(a) A schematic show of the simple and green process of synthesizing porous 3D graphene-based materials.(b) Low magnification and (c) high-resolution scanning electron microscopy (SEM) images of products from the mixtures of PF and GO with optimized ratios, which exhibited sponge-like morphology and porous structure. (d) Low magnification and (e) high-resolution transmission electron microscopy (TEM) images of products from the mixtures of PF and GO with optimized ratios, which also showed a dense 3D pore structure with highly curved or wrinkled surface.

All the graphene domain models were designed as foursquare plane including armchair and zigzag sides for convenience. The models represent graphene domains with different size and the total carbon atoms: G3: 3.2666 × 3.1980 nm², 432 C; G4: 4.1188 × 4.1820 nm², 700 C; G5: 4.9710 × 5.1660 nm², 1032 C; G6: 6.2492 × 6.1500 nm², 1530 C; G7: 7.1014 × 7.1340 nm², 2006 C; G8: 7.9536 × 8.1180 nm², 2546 C. (a) The accessible solvent (N₂) SSA of single layer graphene domains with different dimensional size and edge carbon percent. The accessible solvent (N₂) SSA of graphene domains are significantly higher than the infinite ideal/infinite graphene sheet (2675 m²/g) and increase remarkably with the decrease of graphene domain size, which means that when the graphene domains are small, significant contribution for the SSA comes from the edge part. (b) The accessible solvent (N₂) SSA of graphene stacking domains with different stacking layer number. The layer spacing of graphene stacking domains was set to 0.4 nm. With the same sheet size, the SSA values decrease dramatically with more stacking layers for the graphene domains.

The 3D model of the proposed structure of our porous graphene-based material was established in Materials Studio Modeling (version 4.4, Accelrys), where the units are sp² graphene domains with dimensional size of 4–6 nm and curved and lapped irregularly. This model was first optimized using molecular mechanics method, and its accessible solvent SSA was calculated to be 3536 m²/g using a simple Monte Carlo integration technique where the probe molecule is “rolled” over the framework surface as mentioned above. These results again are consistent with both the experimental and the modeling SSA results above for our products, thus this model could be used as a 3D representative model for our products.

(a) PSD of RP20, G-HA and all the optimized materials, which are based on a slit NL-DFT model from the experimental nitrogen adsorption data. (b) E-SSA of these materials when using EMIMBF₄ as electrolyte for supercapacitor. Based on these experimental PSD and DFT-SSA data from the NL-DFT method, E-SSA is defined as the part of total DFT-SSA above the size of guest molecules or ions. Positive ion EMIM⁺ with size of ~0.76 nm which is larger than the negative balancing ion BF₄⁻ is considered here. As one example, product PF16G-HA could provide large E-SSA (1710 m²/g), 76% from the total DFT-SSA (2250 m²/g) for the supercapacitor application when EMIMBF₄ electrolyte is used. This is contrary to the much lower E-SSA (739 m²/g), 59% of the total DFT SSA (1255 m²/g) for RP20. Our materials not only have ultrahigh overall SSA, but also have much higher E-SSA for guest ion or molecule access compared with the conventional AC and other materials.

Galvanostatic charge/discharge test results of supercapacitors based on the optimized porous 3D graphene-based materials in (a) 1 M TEABF₄/AN and (b) neat EMIMBF₄ electrolytes under different current densities. Galvanostatic charge/discharge curves of PF16G-HA based supercapacitor under different constant currents in (c) 1 M TEABF₄/AN and (d) neat EMIMBF₄ electrolyte. Even under a high current density of 10 A/g, PF16G-HA based supercapacitors still show a very high specific capacitance of 174 F/g in 1 M TEABF₄/AN and 210 F/g in neat EMIMBF₄, indicating excellent capacitance retention and rapid ion transport characteristics; CV curves of PF16G-HA based supercapacitor under different scan rates in (e) 1 M TEABF₄/AN and (f) neat EMIMBF₄ electrolyte. The CV testing of supercapacitors based on our materials in 1 M TEABF₄/AN and in neat EMIMBF₄ electrolyte exhibit nearly rectangular curves over a wide range of voltage scan rates (50-200 mV/s), also indicating an excellent rate performance.

(a) Nyquist plots of PF16G-HA, PF-HA, G-HA and RP20 with the imaginary part (Y axis) vs the real part (X axis) of impedance from EIS studies measured in the frequency range of 100 kHz to 10 mHz at an AC amplitude of 10 mV in neat EMIMBF₄ electrolyte. The inset shows an expanded view for the high frequency range; (b) Frequency response of PF16G-HA, PF-HA, G-HA and RP20 in neat EMIMBF₄ electrolyte. (c) Cycle stability of supercapacitors based on PF16G-HA in different electrolytes at a current density of 1 A/g. No obvious decay of capacitance was observed after 5000 constant current charge/discharge cycles in all the electrolytes. For instance, the devices still keep > 99% capacitance in 1 M TEABF₄/AN system and 94% in EMIMBF₄ system after 5000 cycles.