Supplementary Figure 1. XRD pattern for pristine graphite (PG), graphite oxide (GO) and
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1 Supplementary Figure 1. XRD pattern for pristine graphite (PG), graphite oxide (GO) and expanded graphites (EG-1hr and EG-5hr). The crystalline structures of PG, GO, EG-1hr, and EG-5hr were characterized by D8 Advance with LynxEye and SolX equipment in X-ray Crystallographic Center at University of Maryland, College Park. Powder samples were scanned from 5⁰ - 90⁰ at a scan rate of 0.5⁰ per second in non-spin mode. 1
2 a b c d Supplementary Figure 2. (a) N 2 adsorption-desorption isotherm, (b) tap density, (c) Raman profile, and (d) conductivity of pristine graphite(pg), graphite oxide(go), EG-1hr, and EG-5hr. The BET surface area measurement was conducted by Tristar II 3020 surface area analysis station. In a typical tap density test, ~1g of the sample was put into a graduated measuring cylinder and then tapped for 50 times until no further volume change was observed. The volume was obtained by reading the inner diameter of the cylinder. Raman data was collected by H-J-Y Raman microscope in University of Maryland Nanocenter with laser of 532 nm, over the PG, GO, EG-1hr and EG-5hr powder samples. The electronic conductivity of the samples was measured by four-probe method. In a typical measurement, powder sample with ~0.1g in mass was assembled in a Swagelok cell with an inner diameter of 13mm. The assembled cell was then loaded for 50 Mpa pressure for 3 minutes to achieve the pallets. The pallet samples were then measured employing a four-probe method (Signatone SP4) at University of Maryland Nanocenter. 2
3 Supplementary Figure 3. X-ray photoelectron spectroscopy (XPS) spectra of C 1s spectra of (a) PG, (b) GO, (c) EG-1hr, and (d) EG-5hr. XPS investigation was performed upon powder samples at room temperature. Data was collected by a high sensitive Kratos AXIS 165 spectrometer with survey pass energy of 160 ev and high resolution energy of 20 ev, at University of Maryland Nanocenter. 3
4 Supplementary Figure C MAS spectra of GO (a) without and (b) with 13 C- 1 H dipolar dephasing by 13 C- 1 H REDOR, and (c) the difference spectrum (a) (b). The spectrum in (c) is magnified by 4 times. The 13 C signals were excited by a /2-pulse. The pulse widths for the /2 and -pulses for 13 C are 3.65 s and 7.3 s while that for a 1 H -pulse is 6.28 s. In the 13 C- 1 H REDOR experiments, the data was collected with 13 C -pulse sandwiched by 13 C- 1 H dephasing periods of 4 rotor cycles (rotor cycle: R = 66.7 s) after the direct excitation of 13 C signals by a /2-pulse. The MAS spinning speed was set to 15 khz 10 Hz. The data in Supplementary Fig. 4 were collected (a) without and (b) with two sets of 1 H -pulses applied in each rotor cycle following the pattern of [ R /4- H - R /2- H - R /4] n for the dephasing periods in the REDOR sequence. The total dephasing period was 8 R (533 s). The same experimental conditions as used in Fig. 4 were adopted to analyze EG-1hr and EG-5hr samples in Supplementary Fig. 5, except for the pulse widths. The pulse widths are different between the GO and EGO samples, as the probe efficiency was modulated by loading the mildly conductive EGO samples. 4
5 Supplementary Figure C MAS spectra of (a-c) EG-1h and (d-f) EG-5h (a, d) without and (b, e) with 13 C- 1 H dipolar dephasing by 13 C- 1 H REDOR, together with (c, f) the difference spectra. The spectra in (c, f) are magnified by 8 times. The pulse widths for the /2 and - pulses for 13 C are 5.25 s and 10.5 s while that for a 1 H -pulse is 16 s. 5
6 a b c Supplementary Figure 6. (a) Cyclic voltammograms of EG-1hr from 0.05 to 20 mv s -1. The inset shows the results from 0.05 to 1 mv/s. (b) Sodiation, and (c) desodiation capacity Q versus V -1/2 profile with the dashed line indicating linear fitting between them. All capacities have been normalized by the value under 0.05 mv/s. Cyclic voltammetry experiment was performed by sweeping the cell at various scan rates from 0.05 mv s -1 to 20 mv s -1 in the voltage range from 0V-2V (vs. Na/Na + ) on a Solatron 1260/1287 Electrochemical Interface equipment (Solatron Metrology, UK). 6
7 Supplementary Figure 7. Raman profile for pristine EG-1hr and EG-1hr after sodiation. Ex situ Raman data was collected on a home-made cell, consisting of an EG electrode and a Na counter electrode in 1.0 M NaClO 4 in polycarbonate (PC) solvent liquid electrolyte. Raman data was collected by H-J-Y Raman microscope in University of Maryland Nanocenter with laser of 532 nm. 7
8 Supplementary Figure 8. TEM images showing typical morphologies of EG-1hr (a) after the 6 th sodiation cycle and (b) after the 6 th desodiation cycle. (c), (d) Filtered TEM close-up images corresponding to the boxed areas in (a) and (b), respectively. Images were taken from in situ TEM experiment, during which potentials of -1.0V to -4.0V were applied to EG with respect to Na metal counter electrode to initiate sodiation, and +1.0V to +4.0V for desodiation. 8
9 d EG_AC = 0.42nm Supplementary Figure 9. HRTEM image of EG after 150 cycles (denoted as EG_AC). Contrast profile along the arrow indicates average interlayer spacing of 0.42 nm. The material was cycled in a coin cell for 150 cycles and then held at 2V for 24 h to ensure full desodiation before disassembling for TEM observation. 9
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