Alkaline earth metal carboxylate hydrate-mediated controllable self-assembly of three-dimensional hierarchical nanoporous graphene for high-performance supercapacitors†

Xiao Wu‡ ^ab, Canyu Zhong‡ ^c, Lian Ying Zhang ^d, Jianguo Lu ^e, Qinggang He ^a, Qinghua Zhang ^a, Weiyong Yuan *^ab and Chang Ming Li ^f
aCollege of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, China. E-mail: wyyuan@zju.edu.cn
^bNingbo Innovation Centre, Zhejiang University, Ningbo 315100, China
^cSchool of Vanadium and Titanium & Key Laboratory of Sichuan Province for Critical and Strategic Materials Based on Vanadium and Titanium, Panzhihua University, Panzhihua 617000, China
^dCollege of Materials Science and Engineering, Qingdao University, Qingdao 266071, China
^eState Key Laboratory of Silicon Materials, School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China
^fInstitute for Materials Science and Devices, Suzhou University of Science and Technology, Suzhou 215011, China

First published on 2nd July 2025

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Introduction

Graphene has garnered significant attention over the past decade due to its immense potential in diverse fields such as optoelectronics, biomedicine, and electrochemical energy conversion and storage.^1–3 In particular, it has demonstrated bright prospects as an electrode material for supercapacitors, a key type of highly promising next-generation energy storage device, due to its large specific surface area, excellent conductivity, and high electrochemical stability.^4,5 Nanoporous graphene (NPG), which refers to graphene with nanopores in its basal plane, not only maintains the exceptional properties of graphene nanosheets but also introduces additional unique properties induced by the nanopores, such as greatly reduced resistance to ion diffusion, significantly enlarged surface area, and remarkably enriched edge sites, all of which are favorable to the improvement of the supercapacitor performance.^6,7 The three-dimensional (3-D) nanostructures of NPG offer significant advantages over the conventional two-dimensional ones, as they mitigate nanosheet restacking to increase accessible surface area, offer interconnected pathways to facilitate electron transport, and enhance the stability under harsh electrochemical conditions, thereby further amplifying the unique properties of graphene for supercapacitors.^8,9 Further creation of a hierarchical nanoporous structure by introducing larger pores during the formation of 3-D NPG will induce synergistic effects to simultaneously increase the surface area and promote the ionic diffusion, thus remarkably boosting supercapacitor performance, including the capacitance and rate performance.^5,10 Hence, the fabrication of 3-D hierarchical NPG for supercapacitor applications is highly desirable.

Reported methods to fabricate NPG include electron beam irradiation, ultraviolet-induced oxidative etching, barrier-guided chemical vapor deposition (CVD), block copolymer/nanosphere lithography, catalytic/photocatalytic decomposition and chemical etching.^7,11–16 However, the techniques of electron beam irradiation, ultraviolet-induced oxidative etching and barrier-guided CVD are not suitable for mass production or large-scale pore generation and the methods of electron beam irradiation and barrier-guided CVD require costly and sophisticated equipment;^13,17 although block copolymer/nanosphere lithography is scalable for large-area patterning, the use of a graphene film supported on a planar substrate is required and subsequent reactive ion etching using toxic gases is frequently adopted;¹⁴ catalytic and photocatalytic approaches offer the potential for large-scale production of NPG, but they necessitate intricately designed catalytic reactions and catalysts, as well as external light irradiation for photocatalytic decomposition;^15,18 chemical etching using KOH or H₂O₂ activation/hydrothermal steaming represents a facile approach for the fabrication of NPG, but this process is inherently uncontrollable and often leads to detrimental effects on the intrinsic chemical/electronic structure of graphene.¹⁹ In addition, it remains a formidable challenge to fabricate 3-D NPG using the aforementioned methodologies, and it is even more challenging to fabricate 3-D hierarchical NPG with the existing technologies.^20,21 To date, it has proven as an arduous task to create 3-D hierarchical NPG structures, and it is also elusive to employ them as electrode materials for high-performance supercapacitors. Although there are some reports on using NPG for supercapacitor applications, no one has employed the 3-D hierarchical NPGs as supercapacitor materials. The understanding about the relationship between the structure and supercapacitor performance is still poor due to lack of controllability for the fabrication of porous graphene. In addition, the supercapacitor performances of graphene-based materials need to be further enhanced.

Self-assembly of metal salts on graphene oxide (GO) via their interaction with the oxygen containing groups could be a highly promising strategy for the synthesis of 3-D NPG due to the following great advantages: firstly, the metal salts could be in situ converted to nanoparticles to inhibit the restacking of graphene nanosheets, thus leading to the formation of 3-D graphene;^22,23 secondly, the anions of the salts could be designed to release activation agents during the formation of these nanoparticles for introduction of nanopores;^7,24 thirdly, the nanoparticle size and density could be controlled by changing the self-assembly conditions, thus resulting in the formation of NPG with controlled pore size and pore density;^25,26 lastly, these nanoparticles could be removed after the formation of 3-D NPG.^27,28 To date, utilization of self-assembled metal salts with the function of in situ releasing activation agents for the controllable fabrication of 3-D hierarchical NPG has not been reported.

Carboxylate hydrates of alkaline earth metals (M(RCOO)₂·xH₂O) could be an ideal candidate of the metal salts to be assembled on GO for the synthesis of 3-D hierarchical NPG since it can be decomposed thermally to form alkaline earth metal oxides, CO₂, and H₂O, of which the alkaline earth metal oxides can be easily removed using acid, and CO₂ and H₂O are frequently used activation agents for the introduction of nanopores in the carbon materials.^7,24 In this study, for the first time, 3-D hierarchical NPG was controllably synthesized through self-assembled M(RCOO)₂·xH₂O on GO to simultaneously generate etchants and nanoparticle (NP) spacers, using Mg(CH₃COO)₂·4H₂O (Mg(Ac)₂·4H₂O) as the model M(RCOO)₂·xH₂O. This 3-D hierarchical NPG exhibits several superior properties: (1) it has ultrahigh specific surface area and excellent conductivity, which greatly increase the capacitance of supercapacitors; (2) its extremely abundant nanopores with numerous edge sites can greatly facilitate the electron transfer and ion diffusion, thus remarkably enhancing the capacitance and rate capability; (3) the 3-D graphene-based structure makes it highly stable under harsh electrochemical conditions, thereby promoting the cycling stability of the supercapacitors. The possible mechanism underlying the self-assembly process was investigated. The application of this novel nanostructured graphene as an electrode material for supercapacitors was further explored.

Experimental

Materials

Natural flake graphite, concentrated H₂SO₄ (98%), KMnO₄, NaNO₃, H₂O₂ (30%), and concentrated HCl (37%) were all purchased from Sinopharm Chemical Reagent Co., Ltd. Mg(Ac)₂·4H₂O, Ca(HCOO)₂, and KOH were obtained from Shanghai Aladdin Biochemical Technology Co., Ltd. The deionized (DI) water used throughout all experiments was produced by a Milli-Q water purification system (Millipore).

Preparation of graphene oxide

GO was synthesized using the modified Hummers' method as previously described in the literature.²⁹ 2.0 g of natural flake graphite and 2.0 g of NaNO₃ were carefully added into a flask containing 95 mL of concentrated H₂SO₄ (98%), followed by sonication for 1 h. The mixture was subsequently cooled to 0 °C in an ice bath, followed by the addition of 12.0 g of KMnO₄ under continuous stirring. The flask was then equilibrated to room temperature and subsequently heated at 45 °C in an oil bath. After stirring for 2 h, 100 mL of DI water was added to the flask. The mixture was then allowed to cool for 10 h before dropwise addition of aqueous H₂O₂ (30%) until gas evolution ceased. Finally, the mixture was repeatedly centrifuged and washed using diluted HCl (5 wt%) followed by DI water until a neutral pH was achieved. The GO product was obtained after freeze-drying.

Preparation of 3-D NPG

The GO powder was dispersed in DI water via ultrasonication to form a solution with a concentration of 7.8 mg mL⁻¹. Then 8 mL of the above GO solution was added dropwise into 32 mL of Mg(Ac)₂·4H₂O aqueous solution. After stirring overnight, the precursors were freeze-dried and subsequently calcined in a tube furnace in Ar at 800 °C for 2 h. Finally, the product was filtered and rinsed with diluted HCl (5 wt%) and DI water sequentially. The concentrations of Mg(Ac)₂·4H₂O were adjusted for obtaining different NPG products, denoted as G-0, G-40, G-100 and G-200. The numerical labels corresponded to the amounts (in mg) of Mg(Ac)₂·4H₂O added into 32 mL of DI water. Additionally, the investigation encompassed Ca(HCOO)₂ as another carboxylate hydrate of an alkaline earth metal, and the resulting product was designated as G-Ca-100, with the label indicating the addition of 100 mg of Ca(HCOO)₂ to 32 mL of DI water.

Characterization

Field emission scanning electron microscopy (FESEM) images were obtained using a JSM-7800F electron microscope (JEOL, Tokyo, Japan) operating at 10 kV. During FESEM testing, corresponding EDS (INCA X-Max 250) spectra were collected to analyze the elemental composition of samples. Transmission electron microscopy (TEM) images and selected area electron diffraction (SAED) patterns were acquired on a JEM 2100F electron microscope (JEOL, Tokyo, Japan) operating at 200 kV. XRD patterns were obtained using a Shimadzu XRD-7000 diffractometer with Cu Kα line with the speed of 2° min⁻¹. Brunauer–Emmett–Teller (BET) analysis was implemented by using a Micromeritics (ASAP 2020, ver. 4.02) surface area and pore size analyzer. XPS spectra were recorded on a Thermo Scientific ESCALAB 250Xi XPS using Al Kα radiation as the excitation source.

Fabrication of supercapacitors

The electrode slurry was prepared by homogeneously mixing the NPG sample and poly(vinylidene fluoride) (PVDF) with a weight ratio of 19:1 in N-methylpyrrolidone (NMP). The viscous slurry was uniformly coated on the nickel foam by using an automatic coating machine. After vacuum drying at 80 °C for 12 h, the working electrode was cut into discs with a diameter of 14 mm and the areal mass density of active substance is approximately 4 mg cm⁻². The working electrodes were then immersed in 3 M KOH for 3 h to ensure adequate electrolyte infiltration. A 35 μm-thick cellulose membrane was interposed between two identical working electrodes within a CR2032 button cell. Following injection of moderate 3 M KOH electrolyte and encapsulation, the symmetrical supercapacitor devices were fully assembled.

Electrochemical measurements

The electrochemical measurements were conducted using a CHI 760E electrochemical workstation. Cyclic voltammetry (CV) tests were conducted within the voltage range of 0 to 1 V, with scan rates ranging from 5 to 100 mV s⁻¹. The galvanostatic charge–discharge (GCD) tests were carried out at the same voltage range with current densities between 0.5 to 20 A g⁻¹. Electrochemical impedance spectroscopy (EIS) tests were conducted at open circuit potential (OCP) over a frequency range of 10⁵ to 0.1 Hz with an amplitude of 5 mV. The long-term cycle life test was performed on the battery charging and discharging testing system (Neware Technology Limited). The gravimetric specific capacitance (C_g) was determined from the GCD discharge curve using the following equation:³⁰

Cg = 2 × IΔt/mΔV	(1)

where C_g, I, m, ΔV and Δt correspond to the gravimetric specific capacitance (F g⁻¹), discharge current (A), mass of active material on one electrode (g), voltage change excluding the IR drop (V), and discharging time (s), respectively. The gravimetric energy density (E_g, Wh kg⁻¹) and power density (P_g, W kg⁻¹) of supercapacitors were calculated using the following equations.³¹

Eg = 1/2 × Cg(ΔV)2 × 1000/3600	(2)

Pg = 3600 × Eg/Δt	(3)

Results and discussion

Synthesis and characterization of 3-D hierarchical NPG

The synthesis process of 3-D hierarchical NPG is illustrated in Scheme 1, utilizing Mg(Ac)₂·4H₂O as the model M(RCOO)₂·xH₂O. Firstly, GO@Mg(Ac)₂·4H₂O was formed through the electrostatic interaction and coordination bonding between Mg(Ac)₂·4H₂O and oxygen-containing groups on GO. Then, under high temperature, the decomposition of GO@Mg(Ac)₂·4H₂O results in the formation of CO₂, H₂O, and MgO NPs supported on the reduced graphene oxide (rGO) surface. Subsequently, in situ reaction of CO₂ and H₂O with rGO leads to the formation of nanopores, while MgO NPs acted as spacers between graphene nanosheets to mitigate their restacking. Finally, these MgO NPs were removed through acid wash, yielding 3-D NPGs.

The XRD patterns of G-200 before and after acid wash are shown in Fig. 1A. Prior to washing, three characteristic peaks are observed at 24.1°, 43.0°, and 62.6°, which correspond to (002) planes of graphitic carbon, (200) planes of cubic MgO, and (220) planes of cubic MgO, respectively.³² After acid wash treatment, the two characteristic peaks associated with MgO have disappeared, indicating the removal of spacers. In addition, the G(002) diffraction peak of 3-D NPG shifts from 25.8° to 24.1°, with an increase in Mg(Ac)₂·4H₂O concentration from G-0 to G-200 (Fig. 1B). Consequently, the interlayer distance of graphene increases from 3.44 to 3.68 Å according to the Bragg equation.³³ This suggests that MgO NPs act as the spacers during the synthesis process of 3-D NPG, which will be discussed later. The crystal structure of G-200 after removal of MgO was further investigated via SAED (Fig. S1†). Three diffraction rings are observed, which correspond to (002), (101), and (110) planes of graphitic carbon.³⁴ This result indicates the polycrystalline nature of NPG.

Fig. 1C and D shows the high-resolution XPS spectra of G-200. The C 1s spectrum can be deconvoluted into five peaks located at 284.6, 286.1, 287.1, 289.1, and 292.04 eV, which correspond to C–C/CC, C–O, CO, COOH, and π–π* shake-up, respectively.^35,36 The O 1s spectrum can be well fitted to three peaks located at 533.5, 532.1, and 530.7 eV, which are ascribed to C–OH, CO, and COOH groups, respectively.^35,37 Therefore, there are OH, CO, and COOH groups on the surface of graphene.

The Raman spectra of G-0, G-40, G-100, and G-200 (Fig. S2†) all exhibit two characteristic peaks at 1352 and 1589 cm⁻¹, which correspond to the D and G bands, respectively.³⁸ This result confirms the formation of graphene. The I_D/I_G ratio is an indicator of the degree of graphitization. The I_D/I_G ratios of G-0, G-40, G-100, and G-200 are 0.64, 0.56, 0.46, and 0.40, respectively. The coherence length L_a can be calculated based on the equation:³⁹

La = (2.4 × 10−10) × λ4(ID/IG)−1	(4)

where λ is the Raman laser wavelength (532 nm in this experiment). The calculated coherence lengths of G-0, G-40, G-100, and G-200 are 30.0, 34.3, 41.8, and 48.1 nm, respectively. These results indicate an enhancement in the degree of graphitization of NPG with the increasing concentration of Mg(Ac)₂·4H₂O.^40,41

Fig. 2 depicts FESEM images of graphene synthesized using varied quantities of Mg(Ac)₂·4H₂O before and after acid wash. Uniform distributions of MgO NPs are observed on graphene in G-40, G-100, and G-200 samples before acid wash (Fig. 2B–D). The NP density of MgO on G-100 is significantly higher compared to that on G-40. However, the NP size of MgO on G-200 (∼120 nm) is much larger than those observed on G-100 (∼25 nm) and G-40 (∼10 nm), despite their lower densities. This significant increase in NP size for G-200 can be attributed to the excess amount of Mg(Ac)₂·4H₂O surpassing the available binding sites on GO. After acid wash, no Mg element is detected in EDX spectrum of G-200 sample (Fig. S3†), indicating complete removal of MgO NPs. In addition, these samples exhibit numerous wrinkles, thus forming 3-D interconnected structures with pores among the graphene nanosheets (Fig. 2F–H). In particular, the G-200 sample shows the most wrinkled structure (the height and area of each wrinkle are much larger than that in G-40 and G-100) (Fig. 2F–H). In comparison, G-0 displays a 2-D dense structure due to severe restacking of graphene nanosheets (Fig. 2E). The low-magnification FESEM images of G-200 (Fig. S4A†) and G-0 (Fig. S4B†), along with the corresponding inset of digital photo, provide a more visually comprehensive representation of the disparities between 3-D and 2-D structures.

Fig. 3 presents TEM images of G-0, G-40, G-100, and G-200. No pores exist in G-0 (Fig. 3A and E); however, pores with sizes of 2.81 ± 1.89, 3.42 ± 1.35, and 5.31 ± 1.56 nm (see their size distributions in Fig. S5†) are uniformly distributed in the basal planes of G-40 (Fig. 3B and F), G-100 (Fig. 3C and G), and G-200 (Fig. 3D and H). Therefore, the pore size can be controlled by adjusting the amount of Mg(Ac)₂·4H₂O. The densities of pores are 7500, 6889, and 5445 pores per μm² for G-40, G-100, and G-200, respectively. These pore densities are the highest reported to date.

Fig. 4 displays the N₂ adsorption–desorption isotherms of G-0, G-40, G-100, and G-200. The type IV characteristics is observed for G-200: the steep increase at low relative pressure, the significant hysteresis at medium relative pressures, and the almost vertical tail at a relative pressure close to 1.0 shows the presence of micropores, mesopores, and macropores.^42,43 The BET surface area positively correlates with the concentration of Mg(Ac)₂·4H₂O, except for G-40 (Table 1). G-200 exhibits a specific surface area of 885.87 m² g⁻¹, which is 1.78 times higher than that of G-0 (496.64 m² g⁻¹). The similarity in specific surface area between G-40 and G-0 can be attributed to the formation of smaller-sized MgO NPs in G-40 (Fig. 2B) under these conditions compared to the inter-sheet distance of graphene nanosheets in G-0. The N₂ adsorption capacities of G-100 and G-200 at 0.01P/P₀ is significantly higher compared to G-40 and G-0, indicating a greater number of micropores in G-200 and G-100. Pore size distributions are determined using the BET model and non-local density functional theory (NLDFT) with a carbon slit pore model (Fig. 4B–D), which accurately describes the physical adsorption of N₂ on energetically uniform surfaces and pore size distributions ranging from 0.5 to 100 nm in materials.^44,45 The calculated results exhibit a good agreement with experimental data, except for the relative pressure (P/P₀) range of 0–0.1 in G-0 (Fig. 4B). This discrepancy may be attributed to the scarcity of micropores in G-0, as evidenced by the low amount of adsorbed N₂ in the micropore region (Fig. 4A). The absence of pores with widths smaller than approximately 2.5 nm for G-0, as shown in Fig. 4C, is consistent with the fitting results presented in Fig. 4B. However, the minimum values of pore widths for G-40, G-100, and G-200 reach 1.95, 1.47, and 1.41 nm, respectively. In addition, G-200 exhibits higher values of dV/dW compared to G-0, G-40, and G-100 for pore widths ranging from about 16 nm and above, and thus higher cumulative pore volume in this pore width range. This can be attributed to the incorporation of MgO NPs spacers. When increasing the content of Mg(Ac)₂·4H₂O, the size of MgO NPs increases (Fig. 2B–D), thereby effectively enlarging the interlayer spacing between graphene nanosheets while simultaneously mitigating their restacking.

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The smaller dV/dW of G-40 than that of G-0 across this range of pore widths could be attributed to the dominant crosslinking effect over the spacer effect of ultra-small MgO (4–8 nm), as well as structural restoration through addition of Mg(Ac)₂·4H₂O (Fig. 4B).^46,47

Possible mechanism for the formation of 3-D hierarchical NPG

To investigate the mechanism underlying nanopore formation in the basal plane of graphene, another carboxylate salt Ca(HCOO)₂ with the highest O/C ratio but without crystalline water was employed to synthesize NPG. The BET results in Fig. 5 indicate that the volume of pores with widths smaller than ∼8 nm in the obtained G-Ca-100 is lower compared to the G-100 synthesized using Mg(Ac)₂·4H₂O (no pores larger than 8 nm in the basal planes can be obtained). The higher O/C ratio of Ca(HCOO)₂ compared to Mg(CH₃COO)₂ results in a greater amount of CO₂ formed during pyrolysis, indicating that crystalline H₂O plays a crucial role in the formation of nanopores in the graphene basal plane. Interestingly, graphene with micropores was also obtained from Ca(HCOO)₂ without crystalline water, suggesting that CO₂ is also essential for generating nanopores.

It has been reported that transition metal oxides could interact with graphene basal planes through carbon spill-over from graphene, resulting in the formation of pores. This is attributed to the reduction of transition metal oxides to transition metal carbides at temperatures above 600 °C.^48,49 However, MgO exhibits remarkable thermal stability up to 1000 °C, rendering it unreactive towards graphene in terms of reduction reactions.⁵⁰ As evidence, the XRD pattern in Fig. 1A shows no peaks other than those from graphene and MgO following calcination at 800 °C. Therefore, the presence of MgO NPs does not contribute to the formation of nanopores in the basal plane of graphene. It is worth noting that the volume of mesopores in G-100 and G-200 is greater than that in G-0, and as the concentration of Mg(Ac)₂·4H₂O increases, there is an increase in pore volume. This clearly indicates that the in situ self-assembled MgO NPs are favorable for the development of mesopores and 3-D structures.

Based on the experimental data, the formation of 3-D hierarchical nanoporous graphene could be ascribed to the following reasons: both CO₂ and H₂O are critical for the formation of nanopores in the basal planes of graphene; in addition, the in situ formed MgO NPs act as spacers to promote the generation of 3-D graphene structures with larger pores including the macropores and nanopores.

Supercapacitor performance and mechanism investigation

The 3-D hierarchical NPG samples were utilized as electrode materials for supercapacitors in a two-electrode system. The electrochemical performances of various NPG samples using 3 M KOH as the electrolyte are presented in Fig. 6. The CV curves with a scan rate of 50 mV s⁻¹ are presented in Fig. 6A. All the supercapacitors exhibit regular quasi-rectangular shape without any discernible redox peaks, indicating the typical electrical double layer capacitance (EDLC) characteristics.⁵¹ As the amount of Mg(Ac)₂·4H₂O increases, there is a significant increase in CV curve area (also see the CV curves of G-0, G-40, G-100 and G-200 samples at scan rates ranging from 5 to 100 mV s⁻¹ in Fig. S6†). G-200 exhibits the biggest CV curve area, indicating its largest specific capacitance. Fig. 6B illustrates the galvanostatic charge–discharge (GCD) curves at a current density of 0.5 A g⁻¹. All the NPG samples show a symmetric triangle shape, further indicating the EDLC behavior.⁵² The specific capacitances of G-0, G-40, G-100, and G-200 electrodes are calculated to be 63, 75, 131, and 186 F g⁻¹, respectively. To the best of our knowledge, the value of the G-200 electrode represents the highest reported specific capacitance for supercapacitors utilizing graphene as the electrode materials under identical testing conditions (see Table S1† for comparison with reported representative graphene materials). The IR drop observed during the discharge curve is attributed to the internal resistance of materials. As shown in Fig. S7,† G-200 exhibits a significantly smaller IR drop compared to other samples under a current density of 5 A g⁻¹, indicating its lower equivalent series resistance.^31,53 The GCD curves of different NPG samples under current densities from 0.5 to 20 A g⁻¹ are shown in Fig. S8.† The rate capabilities are calculated based on the above GCD curves and the corresponding results are presented in Fig. 6C. The G-200 sample exhibits the highest specific capacitance among all materials. In addition, a gradual decrease in specific capacitance is observed as the current density increases from 0.5 to 20 A g⁻¹. In terms of capacitance retention rates at a high current density of 20 A g⁻¹, G-200 exhibits a retention rate of 79.6%, while G-0, G-40, and G-100 demonstrate retention rates of 60.3%, 56.1%, and 71.0%, respectively.

The capacitance is mainly determined by the surface area and electronic and ionic conductivity. It is discovered that although the specific surface area of G-200 is only 1.78 times more than G-0, the capacitance of G-200 is 2.95 times that of G-0. Therefore, the surface area is not the main contributor to the much higher capacitance. This is also supported by the fact that the BET surface area of G-200 is only 1.15 times that of G-100 and 1.84 times that of G-40, but its capacitance is 1.42 and 2.48 times, respectively. Here, we argue that the 3-D nanoporous structure of graphene could greatly promote the electron transfer and ion diffusion to enhance both the capacitance and rate performance. The number of edge sites can be estimated through the multiplication of average pore circumference and pore density. The corresponding values calculated from Fig. 3 are 66176, 73980, and 90787 nm μm⁻² for G-40, G-100 and G-200, respectively. Thus, with an increased content of Mg(Ac)₂·4H₂O, the density of edge sites increases significantly, leading to facilitated electron transfer and ion diffusion.^54,55 It is noteworthy that although the edge site density of G-40 is much greater than that of G-0, its capacitance is only slightly higher and its rate capability does not improve. This is due to small inter-sheet distance in G-40 restricting the accessibility of edge sites and retarding the ion diffusion, particularly at high current density. This result indicates that the 3-D macro and mesoporous structure also plays a critical role in the enhanced capacitance and rate performance of 3-D NPG.

The effect of 3-D hierarchical nanoporous structure on the electron transfer and ion diffusion was further explored by EIS, which is a widely utilized technique for evaluating the electron transfer and ion diffusion of supercapacitor electrodes. The Nyquist plots and corresponding equivalent circuit of electrodes are displayed in Fig. 6D. In the high-frequency region, the intersection of the curve and X-axis represents the series resistance (R_s), which includes the intrinsic resistance of electrode materials, electrolyte, and contact resistance between electrodes and current collectors.⁵⁶ The R_s values for these supercapacitors are quite small and almost the same, implying the electrodes are in the same electrolyte environment. The semicircle observed in the mid-frequency region corresponds to the charge transfer resistance (R_ct).⁵⁷ Among these electrodes tested, G-200 exhibits the lowest R_ct value. In addition, the R_ct value decreases with the increase of Mg(Ac)₂·4H₂O concentration and the fitting values are listed in Table 2. This trend is the same as that of the edge site density, further suggesting the nanopores in the graphene basal planes play a critical role in the promotion of the electron transfer. It is worthy of a note that although G-40 has a much higher edge site density than G-0, its R_ct value is only slightly lower than that of G-0. Therefore, this result further indicates the great importance of the 3-D graphene structure. The slopes of the straight lines in the low-frequency region quantify the diffusion rate of electrolyte ions, with higher values indicating faster diffusion rates.⁵⁸ The samples prepared with the addition of Mg(Ac)₂·4H₂O (G-40, G-100, and G-200) exhibit higher slopes compared to that without Mg(Ac)₂·4H₂O (G-0). In addition, the slope increases with increasing the concentration of Mg(Ac)₂·4H₂O, and the G-200 electrode exhibits the highest ion diffusion rate. The essentially vertical low-frequency curve of G-200 also further indicates its ideal capacitive behavior. The ion diffusion coefficient can be calculated by the following formulas:⁵⁹

D = 1/2 × (RT/Aσn2F2C)2	(5)

Zre = Rs + Rct + σω−0.5	(6)

where D is the ion diffusion coefficient (cm² s⁻¹), R is the gas constant (8.314 J mol⁻¹ K⁻¹), T is the room temperature (298.15 K), A is the area of the electrode (cm²), n is the number of transfer electrons, F is the Faraday constant (96485 C mol⁻¹), C is the electrolyte concentration (mol mL⁻¹), σ is the Warburg coefficient (Ω cm² s^−1/2), Z_re is the real part of Nyquist plot, and ω is the angular frequency (rad s⁻¹). According to the formula (6), a linear correlation exists between Z_re and ω^−0.5, as demonstrated by the linear fitting curves in Fig. S9,† with a slope of Warburg coefficient. The Warburg coefficients and ion diffusion coefficients, as presented in Table 2, provide quantitative evidence of the enhanced ion diffusion capability facilitated by the nanoporous structure of graphene. The much higher ion diffusion coefficients of G-100 and G-200 but only slightly higher one of G-40 compared to that of G-0 further indicates the promotion effect of the 3-D hierarchical porous structure on the ion diffusion.

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The Bode plots of different electrodes are shown in Fig. 6E. G-200 has a phase angle of −82.5° at a low frequency of 0.01 Hz. This value is close to the ideal phase angle of −90°, thus confirming its capacitive behavior. When the phase angle is −45°, the frequencies of G-0, G-40, G-100, and G-200 are 0.21, 0.26, 0.28, and 0.35 Hz, respectively (Fig. 6F). According to the equation τ₀ = 1/f₀, the relaxation time constants (τ₀) of G-0, G-40, G-100, and G-200 at −45° are 4.76, 3.85, 3.57, and 2.86 s, respectively. Therefore, G-200 exhibits the shortest relaxation time, indicating it has the highest ion diffusion capability and fastest response during the charging and discharging process.⁶⁰

To further investigate the charge storage mechanism of NPG as supercapacitor electrode materials, the capacitance contributions from surface-controlled and diffusion-controlled processes are analyzed based on the CV curves. For supercapacitor, the correlation between peak current (i) and scan rate (ν) follows the power law:

i = aνb	(7)

where a and b are both constants. As shown in Fig. 7A, there is a linear relation between log(ν) and log(i), with the slope corresponding to the b value. When b equals 1, the charge storage process is surface-controlled and exhibits ideal capacitive behavior; when b is 0.5, the electrode reaction is diffusion-controlled.⁶¹ The calculated b value of G-200 is 0.967, suggesting the charge storage process is controlled by both mechanisms, but with the surface-controlled behavior dominant. The contribution ratios of surface (Q_s, k₁ν) and diffusion (Q_d, k₂ν^1/2) control are determined based on the following equation:⁶²

i(ν) = k1ν + k2ν1/2	(8)

where k₁ and k₂ correspond to the slope and intercept of the line represented by the linear equation (i/ν^1/2 and ν^1/2 as the variables):

i/ν1/2 = k1ν1/2 + k2	(9)

As shown in Fig. 7B, the CV curve of G-200 at 50 mV s⁻¹ is divided into two parts of Q_s and Q_d, with the corresponding areas reflecting the capacitance contributions. The percentages of surface and diffusion-controlled contribution at different scan rates for G-200 is summarized in Fig. 7C. The contribution percentage of surface-controlled capacitance increases from 72.7% to 93.4% as the scan rate is increased from 5 to 100 mV s⁻¹. This is due to the hindrance of the ion diffusion process at the high scan rate. This result further demonstrates the predominance of surface-controlled process, with only a minor contribution from the diffusion-controlled process.

Based on the above experimental data, the high capacitance and rate performance could be ascribed to the following reasons: (1) the 3-D NPG provides ultrahigh surface area; (2) the nanopores in the basal planes of graphene offer numerous edges sites to greatly promote the electron transfer and ion diffusion; (3) the 3-D interconnected structure with macropores and mesopores create fast pathways to facilitate ion transport and enhance the electron transfer. The mechanism for the high supercapacitor performance of the 3-D hierarchical NPG is illustrated in Scheme 2.

The energy density and power density are important parameters for the practical applications of supercapacitors. The Ragone plots of supercapacitors based on NPG samples are shown in Fig. 8A, revealing a gradual decline in energy density as power density increases. The G-200 supercapacitor demonstrates a significantly higher energy density of 25.8 Wh kg⁻¹ at a power density of 500 W kg⁻¹, surpassing that of the G-0 (8.8 Wh kg⁻¹), G-40 (10.4 Wh kg⁻¹) and G-100 (18.2 Wh kg⁻¹) supercapacitors. Even at a high power density of 15000 W kg⁻¹, the energy density remains at a remarkable value of 15.7 Wh kg⁻¹. To our knowledge, the performance in terms of power density and energy density is the highest among the reported graphene-based supercapacitors (see Table S2† for the performance of representative graphene-based supercapacitors).

The stability of supercapacitors is also very critical for their applications. The cycling performances of G-200 and G-0 supercapacitors at a current density of 5 A g⁻¹ are presented in Fig. 8B. The initial specific capacitance of G-200 is 161 F g⁻¹. After undergoing 10000 cycles of charge and discharge, it still exhibits a capacitance of 156.6 F g⁻¹, which is 97.2% of the initial value. In comparison, for G-0, the capacitance decreases from 55 F g⁻¹ to 51 F g⁻¹ after 10000 cycles, and only 93.0% of the initial capacitance is retained. This result unequivocally demonstrates the exceptional cycling stability of the supercapacitor based on G-200. The excellent cycling stability of this supercapacitor is ascribed to the high electrochemical stability of graphene and the robust 3-D structure.^23,63

Conclusions

For the first time, 3-D hierarchical NPG has been synthesized via M(RCOO)₂·xH₂O-mediated controlled self-assembly, in which the noncovalently bonded M(RCOO)₂·xH₂O simultaneously creates metal oxide NPs to serve as spacers and CO₂ and H₂O as pore generators. The pore size and pore density in the graphene basal planes can be tailored by varying the amount of M(RCOO)₂·xH₂O. These unique nanostructured graphenes were subsequently investigated as the electrode materials for supercapacitors, exhibiting a highly tunable specific capacitance. The most outstanding one achieves a specific capacitance of 186 F g⁻¹ at 0.5 A g⁻¹, surpassing all reported graphene-based supercapacitors in the same electrolyte. In addition, it can maintain 79.6% of capacitance retention at 20 A g⁻¹, revealing a superior rate performance compared to reported supercapacitors. Furthermore, no significant decrease in capacitance was observed even after 10000 charge–discharge cycles, demonstrating excellent cycling stability. The ultrahigh capacitance and rate capability are ascribed to the 3-D hierarchical nanoporous structure of graphene with extremely rich edge sites remarkably increasing the surface area and promoting electron transfer and ion diffusion. This study not only presents an innovative strategy for synthesizing unique graphene-based materials with superior capacitive properties but also provides valuable scientific insights into the mechanism underlying the self-assembly process, which could be further extended to fabricate various other 3-D hierarchical nanoporous carbons for diverse important applications.

Data availability

The data supporting this article have been included as part of the ESI.†

Author contributions

Xiao Wu: writing – original draft, investigation. Canyu Zhong: writing – original draft, investigation. Lian Ying Zhang: investigation, validation. Jianguo Lu: investigation, validation. Qinggang He: investigation, validation. Qinghua Zhang: project administration, resources. Weiyong Yuan: writing – review and editing, conceptualization, resources, supervision. Chang Ming Li: investigation, validation.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was financially supported by the Yongjiang Talent Introduction Programme (Grant No. 2021A-155-G), Natural Science Foundation of Ningbo, China (Grant No. 2022J156), Research Fund of Ningbo Innovation Centre, Zhejiang University (Grant No. 704004J20240524 and 704004G20220616), and Start-up Grant from Zhejiang University, China (Grant No. 1140457B20210129).

Notes and references

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Footnotes

† Electronic supplementary information (ESI) available: Raman spectra of G-0, G-40, G-100, and G-200; EDX spectra of G-200 before and after acid wash; low-magnification FESEM images G-200 and G-0; pore size distributions of G-40, G-100, and G-200 directly measured from the TEM images; CV curves of G-0, G-40, G-100, and G-200 at scan rates ranging from 5 to 100 mV s−1; specific capacitance (F g−1) relating to graphene materials in KOH; the IR drop of G-0, G-40, G-100 and G-200 samples under a current density of 5 A g−1; GCD curves of G-0, G-40, G-100 and G-200 samples under current densities from 0.5 to 20 A g−1; the plots of the real part of impedance as a function of the inverse square root of angular frequency for G-0, G-40, G-100, and G-200; comparisons of power density and energy density in graphene-based supercapacitors. See DOI: https://doi.org/10.1039/d5ta02571k

‡ Xiao Wu and Canyu Zhong contributed equally to this work.

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