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1.2 Synthesis process of nanomesh graphene
Porous graphene was synthesized by CH4 cracking at 900 ¡ãC in a vertical quartz reactor with

diameter of 50 mm and length of 1500 mm shown in Fig. S1. A sintered porous plate was used as

the gas distributor at the bottom of the reactor. Gas entered the bottom preheater of the reactor,

then passed through the gas distributor, and finally flowed out into the atmosphere. On the top of

the quartz reactor, there was a stainless steel plate with a hopper for feeding catalyst. In a typical

run, the quartz reactor was mounted in an electrical tube furnace and was heated to 900¡ãC in an

argon flow of 1000 ml/min at atmospheric pressure. When the reaction temperature was reached,

800 ml/min CH4 was introduced into the reactor. Then, the MgO template (about 30 g) was fed

into the reactor over 5 min from the top hopper. After 10 min carbon deposition, CH4 was turned

off and the reactor was cooled to room temperature in an Ar atmosphere. The material obtained

was purified by acid washing (excessive amount of condensed hydrochloric acid diluted by

deionized water, with volume ratio of 1:1) with reflux for 1 hour to remove MgO. This was

followed by filtration and drying at 80 ¡ãC overnight in an oven. The material obtained was

ground into a fine powder for characterization and application.

1.3 Electrochemical testing

Electrodes for supercapacitors were prepared by mixing the porous graphene, carbon black

and poly(tetrafluoroethylene) in a mass ratio of 85:10:5 to give a slurry. The slurry was pressed

onto a nickel foam current collector (1 cm2) and dried at 100¡ãC for 12 h. All electrochemical

measurements were made in a three-electrode setup, in which platinum foil and Hg/HgO

electrodes (saturated calomel electrode, SCE) were used as counter and reference electrodes.

Cyclic voltammetry (CV) and galvanostatic charge/discharge were measured by a CHI 660C

electrochemical workstation in 6 M KOH electrolyte. The specific capacitance of the electrode

was calculated by C = (¡Ò IdV) /(¦ÔmV) , where I was the response current density (A), V was the

potential (V), ¦Ô was the potential scan rate (mV s-1), and m was the mass of the electroactive

materials in the electrodes (g).

1.4 Characterization

The samples for transmission electron microscope (TEM), atomic force microscope (AFM)

and scanning transmission electron microscopy (STEM) characterization were prepared by a

small amount of purified graphene dispersed in ethanol by sonication for 10 min to form a

homogeneous suspension. A drop of the suspension was deposited on a carbon-coated copper

grid for TEM observation (JEM 2010 microscope, operated at 120.0 kV) to get a general view of

the material. Centrifugation was used to remove large pieces of the material from the supernatant.

A drop of the supernatant was deposited on a mica substrate for AFM observation (SPM-9600),

and on a carbon-coated copper grid for STEM observation (FEI Tecnai G2 F20, operated at 200

kV).

Raman measurements at 633 nm excitation were performed with a Renishaw RM2000

Raman spectrophotometer. DWCNTs, MWCNTs and natural graphite were used for Raman

calibration. The DWCNTs were synthesized by methane cracking on Fe/MgO catalysts at

900¡ãC.1 In the DWCNT sample, there was 70% DWCNTs, with the remainder being SWCNTs

(Fig. S2a and b). Neither MWCNTs nor carbon nanofibers (CNFs) were found in wide view field

TEM observations. The DWCNT sample had a diameter distribution from 1 to 5 nm with an

average of 2-3 nm. The MWCNTs were prepared by ethylene cracking in a nano-agglomerate

fluidized bed reactor.2 The MWCNTs had a diameter distribution from 5 to 20 nm with an

average of 10.5 nm. The layer numbers of the MWCNTs were in the range of 5-10 (Fig. S2c and

d). The natural graphite was a purchased chemical with more than 10 graphene layers.

Thermogravimetric analysis (TGA) was performed on a Q500 in air flow with a temperature

scan of 10¡ãC/min. X-ray diffraction (XRD) data were obtained on a D8 ADVANCE

diffractometer utilizing the Cu K¦Á1 line (¦Ë = 0.15406 nm). The pore size distribution and specific  surface area (SSA) were measured on a Micrometritics ASAP 2010 using nitrogen as adsorptive.

A degasification at 300¡ãC (or 600-100¡ãC for calcination) for 10 min was performed before the

nitrogen adsorption. The mesopore distribution (1.7-300 nm) was calculated by the

Barrett-Joyner-Halenda (BJH) method. The micropore distribution (0.5-1.8 nm) was calculated

by the original Horvath-Kawazoe (HK) method. The SSA was calculated by the

Brunauer-Emmett-Teller (BET) method. X-ray photoelectron spectroscopy (XPS) measurements

were performed on a PHI Quantera Scanning X-ray Microprobe.

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