Ultrasmall NiS2 Nanocrystals Embedded in Ordered Macroporous Graphenic Carbon Matrix for Efficiently Pseudocapacitive Sodium Storage

Sodium-ion hybrid capacitor (SIHC) is one of the most promising alternatives for large-scale energy storage due to its high energy and power densities, natural abundance, and low cost. However, overcoming the imbalance between slow Na+ reaction kinetics of battery-type anodes and rapid ion adsorption/desorption of capacitive cathodes is a significant challenge. Here, we propose the high-rate-performance NiS2@OMGC anode material composed of monodispersed NiS2 nanocrystals (8.8 ± 1.7 nm in size) and N, S-co-doped graphenic carbon (GC). The NiS2@OMGC material has a three-dimensionally ordered macroporous (3DOM) morphology, and numerous NiS2 nanocrystals are uniformly embedded in GC, forming a core–shell structure in the local area. Ultrafine NiS2 nanocrystals and their nano–microstructure demonstrate high pseudocapacitive Na-storage capability and thus excellent rate performance (355.7 mAh/g at 20.0 A/g). A SIHC device fabricated using NiS2@OMGC and commercial activated carbon (AC) cathode exhibits ultrahigh energy densities (197.4 Wh/kg at 398.8 W/kg) and power densities (43.9 kW/kg at 41.3 Wh/kg), together with a long life span. This outcome exemplifies the rational architecture and composition design of this type of anode material. This strategy can be extended to the design and synthesis of a wide range of high-performance electrode materials for energy storage applications.


Introduction
Sodium-ion hybrid capacitors (SIHCs) have emerged as an essential alternative for electrochemical energy storage in modern society due to their natural abundance, environmental friendliness, and low cost of sodium resources [1,2]. Generally, a SIHC consists of a battery-type anode with high specific capacity and a supercapacitor-type cathode with high-rate capability, resulting in a promising candidate to achieve considerable energy and power densities simultaneously [3][4][5]. However, the kinetics between the rapid ion adsorption/desorption in capacitive cathodes and the sodiation/desodiation in battery-type anodes are mismatched during the charging/discharging process. In this regard, the major challenge for high-performance SIHCs lies in exploring desirable sodium-ion storage anode materials to overcome the kinetics imbalance [6].
To date, miscellaneous anode candidates of sodium-ion batteries (SIBs) have been attempted as anode materials for SIHCs [3]. There are three sodium storage mechanisms: intercalation, conversion, and alloying [7,8]. Intercalation mechanisms refer to the insertion of sodium ions into lattice materials that exhibit small volume change and thus maintain structural integrity, such as carbon-based materials. Conversion and alloying mechanisms refer to reacting with sodium via multi-electron conversion and forming intermetallic binary compounds by alloying with sodium. The materials of these two mechanisms typically exhibit poor conductivity and undergo significant volume expansion and contraction during charging and discharging, which causes material pulverization and electrode fragmentation, resulting in reduced capacity and poor rate performance [9]. Among conversion-type anode materials, transition metal sulfides, particularly nickel-based sulfides, have attracted tremendous attention due to abundant resources, low price, and high theoretical specific capacity (ca. 446, 591, and 879 mAh/g for Ni 3 S 2 , NiS, and NiS 2 , respectively) [10]. In various nickel-based sulfides, nickel disulfide (NiS 2 ) possesses the highest theoretical specific capacity but suffers from the worst electrical conductivity and the largest volume change [11,12]. Furthermore, metal sulfide anodes in SIBs easily fail due to the generation and dissolution of polysulfides during cycling [13]. Regardless, NiS 2 has been shown to possess strong adsorption of polysulfides and high conversion of soluble polysulfides into insoluble Na 2 S 2 /Na 2 S [14].
Several useful strategies have been employed to alleviate the awful electrical conductivity and volume change of NiS 2 anode materials. A common route is to combine a highly stable and conductive carbon-based matrix (e.g., carbon nanotubes [15], carbon nanofibers [16], and reduced graphene oxide [17]), which can improve electrical conductivity and structural stability to a certain degree. For example, Li et al. [18] fabricated a graphene network-supported NiS 2 nanocrystal, whose reversible capacity reached 580.6 mAh/g at 5.0 A/g. However, the high cost of graphene makes it difficult to be used on a large scale. Furthermore, electrochemical performance, particularly high-rate capability, which is typically limited by sluggish Na + solid diffusion [19], needs to be improved. Tremendous efforts have been made in nanoengineering and structure design to accelerate the sluggish Na + diffusion kinetics. Nanoscale materials greatly diminish the effects of volume change and shorten diffusion paths. Besides, the three-dimensionally ordered macroporous (3DOM) framework has great potential to enhance the rate performance. With the intrinsic hierarchical pores, highly developed channels, and bicontinuous pore structure, the 3DOM architecture has the expected functions of accommodating volume expansion, promoting ion transport, and ensuring electron conduction [19].
Motivated by the above, we developed a 3DOM-structured NiS 2 @OMGC composite through a simple thiourea (CH 4 N 2 S) pyrolysis-assisted colloidal crystal template method. Numerous NiS 2 nanocrystals (~ 8.8 ± 1.7 nm in diameter) are uniformly embedded in the nano-onion GC units of the 3DOM matrix, yielding a core-shell structure locally. This nano-microstructure can not only alleviate the volume change but also will realize high nanocrystallization (< 10 nm in size) and monodisperse distribution of NiS 2 , which is beneficial to improving their rate performances. This conversion-type NiS 2 anode delivers almost 100% pseudocapacitive Na-storage behavior and excellently high-rate performance (355.6 mAh/g at 20.0 A/g), together with remarkable cycling stability due to the synergistic effect between the ultrafine NiS 2 particles and 3DOM GC matrix (68.5 and 31.5 wt%, respectively). The simultaneously high energy and power densities of an as-configured NiS 2 @ OMGC//AC SIHC device, coupled with the NiS 2 @OMGC anode and the commercially available activated carbon (AC) cathode, can further confirm the rationality of the NiS 2 @ OMGC anode in its architecture and composition. Such a design strategy could be effective for many other batterytype electrode materials beyond sodium-based systems.

Materials Synthesis
The polymethyl methacrylate (PMMA) microsphere template was synthesized by the reported method [20]. In a typical procedure, nickel nitrate hexahydrate and citric acid were mixed and dissolved in deionized water with molar concentrations of 2.0 mol/L and 1.0 mol/L, respectively. The structurally ordered template of PMMA microspheres was impregnated in the above solution after vigorous stirring for 1 h until the precursor solution filled its interstitial spaces. The excess precursor solution was then removed by filtration. After drying, the nickel salt-impregnated PMMA template precursors were carbonized for 30 min under a nitrogen atmosphere at 500 °C with a ramp rate of 2 °C/min. After cooling the furnace to room temperature, the product denoted as Ni@OMGC was prepared.
The as-prepared Ni@OMGC underwent a thiourea-treatment process with a mass ratio of 1:5 in a nitrogen atmosphere at 350 °C for 3 h with a ramp rate of 5 °C/min. Ni@OMGC and thiourea were placed downstream and upstream of the tube furnace. The NiS 2 @OMGC product was obtained after the furnace was cooled to room temperature.

Material Characterization
The morphology of the products was characterized using a field-emission scanning electron microscope (SEM, S-4800) and a transmission electron microscope (TEM, JEM-F200) equipped with energy-dispersive spectroscopy (EDS). A Bruker D8 Advance X-ray diffractometer (XRD) was used to scan the product from 10 to 90° with Cu Kα radiation. Raman spectra were obtained using a DXR Microscope spectrometer equipped with a 532 nm laser. The N 2 adsorption/desorption isotherm was measured at 77 K using a BSD-PS(M) volumetric adsorption analyzer for measuring specific surface area and porosity distribution. The pore size distribution (PSD) was calculated using a non-local density functional theory model from the adsorption isotherm. X-ray photoelectron spectroscopy (XPS, ESCALAB Xi+) was examined using monochromatic Al-Kα radiation (1486.6 eV), and the binding energy was calibrated with a correction value of 284.8 eV for C 1s.

Electrochemical Measurements
The working electrodes were prepared by casting a slurry of the as-prepared product (80 wt%), super P (10 wt%), and poly-(vinylidene fluoride) (PVDF, 10 wt%) dispersed in N-methyl-2-pyrrolidone (NMP) onto a copper foil with a doctor blade, followed by drying at 80 °C overnight. The obtained electrodes were cut into circular disks with a diameter of 13.0 mm. The mass loading of NiS 2 @OMGC was 0.8-1.0 mg/cm 2 . The Na + half-cells were assembled in an Ar-filled glovebox using Na foils as the counter and reference electrodes and GF/D glass fibers as the separators. The electrolyte was NaPF 6 of 0.8 mol/L in diglyme (DEGDME).
For the SIHC device, the cathode was prepared by mixing the AC (YP-50, 80 wt%), super P (10 wt%), PVDF (10 wt%) binder in NMP and then coated on an Al foil. For the anode, the NiS 2 @OMGC electrodes in the Na + half-cells were cycled at 0.1 A/g for five cycles before being discharged to 0.01 V and then disassembled from the cells in the glove box. In a SIHC full cell, the active mass ratio of the cathode to the anode was 3:1. The electrolyte was the same 0.8 mol/L NaPF 6 in DEG-DME. Based on the total mass/volume of anode and cathode active materials, the energy densities (E, Wh/kg) and power densities (P, W/kg) of the SIHCs were calculated as follows: where I is the constant current; Δt is the discharge time; m is the total active mass/volume of anode and cathode; t 1 and t 2 are the start time and end time in the discharge process, respectively; V max is the potential at the beginning of discharge after the IR drop; and V min is the terminal voltage in the discharge process.

Kinetic Analyses Methods
Electrochemical impendence spectroscopy (EIS) measurements were performed in situ on an Iviumstat electrochemical workstation in impedance potential scan mode. The implementation was an analog to the impedance constant E (a range of frequencies is applied at a constant DC potential) variant. Meanwhile, it was repeated at the range of 3.0-0.01 V and 0.01-3.0 V, respectively.
The diffusion coefficient of Na + ion (D Na+ ) could be calculated with the following equations [21]: where R is the gas constant; T is the absolute temperature; A is the surface area of the anode; n is the number of electrons per molecule during the reaction; F is the faraday constant; C is the concentration of sodium ion; and the simulation of Warburg factor (σ) was originated from the slope in fitting line of ω −1/2 and Z′.
Galvanostatic intermittent titration technique (GITT) was also used to investigate the Na-storage kinetics of NiS 2 @ OMGC. During the test, a pulse current of 100 mA/g was applied for 30 min and then rested for 60 min to bring the electrode potentials back to equilibrium (Fig. S11).
During the sodiation and desodiation process, the diffusion coefficient D Na+ was calculated using the following equation [22]: where m B is the active mass of the electrode; V m is the molar volume; M B is the molar mass of the electrode; S is the electrochemically active area of the electrode; ΔE s is the difference in open-circuit voltages after two adjacent relaxations; and ΔE τ is the voltage difference between the beginning and termination of a single pulse step.

Facile Fabrication and Physiochemical Characterizations of NiS 2 @OMGC
Scheme 1 depicts the overall synthesizing procedure of the NiS 2 @OMGCcomposite. The structurally ordered template of PMMA microspheres (~ 400 nm in diameter, Fig. S1) was first impregnated in a citric acid-chelated nickel nitrate solution, where its void spaces would be filled with Ni saltsformed gel after drying. Followed by nitrogen-protection calcination at 500 °C and a convenient thiourea-treatment process at 350 °C, the precursor could be transformed into the target NiS 2 @OMGC composite through a Ni@OMGC intermediate of Ni nanocrystals and GC matrix (Figs. 1 and S2) [23]. Figure 1a, b depicts the SEM images, showing that NiS 2 @OMGC inherits the well-defined 3DOM morphology from Ni@OMGC. The TEM images in Fig. 1c, d reveal that the NiS 2 nanoparticles are uniformly embedded in the continuous carbon matrix. Their sizes are distributed within 8.8 ± 1.7 nm (Fig. 1c inset). The high-resolution TEM image (Fig. 1d)  The combined XRD patterns (Fig. 2a) and Raman spectra ( Fig. 2b) of NiS 2 @OMGC and Ni@OMGC can confirm the composition of the target sample as NiS 2 and GC. By indexing each diffraction peak, it is found that all the cubic Ni phases (JCPDS Card#89-7128) in Ni@OMGC have been converted to cubic NiS 2 . As a result of the co-doping of N and S elements during the CH 4 N 2 S pyrolysis, the d 002 value of the GC component appears to have increased slightly (from 0.35 to 0.37 nm) [24]. The enhanced Raman D band (located at 1347 cm −1 , characteristic of disordered carbon) of NiS 2 @OMGC and the increased intensity ratio (from 1.76 to 1.98) between the Raman D and G bands (located at 1589 cm −1 , characteristic of sp 2 hybridized GC) both indicate the heteroatom doping. This doping would enhance the material's local conductivity and greatly enrich its defects to accommodate more Na atoms [25]. Figure 2c shows the nitrogen adsorption/desorption isotherms of NiS 2 @OMGC. The typical IV-type curve, H3-type hysteresis loop, and sharp N 2 uptake at a relative pressure range of 0.9-1.0 indicate the presence of hierarchical nanopores in this sample, Scheme 1 Schematic illustration of the formation process of NiS 2 @OMGC confirmed by the PSD curve based on the adsorption isotherm (Fig. 2c inset). Undoubtedly, such a developed and ordered porous structure would facilitate the mass transfer of both electrolyte and Na + ions. This material also demonstrates a relatively large specific surface area, ca. 230.5 m 2 /g using the Brunauer-Emmett-Teller method. Although forming the solid electrolyte interface (SEI) made it difficult to achieve a high initial Coulombic efficiency (ICE), it greatly benefits achieving superior ions/charges adsorption required by supercapacitor or pseudocapacitor-type electrodes.
The chemical constituents of NiS 2 @OMGC were determined using the analyses of thermogravimetry (TG) in air and XPS. In light of possible reactions (C (s) + O 2 (g) → CO x (g) and NiS 2 (s) + O 2 (g) → NiO (s) + SO 2 (g) [11,26,27]) and the staged weight-remaining ratios indicated by the TG curve (Fig. 2d), the contents of NiS 2 and N, S-co-doped GC are estimated to be ca. 68.5 and 31.5 wt%, respectively. Figure 2e-i presents the chemical states of the surface Ni, S, C, N, and O species (ca. 50.2, 6.4, 29.1, 4.7, and 11.4 at%), respectively. The Ni 2p spectrum (Fig. 2f) can be deconvoluted into six peaks corresponding to Ni 2+ (853.4 and 855.6 eV for Ni 2+ 2p 3/2 , 870.9, and 874.0 eV for Ni 2+ 2p 1/2 ) and two shakeup satellites, confirming the complete conversion of metallic Ni to NiS 2 [28]. For the S species (Fig. 2g), the two obvious peaks at 161.9 and 162.9 eV (for S 2p 1/2 and 2p 3/2 ) are correlated with the spin-orbit characteristics of S 2 2− in NiS 2 . The peak at 164.1 eV is assigned to −C=S− bridging S 2 2− and/or −C−S−C− apical S 2− ligands [11,29]. Furthermore, the binding energy at 168.5 eV can be identified as the −C −SO 2 − bond, which is generally related to slight surface oxidation. As to the C 1s spectrum (Fig. 2h), the three distinct peaks centered at 284.8, 286.1, and 288.7 eV should indicate that there are mainly three types of carbon species, such as the dominated graphenic C atoms, a few heteroatom-bonded C atoms (e.g., C−O, C−N, and C−S), and some oxidized C atoms on edge (e.g., C=O) [26,30,31]. Finally, Fig. 2i depicts the high-resolution XPS spectrum of N 1s. It shows that only a tiny fraction of N atoms (8.4 at% by referring to the peak at 401.4 eV) enter the internal network of the GC matrix. The pyridinic N (399.4 eV, 72.7 at%) [22,23,30] has a significant proportion for functional defects (or active reaction sites) conducive to local electron conductivity of the composite [32]. Figure 3a shows the initial cyclic voltammetry (CV) curves of NiS 2 @OMGC measured at a slow scan rate (v) of 0.1 mV/s and between 3.0 and 0.01 V (vs. Na + /Na). SEI was generated during the first cathodic scan as indicated by the intense peak centered at 1.29 V and those distributed between 0.92 and 0.33 V [33], all of which disappeared in the subsequent cycles. After the SEI formation, several pairs of redox peaks are observed over the highly reversible and stable CV curves. The peaks at 1.73/2.06 and 1.54/1.81 V can be attributed to the stepped conversion reaction between NiS 2 and Na x NiS 2 (i.e., NiS 2 + xNa + + xe − ↔ Na x NiS 2 ) [11,34], whereas the peak of much-enhanced intensity centered OMGC. a XRD patterns and b Raman spectra of NiS 2 @OMGC and Ni@OMGC. c Nitrogen adsorption/desorption isotherms and cor-responding PSD curve. d TG-DTG curves measured in air. e-i XPS spectra: e full spectrum, f Ni 2p, g S 2p, h C 1s, and i N 1s at 0.92/1.61 V should represent the deeper sodiation and regeneration of the Na x NiS 2 phase (i.e., Na x NiS 2 + (4-x) Na + + (4-x)e − ↔ Ni + 2Na 2 S) [11,34]. The sodiation/ desodiation voltages from its initial galvanostatic charge/ discharge (GCD) profiles at 0.2 A/g are in good agreement with the CV curves (Fig. 3b). Moreover, the NiS 2 @OMGC electrode delivers a discharge and charge capacities of 597.9 and 513.4 mAh/g, respectively, achieving a desirable ICE of 85.86%. Subsequently, after 120 cycles at 0.5 A/g, a high reversible capacity of 439.4 mAh/g is retained, with highlevel capacity retention (ca. 91.2%) relative to that of the sixth cycle (Figs. 3c and S4). More importantly, the rate performance of Ni@OMGC and NiS 2 @OMGC electrodes over a wide range of current densities is shown in Fig. 3d; their GCD curves at different current densities are presented in Figs. S5 and 3e. Typically, the initially reversible capacities of NiS 2 @OMGC electrodes were measured to be ~513. 4, 468.8, 437.3, 421.3, 400.3, 378.0, and 355.7 mAh/g at 0.2, 0.5, 1.0, 2.0, 5.0, 10.0, and 20.0 A/g, respectively. When the current density was gradually reduced to 0.2 A/g (Fig. 3d), a reversible capacity of ca. 457.0 mAh/g and high capacity retention (ca. 89.0%) were obtained. Meanwhile, Ni@ OMGC electrodes have a relatively lower specific capacity. Nevertheless, the Ni@OMGC electrodes exhibit a highly stable capacity even if the current increases 100 times. Conversely, the NiS 2 @OMGC electrode's performance is synergistically determined by its NiS 2 phase with high theoretical specific capacity and extremely stable OMGC matrix. Compared with many other NiS x -based electrodes for SIBs [11,16,26,27,[33][34][35][36][37][38][39], such rate performance gives NiS 2 @OMGC a significant competitive advantage, especially at high current densities (Fig. 3f). However, the large-pore structure would inevitably compromise the volumetric performances of NiS 2 @OMGC. Nevertheless, it still outperforms many other electrodes of the same kind for SIBs as well as its precursor (nearly four times that of the initial Ni@OMGC; refer to Fig. 3d) due to its two superior compositions with relatively larger specific capacities (Fig. S6). All of these illustrate the excellent electrochemical energy storage (EES) advantages of NiS 2 @OMGC, especially in applications that do not require high volumetric performance, such as grid-scale battery energy storage stations. We further checked its long-term cycling performances at 10.0 A/g (Fig. 3g). An inevitable capacity loss occurred in the initial tens of cycles before highly stable cycling, which may be related to the slow dissolution and loss of a small amount of S elements [40]. Typically, the reversible capacities reached 308.4 mAh/g after running 1300 cycles at 10.0 A/g. Such a good rate performance and cycling stability, originating from the highly stable structure (Fig. S7), can fully demonstrate the rational composition and structural design of the NiS 2 @OMGC composite.

Electrochemical Na-Storage Mechanism and Kinetic Analyses of NiS 2 @OMGC
Charge storage in an electrode material is achieved either by surface-controlled ion adsorption (like supercapacitors) or solid-state ion diffusion (like batteries). Therefore, it is feasible to distinguish ion behavior in CV measurements by monitoring the response current (i) in an electrochemical reaction as described by the power-law equation: i = av b , where a and b are constants when plotting log(v) vs. log(i) [41]. For fast capacitive ion storage, the b value, namely the slope of the fitted linear plots of log(v) with respect to log(i), is close to 1. However, a typical diffusion-controlled battery behavior has a value of 0.5. Hence, a series of CV measurements were performed between 3.0 and 0.01 V (vs. Na + /Na) by varying scan rates from 2.0 to 0.1 mV/s to explain the high-rate Na-storage performance of NiS 2 @OMGC. The estimated b values for the typical seven-set CV redox peaks labeled in Fig. 4a are all above 0.78 and even reach 0.92−0.99 for the three anodic ones, as shown in Fig. 4a, b. Thus, the sodiation and desodiation of the NiS 2 @OMGC electrode (or its two components) are both highly desirable (pseudo-)capacitive behaviors. To support this statement, the capacitive contributions at different scan rates were calculated using the approximate equation i(v) = k 1 v + k 2 v 0.5 , where i(v) and the two k values represent the total response current at a specific voltage (V) and the fitting constants, respectively [42]. The charge storage in the NiS 2 @OMGC electrode is almost dominated by the (pseudo-)capacitive behavior, as shown by the nearly overlapping CV curves (Figs. 4c and S8). The capacitive contribution reaches ~100% at small scan rates (Fig. 4d), accounting for its excellent Na-storage rate performance and cycling stability. Many factors about ion and electron conduction properties (Na + + e − ⇌ Na 0 ) can be used to interpret the extraordinarily "extrinsic" pseudocapacitive EES performances of NiS 2 @OMGC, such as its well-defined 3DOM morphology with both developed nanoporous structure and excellent overall electrical conductivity, its heteroatom-doped GC matrix with both superior interlayer spacing and local electrical conductivity, and its monodispersed NiS 2 active constitutes with all dimensions less than 10 nm [43].
To further investigate the NiS 2 @OMGC electrodes, in situ EIS [44] and GITT [21] techniques were used for Na-storage kinetics. Figure 4e, f depicts the typical Nyquist plots of a mature NiS 2 @OMGC-based electrode upon the repeated potential drop and increase. The Randle-type equivalent circuit can fit all plots well (Fig. S9), showing that the potential gradually decreased from 3.0 to 0.01 V (corresponding to the sodiation process). And the total resistance (R tot ) is composed of the intrinsic resistances from the electrode, electrolyte, and separator (R s ), the interfacial resistance related to the SEI (R sei ), and the charge transfer resistance at the electrode-SEI interface (R ct ) (Fig. S10) [45], only increases by 4.6 Ω·cm 2 (from 15.9 to 20.5 Ω·cm 2 ; Fig. 4g). Moreover, two large and one slight stepwise increase seems to appear around 1.6/0.9 V and 0.3 V, respectively, in good line with the electrochemical reaction potentials over the CV curves. During the desodiation process, similar phenomena occur, but the phase transformation of metallic Ni to nonconductive NiS 2 leads to a large R tot increase (by 5.0 Ω·cm 2 ) between 1.6 and 2.1 V. Figure 4e, f depicts the regular evolutions of the Warburg regions, namely the linear part of the Nyquist plots associated with the Na + ion diffusion in the electrode. Thus, the apparent diffusion coefficients of Na + ions (D Na+ ) at various stages can be obtained, shown in Fig. 4g, based on the reported Warburg impedance method (in the supporting information) [44]. It is found that the D Na+ values range between 10 −9 and 10 −8 cm 2 /s, ca. 8.3 × 10 −10 cm 2 /s for the NiS 2 -based conversion reaction and 7.4 × 10 −9 cm 2 /s for the GC-based intercalation reaction. Besides, the Ni-NiS 2 redox reactions (such as at the discharged 1.6 and 1.1 V, as well as the charged 1.6 and 2.0 V) would promote the Na + ion diffusion, which may result from the improved ion transfer kinetics at their constantly reconstructed interfaces. Consistent conclusions could be drawn from the GITT experiment (Figs. 4h and S11), including the order of magnitude of the D Na+ values and their variation tendency [21]. Overall, the different Na + diffusion rates of its two components for this specific NiS 2 @OMGC electrode indicate that the multilayered GC shell would provide Na + ions with a convenient diffusion pathway to approach the encapsulated NiS 2 nanocrystal rather than impede this process. The relatively small three dimensions of the NiS 2 nanocrystals over the entire conductive graphenic matrix allow this phase to undergo rapid surface redox reactions, ensuring the superior "extrinsic" pseudocapacitive performance of NiS 2 @OMGC throughout the EES process [43,46].

Performance Evaluation of a NiS 2 @OMGC-based SIHC Device
In order to further evaluate the potential of NiS 2 @OMGC in practical application, SIHC full-cell devices were fabricated using AC as cathode and 0.8 mol/L NaPF 6 dissolved in DEGDME as electrolyte (denoted as NiS 2 @OMGC//AC SIHC, with the mass ratio of NiS 2 @OMGC and AC at 1:3). During discharging (shown in Fig. 5a), when cations (i.e., DEGDME-Na + ) are stored in NiS 2 @OMGC, anions from the electrolyte (PF 6 -) are absorbed by AC. Consequently, a wide voltage window of 4.0-0.01 V was applied to operate the SIHC device because of the safety voltages of the as-applied electrolyte and electrodes (i.e., 4.0-2.5 V and 3.0-0.01 V for AC and NiS 2 @OMGC, respectively; Figs. 5b and S12). Figure 5c depicts its typical CV curves at scan rates ranging from 0.5 to 5 mV/s, where the approximate rectangular shape indicates the superior reversibility and remarkably pseudocapacitive feature of this device [21,46]. Figure S13 depicts specific capacitances of the device, showing that the capacitance reaches up to 43.1 F/g at 1 mV/s. The approximately linear profile of GCD curves at 20.0-0.1 A/g, together with their symmetric triangular shape, also demonstrates the nearly ideal capacitive behavior of the NiS 2 @OMGC//AC SIHC device (Fig. 5d, e). In particular,  (Fig. S14), respectively, rather competitive compared with the reported values (Table S1). The results agreed with the CV results and indicated its superior rate capability. A Ragone plot of power density vs. energy density (based on the total active mass) was also obtained to demonstrate the SIHC device. As shown in Fig. 5f, the maximum energy density of 197.4 Wh/kg was achieved at 0.1 A/g, following a power density of 398.8 W/ kg and thus a current-drain time (E/P) of 29.7 min. The maximum power density of 43.9 kW/kg was achieved at 20.0 A/g, following an energy density of 41.3 Wh/kg and a current-drain time of 3.4 s. Such a comprehensive performance is far superior compared with most of those reported SIHCs [21,30,32,38,42,[47][48][49][50][51]. Finally, we examined its longterm cycling stability at a large current density of 5.0 A/g. Figure 5g exhibits nearly 100% of Coulombic efficiency over all 3000 cycles, confirming the structural stability of NiS 2 @ OMGC as a high-capacity anode for SIHC.

Conclusion
We developed a NiS 2 @OMGC composite with numerous ultrasmall NiS 2 nanocrystals embedded in a 3DOM-structured N, S co-doped GC matrix using a facile thiourea pyrolysis-assisted colloidal crystal template method. The NiS 2 @ OMGC electrode, which benefits from the distinguished 3DOM nano-microstructure, ultrafine NiS 2 nanoparticles, Fig. 5 Electrochemical performances of the NiS 2 @OMGC//AC SIHC device. a Schematic illustration of the working mechanism of the device. b Individual CV curves of its two electrodes in a Na half-cell. c CV curves at different scan rates ranged from 5 to 0.5 mV/s. GCD profiles at current densities of d 1.0-0.1 A/g and e 20.0-2.0 A/g. f Compared Ragone plots of the NiS 2 @OMGC//AC SIHC device with other reported similar systems. g Cycling performance at 5.0 A/g and GC matrix, demonstrates a dominant pseudocapacitive energy storage mechanism and excellent Na-storage performances, such as ultrahigh-rate capabilities and long-term cycling stability to endow a SIHC with simultaneously large energy and power densities. Our developed strategy could be applied to other metal sulfides/oxides/phosphides/selenidebased electrodes for various EES devices.