Flexible Nb 4 N 5 /rgo Electrode for High-Performance Solid State Supercapacitors. Huazhong University of Science and Technology Wuhan , China

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1 Copyright 2018 American Scientific Publishers All rights reserved Printed in the United States of America Article Journal of Nanoscience and Nanotechnology Vol. 18, 30 38, Flexible Nb 4 N 5 /rgo Electrode for High-Performance Solid State Supercapacitors Chao Huang 1 2,YuanYang 1, Jijiang Fu 1,JiaweiWu 1, Hao Song 1, Xuming Zhang 1, Biao Gao 1,PaulK.Chu 2, and Kaifu Huo 3 1 The State Key Laboratory of Refractories and Metallurgy, Wuhan University of Science and Technology, Wuhan , China 2 Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, , China 3 Wuhan National Laboratory for Optoelectronics (WNLO), School of Optical and Electronic Information Huazhong University of Science and Technology Wuhan , China Flexible supercapacitors (SCs) are desirable for elastic and clothing electronic products owning to their considerable safety, high foldability and outstanding power density. Herein, multilayered films composed of alternating mesoporous Nb 4 N 5 nanobelts and rgo nanosheets (Nb 4 N 5 /rgo) are designed and fabricated exhibiting good flexibility. The folding Nb 4 N 5 /rgo film electrode reveals an areal capacitance of 141 mf cm 2 (at 1 ma cm 2 along with remarkable cycling stability (the capacitance retention is 90% after 6,000 cycles). The flexible SCs devices were constructed by interlayer couple films of Nb 4 N 5 /rgo electrodes with PVA/H 2 SO 4 gel as the electrolyte, which exhibited huge volumetric capacitance of 19 F cm 3 (at 0.1 A cm 3 and a considerable energy density of 0.98 mw h cm 3 with a power density of W cm 3. Additionally, the as-obtained folding devices bode outstanding cycling stability with capacitance retention of 89% after 4,000 cycles measured by cyclic voltammetry method (at 100 mv s 1. Above results about niobium nitride based flexible electrodes and devices exploit a platform for wearable electronics and flexible devices. Keywords: Nb 4 N 5 Nanobelts, Graphene, Flexible, Solid State Supercapacitors. 1. INTRODUCTION The development of wearable electronics and flexible devices dramatically boost the demand of flexible energy storage devices. Supercapacitors (SCs) are promising energy storage devices connecting conventional capacitors and batteries because of high power density, considerable energy density and high cycling stability. 1 5 Flexible solid state SCs can be assimilated into flexible/wearable electronic devices for safe, portable, light, and environmentally friendly application The electrodes in flexible SCs should have both excellent capacitive properties and sturdy mechanical flexibility, however, it is also a challenge to design and manufacture electrode materials in order to gain the high conductivity, large specific capacitance, flexibility and good cycling stability Transition metal nitrides (TMNs) with intrinsically high electrical conductivity and large specific capacitance act as promising electrode materials for next-generation Authors to whom correspondence should be addressed. high-performance SCs such as TiN, VN, Mo 2 N, NbN, and Nb 4 N Compared to carbon-based materials, TMNs can generally deliver larger specific capacitances and volumetric energy densities. In addition, TMNs have a larger power density and better rate performance than transitional metal oxides (TMOs) due to the higher conductivity, especially at high current densities which can also provide considerable performance Asymmetrical pliable SCs devises based on VN and VOx nanowires were assembled with LiCl/PVA gel electrolyte by Lu and coauthors. 23 Our previous research depicted that bondable SCs constructed hybrid mesoporous VN/CNTs materials with 70 wt% mass loading of VN NWs and H 3 PO 4 /PVA gel electrolyte exhibited a huge volumetric capacitance of 7.9 F cm 3 (1.1 ma cm More recently, we reported high performance symmetric all-solid-state SCs heaping a couple of paper-like composite film consisting of mesoporous Mo 2 N and rgo with the H 3 PO 4 -based gel as electrolyte. The volumetric capacitance of the as-obtained flexible device is as high as 15.4 F cm 3 on basis of the whole volume of the cell J. Nanosci. Nanotechnol. 2018, Vol. 18, No /2018/18/030/009 doi: /jnn

2 Flexible Nb 4 N 5 /rgo Electrode for High-Performance Solid State Supercapacitors Among those different types of TMNs, the typical niobium nitride is attractive due to following reasons: Firstly, niobium nitride with the valence (+5) of Nb ions facilitates the electrochemical activity enhancing multistep electrochemical reactions. 20 Secondly, the great electrical conductivity of niobium nitride plays a significant role in enhancing electron transfer and promotes the power density for SCs Thirdly, the large density 8.47 g cm 3 of the niobium nitride with considerable capacitance can boost large volumetric energy density. 27 For instance, Choi et al. fabricated niobium nitride nanoparticles and investigated their electrochemical behaviors. 28 In recently, the mesoporous niobium nitride nanobelt arrays with considerable specific capacitance of 37.4 mf cm 2 at charge/discharge current density of 0.2 ma cm 2 and outstanding rate performance were synthesized directly on Nb substrate by our research groups. 29 Cui et al. prepared porous Nb 4 N 5 nanostructure, which achieved a high capacity of about mf cm 2 (at a change/discharge current density of 0.5 ma cm However, Nb 4 N 5 based flexible and binder-free electrodes suitable for solid state and flexible SCs have rarely been reported. Herein, alternating mesoporous Nb 4 N 5 nanobelts (NBs) and rgo nanosheets (Nb 4 N 5 /rgo) are prepared by selfassembly of Nb 2 O 5 and graphene oxide and subsequent annealing in NH 3. The free-standing and binder free Nb 4 N 5 /rgo film electrode exhibits large areal capacitance of 164 mf cm 2 at a current density of 0.75 ma cm 2,and excellent cycling stability with a high capacitance retention of 90% after 6,000 cycles. The solid state flexible SCs consisting of a double of standalone Nb 4 N 5 /rgo films with PVA/H 2 SO 4 gel as the electrolyte exhibits a high volumetric capacitance of 19 F cm 3 and energy density of 0.98 mw h cm 3 at a current density of 0.1 A cm MATERIALS AND METHODS 2.1. Preparation of Niobic Acid NBs The chemicals were purchased from Sigma. A simple hydrothermal method was employed to fabricate niobic acid NBs. In brief, remarks at experiment, 0.26 g of Nb powders (99.5%) were dispersed in 40 ml of 10 M NaOH, under magnetic stirring. Then, the mixture was transferred into a 60 ml autoclave, heated to 130 C and kept for 18 h. The white product was gathered and washed by deionized water (DW) for three times to obtain sodium niobate nanobelts. By hydrogen ion exchange process in diluted hydrochloric acid (HCl) three times, the niobic acid NBs was obtained and more details can be found in our previous work Fabrication of Graphene Oxide (GO) GO sample was obtained via advanced Hummers method. 31 Natural graphite powders were oxidized by KMnO 4,NaNO 3, and 98% H 2 SO 4 and then the GO dispersion was obtained by centrifuging and rinsing the brown product a few times Synthesis of Free-Standing Nb 4 N 5 /rgo Film In brief, 0.26 g of niobic acid NBs were dispersed in DW (40 ml) under dramatic stirring. Afterwards, 1 ml poly diallyl dimethyl ammonium chloride (PDDA) liquid was added into the mixture solution and stirred for 2 h to obtain the positively-charged niobic acid-pdda NBs. The redundant PDDA was removed by centrifugation method and then the solution was added into the GO suspension drop by drop. The suspension was collected by vacuumfiltering and washed with DW for several times. Before freeze-drying overnight, the film was stripped off from the filtration membrane and then annealed at 700 Cfor3hin NH 3 to produce the free-standing Nb 4 N 5 /rgo paper-like film Assembly of Flexible Nb 4 N 5 /rgo Based SCs Two slices of the Nb 4 N 5 /rgo films were incorporated by H 2 SO 4 /PVA gel to form all solid state Nb 4 N 5 /rgo based device. The gel electrolyte was obtained by dissolving 1 M PVAand1MH 2 SO 4 in DW under stirring at 80 Cfor 6 h. After immersing in H 2 SO 4 /PVA solution for 15 min, two electrode films were overlapped and solidified at 25 C for 10 h to remove superfluous water Samples Characterization The structure, morphology, and composition of the samples were characterized by field-emission scanning electron microscopy (SEM, FEI Nova 450 Nano), transmission electron microscopy (HR-TEM, FEI TITAN), X-ray diffraction meter using Cu K radiation ( = Å, XRD, Philips X Pert Pro), Raman spectrometer (HR RamLab), and X-ray photoelectron spectrum (XPS, PHI quantera ii). The rgo content of Nb 4 N 5 /rgo hybrid were evaluated by thermogravimetric analysis (TG, STA449) and differential thermal analysis (DTA, STA449) from 100 to 500 C with the heating rate of 10 Cmin Electrochemical Test The electrochemical performance of the Nb 4 N 5 and Nb 4 N 5 /rgo film was characterized in three electrode system with the platinum foil as counter electrode, and a saturated calomel electrode (SCE) as reference electrode. The electrolyte was 1 M H 2 SO 4 solution. The cyclic voltammetry (CV) and galvanostatic charging/discharging (GCD) tests were carried out on an electrochemical workstation (CH Instruments, 760e) and the voltage range was between 0 and 0.6 V. The Nyquist plots were measured in a frequency range from 0.1 Hz to 100 KHz. 31

3 The capacitance of electrode is computed by following equations:18 I t and U I t C Cs = = S S U C= (1) (2) where C (F g 1 or F cm 3 is the specific capacitance, I (A g 1 or A cm 3 represents for the charge/discharge current density, t (s) is the discharge time, U (V) is the potential window of discharge, V (cm3 is the device volume. The volumetric energy density (E) and power density (P ) of SCs device can be calculated as follows:19 E= 1 CU 2 and 2 V E P= t (3) (4) 3. RESULTS AND DISCUSSION Figure 1 illustrates the fabrication process of the flexible Nb4 N5 /rgo composite electrodes. Firstly, the as-obtained positively-charged niobic acid-pdda were added into the negative GO suspension to form niobic acid/go composites under strong stirring via static electricity interactions method. The paper-like niobic acid/go films were produced by filtering and freeze-drying. Finally, freestanding Nb4 N5 /rgo hybrid films were fabricated by heat treating niobic acid/go hybrid film in NH3 during which the niobic acid NBs transform into Nb4 N5 NBs and GO turns into rgo. The niobic acid NBs obtained by hydrothermal treatment exhibits a diameter of 80 nm and length of tens of micrometers (Not provided). In order to search a suitable annealing temperature, the as-obtained niobium acid NBs were annealed at different temperature of 500, 600, 700, and 800 C. The XRD patterns of the precursor nitrided at 500 C can be indexed to orthorhombic Nb2 O5 (JCPSD No: ) as shown in Figure However, the XRD diffraction peaks of products correspond to tetragonal Nb4 N5 (JCPDS No: ) above 600 C, indicating the transformation of orthorhombic Nb2 O5 into tetragonal Nb4 N5 during annealing Increasing the temperature to 700 and 800 C, the intensity of all the peaks goes up implying better crystallinity. Figure Schematic illustration of the preparation of Nb4 N5 /rgo. Figure 2. XRD pattern of Nb2 O5 and Nb2 O5 annealing in NH3 atmosphere at different temperature from 500 to 800 C. The SEM images of samples annealed at 500, 600, 700 and 800 C are depicted in Figure 3. The SEM images of samples obtained by annealing at 500 C indicate that the NBs are almost the same as the niobic acid NBs. Even after annealing at 600 C and 700 C, the one-dimensional structure is mostly retained while some pores are found in the surface of the NBs. The porous structure of Nb4 N5 after annealing at 700 C is more remarkable than that of samples obtained from 600 C as shown in Figure 3. The N2 adsorption desorption isotherm is acquired to study the porous structure of Nb4 N5 and the corresponding pore size distribution shows a wide mesoporous distribution with a specific surface of 38.6 m2 and an average pores about 13 nm. However, the NBs are destroyed and turn into nanoparticles at 800 C as shown in Figure 3(d). Figure 3. Nb2 O5 at different temperature annealing in NH3 atmosphere of (a) 500 C (b) 600 C; (c) 700 C; (d) 800 C.

4 Figure 4. (a) CV curves of different samples at 50 mv s 1 in 1 M H2 SO4 (b) GCD curves. The electrochemical performance of the samples annealed at 500, 600, 700, and 800 C is assessed in 1 M H2 SO4 and the CV curves show a rectangular shape (Fig. 4(a)). The specific capacitance values are 7.18, 86.6, 133, and 65.2 mf cm 2 at a current density of 1 ma cm 2 for the samples annealed at 500, 600, 700, and 800 C (Fig. 4(b)), respectively. The Nb4 N5 after annealing at 700 C exhibits the largest specific capacitance due to the porous structure and is used in the subsequent experiments. The SEM image of the Nb4 N5 /rgo film in Figure 5(a) shows that the rgo nanosheets are uniformly distributed on the Nb4 N5 NBs. The cross-view SEM picture in Figure 5(b) clearly indicates that the freestanding Nb4 N5 /rgo film is about 14 m in thickness consisting of mesoporous Nb4 N5 NBs and rgo nanosheets. The TEM image (Fig. 5(c)) further indicates that the Nb4 N5 NBs and rgo are strongly bonded even after ultrasonication in ethanol for a quarter minutes prior to TEM characterization. The Nb4 N5 NBs inherit the original morphology and are bonded well with rgo. The three-dimensional rgo nanosheets offer the mechanical network to support the Nb4 N5 NBs enabling the formation of a flexible film. The digital picture in Figure 5(d) shows that the Nb4 N5 /rgo paper-like film has excellent flexibility which is better than that of the compound Nb4 N5 (95% Nb4 N5 and 5% PTFE) film. The XRD patterns of Nb4 N5 and Nb4 N5 /rgo (Fig. 6(a)) can be ascribed to the tetragonal Nb4 N5 except for a broad peak at 27 which can be related to graphene.19 The Raman scattering spectra of Nb4 N5, GO, and Nb4 N5 /rgo in Figure 6(b) describe two typical peaks at 1352 and 1590 cm 1 relating to D-band and G-band of graphitic structure.34 The other peaks at 260, 656, and 980 cm 1 correspond to vibrational modes of orthorhombic Nb2 O535 resulting from surface oxidation of Nb4 N5. This phenomenon has been observed from other metal nitrides The TG and DTA curves of Nb4 N5 and Nb4 N5 /rgo acquired in air with a heating speed of 10 C min 1 are displayed in Figure 6(c). Between 300 C and 400 C, the characteristic exothermal peaks in the DTA curves and mass increase in the TG curves are attributed to oxidation of Nb4 N5 to Nb2 O The content of the rgo in Nb4 N5 /rgo calculated by comparing the TG curves of Nb4 N5 and Nb4 N5 /rgo is as small as 4.06%, which is less than that of other graphene-based composites XPS is employed to determine the detailed composition of the Nb4 N5 /rgo NBs in Figure 6(d). The fine XPS spectra of Nb 3d of Nb4 N5 /rgo can be fitted into three peaks. The high bonding energy peaks of and ev arise from Nb 3d3/2 and Nb 3d5/2 of Nb O due to surface oxidization of Nb4 N5 similar to that of TiN and VN The peaks at and 205 ev are associated with niobium oxynitride (Nb N O) bond as a result of incomplete nitridation of Nb2 O5 and those at and ev stem from Nb 3d3/2 and Nb 3d5/2 of the Nb N bond The electrochemical properties of the Nb4 N5 /rgo electrode are evaluated by CV and GCD in a 1 M H2 SO4 aqueous solution. The CV curves of specific gravimetric capacitance and area capacitance of the Nb4 N5 /rgo electrode at different scan rates between 10 and 200 mv s 1 are depicted in Figures 7(a) and (c), respectively, which Figure 5. (a) SEM image of Nb4 N5 /rgo at the top view; (b) SEM image of cross-sectional of Nb4 N5 /rgo; (c) TEM image of the Nb4 N5 /rgo hybrid electrode; (d) digital image of the bending Nb4 N5 /rgo film. 33

5 Figure 6. (a) XRD patterns of Nb4 N5 /rgo and Nb4 N5 ; (b) Raman scattering spectra of Nb4 N5 /rgo, GO, and Nb4 N5 ; (c) TG and DTA results acquired from the freestanding Nb4 N5 /rgo and Nb4 N5 ; (d) the Nb 3d of XPS spectrum stem from the Nb4 N5 /rgo film. show a rectangular shape suggesting a good capacitive behavior of Nb4 N5 /rgo electrode. The GCD results collected at various current densities are presented in Figures 7(b) and (d). Even at large current densities no any obvious voltage drop in GCD curves implying remarkable electrochemical performance. In Figure 7(b), the gravimetric capacitance of the Nb4 N5 /rgo paper-like electrode (175.2 F g 1 at current density of 1 A g 1 is larger than those of earlier literature reported such as NbN (73 F g 1 24, WN (30 F g 1 28 and Mo2 N (173 F g 1.19 The specific capacitance of the flexible film is 164 mf cm 2 at a current density of 0.75 ma cm 2 which is calculated by the GCD curve. At the current density of 1 ma cm 2, the Nb4 N5 /rgo electrode can obtain a high areal capacitance of 141 mf cm 2, which is also higher than that of carbon nanoparticles/mno2 hybrid structure electrode (110 mf cm 2 44 as well as ZnO and carbon shell-core structure electrode (139 mf cm 2.45 Even the current density was increased 133-fold to 100 ma cm 2, the Nb4 N5 /rgo film achieves a capacitance of 60 mf cm 2. Moreover, the materials have a long cycling lifetime with 90% capacitance retained after 6,000 cycles as shown in Figure 5(d). The superb electrochemical performance in SCs can be ascribed to the following reasons: First of all, the mesoporous Nb4 N5 NBs possess a large specific surface area and high mass loading (94.96 wt.%) offering not only galore active sites for the redox reaction but also channels facilitating transportation and storage of ions. Secondly, the two-dimensional graphene 34 nanosheets separated by Nb4 N5 NBs form a hierarchical three-dimensional network allowing permeation of the electrolyte and electron transfer. Thirdly, the Nb4 N5 NBs and rgo compound has a great structural stability thereby obviating the failure of electrode. All solid state SCs devices with considerable flexibility are constructed using the Nb4 N5 /rgo freestanding films with H2 SO4 /PVA as both the electrolyte and separator. The CV curves of the Nb4 N5 /rgo based device in a range of potential between 0 and 0.6 V are depicted in Figure 8(a) with different scanning rates of mv s 1, which are of similar rectangular shape indicating typical capacitive characteristics. The GCD plots obtained from the Nb4 N5 /rgo//nb4 N5 /rgo devices at current densities range between 0.1 and 2 A cm 3 are displayed in Figure 8(b). The volume of the cell including the electrodes, electrolyte, and separator is about cm3 (1.4 cm 0 5 cm cm) and according to Eq. (1), the volumetric capacitance values derived from the GCD plots are 19, 16.4, and 10.3 F cm 3 at current densities of 0.1, 0.2, and 1 A cm 3, respectively, which are generally larger than others results on all solid state SCs, for example intertwined mesoporous VN and CNT composite electrodes based device (7.9 F cm 3 at 25 ma cm 3,16 laser scribing flexible graphene electrodes based device (0.5 F cm 3 at 5 ma cm 3,46 oxygendeficient hematite nanorods for flexible device (9.5 F cm 3 at 12.5 ma cm 3,47 as well as Mo2 N and graphene composite film based device (15.4 F cm 3 at 100 ma cm 3.19 Moreover, the Nb4 N5 /rgo//nb4 N5 /rgo devices also show

6 Figure 7. CV curves of the Nb4 N5 /rgo paper-like electrode at different scanning rates from 10 to 200 mv s 1 in 1 M H2 SO4 (0 0.6 V) (a) specific gravimetric capacitance of electrode (c) area capacitance of electrode (b) GCD curves of Nb4 N5 /rgo compound at current densities between 1 A g 1 and 10 A g 1 ; (d) GCD curves of Nb4 N5 /rgo compound at current densities between 0.75 and 10 ma cm 2 ; (e) The relationship of areal specific capacitance of Nb4 N5 /rgo film electrode and current density; (f) cycling stability of Nb4 N5 /rgo film electrode obtained by CV test at a scanning rate of 100 mv s 1. a considerable rate capability. The volumetric capacitance is as high as 5 F cm 3 at 5 A cm 3 as shown in Figure 8(c). The Nyquist data in Figure 8(d) indicates that the niobium nitride based device exhibits a low resistance of 6.2 cm2 representing an excellent capacitive behavior. Figure 8(e) reveals that Nb4 N5 /rgo//nb4 N5 /rgo devices possess superior cycle capability with only 10% capacitance decay after 4,000 cycles. The Ragone plots associated to the characteristics of the energy-power are presented in Figure 8(f). A large energy density of 0.98 mwh cm 3 is achieved at a power density of W cm 3. The volumetric energy density is superior to these of other solid state SCs devices including flexible porous graphene-based SCs (0.098 mwh cm 3,48 carbon micro-scs (0.438 mwh cm 3,49 laser-induced porous graphene films based SCs (0.5 mwh cm 3,50 ZnO fiber based SCs (0.05 mwh cm 3,51 carbon/mno2 core shell fiber based SCs (0.23 mw h cm 3,52 and carbon coating TiO2 nanowires based SCs (0.012 mwh cm 3.53 To further test the function of the structure, three identical Nb4 N5 /rgo//nb4 N5 /rgo based SCs indicated as A, B, and C are joined in series circuit or parallel circuit. The demonstration of practical feasibility of our device as a flexible energy storage, CV tests were conducted under different bending condition. The GCD curves show no obvious different at different bending conditions as shown in Figure 9(a). Figure 9(b) depicts the GCD plots collected for parallel/series combinations of three devices at a current density of 0.2 A cm 3. The specific capacitance are 91.6, 92.4, and 92.2 mf for A, B and C device, respectively. The whole potential of the three series-wound devices is 1.8 V, which is triple that of the single one. The 35

7 Figure 8. Electrochemical performance of Nb4 N5 /rgo//nb4 N5 /rgo all solid state SCs devic: (a) CV curves at the current density from mv s 1 ; (b) GCD plots of the current density A cm 3 ; (c) capacitance variation versus the current density; (d) Nyquist plots; (e) cycling lifetime collected from CV curves at a scan rate of 100 mv s 1 ; (f) Ragone plot of all solid devices, the inserts are laser-induced graphene-sc48 carbon micro-sc49 graphene-micro-sc50 HZM-SC51 carbon/mno2 -SC53 Figure 9. (a) GCD curves collected from all-solid-state supercapacitor device at a current density of 0.2 A cm 3 under different bending states. The inserts are images under the test conditions. (b) GCD curves of the solid state SCs at a current density of 0.2 A cm 3 ; (c) digital picture of two yellow LEDs powered by four devices arranged in series and bent. 36

8 Flexible Nb 4 N 5 /rgo Electrode for High-Performance Solid State Supercapacitors capacitance three shunt-wound devices from GCD curves reaches 256 mf closing to the theory value (276 mf). Further demonstration, four flexible devices in series are bent while powering two yellow light-emitting diodes (LED) as showninfigure9(c). 4. CONCLUSION Flexible Nb 4 N 5 /rgo films with a large Nb 4 N 5 concentration of wt.% are designed and fabricated by self-assembly of Nb 2 O 5 and graphene oxide followed by annealing in NH 3. The nano-structured electrode with a small resistance of 6.2 cm 2 shows a capacity of 141 mf cm 2 at 1 ma cm 2, good rate performance, and remarkable long life stability (about 10% capacitance loss after 6,000 cycles). The solid device with high flexibility was made by a couple of Nb 4 N 5 /rgo films and H 2 SO 4 based gel electrolyte exhibiting a huge capacitance of 19 and 5 F cm 3 at current densities of 0.1 and 5 ma cm 3. Additionally, the Nb 4 N 5 /rgo//nb 4 N 5 /rgo device also show a considerable energy density of 0.98 mw h cm 3 at a power density of W cm 3 as well as superb cycling stability with about 90% capacitance retention after 4,000 cycles. The outstanding results of the niobium nitride based flexible electrodes are suitable for high-performance wearable SCs. Acknowledgments: C. Huang and Y. Yang contributed equally in this work. This work was financially supported by Natural Science Foundation of China ( , , ), Project of Hubei Provincial Education Office (B ), Outstanding Young and Middle-aged Scientific Innovation Team of Colleges and Universities of Hubei Province (T201402), and City University of Hong Kong Applied Research Grant (ARG) No References and Notes 1. Y. Zhu, S. Murali, M. Stoller, K. Ganesh, W. Cai, P. Ferreira, A. Pirkle, R. Wallace, K. Cychosz, M. Thommes, D. Su, E. Stach, and R. Ruoff, Science 332, 1537 (2011). 2. B. E. Conway, V. Birss, and J. Wojtowicz, J. 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