Experimental investigation on thermal conductivity of

JOURNAL OF APPLIED PHYSICS 107, 094317 共2010兲

Experimental investigation on thermal conductivity of nanofluids containing graphene oxide nanosheets Wei Yu, Huaqing Xie,a兲 and Wei Chen School of Urban Development and Environmental Engineering, Shanghai Second Polytechnic University, Shanghai 201209, China

共Received 22 January 2010; accepted 27 February 2010; published online 7 May 2010兲 Nanofluids containing graphene oxide nanosheets have substantially higher thermal conductivities than the base fluids. The thermal conductivity enhancement ratios with the loading 5.0 vol % are up to 30.2%, 62.3%, and 76.8%, when the base fluids are distilled water, propyl glycol and liquid paraffin, respectively. The enhancement ratios of the nanofluids are almost constant with the tested temperature varying, and they are reduced with the increasing thermal conductivity of the base fluids. Heat transport along the graphene oxide plane is proposed to be the major contributions to the increase in the thermal conductivity. © 2010 American Institute of Physics. 关doi:10.1063/1.3372733兴 I. INTRODUCTION

Graphene, a single-atom-thick sheet of hexagonally arrayed sp2-bonded carbon atoms, has attracted much attention since it was discovered by Novoselov et al.1 in 2004. The two-dimensional 共2D兲 material exhibits exceptionally high crystal and electronic quality, and it has already revealed a cornucopia of new physics and potential applications.2 The remarkable properties of graphene reported so far include high values of its Young’s modulus, fracture strength, mobility of charge carriers, and specific surface area, plus fascinating transport phenomena such as the quantum Hall effect.3 The recent research revealed that the in-plane thermal conductivity of a suspended single-layer graphene was up to 5200 W/mK.4 Nika et al.5 proposed a simple model for the lattice thermal conductivity of graphene in the framework of Klemens approximation. The calculations show that Umklapp-limited thermal conductivity of graphene grows with the increasing linear dimensions of graphene flakes and can exceed that of the basal planes of bulk graphite when the flake size is on the order of a few micrometers. Then, they investigated theoretically the phonon thermal conductivity of single-layer graphene. It was found that the near roomtemperature thermal conductivity of single-layer graphene, calculated with a realistic Gruneisen parameter, is in the range 2000–5000 W/mK depending on the flake width, defect concentration, and roughness of the edges.6,7 The extremely high value of the thermal conductivity suggests that graphene can perform well as carbon nanotube in heat conduction. The superb thermal conduction property of graphene is beneficial for the proposed electronic applications and establishes graphene as an excellent material for thermal management. Nanofluids, which are the suspensions of nanoparticles in fluids, have promising potential applications in microelectronics, energy supply and transportation because of their intriguing properties such as the increase in thermal conduca兲

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tivity, long-term stability, and prevention of clogging in microchannels.8 The researchers from over 30 organizations worldwide completed a benchmark study on the thermal conductivity of nanofluids9 and the results demonstrated that the experimental data were in good agreement with the effective medium theory developed for dispersed particles by Maxwell in 1881 and recently generalized by Nan et al.10 The paper suggested that no anomalous enhancement of thermal conductivity was achieved in the nanofluids tested in the exercise. Graphene has superior thermal conductivity, and it is expected to be a good additive of nanofluids. In addition, according to the prediction by Hamilton and Crosser,11 when the particle-to-liquid conductivity ratio of a suspension was above 100, the particle shape had a substantial effect on the effective thermal conductivity of the suspension. Graphene is a 2D material, and the heat transfer properties may be different from the zero dimensional nanoparticles and one dimensional carbon nanotube. Therefore, it is very interesting to investigate the thermal conductivities of the suspensions containing graphene nanosheets. Graphene can be prepared in many methods, such as intercalation,12 sonication in various solvents,13 solvothermal synthesis,14 and chemical vapor deposition.15 Among these methods, chemical methods for the production of graphene are both versatitle and scalable.16 The chemical methods will afford the possibility of high-volume production, and versatile in terms of being well-suited to chemical functionalization. Due to the hydrophobic property of graphene, it cannot be dispersed in polar solvents directly, therefore, we selected the hydrophilic graphene oxide as the additive in nanofluid, and graphene oxide with rich oxygencontaining groups could be modified easily, and graphene oxide modified by the alkyl-chain could be dispersed in organic solvents after sonication.17 The precursor of graphene oxide is graphite oxide, and graphene oxide is always prepared by the exfoliation of graphite oxide under ultrasonic vibration. The precise chemical structure of graphite oxide has been the subject of considerable debate over the years, and even to this day no

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unambiguous models exist.18 Some papers proposed that graphene oxide is graphene with hydrophilic oxygencontaining groups such as carboxyl, hydroxyl, and epoxide.19 In this paper, the chemical method was applied to produce graphene oxide nanosheets 共GONs兲. In our recent work,20 we investigated the heat transfer property of ethylene glycol based nanofluid containing GONs, and the results demonstrate that graphene oxide is a good additive to enhance the thermal conductivity of base fluids, while further work should be done in order to solve some scientific problems. For example, how to enhance the dispersion of GO in nonpolar solvents. This is a challenging work. Due to the hydrophilic nature, GO is hard to be dispersed into nonpolar base fluids. The effect of base fluids on the heat transfer enhancement of nanofluids containing GO is another important scientific issue. The third challenging work is to investigate the major factor influencing the thermal conductivity enhancement of nanofluids. Although the GO contained nanofluids exhibits much higher thermal conductivities than those containing spherical nanoparticles, the thermal conductivity enhanced ratio of nanofluids containing GO is lower than those containing carbon nanotubes 共CNTs兲. It is very important to find the major influencing factors. In this paper, another three kinds of nanofluids were prepared, using distilled water 共DW兲, propyl glycol 共PG兲, and liquid paraffin 共LP兲 as base fluids, respectively, and the thermal conductivity improvement of nanofluids containing GONs were reported. The influencing factors including volume fractions, temperature, base fluids, and defects were investigated in detail. II. EXPERIMENTAL SECTION

The two-step method was used to prepare the graphene oxide nanofluids. The first step was to prepare GONs. The functionalized GONs were gained through a modified Hummers method as described elsewhere.20,21 GONs were obtained by exfoliation of graphite in anhydrous ethanol. The product was a loose brown powder and it had good hydrophilic nature, therefore, graphene could be dispersed in polar solvents DW and PG well without the use of surfactant. For LP based nanofluid, oleylamine was used as the dispersant. The fixed quality of GONs with different volume concentrations 共␸: 0.01–0.05兲 was dispersed in the base fluids. The volume fraction of the powder was calculated from the weight of dry powder using the density of graphite 共2.62 g / cm3兲 provided by the supplier and the total volume of the suspension. When ␸ = 0.01, 0.02, 0.03, 0.04, and 0.05, the mass concentrations for DW 共PG, LP兲 based nanofluids are 2.58 共2.49, 2.89兲, 5.09 共4.91, 5.67兲, 7.52 共7.25, 8.34兲, 9.88 共9.53, 10.93兲, and 12.16 共11.75, 13.42兲%, respectively. The nanofluid mixture was stirred and sonicated 共40 kHz, 150 W兲 continuously for 3 h. This ensured uniform dispersion of GONs in the base fluid. Transmission electron microscopy 共TEM, JEOL 2100F兲 was used to examine the size and morphology of the GONs. Fourier transform infrared 共FTIR兲 spectra were obtained using Bruker vertex 70 with KBr method. GONs modified by oleylamine 共GONs-OA兲 were separated by centrifugation at 4000 r/min from the GON suspension in LP. Then GON-OA

J. Appl. Phys. 107, 094317 共2010兲

FIG. 1. FT-IR spectra of GONs 共a兲 and GONs-OA 共b兲.

was washed with hot ethanol for five times to remove excess oleylamine. Atomic force microscopy 共AFM兲 images were taken on a MultiTask AutoProbe CP/MT scanning probe microscope 共Veeco Instruments, Woodbury, NY兲. The UV-Vis spectra of the nanofluid were measured on a Shimadzu UV2550 UV-Vis spectrometer. X-ray photoelectron spectrum 共XPS兲 was obtained using Kratos Axis Ultra DLD x-ray photoelectron spectroscopy, the system uses a monochromatic Al Ka X-ray source, a hemispherical analyzer and a multichannel detector. A transient short hot-wire technique was applied to measure the thermal conductivities of the nanofluids in the temperature range of 10–60 °C.22 In addition to hot-wire system, a temperature-controlled bath was used to maintain different temperatures of nanofluids during the measurement process. The experimental apparatus was calibrated by measuring the thermal conductivity of deionized water, and the accuracy of these measurements was estimated to be within ⫾1%. In the thermal conductivity measurements, the vessel containing the tested sample was placed in a temperaturecontrolled bath and a thermocouple inside the vessel was used to monitor the sample temperature. III. RESULTS AND DISCUSSION

The DW and PG based nanofluids containing GONs exhibit a long-term stability, which is similar to the results of Paredes.23 The fact shows GONs have good compatibility with polar solvents, which is confirmed by the FTIR spectrum of GONs. In the FTIR spectrum of GONs, 关Fig. 1共a兲兴, the most characteristic feature is the broad, intense band at 3400 cm−1, assigned to the O u H stretching vibrations. The band at 1730 cm−1 is related to the C v O stretching of carboxyl groups situated at edges of GONs. The absorption due to the O u H bending vibration is observed around 1630 cm−1. The band at 1184 cm−1 corresponds to stretching vibration of C u O u C. Due to the hydrophilic nature of GONs, it is difficult for them to be dispersed in nonpolar solvent without dispersant, and GONs are easy to form large bulk in organic solvents. Therefore, for the nonpolar fluid LP, oleylamine as oil soluble surfactant was selected to make a stable nanofluid. Figure 1共b兲 demonstrates that oleylamine


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(a) (a)

(b)

FIG. 3. 共Color online兲 A tapping mode AFM image of GONs 共a兲 and the height profiles in selected location 共b兲.

(b) FIG. 2. TEM images of GONs 共a兲 bar 2 ␮m; 共b兲 bar 100 nm, one sheet coiled at the edge with defect.

was absorbed on the surface of GONs, and hot ethanol could not remove the absorbed oleylamine completely, indicating the strong interaction between GONs and oleylamine. Oleylamine is an effective surface-modified agent for GONs, GONs-OA nanosheets can be dispersed in LP well. Figure 2 shows the typical TEM images of GONs. The sizes of nanosheets are in the range of 0.5– 3 ␮m, and few of them are larger than 4 ␮m. Most GONs exist in style of thin few-layer graphene, and some of them are fold and coiled at the edge of nanosheets. There are always some defects on the surface of GONs, caused by the strong oxidization 关Fig. 2共b兲兴, and even some researches demonstrated that the GONs were amorphous in structure.24 GONs were imaged using tapping mode AFM 共Fig. 3兲, and the height of GONs ranges from 0.6 to 1.1 nm. The theoretical height for a single-layer graphene is 0.34 nm, while the single-layer graphene oxide with covalently bound carboxyl groups or hydroxyl groups is about 0.6 nm.25 Therefore, GONs may be

composed of single or bilayers of graphene oxide sheets. Figure 4 shows UV-Vis absorption spectra of graphene oxide aqueous solution and GON suspension in LP. The spectrum of graphene oxide aqueous solution presents the characteris-

FIG. 4. The UV-Vis spectra of diluted GON aqueous suspension 共a兲 and GON suspension in LP 共b兲.


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FIG. 5. Thermal conductivity enhancement ratios of the nanofluids as a function of loading.

tic features with peak at 227 nm, corresponding to ␲ − ␲ⴱ transitions of aromatic C u C bonds, while the absorption peak is shifted to 263 nm for GON suspension in LP according to the influence of oleylamine. Figure 5 depicts the thermal conductivity enhancement ratios of the nanofluids as a function of the volume fraction of GONs. In this paper, k and k0 represent the thermal conductivities of the nanofluid and base fluid, respectively, and 共k − k0兲 / k0 is the thermal conductivity enhancement ratio. ␸ is the volume fraction of GONs. Substantial increases in thermal conductivity are seen for all measured GON suspensions, and the thermal conductivity enhancement ratios of the nanofluids with 5.0 vol % are up to 30.2%, 62.3%, and 76.8% for DW, PG, and LP, respectively. There is an approximately linear relationship between the thermal conductivity enhancement ratios and the volume fraction of GONs. According to the statistics data,26 the nanofluids containing GONs would show larger thermal conductivity enhancement than those containing spherical nanoparticles. It demonstrates that GONs are good additive to enhance the thermal conductivity of base fluid. It was reported that thermal conductivity augmentation ratios decreased with the thermal conductivity of the base fluid for nanofluids containing alumina nanoparticles27 and carbon nanotubes.28 As shown in Fig. 6, dramatic improvement in thermal conductivity of GON suspension is seen for a base fluid with lower thermal conductivity. For the base fluid with lower thermal conductivity, the thermal conductivity difference between GONs and base fluid is larger, and the effect of additive is more obvious. The temperature has great influence on the thermal conductivity of base fluid. For nanofluids, there are relative fewer effective data to reach the unanimous conclusion about the influence of temperature on the enhancement ratios of thermal conductivity. Several groups have reported studies of the thermal conductivity enhancement at elevated temperatures29–31 and some of them attributed the facts to the Brownian motion of the suspended nanopartices and the mi-

J. Appl. Phys. 107, 094317 共2010兲

FIG. 6. Thermal conductivity enhancement ratios as a function of the thermal conductivities of the base fluids with different volume fraction.

croconvection caused by the Brownian motions. However, some researchers have reported the contrary results.32 Figure 7 shows the effect of temperature on the thermal conductivity enhancement ratios of nanofluids. For the three kinds nanofluids containing GONs, the thermal conductivities of the nanofluids track the thermal conductivities of the base fluid, and the enhancement ratios are almost constant in the temperatures rang from 10– 60 ° C, which is similar to the conclusion of Timofeeva32 and Chen.33 According to the prediction by Hamilton and Crosser,11 the particle shape had a substantial effect on the effective thermal conductivity of the suspension. Xue34 predicted that the effective thermal conductivity increased rapidly with increasing CNT length, the large length of the CNTs embedded played a key role in the thermal conductivity enhancement. Gao and Zhou35 presented differential effective medium theory to estimate the effective thermal conductivity in nanofluids. It was found that the adjustment of the nanoparticles

FIG. 7. Thermal conductivity enhancement ratios of nanofluids with the tested temperature varying.


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and the facts may influence the thermal conductivity greatly. Therefore, large graphene without much defect will be the better alternative to further enhance the thermal conductivities of nanofluids, and this is a challenging work. IV. CONCLUSIONS

FIG. 8. XPS spectrum of as-prepared GONs.

shape was really helpful to achieve appreciable enhancement of effective thermal conductivity. For the nanofluids containing GONs, due to the large dimension of GONs, the effect of Brownian motion is not obvious, so the microconvection caused by the Brownian motions can be ignored. The thermal conductivity of GONs is highly anisotropic, and heat flux is confined to the plane. Because of the large size of GONs, in our opinion, heat transport along the GON is one of the major contributions to the increase in the effective thermal conductivity of nanofluids. Although the nanofluids containing GONs have higher thermal conductivities than the base fluids, the enhancement ratios of nanofluids containing GONs are less than what we expected. In our opinion, several factors may contribute to the facts. First, when graphite is oxidized, some of sp2-bonded carbon atoms become sp3-bonded atoms. XPS was employed to analyze the samples of GONs 共Fig. 8兲. From the semiquantitative analysis by XPS, it was found that around 17% of the carbon atoms in the sample were oxygenated. Therefore, the electrical conductivity was reduced largely.36 At the same time, the thermal conductivity of graphene oxide was far below that of graphene itself. Second, the perfect structure of graphene was damaged when graphite was chemically oxidized by treatment with strong oxidants, and it would cause some defects, which was confirmed by the TEM analysis. There is no doubt that the high thermal conductivity is diminished by defects, and the defects have direct influence on the heat transport along the 2D structure. The theoretical calculation6 demonstrated that the thermal conductivity of graphene depended strongly on the size of graphene, the rough of edge and the concentration of defects. For larger size graphene, the thermal conductivity is high. Xu et al.’s study37 also showed that the defect concentration and the rough of edge would reduce the thermal conductivity of graphene nanoribbons largely. In the paper, Graphene oxide is prepared by the exfoliation of graphite oxide under ultrasonic vibration. Ultrasonic vibration is an effective means to exfoliate graphite oxide to few-layer graphene oxide, while at the same time it would break the large graphene oxide into fragments. The TEM shows that GONs are always fold and coiled at the edge of nanosheets,

In summary, three kinds of stable nanofluids containing GONs have been prepared by the two-step method. GONs were prepared by the modified Hummers method, and GONs were characterized by TEM, AFM, FTIR, UV-Vis, and XPS. The heat transfer properties of three nanofluids containing GONs have been studied, and the effects of the particle volume fraction, measured temperature, and base fluid on the thermal conductivity enhancement were investigated in detail. The experimental results show the addition of GONs leads to substantial enhancement of thermal conductivity. The thermal conductivity enhancement ratios of the nanofluids are almost constant with tested temperatures varying. The thermal conductivity enhancement increases with the increase in GON loading, but is reduced with thermal conductivity increase in the base fluid. The enhancement ratios of nanofluids containing GONs are less than those containing carbon nanotubes with the same loading, maybe due to the oxidation and defects of graphene. ACKNOWLEDGMENTS

The work was supported by Program for New Century Excellent Talents in University 共NECT-10-883兲, Innovation Program of Shanghai Municipal Education Commission 共Grant No. 10YZ199兲, Shanghai Educational Development Foundation and Shanghai Municipal Education Commission 共Grant No. 08CG64兲, and the Program for Professor of Special Appointment 共Eastern Scholar兲 at Shanghai Institutions of Higher Learning. 1

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 共2004兲. 2 A. K. Geim and K. S. Novoselv, Nature Mater. 6, 183 共2007兲. 3 S. Stankovich, D. A. Dikin, G. H. B. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, Nature 共London兲 442, 282 共2006兲. 4 A. A. Balandin, S. Ghosh, W. Z. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, Nano Lett. 8, 902 共2008兲. 5 D. L. Nika, S. Ghosh, E. P. Pokatilov, and A. A. Balandin, Appl. Phys. Lett. 94, 203103 共2009兲. 6 D. L. Nika, E. P. Pokatilov, A. S. Askerov, and A. A. Balandin, Phys. Rev. B 79, 155413 共2009兲. 7 S. Ghosh, D. L. Nika, E. P. Pokatilov, and A. A. Balandin, New J. Phys. 11, 095012 共2009兲. 8 H. Q. Xie, W. Yu, Y. Li, and L. F. Chen, Proc. ASME Micro/Nanoscale Heat Transf. Int. Conf., MNHMT2009-18445 共2009兲. 9 J. Buongiorno, D. C. Venerus, N. Prabhat, T. McKrell, J. Townsend, R. Christianson, Y. V. Tolmachev, P. Keblinski, L. W. Hu, J. L. Alvarado, I. C. Bang, S. W. Bishnoi, M. Bonetti, F. Botz, A. Cecere, Y. Chang, G. Chen, H. S. Chen, S. J. Chung, M. K. Chyu, S. K. Das, R. D. Paola, Y. L. Ding, F. Dubois, G. Dzido, J. Eapen, W. Escher, D. Funfschilling, Q. Galand, J. W. Gao, P. E. Gharagozloo, K. E. Goodson, J. G. Gutierrez, H. Hong, M. Horton, K. S. Hwang, C. S. Iorio, S. P. Jang, A. B. Jarzebski, Y. Jiang, L. Jin, S. Kabelac, A. Kamath, M. A. Kedzierski, L. G. Kieng, C. Kim, J. H. Kim, S. Kim, S. H. Lee, K. C. Leong, I. Manna, B. Michel, R. Ni, H. E. Patel, J. Philip, D. Poulikakos, C. Reynaud, R. Savino, P. K. Singh, P. Song, T. Sundararajan, E. Timofeeva, T. Tritcak, A. N. Turanov, S. V. Vaerenbergh, D. S. Wen, S. Witharana, C. Yang, W. H. Yeh, X. Z. Zhao, and S. Q. Zhou, J. Appl. Phys. 106, 094312 共2009兲.


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C. W. Nan, R. Birringer, D. R. Clarke, and H. Gleiter, J. Appl. Phys. 81, 6692 共1997兲. 11 R. L. Hamilton and O. K. Crosser. I & EC Fundamentals 1, 187 共1962兲. 12 X. L. Li, G. Y. Zhang, X. D. Bai, X. M. Sun, X. R. Wang, E. Wang, and H. J. Dai, Nat. Nanotechnol. 3, 538 共2008兲. 13 Y. Hernandez, V. Nicolosi, M. Lotya, and F. M. Blighe, Nat. Nanotechnol. 3, 563 共2008兲. 14 M. Choucair, P. Thordarson, and J. A. Stride, Nat. Nanotechnol. 4, 30 共2009兲. 15 A. N. Obraztsov, Nat. Nanotechnol. 4, 212 共2009兲. 16 S. Park and R. S. Ruoff, Nat. Nanotechnol. 4, 217 共2009兲. 17 K. A. Worsley, P. Ramesh, S. K. Mandal, S. Niyogi, M. E. Itkis, and R. C. Haddon, Chem. Phys. Lett. 445, 51 共2007兲. 18 D. R. Dreyer, S. Park, C. W. Bielawski, and R. S. Ruoff, Chem. Soc. Rev. 39, 228 共2010兲. 19 G. X. Wang, B. Wang, J. Park, J. Yang, X. P. Shen, and J. Yao, Carbon 47, 68 共2009兲. 20 W. Yu, H. Q. Xie, and D. Bao, Nanotechnology 21, 055705 共2010兲. 21 W. S. Hummers, Jr. and R. E. Offeman, J. Am. Chem. Soc. 80, 1339 共1958兲. 22 H. Q. Xie, H. Gu, M. Fujii, and X. Zhang, Meas. Sci. Technol. 17, 208 共2006兲. 23 J. I. Paredes, S. Villar-Rodil, A. Martnez-Alonso, and J. M. D. Tascon, Langmuir 24, 10560 共2008兲.

24

G. X. Wang, B. Wang, J. Park, J. Yang, X. P. Shen, and J. Yao, Carbon 47, 68 共2009兲. 25 S. Stankovich, D. A. Dikin, R. D. Piner, K. A. Kohlhass, A. Kleinhammes, Y. Y. Jia, Y. Wu, S. T. Nguyen, and R. S. Ruoff, Carbon 45, 1558 共2007兲. 26 X. Q. Wang and A. S. Mujumdar, Int. J. Therm. Sci. 46, 1 共2007兲. 27 H. Xie, J. Wang, T. Xi, Y. Liu, F. Ai, and Q. Wu, J. Appl. Phys. 91, 4568 共2002兲. 28 X. Q. Xie, H. Lee, W. Youn, and M. Choi, J. Appl. Phys. 94, 4967 共2003兲. 29 C. H. Chon, K. D. Kihm, S. P. Lee, and S. U. S. Choi, Appl. Phys. Lett. 87, 153107 共2005兲. 30 S. P. Jang and S. U. S. Choi, Appl. Phys. Lett. 84, 4316 共2004兲. 31 S. M. S. Murshed, K. C. Leong, and C. Yang, Int. J. Therm. Sci. 47, 560 共2008兲. 32 E. V. Timofeeva, A. N. Gavrilow, J. M. Mccloskey, Y. V. Tolmachev, S. Sprunt, L. M. Lopatina, and J. V. Selinger, Phys. Rev. E 76, 061203 共2007兲. 33 L. F. Chen, H. Q. Xie, L. Yang, and W. Yu, Thermochim. Acta 477, 21 共2008兲. 34 Q. Z. Xue, Nanotechnology 17, 1655 共2006兲. 35 L. Gao and X. F. Zhou, Phys. Lett. A 348, 355 共2006兲. 36 S. Park, J. An, R. D. Piner, I. Jung, D. Yang, A. Velamakanni, S. T. Nguyen, and R. S. Ruoff, Chem. Mater. 20, 6592 共2008兲. 37 J. N. Hu, X. L. Ruan, and Y. P. Chen, Nano Lett. 9, 2730 共2009兲.
