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1 Supporting Information Defect-Free, Size-Tunable Graphene for High-Performance Lithium Ion Battery Kwang Hyun Park, Dongju Lee, Jungmo Kim, Jongchan Song, Yong Min Lee *,, Hee-Tak Kim *,, and Jung-Ki Park *, 1 Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, , Republic of Korea 2 Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon , Republic of Korea 3 Department of Chemical and Biological Engineering, Hanbat National University, Daejeon, , Republic of Korea *Corresponding author address: jungpark@kaist.ac.kr (Jung-Ki Park), Fax number: *Co-corresponding authors Yong Min Lee: yongmin.lee@hanbat.ac.kr, Hee-Tak Kim: heetak.kim@kaist.ac.kr 1

2 Experimental S1 Materials S2 Methods S3 Equipment & Techniques Characterizations Figure S1 Solvation of potassium metal with various solvents with different property indexes. Figure S2 Characterization of graphene flakes exfoliated in various solvents with different property indexes. Figure S3 Characterization of graphene exfoliated by scotch tape method. Figure S4 Chemical compositions of the graphite and df-g. Figure S5 Comparison of I D /I G ratio obtained from graphene oxide, reduced graphene oxide, and df-g. Figure S6 Representative AFM images of df-g with different layer thickness. Figure S7 Representative TEM images of df-g with different layer thickness. Figure S8 BET surface area of df-g determined by N 2 adsorption/desorption at 77 K Figure S9 Characterization of the graphite, the reduced graphene oxide (RGO), and df-g Figure S10 Characterization of Co 3 O 4 and df-g/co 3 O 4 composite. Performance of Co 3 O 4, RGO/Co 3 O 4, and df-g/co 3 O 4 as anode materials in Li ion battery Figure S11 Cyclic voltammograms of the df-g/co 3 O 4 samples composed of df-gs of different sizes. (~10.5 μm 2 for 5 C, ~5.8 μm 2 for 30 C, and ~3.6 μm 2 for 50 C) Figure S12 Cycle performance of df-g/co 3 O 4 (5 C, 30 C, and 50 C), RGO/Co 3 O 4 and 2

3 Co 3 O 4 at a current density of 500 ma g -1. Figure S13 Charge/discharge voltage profiles of df-g/co 3 O 4 (5 C) and RGO/Co 3 O 4 at current densities of 500 ma g -1 and 1000 ma g -1. Figure S14 Equivalent circuit model and Nyquist plots of impedances for df-g/co 3 O 4 and RGO/Co 3 O 4. Experimental S1. Materials Graphite powder and potassium metal were purchased from Bay Carbon, Inc. (SP-1 graphite powder) and Kojundo Korea, Co., Ltd (KKE02GB, stored in oil), respectively. Hexane, toluene, tetrahydrofuran (THF), ethanol (EtOH), pyridine, dimethylformanmide (DMF), and dimethyl sulfoxide (DMSO) having different property indexes were purchased from Sigma-Aldrich. S2. Methods Defect-free graphene (df-g) and df-g/co 3 O 4 composite A Pyrex tube with open ends (diameter: 6 mm) filled with graphite powder (1g, M) was inserted into a larger Pyrex tube (diameter: 10 mm) and then the space between the two Pyrex tubes was filled with potassium metal (0.407 g, M). The tube set was then sealed after evacuation for 30 min, and kept at 110 C for 1 h in a glove box under argon atmosphere. 200 mg of KC 8 synthesized by potassium insertion was added into 10 ml of the selected solvents, and the samples were kept at different temperatures in the range of 0-80 C for 24 h, allowing the formation of graphene nanosheet (GNS) with regular interlayers. Then, the expanded GNS was exfoliated into 3

4 graphene flakes with mild sonication in water bath for 1 h at different temperatures (5, 30, and 50 C). The quality and size distribution for the as-prepared graphene samples were carefully characterized by various analytical techniques. The analytical results suggest the following optimal fabrication conditions. i) The GNS with regular interlayers in graphite crystals was fabricated at 0 C for 24 h in pyridine, and ii) the df- G without any notable damages was produced with mild sonication at 5 C in a water bath. To synthesize the graphene/metal oxide composite, the dispersion of df-g in pyridine (20 mg graphene /ml pyridine ) obtained at the optimal condition was mixed with the dispersion of Co 3 O 4 powder in pyridine (80 mg Co3O4 /ml pyridine ). The synthesized samples were washed by warm distilled (DI) water (~40 C), filtrated to remove any potassium ion residues, and dried at 110 C for 24 h in oven. Electrochemical Measurement The working electrodes were fabricated by slurry casting the mixture of df- G/Co 3 O 4, super-p, and polyvinylidene fluoride (PVDF, Aldrich) at a weight ratio of 80:10:10 on a copper foil. The electrodes were then dried at 60 C for 12 h in vacuum. The typical active mass loading was in the range of mg cm -2. A piece of 450 μm lithium foil (Honjo metal), polyethylene separator (Asahi Kasei), and electrolyte containing 1 M LiPF 6 in ethylene carbonate (EC) and dimethyl carbonate (DMC) at 1:1 volume ratio (Panax ETEC) were chosen. A CR-2032 coin type cell was selected and the cell assembly was conducted in a glove box under argon atmosphere. The cycling and rate performances were tested at various current densities after a 30 ma g -1 precycle at a voltage ranging from V. The cyclic voltammetry (CV) and 4

5 electrochemical impedance spectroscopy (EIS) measurements were carried out on an electrochemical workstation of a Solartron 1255 frequency response analyzer (FRA) coupled with Solartron 1287 electrochemical interface. The cyclic voltammetry measurements were performed over the potential range of V at a scan rate of 0.5 mv s -1 and the impedance spectra were recorded by applying a sine wave with 10mV amplitude over a frequency range of 100 khz to 0.01 Hz. S3. Equipment and Techniques The crystallographic structures of the samples were analyzed by X-ray diffraction (D/MAX-2500 (18kW)) with Cu Kα radiation (λ=1.518 Å). The surface functional groups of the samples were measured by X-ray photoelectric spectroscopy (XPS, Sigma Probe). Thermal gravimetric analysis (TGA, G 209 F3) of all the samples was conducted at a temperature up to 900 C with heating rate of 10 C min -1 under air atmosphere. Raman spectroscopy (excitation at 532 nm) and atomic force microscopy (AFM) measurements of all the samples were performed on a N8 NEOS with RAMAN AFM/SPM System (SENTERRA, Bruker GmbH). Additionally, the morphology of the graphene flakes was analyzed by a field emission scanning electron microscope (FE- SEM, Philips XL30SFEG) and transmission electron microscope (TEM, JEOL JEM- 2200FS). BET surface area of sample was determined by N 2 adsorption/desorption at 77 K (Micromeritics Tristar II volumetric adsorption analyzer). Characterizations Figure S1. Solvation of potassium metal with various solvents with different property indexes 5

6 Figure S1a shows properties of different solvents in terms of polarity, Gutmann acceptor/donor number (AN/DN), electric constant (ε), solvation of potassium metal. Figure S1b presents plotting of dielectric constant (ε) vs AN for solvents (left) and digital images as a function of time (right). Potassium metal was extremely solvated by DMSO, DMF, and EtOH having relatively high dielectric constant and acceptor number, and color of potassium solvated in DMSO and DMF was significantly changed to dark yellow and pink, respectively. In contrast, a significant change of potassium metal in Hexane, Toluene, THF, and Pyridine was not shown. Figure S1. Solvation in various solvents with different property indexes. a, Table for different property indexes of solvents. b, Plotting for dielectric constant vs accept number (left) and Optical images for solvation of potassium metal (right). Figure S2. Characterizations of graphene flakes exfoliated in various solvents with 6

7 different property indexes A negligible evolution of hydrogen gas in the hexane, toluene, pyridine, and DMF solvents was observed at 0 C in contrast with the tetrahydrofuran (THF), EtOH, DMSO, and DI water, which were explosively reacted with potassium-graphite intercalation compound. After water batch sonication at 5 C for 1 h, THF, EtOH, pyridine, and DMF exhibit a good dispersion, as shown in Figure S2a. The structural property of the resulting graphene samples is characterized by Raman spectroscopy. Interestingly, the graphene sample exfoliated by the pyridine exhibits a structural perfection on the basal plane. Its I D /I G ratio is remarkably lower than those of the previously reported RGO (Figure S2b and c), and is comparable with that of the mechanical cleavage (Figure S3). This result indicates that the pyridine solvent facilitates the introduction into potassium-gic through a stable entropy gain without causing any damages to the graphene structure by a harsh chemical reaction. Figure S2. Characterizations of graphene flakes exfoliated in various solvents with different polarity index. a, Optical images of the GNS and the df-g. b, Raman spectra for graphene sheets exfoliated by different solvents. c, Comparison of D band intensity/g band intensity (I D /I G ). Figure S3. Characterizations of graphene exfoliated by scotch tape method 7

8 To evaluate the quality of df-g prepared in our study, in-situ AFM/Raman spectra of the supreme quality graphene sheets produced by scotch tape were obtained. As shown in Figure S3a-e, the I D /I G ratio is ~0.01, and the G band and 2D band demonstrate significant changes in both location and shape depending on the stacked graphene layers (Figure S3d). Moreover, the gap between layers in the graphene was ~0.5 nm as determined by the thickness profile (Figure S3e), which is in agreement with the result in the previous work 1. Figure S3. Characterizations of graphene produced by scotch tape method. a, Optical image of 1 5 layers. b, AFM image (Topology). c, Raman I D /I G mapping image. d, Raman spectra of samples composed of 1-5 layers. e, Thickness profiles of sample (i, ii, iii, iv, v in b). Figure S4. Chemical compositions of graphite and df-g 8

9 Figure S4 displays XPS spectra of graphite and df-g that consists of carbon (96.7%) and oxygen (3.3%) according to Figure S4a and b. The increased oxygen content of the df-g is probably because of the adsorbed moisture on the surface or trivial edge oxidation (Figure S4c and d). Figure S4. Chemical compositions of graphite and df-g. a, Table for atomic percentage of graphite and df-g. b, XPS survey spectra. c, Comparison of C1s peaks (C-C; ev, C-O; ev). d, Comparison of O1s peaks (OH; ev, H 2 O; ev). Figure S5. Comparison of I D /I G ratio obtained from graphene oxide, reduced graphene oxide, and df-g. Figure S5a and b presents in-situ AFM/Raman results for GO (by modified hummer s method), RGO (by thermal reduction under hydrgen gas at 800 C for 6 h), and df-g. The I D /I G ratio (~0.02) of the df-g is considerably lower than that of GO (~0.99) and RGO (~1.14), as shown in Figure S5b and c. 9

10 Figure S5. Comparison of I D /I G ratio of graphene oxide (GO), reduced graphene oxide (RGO), and df-g. a, Optical microscopy (OM) and AFM images. b, Raman spectra. c, Comparison of I D /I G ratio in the present work and results from other studies. Figure S6. Representative AFM images of the df-g with different layer thickness Representative AFM images of the df-g with different layer thicknesses are shown in Figure S6. The thickness of the monolayer (a), 3 layers (b), and 7 layers (c) samples ~1, ~2, and ~4 nm, respectively. 10

11 Figure S6. Representative AFM images of df-g. a, 1 layer. b, 3 layers. c, 7 layers. Figure S7. Representative TEM images of the df-g with different layer thickness Representative HR-TEM images and diffraction patterns of the df-g of monolayer, 2 layers, 3 layers, and multilayers are shown in Figure S7a-d. The layers of the df-g can be clearly discriminated by observing their edges with a regular distance of 0.34 nm between each layer and the intensity identification of I (0-110) /I (1-210). 11

12 Figure S7. Representative HR-TEM images and diffraction patterns of df-g. a, Monolayer. b, 2 layers. c, 3 layers. d, Multilayers. Figure S8. Textual property of df-g determined by N 2 adsorption/desorption at 77 K Figure S8 shows N 2 adsorption/desorption isotherm and the pore size distribution calculated by Barrett-Joyner-Halenda (BJH) equation. The isotherm of df-g exhibits an H3 hysteresis loop during desorption, which is generally known to be typical 12

13 of nonporous or macroporous materials. Also, the Brunauer-Emmett-Teller (BET) surface area of the df-g is found to be m 2 g -1 and its pore size distribution, as calculated by BJH equation, exhibits wide dispersivity of the pore size within 40 nm. Although BET surface area of our sample did not approach to theoretical value, the main reason is well clarified by previous works Especially, low surface area in spite of high monolayer contents is mostly ascribed to the limited accessibility of N 2 gas on bulk graphene powder which is formed by agglomeration and re-stacking between graphene sheets during solidification process. Accordingly, the BET result in our study indicates that the bulk geometric structure of the df-g sheets would be overlapped more tightly and crumpled extremely during solidification by freeze drying because of a strong electrostatic attraction between graphene sheets. Also, the result is in quite consistent with XRD results (Figure 1i). Consequently, novel approaches for preventing re-stacking and agglomeration between graphene sheets are still required and are under investigation. Figure S8. Textual property of df-g determined by N 2 adsorption/desorption at 77 K. a, N 2 adsorption/desorption isotherm and BET surface area. b, BJH pore size distribution. 13

14 Figure S9. Characterizations of graphite, reduced graphene oxide, and defect-free graphene Textural/chemical properties of graphite, RGO, and df-g are characterized by SEM, Raman spectroscopy, XRD, and XPS measurements. As can be seen from the SEM images in Figure S9a, df-g shows a lateral size (>5 μm) larger than that of RGO (~2 μm). Figure S9b, c and d illustrate that df-g preserves the intrinsic textural structure of graphene without introduction of any elements on the basal plane. A minute oxygen content of 3.3% can be observed, while its crystallographic structure attributable to Bernal stacking is diminished. On the other hand, the RGO underwent an incomplete recovery of the original graphene crystalline, in spite of a low oxygen content of ~6.7 % and heterogeneous agglomeration between them. Figure S9. Characterizations of graphite, reduced graphene oxide (RGO), and df-g using a, SEM images. b, Raman spectroscopy. c, X-ray diffraction (XRD). d, X-ray photoelectric spectroscopy (XPS). 14

15 S10. Characterizations of Co 3 O 4 and df-g/co 3 O 4 composite Figure S10a shows the SEM image of Co 3 O 4 powder, which aggregates into a secondary particle with a diameter of ~100 μm. With a homogeneous dispersion of Co 3 O 4 in pyridine solution, the Co 3 O 4 secondary particles in the size of nm are wrapped by the df-g, as shown in Figure S10b. Figure S10c demonstrates that the distribution of carbon (C) is highly uniform, indicating a homogeneous composition of the df-g/co 3 O 4 composite. Figure S10. Characterizations of Co 3 O 4 and df-g wrapped Co 3 O 4. a, b, SEM images. c, SEM image, as well as and cobalt and carbon elemental mapping images. Performance of Co 3 O 4, RGO/Co 3 O 4, and defect-free graphene/co 3 O 4 as anode material in Li ion battery 15

16 Figure S11. Cyclic voltammograms of the df-g/co 3 O 4 samples composed of df-gs of different sizes (~10.5 μm 2 for 5 C, ~5.8 μm 2 for 30 C, and ~3.6 μm 2 for 50 C) obtained at a scanning rate of 0.5 mv s -1 for the 1 st, 2 nd, 50 th, and 100 th cycles. Figure S12. Cycling performance of df-g/co 3 O 4 (5 C, 30 C, and 50 C), RGO/Co 3 O 4 and Co 3 O 4 at a current density of 500 ma g -1. Figure S13. Charge/discharge voltage profiles of df-g/co 3 O 4 (5 C) and RGO/Co 3 O 4 at current densities of 500 ma g -1 and 1000 ma g -1. Figure S13a and b show the charge/discharge profiles of df-g/co 3 O 4 and RGO/Co 3 O 4 composite for the 1 st, 2 nd, 50 th, and 100 th at different currents (500 ma g -1 and 1000 ma g -1 ). The sloping reduction/oxidation curves of the df-g/co 3 O 4 (5 C) are 16

17 certainly maintained with a gradual increase of the reversible capacity at a current density of 500 ma g -1 after 100 th cycles, even increase of a current density to 1000 ma g -1. In contrast, those of the RGO/Co 3 O 4 are severely changed with the decrease of the reversible capacity during 100 cycles. This result suggests that the RGO/Co 3 O 4 fabricated by RGO with damaged crystallinity is still insufficient to prevent electrical isolation and detachment of pulverized Co 3 O 4 particles from the electrode during Li + insertion/deinsertion. Figure S13. Charge/discharge voltage profiles of a, df-g/co 3 O 4 (5 C) and b, RGO/Co 3 O 4 at current densities of 500 ma g -1 and 1000 ma g -1 for the 1 st, 2 nd, 50 th, and 100 th cycles Figure S14. Equivalent circuit model and Nyquist plots of impedances for df-g/co 3 O 4 and RGO/Co 3 O 4. The solid electrolyte interface resistance (R SEI ) and the charge transfer resistance (R ct ) for the df-g/co 3 O 4 and the RGO/Co 3 O 4 are calculated by equivalent 17

18 circuit model (Figure S14a) and the results are listed in Figure S15b. The values of R SEI and R ct for the df-g/co 3 O 4 are significantly decreased with cycling, whereas the values of R SEI and R ct for the RGO/Co 3 O 4 are increased. Figure S15c shows the Nyquist plots of impedances for the df-g/co 3 O 4 and RGO/Co 3 O 4 containing depressed semicircle in the high frequency region and an inclined line with varying slop in the low frequency region. The df-g/co 3 O 4 (5 C) exhibits the low-frequency line shortened with the cycling, indicating faster solid state Li + diffusion rate and further maintains the line slope of 50 without a traceable change, demonstrating homogenous solid state diffusion of Li +. On the other hand, the RGO/Co 3 O 4 shows a lengthening of the line, revealing slower Li + diffusion rate, and the irregular slope in the range with the cycling, indicating partial conjugation between the pulverized particles and rising heterogeneity of it. These results suggest that the df-g/co 3 O 4 synthesized by the as-prepared defect-free and largesize graphene can retain its initial morphology with stable reversibility on the high performance after 100 cycles. 18

19 Figure S15. Equivalent circuit model and Nyquist plots of df-g/co 3 O 4 (5 C) and RGO/Co 3 O 4 for the 1 st, 2 nd, 50 th, 100 th cycles. a, Equivalent circuit model. b, Values of R SEI and R ct. c, Comparison of real data and fitted result using equivalent circuit model. Reference (1) Ferrari, A. C.; Meyer, J. C.; Scardaci, V.; Casiraghi, C.; Lazzeri, M.; Mauri, F.; Piscanec, S.; Jiang, D.; Novoselov, K. S.; Roth, S.; Geim, A. K. Phys. Rev. Lett. 2006, 97, (2) Schniepp, H. C.; Li, J.-L.; McAllister, M. J.; Sai, H.; Herrera-Alonso, M.; Adamson, D. H.; Prud'homme, R. K.; Car, R.; Saville, D. A.; Aksay, I. A. J. Phys. Chem. B 2006, 110,

20 (3) McAllister, M. J.; Li, J.-L.; Adamson, D. H.; Schniepp, H. C.; Abdala, A. A.; Liu, J.; Herrera-Alonso, M.; Milius, D. L.; Car, R.; Prud'homme, R. K.; Aksay, I. A. Chem. Mater. 2007, 19, (4) Stankovich, S.; Dikin, D. A.; Piner, R. D.; Kohlhaas, K. A.; Kleinhammes, A.; Jia, Y.; Wu, Y.; Nguyen, S. T.; Ruoff, R. S. Carbon 2007, 45, (5) Wang, D.-W.; Li, F.; Wu, Z.-S.; Ren, W.; Cheng, H.-M. Electrochem. Commun. 2009, 11, (6) Wang, Y.; Shi, Z.; Huang, Y.; Ma, Y.; Wang, C.; Chen, M.; Chen, Y. J. Phys. Chem. C 2009, 113, (7) Srinivas, G.; Zhu, Y.; Piner, R.; Skipper, N.; Ellerby, M.; Ruoff, R. Carbon 2010, 48, (8) Sridhar, V.; Jeon, J.-H.; Oh, I.-K. Carbon 2010, 48, (9) Dreyer, D. R.; Park, S.; Bielawski, C. W.; Ruoff, R. S. Chem. Soc. Rev. 2010, 39, (10) El-Kady, M. F.; Strong, V.; Dubin, S.; Kaner, R. B. Science 2012, 335, (11) Jabari Seresht, R.; Jahanshahi, M.; Rashidi, A.; Ghoreyshi, A. A. Appl. Surf. Sci. 2013, 276, (12) Kim, K. H.; Yang, M.; Cho, K. M.; Jun, Y.-S.; Lee, S. B.; Jung, H.-T. Sci. Rep-Uk. 2013, (13) Li, W.; Wang, F.; Feng, S.; Wang, J.; Sun, Z.; Li, B.; Li, Y.; Yang, J.; Elzatahry, A. A.; Xia, Y.; Zhao, D. J. Am. Chem. Soc. 2013, 135,

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