Graphite Nanoplatelet−Epoxy Composite Thermal Interface

Rafael Hernández , Jordi Riu , Johan Bobacka , Cristina Vallés , Pablo Jiménez ..... Siddiqui , Abul Fazal M. Arif , Syed Sohail Akhtar , Abbas Sae...
0 downloads 0 Views 462KB Size
Download PDF
7565

2007, 111, 7565-7569 Published on Web 05/10/2007

Graphite Nanoplatelet-Epoxy Composite Thermal Interface Materials Aiping Yu, Palanisamy Ramesh, Mikhail E. Itkis, Elena Bekyarova, and Robert C. Haddon* Center for Nanoscale Science and Engineering, Departments of Chemistry and Chemical and EnVironmental Engineering, UniVersity of California RiVerside, RiVerside, California 92521 ReceiVed: March 5, 2007; In Final Form: April 25, 2007

Natural graphite was intercalated, thermally exfoliated, and dispersed in acetone to prepare graphite nanoplatelets (GNPs, Gn) of controlled aspect ratio. Thermal conductivity measurements indicate that few graphene layer Gn, where n ∼ 4, with a thickness of ∼2 nm function as a very efficient filler for epoxy composites. When embedded in an epoxy matrix, the G4 GNPs provide a thermal conductivity enhancement of more than 3000% (loading of ∼25 vol %), and a thermal conductivity κ ) 6.44 W/mK, which surpasses the performance of conventional fillers that require a loading of ∼70 vol % to achieve these values. We attribute the outstanding thermal properties of this material to a favorable combination of the high aspect ratio, two-dimensional geometry, stiffness, and low thermal interface resistance of the GNPs.

1. Introduction The progress in miniaturizing device components has aggravated the problems associated with heat dissipation in the electronics industry, and this has produced a need for improved thermal interface materials (TIMs) in modern chip packaging. Current TIMs are based on polymers, greases, or adhesives filled with thermally conductive particles such as silver, alumina, or silica which require 50-70 vol % of filler to achieve thermal conductivity values of 1-5 W/mK.1 A number of nanomaterials have been explored as candidates for improving the thermal conductivity of polymer composites, and carbon nanotubes (CNTs) have emerged as an efficient filler because of their superior thermal conductivity (∼3,000 W/mK along the tube axis) and high aspect ratio.2-10 However, the cost of CNTs is inhibiting industrial applications. In the present manuscript, we show that graphite nanoplatelets (GNPs), prepared from exfoliated natural graphite, provide excellent thermal enhancement when embedded in an epoxy matrix. We demonstrate an industrially viable procedure for the bulk processing of natural graphite that yields few-layer GNPs of similar aspect ratio to that of single-wall carbon nanotubes (SWNTs) but with twice the increase in the thermal conductivity when embedded in an epoxy composite;10 the application of these materials promises an economical route to a new class of efficient thermal management materials.1 Graphite, an allotrope of carbon, consists of superimposed lamellae of two-dimension (2D) carbon-carbon covalent networks, referred to as graphene, which stack along the c-axis as a result of strong van der Waals forces, and the separation of these layers is a considerable challenge.11 The focus on the extraordinary electronic properties of graphene11-21 has prompted a search for efficient routes to bulk materials, and chemical processing has already been employed to study the solutionphase properties of single-layer graphene,11 and to prepare * Corresponding author. E-mail: [email protected].

10.1021/jp071761s CCC: $37.00

individual oxygenated graphene sheets, which were utilized for the fabrication of electrically conductive composites with a very low percolation threshold.19 Exfoliation of graphite is an alternative route to the separation of graphene layers;22-27 however, the lack of functional groups in the graphene sheets promotes the reaggregation of the material into micron-sized clusters. Significant efforts have already been applied to embed nanometer-sized graphite particles in polymer matrices using a variety of techniques,25,28,29 and these composites, which contain nanometer-sized particles (5-10 nm), have been reported to show enhanced thermal and electrical conductivities.25,28-30 In the present manuscript, we report a systematic investigation of the exfoliation and dispersion of natural graphite to prepare graphite nanoplatelets of desired aspect ratio, and we provide the first study of the effect of the aspect ratio of the 2D-graphitic filler material on the thermal conductivity. The controlled exfoliation and dispersion process described in this study plays a key role in manipulating the thickness of the GNPs, and we demonstrate the power of this technology in achieving a remarkable thermal conductivity enhancement in epoxy composites. 2. Experimental Section 2.1. Graphite Nanoplatelets Preparation. Natural graphite flakes with an average size of 500 µm were obtained from Asbury Graphite Mills Inc., NJ, and Vulcan XC72R carbon black was obtained from Cabot Corporation. In a typical experiment, 1 g of natural graphite flakes was treated overnight at room temperature with 12 mL of a mixture of concentrated sulfuric and nitric acids (3:1). The intercalated graphite was filtered, washed with distilled water, and air-dried for 2 days. The intercalated graphite was exfoliated by thermal shock on rapid exposure to temperatures of 200, 400, and 800 °C in nitrogen for 2 min.24 The exfoliated graphite was dispersed in acetone by highshear mixing for 30 min followed by bath sonication for 24 h © 2007 American Chemical Society

7566 J. Phys. Chem. C, Vol. 111, No. 21, 2007

Figure 1. Images of natural graphite before and after exfoliation. (a) Side view of a starting natural graphite flake. (b) Natural graphite flakes expanded along the c-axis as a result of the acid intercalation and thermal exfoliation illustrating the overall volume increase with increased exfoliation temperature (shown next to the product).

(sonic power 270 W) to obtain GNP dispersions at a concentration of 2 mg/mL. The postprocessing treatment applied to the exfoliated GNPs is the key to stabilizing very thin nanoplatelets and realizing improved properties.29,30 Graphite microparticles (GMPs) were prepared by grinding and sieving natural graphite flakes to achieve particles with an average lateral dimension, L ≈ 30 µm, and an average thickness, t ≈10 µm. 2.2. Composite Processing. Monoliths of GNP-epoxy composites were prepared as follows: epoxy resin (diglycidyl ether of bisphenol A, EPON 862) was added to the GNP suspension and was subjected to 30 min of high-shear mixing. The solvent was removed at 50 °C in a vacuum oven, and the curing agent (diethyltoluenediamine, EPI-CURE W) was added under continuous stirring in a ratio of epoxy to curing agent of 100:26 by weight. The mixture of epoxy with the homogeneously dispersed GNPs was loaded into a custom stainless steel mold, degassed and heated in vacuum for curing. The composites were cured at 100 °C for 2 h and at 150 °C for additional 2 h to complete the curing cycle. A series of composite monoliths were prepared with GNP loadings between 0.1 and 10 vol %. For comparison studies, epoxy composites filled with GMPs and carbon black were prepared using the procedure described above. The densities used for the calculation of the vol % loading are: graphite and GNPs, 2.26 g/cm3; SWNTs, 1.4 g/cm3; carbon black, 1.8 g/cm3; and epoxy, 1.17 g/cm3. 2.3. Characterization Techniques. Tapping mode atomic force microscopy (AFM) images were obtained on mica substrates using a Digital Instruments Nanoscope IIIA. Highresolution transmission electron microscopy (TEM) was performed with a FEI-Philips CM300 microscope operating at an accelerating voltage of 200 kV. The thermal conductivity (κ) of disc-shaped composite samples with a 1 in. diameter was measured with a FOX50 (LaserComp, Inc), steady-state heat flow measurement apparatus, employing a dual thickness measurement cycle to eliminate the thermal contact resistance to the sample; a value of κ0 ) 0.201 W/mK was obtained for pristine epoxy. 3. Results and Discussion We utilized natural graphite flakes of nominal diameter 500 µm as the starting material (Figure 1a) for the production of the GNPs. The interlamellar space between the graphene layers can be intercalated by a range of ionic species.11,13-19 In our procedure, the natural graphite was intercalated with a mixture of sulfuric and nitric acids; upon thermal shock the acid trapped between the graphene layers vaporizes and the increase in volume leads to expansion along the graphite c-axis. We

Letters employed three different exfoliation temperatures: 200, 400, and 800 °C for inducing thermal shock; the volume of the graphite flakes abruptly increased by more than 100 times at the threshold exfoliation temperature (∼200 °C) and further increases were realized up to 800 °C (Figure 1b). This result correlates with earlier observation that the exfoliation temperature controls the apparent volume and surface area of the exfoliated graphite.24 Scanning electron microscopy of the exfoliated graphite particles revealed that despite the enormous increase of the total volume, the individual GNPs are still held together in macrostructures due to strong van der Waals forces and the measured resistance along the length of the fibers was about 10Ω. To take advantage of the unique properties of GNPs, it is essential to further process the exfoliated material so as to physically separate and stabilize the individual GNPs. Conventional powdering techniques, which are routinely utilized for physical separation such as grinding, can lead to reaggregation of the graphite nanoplatelets into multilayer compressed sheets due to the flexible nature of the exfoliated graphite. Therefore, we shear mixed the exfoliated graphite in acetone for 30 min followed by 24 h of ultrasonication (270 W sonic power) to obtain a stable suspension of GNPs; this step is essential for the practical utilization of the few-layer GNPs. Figure 2a shows the AFM images of the material after exfoliation at 200 °C and subsequent physical separation. The average lateral dimension (L) and average thickness (t) of the GNPs assessed from the AFM are L ≈ 1.7 µm and t ≈ 60 nm. Given the average size of the natural graphite starting material (500 µm), we estimate that the average particle size was reduced by a factor of ∼250 after the exfoliation and dispersion. Exfoliation at 400 °C resulted in further reduction in particle size: L ≈ 1.1 µm and t ≈ 25 nm (GNP-400, Figure 2b). The AFM analysis showed that the GNP-200 and GNP-400 materials consist of nanoplatelets of irregular shape and a wide thickness distribution. In contrast, at an exfoliation temperature of 800 °C the nanoplatelets exhibit average dimension L ≈ 0.35 µm and a narrow platelet thickness distribution centered around t ≈ 1.7 nm (GNP-800, Figure 2c), which corresponds to the full exfoliation of the stage 4 intercalation compound into individually stabilized GNPs. On the basis of these observations, we assume that GNP-800 predominantly contains G4 stacking motifs (where Gn denotes the number of graphene layers, n, in GNPs). Several AFM images from different batches GNPs were obtained for statistical analysis. The AFM data analysis indicates average aspect ratios of ∼30, ∼50, and ∼200 for GNP-200, GNP-400, and GNP-800, respectively. The GNPs were embedded into an epoxy matrix using the in situ cross-linking technique previously employed for the SWNT-epoxy composite preparation.10 The epoxy was mixed with a suspension of GNPs in acetone under continuous shear mixing. This step ensures the homogeneous incorporation of individual GNPs and their stabilization in the epoxy matrix thereby preventing reaggregation. The dispersion was then mixed with the curing agent and subsequently was cured as described in the experimental section. The TEM cross-sectional images of the epoxy composites (Figure 2d-f) show readily observable graphitic laminar structures within the polymer matrix. It is clear that the number of graphene layers decreases significantly from GNP-200 to GNP-800 in accord with the AFM measurements (Figure 2a-c) and confirms that the degree of graphite exfoliation increases as the temperature of the thermal shock treatment increases. The 200 and 400 °C thermal

Letters

J. Phys. Chem. C, Vol. 111, No. 21, 2007 7567

Figure 2. AFM and TEM micrographs of GNPs. The micrographs illustrate the degree of exfoliation and number of graphene layers in the nanographitic materials as a function of exfoliation temperatures Texf. AFM images of (a) GNP-200, Texf ) 200 °C; (b) GNP-400, Texf ) 400 °C; and (c) GNP-800, Texf ) 800 °C. Cross-sectional TEM images of the epoxy composites filled with (d) GNP-200, (e) GNP-400, and (f) GNP-800.

shock treatments are only partially effective, whereas complete exfoliation occurs at 800 °C, which facilitates the final separation of the individual GNPs (Figure 2f). Figure 3 compares the thermal conductivity (κ) of epoxybased composites prepared with 5.4 vol % graphitic filler at 30 °C. To assess the performance of the GNPs, we also prepared epoxy composites containing GMPs with an aspect ratio of ∼3 (L ≈ 30 µm, t ≈ 10 µm). Figure 3 shows that the GMPs improve the thermal conductivity of the epoxy composites to 0.54 W/mK, as compared to the value of κ0 ) 0.201 W/mK in pristine epoxy. Clearly, the GNP fillers provide substantially greater thermal conductivity enhancement when embedded into epoxy as compared to GMPs; furthermore, the κ values increase as the

degree of exfoliation increases, and at the highest degree of exfoliation (GNP-800) the thermal conductivity of the composite at ∼5 vol % loading reaches a value of κ ≈1.45 W/mK, which compares very favorably with currently available thermal interface materials (TIMs), which require about 10 times the filler volume (50-70 vol %) to achieve comparable thermal conductivities.1 The contribution of the graphitic fillers to the thermal conductivity increases as the nanoplatelet size is reduced and the aspect ratio increases; the high aspect ratio is apparently responsible for the improved thermal performance of the GNPs in comparison with previous measurements on similar fillers, which showed 2-3% enhancement at 1 vol % loading.30

7568 J. Phys. Chem. C, Vol. 111, No. 21, 2007

Letters

Figure 3. Thermal conductivities of epoxy composites at 30 °C prepared with 5.4 vol % loading of graphitic fillers: GMP, average particle size L ≈ 30 µm, t ≈ 10 µm. Nanographite materials obtained by exfoliation at different temperatures: Texf ) 200 °C (GNP-200, L ≈ 1.7 µm, t ≈ 60 nm); Texf ) 400 °C (GNP-400, L ≈ 1.1 µm, t ≈ 25 nm); Texf ) 800 °C (GNP-800, L ≈ 0.35 µm, t ≈ 1.7 nm). The thermal conductivity of pristine epoxy is included for comparison. Top scale shows the average aspect ratios of the graphite micro- and nano-filler particles.

Figure 4a shows the thermal conductivity enhancement (κ κ0)/κ0 at 30 °C as a function of the filler loading, and the results confirm the improvement of the thermal performance of the composites with increasing the degree of exfoliation. The highest value of (κ - κ0)/κ0 is achieved for GNP-800 (>3000% at 25 vol % loading, where κ ) 6.44 W/mK) and corresponds to an enhancement of more than 100% per 1 vol % loading, an outstanding value for filler efficiency. Traditional fillers typically show an enhancement of ∼20% per 1 vol % filler loading.1 Recently, a thermal conductivity of ∼4 W/mK was reported for nylon composites prepared with 20 vol % loading of graphite nanoplatelets (κ0 ) 0.4 W/mK for nylon);29 direct comparison of our results with those obtained in this study is complicated by the uncertainty in the degree of graphite exfoliation and the different nature of the polymers utilized for composite preparation. Nevertheless, the enhancement factor per 1 vol % loading of GNP-800 in epoxy composites reported here is higher than the values obtained previously for nanographite-epoxy and nanographite-nylon composites.29,30 Figure 4b shows the temperature dependence of the thermal conductivity of the sample prepared at a 25 vol % loading of GNP-800 in epoxy; the thermal conductivity of the composite is found to increase as a function of temperature. In general, most of the computer processors operate at elevated temperatures, and the higher thermal conductivity (6.87 W/mK) of GNP-epoxy at elevated temperatures can ensure efficient heat transfer. The efficient heat transmission of these composites at elevated temperatures makes them potentially suitable for the next generation TIMs. The GNPs provide very efficient thermal conductivity enhancement compared to other carbon materials, including SWNTs, although the intrinsic thermal conductivities of the two materials are similar. Furthermore, the addition of GNPs to epoxy has a much smaller effect on the viscosity than the addition of SWNTs; minimizing the viscosity of TIMs is important in improving the processability and reducing the thickness and overall thermal resistance of the thermal interface layer.1 The efficiency of the GNP in increasing the thermal performance of epoxy composites is compared with that of purified SWNTs10 in Figure 4a. The SWNTs perform better than the GMPs because of the higher aspect ratio (100-1000 for the SWNTs) and more homogeneous dispersion in the polymer

Figure 4. (a) Thermal conductivity enhancement of epoxy-based composites at 30 °C. Utilized graphitic fillers: graphitic microparticles (GMP), GNPs exfoliated at 200 °C (GNP-200) and 800 °C (GNP800), carbon black (CB), and purified SWNTs.10 (b) Temperature dependence of thermal conductivity (κ) for the composites with 25 vol % loading of GNP-800.

matrix.10 However, even the partially exfoliated GNP-200 material demonstrates a better thermal filler performance than the SWNTs, while the completely exfoliated GNP-800 nanoplatelets show ∼2.5 times the enhancement achieved with the SWNTs (Figure 4a). In view of the similar intrinsic thermal conductivities and comparable aspect ratios of the two materials, the dominant thermal performance of the GNPs over SWNTs is remarkable; clearly, other factors militate in favor of the GNPs such as the dimensionality and rigidity of the nanoplatelets and the thermal interface resistance between the nanoplatelets and polymer matrix. Despite significant recent progress, carbon nanotube-based composites do not reach the theoretically predicted level of thermal conductivity,2-5,7-10 which is usually attributed to the high thermal interface resistance between the nanotubes and polymer matrix.8,31-34 Theoretical modeling of thermal transport in composites suggests that the contribution of the phonon acoustic mismatch to the interface contact resistance increases with decreasing radius of the nano particles, and in the case of SWNTs this can significantly increase the total thermal resistance of the composite.1 In contrast to the SWNTs, the flat surface of the few-layer GNPs nanoplatelets minimizes the geometric contribution to the thermal interface resistance. Figure 4a shows the dependence of (κ - κ0)/κ0 on the SWNT loading, and it is apparent that the enhancement of the thermal conductivity by SWNTs is sublinear; this is usually associated with the reduced effective aspect ratio due to nanotube bending at high SWNT loadings.9,10 In contrast, the GNP materials show a slightly superlinear (κ - κ0)/κ0 dependence on the loading

Letters presumably due to the more rigid 2D structure of the nanoplatelets, which minimizes the bending and preserves the high aspect ratio. We suggest that the dimensionality and rigidity of the 2D GNPs are responsible for the superior thermal conductivity enhancement compared to that of the one-dimensional SWNTs (Figure 4a). We posit that the few-layer GNPs represent the optimum nanographite for advanced composites, because it has been shown that individually exfoliated graphene sheets roll up into nanoscrolls and thereby reduce the dimensionality of the material.13 Further enhancement in thermal conductivity of GNPs-based composites may be possible if the interfacial bonding between the GNPs and the polymer matrix is improved. This might be achieved by introducing chemical functionalities on the surface of the nanoplatelets as proposed for the SWNT-based composites.35 The chemistry of SWNTs is now well developed,36 including interfacial bonding with polymers,37 and in most cases similar functionalization schemes can be applied to graphite nanoplatelets. In the few-layer GNPs, the inside layers function as highly conductive channels for thermal transport, while the chemically functionalized outside layers can facilitate the phonon transfer from the GNPs to the polymer matrix, an additional advantage in comparison with the individual graphene sheet. Theoretical modeling predicts that the thermal conductivity of composites increases with the filler aspect ratio, 38 whereas we observe a trend toward saturation of the thermal conductivity enhancement at an aspect ratio between 30 and 200 (Figure 3), and thus GNP-800 with an aspect ratio of ∼200 is close to the optimum filler for TIM applications. We anticipate that it will be possible to optimize the GNPs for utilization in other advanced composites and to develop economical solutions for applications that require high strength or electrically conductive materials. 4. Conclusions In summary, we report an efficient process for converting natural graphite into few-layer GNPs utilizing a simple procedure of acid intercalation, thermal exfoliation, physical separation, and dispersion. When embedded in a polymer matrix, the GNP material (Gn, where n is small) demonstrates a remarkable enhancement of the thermal conductivity at low-volume loadings and significantly outperforms carbon nanotube-based fillers. This material offers an economical solution for the development of a new generation thermal interface materials for electronic packaging and advanced composites. Acknowledgment. This research was supported by DOD/ DARPA/DMEA under Award No. H94003-05-2-0505 and H94003-06-20604. References and Notes (1) Prasher, R. S.; Chang, J.-Y.; Sauciuc, I.; Narasimhan, S.; Chau, D.; Chrysler, G.; Myers, A.; Prstic, S.; Hu, C. Intel Tech. J. 2005, 9, 285. (2) Kim, P.; Shi, L.; Majumdar, A.; McEuen, P. L. Phys. ReV. Lett. 2001, 87, 215502. (3) Biercuk, M. J.; Llaguno, M. C.; Radosavljevic, M.; Hyun, J. K.; Johnson, A. T.; Fischer, J. E. Appl. Phys. Lett. 2002, 80, 2767.

J. Phys. Chem. C, Vol. 111, No. 21, 2007 7569 (4) Hone, J.; Liaguno, M. C.; Biercuk, M. J.; Johnson, A. T.; Batlogg, B.; Benes, Z.; Fischer, J. E. Appl. Phys. A 2002, 74, 339. (5) Liu, C. H.; Huang, H.; Wu, Y.; Fan, S. S. Appl. Phys. Lett. 2004, 84, 4248. (6) Thostenson, E. T.; Li, C. Y.; Chou, T.-W. Compos. Sci. Technol. 2005, 65, 491. (7) Huang, H.; Liu, C. H.; Wu, Y.; Fan, S. S. AdV. Mater. 2005, 17, 1652. (8) Bryning, M. B.; Milkie, D. E.; Islam, M. F.; Kikkawa, J. M.; Yodh, A. G. Appl. Phys. Lett. 2005, 87, 161909. (9) Song, P. C.; Liu, C. H.; Fan, S. S. Appl. Phys. Lett. 2006, 88, 153111. (10) Yu, A.; Itkis, M. E.; Bekyarova, E.; Haddon, R. C. Appl. Phys. Lett. 2006, 89, 133102. (11) Niyogi, S.; Bekyarova, E.; Itkis, M. E.; McWilliams, J. L.; Hamon, M. A.; Haddon, R. C. J. Am. Chem. Soc. 2006, 128, 7720. (12) Affoune, A. M.; Prasad, B. L. V.; Sato, H.; Enoki, T.; Kaburagi, Y.; Hishiyama, Y. Chem. Phys. Lett. 2001, 348, 17. (13) Viculis, L. M.; Mack, J. J.; Kaner, R. B. Science 2003, 299, 1361. (14) Berger, C.; Song, Z.; Li, T.; Li, X.; Ogbazghi, A. Y.; Feng, R.; Dai, Z.; Marchenkov, A. N.; Conrad, E. H.; First, P. N.; de Heer, W. A. J. Phys. Chem. B 2004, 108, 19912. (15) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Nature 2005, 438, 197. (16) Zhang, Y.; Tan, Y. W.; Stormer, H. L.; Kim, P. Nature 2005, 438, 201. (17) Viculis, L. M.; Mack, J. J.; Mayer, O. M.; Hahn, T.; Kaner, R. B. J. Mater. Chem. 2005, 15, 974. (18) Berger, C.; Song, Z. M.; Li, X. B.; Wu, X. S.; Brown, N.; Naud, C.; Mayo, D.; Li, T. B.; Hass, J.; Marchenkov, A. N.; Conrad, E. H.; First, P. N.; de Heer, W. A. Science 2006, 312, 1191. (19) Stankovich, S.; Dikin, D. A.; Dommett, G. H. B.; Kohlhaas, K. M.; Zimney, E. J.; Stach, E. A.; Piner, R. D.; Nguyen, S. T.; Ruoff, R. S. Nature 2006, 442, 282. (20) Ohta, T.; Bostwick, A.; Seyller, T.; Horn, K.; Rotenberg, E. Science 2006, 313, 951. (21) Schniepp, H. C.; Li, J. L.; McAllister, M. J.; Sai, H.; HerreraAlonso, M.; Adamson, D. H.; Prud’homme, R. K.; Car, R.; Saville, D. A.; Aksay, I. A. J. Phys. Chem. B 2006, 110, 8535. (22) Chung, D. D. L. J. Mater. Sci. 1987, 22, 4190. (23) Ramesh, P.; Sampath, S. Chem. Comm. 1999, 2221. (24) Ramesh, P.; Sampath, S. Anal. Chem. 2003, 75, 6949. (25) Chen, G. H.; Wu, D. J.; Weng, W. U.; Wu, C. L. Carbon 2003, 41, 619. (26) Inagaki, M.; Tashiro, R.; Washino, Y.; Toyoda, M. J. Phys. Chem. Solids 2004, 65, 133. (27) Celzard, A.; Mareche, J. F.; Furdin, G. Prog. Mater. Sci. 2005, 50, 93. (28) Chen, G. H.; Weng, W. G.; Wu, D. J.; Wu, C. L. Eur. Polym. J. 2003, 39, 2329. (29) Fukushima, H.; Drzal, L. T.; Rook, B. P.; Rich, M. J. J. Therm. Anal. Calorim. 2006, 85, 235. (30) Hung, M.-T.; Choi, O.; Ju, Y. S.; Hahn, H. T. Appl. Phys. Lett. 2006, 89, 023117. (31) Nan, C. W.; Birringer, R.; Clarke, D. R.; Gleiter, H. J. Appl. Phys. 1997, 81, 6692. (32) Huxtable, S. T.; Cahill, D. G.; Shenogin, S.; Xue, L.; Ozisik, R.; Barone, P.; Usrey, M. L.; Strano, M. S.; Siddons, G.; Shim, M.; Keblinski, P. Nature Mater. 2003, 2, 731. (33) Nan, C. W.; Liu, G.; Lin, Y. H.; Li, M. Appl. Phys. Lett. 2004, 85, 3549. (34) Shenogin, S.; Xue, L. P.; Ozisik, R.; Keblinski, P.; Cahill, D. G. J. Appl. Phys. 2004, 95, 8136. (35) Shenogin, S.; Bodapati, A.; Xue, L.; Ozisik, R.; Keblinski, P. Appl. Phys. Lett. 2004, 85, 2229. (36) Niyogi, S.; Hamon, M. A.; Hu, H.; Zhao, B.; Bhowmik, P.; Sen, R.; Itkis, M. E.; Haddon, R. C. Acc. Chem. Res. 2002, 35, 1105. (37) Gao, J.; Zhao, B.; Itkis, M. E.; Bekyarova, E.; Hu, H.; Kranak, V.; Yu, A.; Haddon, R. C. J. Am. Chem. Soc. 2006, 128, 7492. (38) Nielsen, L. E. Ind. Eng. Chem. Fundam. 1974, 13, 17.