Letter pubs.acs.org/NanoLett
Building 3D Structures of Vanadium Pentoxide Nanosheets and Application as Electrodes in Supercapacitors Jixin Zhu,†,‡ Liujun Cao,†,§ Yingsi Wu,† Yongji Gong,∥ Zheng Liu,† Harry E. Hoster,‡ Yunhuai Zhang,§ Shengtao Zhang,§ Shubin Yang,*,† Qingyu Yan,*,‡,⊥ Pulickel M. Ajayan,† and Robert Vajtai*,† †
Department of Mechanical Engineering & Materials Science, Rice University, Houston, Texas 77005, United States TUM CREATE, 1 CREATE Way, #10-02 CREATE Tower, 138602, Singapore § School of Chemistry and Chemical Engineering, Chongqing University, Chongqing, 400044, China ∥ Department of Chemistry, Rice University, Houston, Texas 77005, United States ‡
S Supporting Information *
ABSTRACT: Various two-dimensional (2D) materials have recently attracted great attention owing to their unique properties and wide application potential in electronics, catalysis, energy storage, and conversion. However, largescale production of ultrathin sheets and functional nanosheets remains a scientific and engineering challenge. Here we demonstrate an efficient approach for large-scale production of V2O5 nanosheets having a thickness of 4 nm and utilization as building blocks for constructing 3D architectures via a freezedrying process. The resulting highly flexible V2O5 structures possess a surface area of 133 m2 g−1, ultrathin walls, and multilevel pores. Such unique features are favorable for providing easy access of the electrolyte to the structure when they are used as a supercapacitor electrode, and they also provide a large electroactive surface that advantageous in energy storage applications. As a consequence, a high specific capacitance of 451 F g−1 is achieved in a neutral aqueous Na2SO4 electrolyte as the 3D architectures are utilized for energy storage. Remarkably, the capacitance retention after 4000 cycles is more than 90%, and the energy density is up to 107 W·h·kg−1 at a high power density of 9.4 kW kg−1. KEYWORDS: 2D layers, V2O5, 3D architectures, high energy density, supercapacitor
S
However, these carbon-based electrochemical double-layer capacitors have a low capacitance, especially at high charge/ discharge rates. Metal oxides and hydroxides overcome these limitations of carbon and commonly exhibit high capacitance for energy storage owing to their more efficient energy storage mechanism, and they have potential to be the electrode material of supercapacitors having high energy density.9−13 In this respect, vanadium pentoxide (V2O5) has been widely studied in devices with both aqueous electrolyte and organic electrolyte due to its very stable crystal structure, high Faradaic activity, and wide potential window.14 Many investigations demonstrated that the structure of V2O5 has a significant influence on the energy density; for example, bulk V2O5 delivers only a low energy density of 11.6 W h kg−1,15 whereas the porous, paper-like V2O5 framework built from carbon fiber coated with a thin V2O5 layer can exhibit energy density of 45.0 W·h·kg−1.16 Thus, developing V2O5 nanomaterials with suitable structure is the key to further improve their energy density. At the same time, the specific capacitance and energy density of
upercapacitors, also called electrochemical capacitors or ultracapacitors, are extensively studied as they complement lithium-ion batteries due to their high power density, fast delivery rate, and long lifespan. However, the low energy density of supercapacitors largely obstructs the way of their applications as standalone devices. The energy density (E) of a supercapacitor is determined by its specific capacitance (C) and the cell voltage (V) according to the equation of E = 1/2CV2.1,2 Thus, improving the specific capacitance of electrode materials is an efficient way to achieve supercapacitors with a high energy density. Generally, high-capacitance electrode materials possess a high surface area and good electrical conductivity since these properties are strongly related to the electrochemical double layer capacitance or electroactive surface for redox-reactions, resulting in pseudocapacitance within an electrode. To date, a large number of high-surface-area carbonaceous materials such as activated carbon, carbon nanotubes, and graphene have been employed as electrode materials for supercapacitors.3−7 In particular, it was shown that graphene, a 2D monolayer of carbon atoms, is an excellent building block for constructing 3D architectures having improved electrochemical performance advantageous for energy storage devices.6,8 © 2013 American Chemical Society
Received: August 7, 2013 Revised: October 7, 2013 Published: October 22, 2013 5408
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Figure 1. Schematics of the fabrication steps of the 3D V2O5 architectures: (1) producing thin and flexible V2O5 nanosheets via the hydrothermal treatment of V2O5 powder with H2O2 at 190 °C; (2) removal of water from the as-prepared V2O5 nanosheet samples via freeze-drying.
sealed into a 40 mL Teflon-autoclave and heated at 190 °C for 5−20 h. During this hydrothermal process, the high viscous red gelation was generated, which was consisted of numerous V2O5 nanosheets. The formation of nanosheets should be attributed to the preferably regrowth of V2O5 along its [a] and [b] directions from [VO2]+ during the synthesis process (see below a discussion of high-resolution TEM analysis).21 Finally, the high viscous V2O5 gel composed of random interconnected nanosheets was frozen by liquid nitrogen and was dried by high-level vacuum pump to sublime the ice. As a result, a 3D V2O5 architecture with high surface area was obtained. Note that the yield of the product in such simple template-free methodology is only dependent on the volume of autoclaves and the mass of precursors used during our synthesis process, which is favorable for the mass production. The morphology and structure of the as-prepared 3D architectures were systematically investigated by field-emission scanning electron microscopy (FE-SEM) and transmission electron microscopy (TEM). As shown in Figure 2a and b, the highly interconnected and porous 3D architectures are built from numerous nanosheets, similarly to those reported for 3D graphene networks and aerogels.17,22−26 Further investigations reveal that the building block nanosheets have lateral sizes from 500 nm to tens of micrometers, and they are randomly selfassembled in the 3D architectures. The pores sized from several micrometers to tens of micrometers can be identified; the pore structure is derived from the removal of water during the freeze-drying process. The porosity of the samples was further studied by nitrogen physisorption measurements. The adsorption/desorption isotherm exhibits a typical H3 hysteresis loop.27 The adsorption analysis via the Brunauer−Emmett− Teller (BET) method reveals a high surface area value of 133 m2 g−1 (Figure 3c), which is much higher than those of stacked V2O5 films (27 m2 g−1) and commercial bulk V2O5 (5.4 m2 g−1). Moreover, the surface area of our 3D V2O5 architectures is comparable to those reported for liquid-phase exfoliated V2O5 nanosheets with the thicknesses of 2−4 nm (147.5 m2 g−1) and the hollow V2O5 hierarchical architectures built from nanosheets with the thickness of 20 nm (60 m2 g−1).28−30 Note that the formation process of the 3D vanadium pentoxide architectures is fundamentally different from the one used in graphene oxide nanosheets to build 3D graphene foams; in that process one needs to use a linking agent such as a surfactant (e.g., ethylenediamine)26 or biomolecules (e.g., DNA).31 A typical high-resolution TEM (HRTEM) image further shows that the nanosheet building blocks contain wrinkles, from these their thickness is estimated to be ∼4 nm (an example is marked by arrows in Figure 2c). The lattice periodicity of 0.19 and 0.18 nm is clearly observed in Figure 2d, corresponding to the
V2O5 electrodes can be further increased by using organic electrolyte having higher voltage windows than the aqueous electrolytes,1,17 for example, an energy density of 65.9 W·h·kg−1 delivered at a power density of 8.32 KW kg−1 for Li+ exchanged V2O5 nanowire/carbon nanotubes (CNTs) samples in lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) electrolyte. To the best of our knowledge, this is the highest value reported for any V2O5-based materials until now, and the energy density of V2O5 still needs to be improved for the practical application. Here, we report an approach for large-scale production of ultrathin V2O5 nanosheets with a thickness of 4 nm and lateral dimension up-to tens of micrometers that are ideal building blocks of 3D architectures produced via a freeze-drying process. Such a porous architecture possesses a high surface area usable for electrolyte/electrode interfaces, and the ultrathin nature of V2O5 walls can efficiently reduce the diffusion length of both electrons and ions. As a result, the resulting 3D V2O5 architectures exhibit a high capacitance, large rate-capability, excellent stability, and large energy density as they are utilized as electrode materials for symmetric supercapacitor in a neutral aqueous Na2SO4 electrolyte. As illustrated in Figure 1, a gel constructed of large number of V2O5 nanosheets was fabricated via a simple hydrothermal treatment and a subsequent freeze-drying approach. Typically, bulk V2O5 was first dispersed into a mixture of H2O2 (30 wt %) and deionized water, where their volume ratio was constant at 1:5. Then the mixture was sonicated for 2−3 min for the quick dissolution of V2O5. Interestingly, during the sonication process, the orange mixture was gradually transformed into a transparent red solution associated with vigorous bubbles.18,19 This phenomenon should be derived from the following complicated chemical reactions of V2O5 with H2O2, similar to that reported in previous literature.18−20 V2O5 + 4H 2O2 → 2[VO(O2 )2 (OH 2)]− + 2H+ + H 2O (1)
V2O5 + 2H+ + 2H 2O2 + 3H 2O → 2[VO(O2 )(OH 2)3 ]+ + O2
(2)
2[VO(O2 )2 (OH 2)]− + 4H+ + 2H 2O → 2[VO(O2 )(OH 2)3 ]+ + O2
2[VO(O2 )(OH 2)3 ]+ → 2[VO2 ]+ + O2 + 6H 2O
(3) (4)
Thus, it was clear that the bubbles and the color change resulted from the release of O2 gas and the generation of intermediate phases during the complicated chemical reactions, respectively. Subsequently, the transparent red solution was 5409
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interplane spacing of (600) and (020) crystal planes of orthorhombic V2O5, respectively. The associated diffraction patterns (Figure 2d, inset) generated by fast Fourier transformation (FFT) are indexed to the zone axis of [001], corresponding to the exposure of (001) facets of V2O5.28,32 The composition of as-prepared V2O5 sheets is demonstrated by energy dispersive X-ray (EDX) and elemental mapping analysis. As shown in Figure 2e−g, the V and O atoms are homogeneously distributed in the nanosheets. The crystal structure and phase of the 3D architectures were examined by X-ray diffraction measurements. As illustrated in Figure 3 and Figure S1 with high-magnified curves (see Supporting Information), the main peak of V2O5 architecture is located at 7.6, and two smaller intensity peaks are located at 22.8 and 30.4, corresponding to (001), (003), and (004) facets of orthorhombic V2O5 (JCPDS no. 40-1296), respectively.17 These patterns are different from those of V2O5 powder (JCPDS no. 41-1426, space group: Pmmn (59)); our bulk sample has particle size of 100 nm to several micrometers (see Figure S2 in the Supporting Information). To gain insight into the reason of this difference, we fabricated stacked V2O5 films (see Figure S3 in the Supporting Information) using the same V2O5 gel via a filtration procedure and then drying in vacuum oven. Apparently, in the XRD patterns of the stacked V2O5 film (Figure 3a and Figure S1b, Supporting Information), the (005), (006), and (007) reflection peaks appear besides the (001), (003), and (004) peaks of 3D V2O5 architecture (see Figure S1a in the Supporting Information), validating that the V2O5 architecture consists of ultrathin sheets with large exposure (001) facets and well consistent with the observations from HRTEM images (Figure 2d). Notably, the diffraction intensity
Figure 2. Characterization of the 3D V2O5 constructs. (a−b) Typical field emission scanning electron microscopy (FESEM) images of the 3D V2O5 architecture constructed from nanosheets; (c−d) transmission electron microscopy (TEM) image of a nanosheet showing wrinkles and corresponding high-resolution TEM image (FFT, inset); (e−g) scanning transmission electron microscopy (STEM) image and corresponding elemental mapping of (f) oxygen and (g) vanadium, indicating the homogeneous distribution of V and O in the nanosheet.
Figure 3. (a) X-ray diffraction (XRD) patterns, indicating the differences between the layered structures of the 3D V2O5 architecture and the stacked V2O5 film, and the bulk, orthorhombic V2O5 crystal; (b) Raman spectra of the 3D V2O5 architecture, the stacked V2O5 film, and the commercial bulk V2O5 materials, indicating that the V2O5 in the 3D architecture and stacked film samples have the same in-plane behavior as the bulk V2O5; (c) nitrogen adsorption/desorption isotherms of the 3D V2O5 architecture, the stacked V2O5 film, and the commercial bulk V2O5 samples, showing that the 3D architecture has the highest surface area; (d) X-ray photoelectron spectroscopy (XPS) of V2O5 3D architecture, indicating the presence of V5+ in the sample. 5410
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Figure 4. Electrochemical performance of 3D V2O5 architecture, stacked V2O5 film, and bulk V2O5 for supercapacitors. (a) Specific capacitances calculated from the cyclic voltammetry curves measured with various scan rates shown in Figures S5−S7. (b) Galvanostatic charge/discharge at a current density of 0.5 A·g−1 in the range of −1.0 to +1.0 V in 1 M Na2SO4 aqueous solution. (c) Specific capacitances calculated from galvanostatic charge/discharge with various current densities. (d) Power density and energy density of V2O5 3D architecture, stacked V2O5 film, and bulk V2O5 electrodes.
and −0.74 V are presented in the CVs of 3D V2O5 architectures (see Figure S4a in the Supporting Information), indicating their pseudocapacitive behavior. In comparison, this phenomenon is invisible in the stacked V2O5 film and bulk V2O5 due to their unfavorable access of electrolyte to the interior. From the CV curves, the specific capacitances can be calculated based on an equation of C = Q/(ΔVm), where C is the specific capacitance, m is the mass of the active material in the working electrode, Q is the average charge during the charging and discharging process, and ΔV is the potential window. High specific capacitance of 521 F g−1 is achieved at a scan rate of 5 mV· s−1 for the 3D V2O5 architectures (Figure 4a). This value is much higher than those for the stacked V2O5 films (360 F g−1), bulk V2O5 (142 F g−1) measured in this study, and for the porous V2O5/carbon nanotubes composites reported in ref 17. At a scan rate of 100 mV·s−1, the specific capacitance of 3D V2O5 architecture is as high as 279 F g−1, showing high-rate storage capability (Figure 4a). In contrast, the capacitances of stacked V2O5 film and bulk V2O5 largely decrease at this scan rate to 168 and 51 F g−1, respectively (Figure 4a). To further compare the electrochemical performances of V2O5 architecture, stacked V2O5, and bulk V2O5, we conducted galvanostatic charge/discharge measurements at various current densities from 0.5 A·g−1 to 50 A·g−1 over the potential range from −1.0 to +1.0 V in 1 M Na2SO4 aqueous solution (for detailed results, see Figures S5, S6, and S7 in the Supporting Information). The typical galvanostatic charge/discharge curves of V2O5 architecture, stacked V2O5, and bulk V2O5 measured at a current density of 0.5 A·g−1 are shown in Figure 4b. The discharge slope of 3D V2O5 architecture is much smaller than
of 3D V2O5 architecture is much weaker than that of the stacked V2O5, which should be related to the less loading of the 3D V2O5 architecture sample by using the same height holder during our XRD measurements. The crystalline nature of the 3D V2O5 architecture is consistent with stacked V2O5 because both of the samples are fabricated from the same as-prepared precursor V2O5 gel. The Raman scattering spectra show five well-resolved peaks at 139.5, 192.5, 282.5, 406.8, and 695.2 cm−1 for both the 3D V2O5 architectures, and the stacked V2O5 film, the same as that of bulk V2O5, clearly demonstrates that the V2O5 in the 3D architecture and stacked film samples have the same stack behavior as the bulk V2O5 (Figure 3b). Associated with X-ray photoelectron spectroscopy (XPS) curves (Figure 3d), where the characteristic satellites of V5+ 2p3/2 and 2p1/2 bands located at the binding energies of 517.5 and 525 eV are presented, it is clearly known that V2O5 formed in our 3D architecture.17 Such unique structural features of the V2O5 architectures including high surface area, ultrathin sheets, and porous structure render large electrode/electrolyte contact and short electron/ion diffusion paths when they are used as electrode materials in energy storage devices. As a proof of concept, the electrochemical behavior of the 3D V2O5 architecture was first evaluated via cyclic voltammetry (CV) measurements over a range of scan rates of 5−100 mV·s−1 in symmetric electrochemical cells with 1 M Na2SO4 aqueous electrolyte (see Figures S4, S5, and S6 in the Supporting Information). For comparison, the electrochemical properties of stacked V2O5 film and bulk V2O5 are also tested under the same conditions. Obviously, a pair of reversible redox peaks at around −0.54 V 5411
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V2O5 architecture electrode shows the smallest diameter of semicircle compared with those of stacked V2O5 and bulk V2O5. The kinetic differences of these V2O5 electrodes were further investigated via the common R-C equivalent circuit (Figure S10), and the kinetic parameters were summarized in Table S1. Apparently, their solution resistances are almost the same owing to the same electrolyte testing system. In contrast, the charge transfer resistance of 3D V2O5 architecture is only 10.0 Ω, which is much lower than that of stacked V2O5 (32.4 Ω) and bulk V2O5 (62.8 Ω) electrodes, clearly demonstrating the highest electrochemical activity of 3D V2O5 architecture for energy storage. This should be resulted from its high surface area, ultrathin walls, and 3D interpenetrating structure as we expected. In summary, a new efficient approachhydrothermal treatment and a freeze-drying processhas been developed for large-scale production of 3D V2O5 architectures that constructed from ultrathin V2O5 nanosheets having a thickness of 4 nm and lateral dimension of up to micrometers. Such unique 3D V2O5 architecture provides high surface area for enhanced electrolyte/electrode interaction and also reduces the diffusion path both for electrons and ions. These advantageous properties lead to the excellent electrochemical performance high specific capacitance, excellent rate capability, and charge− discharge stabilityusable for energy storage. We believe that our 3D V2O5 architecture with its unique structure can be further extended to broad applications in lithium ion batteries, sensors, and electronics. Experimental Methods. In a typical fabrication of 3D V2O5 architectures, 0.36 g of V2O5 bulk, 5 mL of 30% H2O2, and 30 mL of H2O were mixed to afford a clear solution, and then 30 mL of the mixture was sealed into a 40 mL Teflon autoclave. The mixture was then maintained at 190 °C for 5− 20 h to generate V2O5 gel. Subsequently, the as-prepared gel was frozen by liquid nitrogen and then dried by a cryodesiccation process to preserve the high surface area during the removal of the residual water. For comparison, the stacked V2O5 film was fabricated from the same gel and dried in a conventional vacuum oven. The electrochemical performances for energy storage of the as-prepared samples were investigated via a symmetric twoelectrode supercapacitor system. The electrodes were prepared by making slurry of 80 wt % active materials, 10 wt % acetylene black, and 10 wt % polytetrafluoroethylene (PTFE; 60 wt % dispersion in water) in ethanol. The obtained slurry was then coated onto 2 × 1 cm2 graphite papers within an area of 1 × 1 cm2, which were then dried in vacuum at 60 °C for 12 h to remove the solvent. A 1 M neutral aqueous Na2SO4 was used as an electrolyte, and two pieces of nickel foils were connected to the back of graphite papers as the current collectors. The morphology and microstructure of the samples were systematically investigated by FE-SEM (JEOL 6500), TEM (JEOL 2010), HRTEM (field emission JEOL 2100), XPS (PHI Quantera X-ray photoelectron spectrometer), and XRD (Rigaku D/Max Ultima II powder X-ray diffractometer) measurements. Nitrogen adsorption isotherms for calculating the Brunauer−Emmett−Teller (BET) surface area were measured at 77 K with a Quantachrome Autosorb-3B analyzer (USA). The electrochemical behavior of the V2O5 samples is evaluated via cyclic voltammetry (CV) measurements over a range of scan rates of 5−100 mV·s−1 in symmetric electrochemical cells with 1 M Na2SO4 aqueous electrolyte between −1.0 and +1.0 V. The galvanostatic charge/discharge measure-
these of stacked V2O5 and bulk V2O5, demonstrating the higher electrochemical activity behavior in 3D V2O5 architecture electrodes. In the case of 3D V2O5 architecture, a high specific capacitance of 451 F g−1 is obtained at a current density of 0.5 A·g−1 (Figure 4c). This is much higher than those of stacked V2O5 (314 F g−1) and bulk V2O5 (108 F g−1) at the same testing conditions, in coherence with the CVs analysis. The specific capacitance can be still maintained as high as 150 F g−1 at a very fast charge−discharge rate of 50 A·g−1, comparable to that of the double layer supercapacitor. To further optimize, we fabricated several 3D V2O5 architectures via adjusting the synthesis temperature from 190 to 150 °C. As shown in Figure S8, with decreasing the temperature from 190 to 170 °C, the capacitances at various current densities are almost the same. However, with further decreasing the temperature to 150 °C, the capacitance and high-rate performance significantly decrease. Thus, we chose the best 3D V2O5 architecture synthesized at 190 °C to study their electrochemical performances in this context. From the galvanostatic charge/discharge results, the energy density (E) and power density (P) of the V2O5 electrodes can be determined via the following equations: E = 1/2C(ΔV)2 and P = E/t. Strikingly, the 3D V2O5 architectures possess a high energy density of 247.9 W·h·kg−1 at a power density of 497.1 W·h·kg−1 to 43.2 W·h·kg−1 at a power density of 39.9 kW·kg−1 within different current densities (Figure 4d). These values are significantly higher than those of stacked V2O5 film (172 W·h·kg−1) and bulk V2O5 (58 W·h·kg−1), as well five times higher than those reported for V2O5-based materials and commercial supercapacitor devices (see Figure S7 in the Supporting Information).1,14,16,17,33 Moreover, this 3D V2O5 architecture exhibits excellent cycle performance. As shown in Figure S9, the capacitance retention is ∼90% after 4000 cycles at a constant current density of 5 A· g−1. To the best of our knowledge, the excellent electrochemical behaviors of 3D V2O5 architecture for energy storage are the best for all of the reported V2O5-based materials,1,14,16,17,34 holding a great promising application for supercapacitors. To reveal the reason of the excellent electrochemical behavior of the 3D V2O5 architecture, the electrochemical impedance spectroscopy (EIS) was carried out over a frequency range of 100 kHz to 0.01 Hz. As shown in Figure 5, the 3D
Figure 5. Nyquist plots of the 3D V2O5 architecture, stacked V2O5 film, and bulk V2O5 electrodes obtained over the frequency range of 100 kHz to 0.01 Hz by applying a sine wave with an amplitude of 5.0 mV; the smallest circle diameter indicates the lowest of resistance in 3D V2O5 architecture electrode (magnified figure at the high frequency, inset). 5412
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ments are carried out at various current densities from 0.5 to 50 A·g−1 over the potential range from −1.0 to +1.0 V in 1 M Na 2 SO 4 aqueous solution using autolab equipment (PGSTAT302N). The specific capacitance of the V2 O5 electrodes are estimated from the galvanostatic discharge curves according to the equation: C = IΔt/ΔV, where I is the constant discharging current density and Δt is the discharging time (Figure 5c). Electrochemical impedance spectroscopy (EIS) measurements were carried out over the frequency range from 100 kHz to 0.01 Hz by applying a sine wave with amplitude of 5.0 mV under autolab equipment (PGSTAT302N).
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ASSOCIATED CONTENT
* Supporting Information S
X-ray diffraction patterns of a 3D V2O5 architecture and a stacked V2O5 film; FESEM images of commercially available bluk V2O5 materials and stacked V2O5 films; CV curves of the 3D V2O5 architecture, stacked V2O5 film, and bulk V2O5; Ragone plot for 3D V2O5 architecture, stacked V2O5 film, and bulk V2O5; specific capacitance vs current density curves and charge−discharge performance of 3D V2O5 architecture; equivalent circuit diagram for fitting EIS profiles; and calculation results from the EIS profiles. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected] (S.Y.). *E-mail:
[email protected] (Q.Y.). *E-mail:
[email protected] (R.V.). Present Address ⊥
School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore.
Author Contributions
J.Z. and L.C. contributed equally to this work. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was financially supported by U.S. Army Research Office through a MURI grant (W911NF-11-1-0362) on Novel Free-Standing 2D Crystalline Materials focusing on “Atomic Layers of Nitrides, Oxides, and Sulfides”. S.Y. and P.M.A. also acknowledge funding sponsorship from the U.S. Department of Defense: U.S. Air Force Office of Scientific Research through a MURI grant (FA9550-12-1-0035) on “Synthesis and Characterization of 3-D Carbon Nanotube Solid Networks”. Q.Y. acknowledges the Singapore National Research Foundation under CREATE programs: EMobility in Megacities, A*STAR SERC grant 1021700144.
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