum oven at 100°C, the anode electrode was punched into disklike shape with mass loading of 0.7-1.0 mg cm −2 . The CR2032type button cells were assembled with Li foil worked as counter electrodes and glass fiber (GF/D) as separator in 1.0 M LiPF 6 in ethylene carbonate (EC)/ ethyl methyl carbonate (EMC)/ dimethyl carbonate (DMC) (1:1:1 by volume) with lithium difluorooxalato borate (LiDFOB) as functional additive. The dual-carbon LICs were assembled with DHPCs-800 as cathode and prelithiated DHPCs-800 as anode. The pre-lithiation process of anode is galvanostatically charged and discharged at 0.1 A g −1 for 10 cycles within 0.02-3 V, and last cycle is cut off at 0.02 V.
The specific capacitance (C, F g −1 ), energy density (E, Wh kg −1 ) and power density (P, W kg −1 ) of LICs were determined based on the following equations: where t (s) means the discharge time of full cell, I (A) represents the discharge current, M (g) means the total mass of active materials in both electrodes and V max and V min (V) mean the voltage at the beginning and the end during discharge process, respectively. The CV and EIS measurements were conducted on the CHI760E electrochemical working station. The rate capability and cycling stability were performed on a Land CT2001A. In LICs test, the CV and GCD tests were conducted on CHI760E electrochemical working station, and the cycling stability was measured on a LANHE M340A test system.
Computational simulation: The Materials Studio 8.0 package integrated with CASTEP code was adopted to carry out theoretical simulations. The different geometrical models of pure graphene, defective graphene and defective graphene with N and S doping were established to obtain their adsorption energies (E ads ) with Li atom. The adsorption energy of each investigated model with Li could be obtained by the following equation of E ads = E M-Li -E Li -E M . Where the E M-Li means the energy of Li atom adsorbed on graphene in its relaxed state, the E Li and E M represent the energy of a single Li atom and substrate without Li adsorption respectively.