Thermal conductivity of carbon nanotubes and graphene in epoxy nanofluids and nanocomposites

  • Mario Martin-Gallego1,

    Affiliated with

    • Raquel Verdejo1,

      Affiliated with

      • Mohamed Khayet2,

        Affiliated with

        • Jose Maria Ortiz de Zarate2,

          Affiliated with

          • Mohamed Essalhi2 and

            Affiliated with

            • Miguel Angel Lopez-Manchado1Email author

              Affiliated with

              Nanoscale Research Letters20116:610

              DOI: 10.1186/1556-276X-6-610

              Received: 19 August 2011

              Accepted: 1 December 2011

              Published: 1 December 2011


              We employed an easy and direct method to measure the thermal conductivity of epoxy in the liquid (nanofluid) and solid (nanocomposite) states using both rodlike and platelet-like carbon-based nanostructures. Comparing the experimental results with the theoretical model, an anomalous enhancement was obtained with multiwall carbon nanotubes, probably due to their layered structure and lowest surface resistance. Puzzling results for functionalized graphene sheet nanocomposites suggest that phonon coupling of the vibrational modes of the graphene and of the polymeric matrix plays a dominant role on the thermal conductivities of the liquid and solid states.

              PACS: 74.25.fc; 81.05.Qk; 81.07.Pr.


              carbon nanotubes graphene nanocomposites nanofluids thermal conductivity


              Due to the increasing importance of energy dissipation in the electronic industry, thermal conductivity of cured epoxy resins has been widely investigated over the years. One strategy to improve the thermal transport of epoxy resins has been the addition of highly conductive fillers, such as carbon-based or metallic fillers [1]. However, the effect of such additions on either the uncured system or the cure reaction of resins has not yet been fully established. The thermal conductivity of the uncured liquid resin plays an important role to define the variables involved in the transformation process, such as time, applied heat, or cooling time, which will then have a profound effect on the cross-link density and hence, on the final properties of the system. Thus, we aimed at studying the effect of two types of carbon-based nanofillers, in particular, nanotubes and graphene sheets, on the thermal conductivity of an uncured liquid epoxy resin.

              There have been considerable interest and effort in the transport properties of carbon nanotube [CNT] filled polymer nanocomposites [2, 3]. Electrical conductivity of epoxy nanocomposites increases by several orders of magnitude with CNT concentration [4]; this effect can be explained by the established percolation theory [5] with the shift from an insulator into a conductive material when a critical concentration of the conductive filler is reached, commonly known as percolation threshold. However, the thermal conductivity has shown at best linear enhancements with nanotube content with a lack of thermal percolation. The main reason for this fact is the relatively small thermal conductivity ratio (K cnt /K matrix) by comparison with the corresponding ratio of electrical conductivities [6].

              Graphene is a two-dimensional carbon nanofiller with a one-atom-thick sheet of sp 2 bonded carbon atoms that are densely packed in a honeycomb crystal lattice [7, 8]. Single layer graphene is predicted to have a remarkable performance, such as high thermal conductivity of 5,000 W/mK, which corresponds to the upper bound of the highest values reported for single-walled carbon nanotube bundles [9], high electrical conductivity of up to 6,000 S/cm [10], and superior mechanical properties with Young's modulus of 1 TPa and ultimate strength of 130 GPa [11]. In addition to these outstanding properties, the recent developments on graphene synthesis routes and on the understanding of their unique properties have prompted the development and study of graphene filled nanocomposites [12, 13].

              This communication analyzes the epoxy-nanofiller blend in the liquid state as a nanofluid and takes into consideration the current theories to explain its transport properties, particularly, the thermal conductivity. Some studies report large thermal enhancements by adding a small percentage of nanoparticles to a fluid [14]. This anomalous behavior, far away from the predicted data by standard theoretical models, is explained by several physical mechanisms like the Brownian motion of the particles or changes in the distribution of the molecules in the liquid state at the particle/liquid interface [15].



              Diglycidyl ether of bisphenol-A epoxy resin (product number: 405493), diethylene triamine curing agent (D93856), and single-walled nanotubes [SWNTs] (519308; diameter 1.2 to 1.5 nm; length 2.5 μm; and specific surface area 1,300 m2/g) used in this study were purchased from Sigma-Aldrich (St. Louis, MO, USA), while multiwalled nanotubes [MWNTs] (diameter 40 nm; length 120 μm, and specific surface area 250 to 300 m2/g) were synthesized in-house by a chemical vapor deposition technique [16]. These MWNTs were then functionalized [f-MWNT] with a 3:1 concentrated H2SO4/HNO3 mixture refluxed at 120°C for 30 min and thoroughly washed with distilled water until neutral. Functionalized graphene sheets [FGS] were also synthesized in-house by the rapid thermal expansion of graphite oxide [GO] at 1,000°C under an inert atmosphere. This results in a high surface area carbon material consisting of graphene layers with residual hydroxyl, carbonyl, and epoxy groups. GO was synthesized from natural graphite flakes obtained from Sigma-Aldrich (St. Louis, MO, USA; universal grade, purum powder ≤ 0.1 mm, 200 mesh, 99.9995%), according to the Brödie method. Full characterization of the FGS used in this work is described elsewhere [17].

              Sample preparation and characterization

              Nanoparticles were mixed under high shear in the resin for 8 h at room temperature to ensure a homogeneous dispersion. The thermal conductivity of the uncured nanofluids (the samples do not contain the curing agent) was measured with a KD2 probe (Decagon Devices Inc., Pullman, WA, USA), based on the hot wire technique, and consisting of a needle located inside the sample. As can be seen in the experimental setup (Figure 1), the hot wire enabled us to obtain the thermal conductivity in a direct and easy way. The needle had a waiting time of 30 s until the sample temperature was stable and heated up the sample for 30 s. Then, it was used to monitor the cooling rate and calculate the thermal conductivity with an accuracy of 5%. The measurements were carried out over a temperature range from 30°C to 60°C. In this range of temperature, no convection was present in the liquid. The results were the average of at least six measurements for each sample. On the other hand, the thermal conductivity of the cured samples was measured using a hot disk apparatus. This method was based on a heat balance in the steady state between the sample and the three disks of the apparatus that allowed us to calculate the thermal resistivity of the solid sample. Testing samples with different thicknesses were used to obtain the thermal conductivity of the material. The next protocol was followed to cure the formulations: the liquid formulations containing nanoparticles and epoxy resin were mixed with diethylene triamine in a stoichiometric ratio; the blends were degassed for 10 min in a vacuum chamber and casted in Teflon molds. Thermal treatments of 60 min at 70°C and 90 min at 130°C were applied to complete the curing reaction [18]. The morphology of the samples was observed using a Philips Tecnai 20 (Philips, Amsterdam, The Netherlands) transmission electron microscope at an acceleration voltage of 200 kV.
              Figure 1

              Experimental setup.

              Results and discussion

              In Figure 2, we show the morphology of the uncured formulations with the highest concentrations of MWNT and FGS by transmission electron microscopy [TEM] analysis. In both cases, a homogeneous dispersion state was obtained.
              Figure 2

              TEM images of nanofluids. (a) Resin loaded with 1 wt.% MWNTs and (b) with 1 wt.% FGS.

              The thermal conductivity [K] of CNTs depends on several factors such as the morphology, the chirality, the diameter and length of the tubes, the number of structural defects, and the specific surface area [19, 20]. Thus, a description of the thermal conduction mechanisms is nontrivial. Liu et al. [21] reported a K for a SWNT and a MWNT of 2,400 W/mK and 1,400 W/mK, respectively, measured using the non contact Raman spectra shift method. The lower intrinsic conductivity of MWNTs was assigned to the fact that thermal transport mainly occurs by the outermost wall and by the existence of intertube Umklapp scattering processes. In addition, SWNTs exhibit a higher number of phonon vibrational modes and a lower defect density in relation to MWNTs, leading to a higher intrinsic K[22, 23]. CNTs are characterized by a large aspect ratio and a huge surface area. It is assumed that the K of CNTs will be higher for CNTs with a greater aspect ratio [24]. In this study, both CNTs exhibit a similar aspect ratio, so this issue does not seem to affect the K of the nanofluid. Another factor that determines the K of CNTs is the presence of structural defects. Che et al. [25] revealed that the K of CNTs decreased with increasing defect concentration. Finally, the heat transfer mechanism of CNTs takes place with phonons and electrons and depends on their chirality [1]. However, to simplify the discussion, we assumed that the thermal conductance mainly occurs via a phonon conduction mechanism since the aim of this article is to provide a general description of the experimentally determined K.

              Table 1 presents the K measurements of the nanofluids only at 30°C as no significant changes with the temperature were observed. The results indicate that MWNTs are the most effective carbon nanofillers to improve the K of liquid resins. Indeed, the K of the nanofluids gradually increased as a function of MWNT content, reaching a 70% improvement at 1 wt.% loading. The better performance of MWNTs can be due to their lower specific surface area [SSA], as compared with SWNTs, and to the presence of the internal layers which enable phonon conduction and hence minimize coupling losses. K of nanocomposites is sensitive to the quality of the interfacial bonding between the filler and the matrix, intimately related to a phonon coupling mechanism. This mechanism is influenced by numerous factors such as the length of free path for phonons, the boundary surface scattering, the number of vibration modes, and the resistance to heat flow at the interface, known as Kapitza resistance [26]. In general, the Kapitza resistance increases with the SSA, decreasing the efficiency of phonon transport.
              Table 1

              Thermal conductivity of epoxy nanofluids and nanocomposites


              K liq


              K sol


              Neat resin

              0.150 ± 0.001

              0.22 ± 0.07

              0.2 wt.% MWNT

              0.162 ± 0.004


              0.4 wt.% MWNT

              0.176 ± 0.009


              0.6 wt.% MWNT

              0.202 ± 0.004

              0.29 ± 0.05

              0.8 wt.% MWNT

              0.220 ± 0.001


              1 wt.% MWNT

              0.250 ± 0.001

              0.38 ± 0.07

              0.6 wt.% f-MWNT

              0.180 ± 0.001


              0.6 wt.% SWNT

              0.180 ± 0.001


              1 wt.% FGS

              0.150 ± 0.001

              0.36 ± 0.04

              1 wt.% Graphite

              0.176 ± 0.005


              1 wt.% GO

              0.150 ± 0.001


              A lower improvement was obtained with the acid-treated carbon nanotubes (f-MWNTs), even though the functionalization decreases the SSA of the nanotubes. This result can be explained by the presence of the functional groups, hydroxyl and carbonyl, that act as scattering points on the surface where phonons can be transferred from the nanotube crystalline structure into the insulating polymer matrix. This behavior has already been observed in cured resins [27, 28], but not in the pre-cured state.

              The addition of nano-dispersed FGS caused no improvement of the K in the liquid resin. To better understand this result, we also measured dispersions of both the starting natural graphite and GO. The natural graphite showed a slight enhancement of K, while no improvement was observed in the oxidized system. These results support the previous discussion of the negative effect of the presence of functional groups on the nanoparticle surfaces [29], the presence of only one carbon layer, and the large SSA (see Figure 3). Hence, FGS cannot be considered as suitable fillers to enhance the K of liquid resins.
              Figure 3

              Schema of the phonon coupling losses and the boundary phonon scattering at the nanoparticle interphase.

              The enhancement in the K of MWNT nanofluids were fitted with the Hamilton-Crosser [30] model (Equation 1) traditionally used to predict the thermal enhancement of solid/liquid suspensions:
              K e K f = 1 + n α - 1 ϕ α + n - 1 - α - 1 ϕ
              where K e and K f are the effective thermal conductivities of the suspension and the base fluid, respectively; α = K p K f is the K ratio, K p is the particle conductivity, n is the particle shape factor (n = 6 for cylinders, n = 3 for spheres in which case, Equation 1 reduces to the Maxwell model), and φ is the particle volume fraction calculated using the true density of the nanotubes [31]. The theoretical thermal conductivities are calculated with both values due to the bent conformation adopted by CNTs when dispersed in a matrix; thus, their shape factor would be between 3 and 6. Figure 4 compares the experimental results for the MWNT samples with the theoretical ones from the proposed model.
              Figure 4

              Comparison of the measured data for MWNT nanofluids and the theoretical values.

              We observe an anomalous enhancement of the experimental K. This behavior could be related to two effects. The first effect is the presence of an organized structure of the molecules in the liquid state at the solid/liquid interface that facilities the coupling between the solid particles and the fluid [32]. The second effect could be contributions from the Brownian motions of the particles that modify the heat transfer in the fluid [33].

              We finally measured the K of the cured samples for some of the nanocomposites with a classical hot-plate apparatus. TEM microphotographs show a finely and homogeneous dispersion of the carbon nanostructures, MWNTs, and FGS in the cured epoxy samples (Figure 5). The improvements obtained for the cured MWNT nanocomposites are approximately the same as those in the liquid state and are in agreement with the data found in the literature [27, 28, 34]. The cured FGS sample revealed a similar enhancement of the K as the MWNT sample. This increase of K in cured epoxy resin due to the addition of FGS has already been reported [35, 36], but not the uncured/cured transition. This transition suggests that the results can be attributed to the differences in the media surrounding the nanoparticles when the resin is in the liquid or solid state. While the FGS are dispersed in a liquid media, they are not able to transfer the heat because the vibrational modes are not compatible. However, when the FGS are surrounded by the more rigid cured matrix, the differences between the frequencies of vibrational modes are smaller and enable phonon coupling. This result corroborates a current theory postulating that the dominant factor in nanocomposite heat conduction is the low frequency modes and their coupling with high vibrational modes at the interface [37, 38]. This transition does not exist in the MWNT samples because the phonon transport through the inner tubes should be relatively unperturbed by the surrounding matrix.
              Figure 5

              TEM images of cured epoxy samples. (a) Resin loaded with 1 wt.% MWNT and (b) with 1 wt.% FGS.


              We employed an easy and direct method based on the hot wire technique to measure the thermal conductivity of epoxy nanofluids. We also studied the differences in heat conduction mechanisms using graphene sheets and different types of CNTs analyzing the role of surface functionalization and resistance to heat flow at the interface in the thermal conductivity. The results show that the layered structure of MWNTs enables an efficient phonon transport through the inner layers, while SWNTs present a higher resistance to heat flow at the interface due to its higher SSA, and f-MWNTs have functional groups on their surface acting as scattering points for the phonon transport. The dominant role of coupling vibrational modes between the matrix and the filler is evident in the case of FGS which induces a transition from a non thermal conductive nanofluid into a thermal-conductive nanocomposite in the solid state.



              The work was supported by the Spanish Ministry of Science and Innovation (MICINN) under project MAT 2010-18749. MMG thanks the CSIC for a JAE-Pre grant.

              Authors’ Affiliations

              Instituto de Ciencia y Tecnologia de Polimeros, ICTP-CSIC
              Faculty of Physics, Complutense University


              1. Han Z, Fina A: Thermal conductivity of carbon nanotubes and their polymer nanocomposites: a review. Prog Polym Sci 2011, 36: 914–944. 10.1016/j.progpolymsci.2010.11.004View Article
              2. Berber S, Kwon YK, Tománek D: Unusually high thermal conductivity of carbon nanotubes. Phys Rev Lett 2000, 84: 4613–4616. 10.1103/PhysRevLett.84.4613View Article
              3. Hone J, Batlogg B, Benes Z, Johnson AT, Fischer JE: Quantized phonon spectrum of single-wall carbon nanotubes. Science 2000, 289: 1730–1733. 10.1126/science.289.5485.1730View Article
              4. Allaoui A, Bai S, Cheng HM, Bai JB: Mechanical and electrical properties of a MWNT/epoxy composite. Compos Sci Technol 2002, 62: 1993–1998. 10.1016/S0266-3538(02)00129-XView Article
              5. Kirkpatrick S: Percolation and conduction. Rerv Mod Phys 1973, 45: 574–588. 10.1103/RevModPhys.45.574View Article
              6. Shenogina N, Shenogin S, Xue L, Keblinski P: On the lack of thermal percolation in carbon nanotube composites. Appl Phys Lett 2005, 87: 133106. 10.1063/1.2056591View Article
              7. Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Grigorieva IV, Firsov AA: Electric field effect in atomically thin carbon films. Science 2004, 306: 666–669. 10.1126/science.1102896View Article
              8. Novoselov KS, Geim AK, Morozov SV, Jiang D, Katsnelson MI, Grigorieva IV, Firsov AA: Two-dimensional gas of massless Dirac fermions in graphene. Nature 2005, 438: 197–200. 10.1038/nature04233View Article
              9. Balandin AA, Ghosh S, Bao W, Calizo I, Teweldebrhan D, Miao F, Lau CN: Superior thermal conductivity of single-layer graphene. Nano Lett 2008, 8: 902–907. 10.1021/nl0731872View Article
              10. Du X, Skachko I, Barker A, Andrei EY: Approaching ballistic transport in suspended graphene. Nature Nanotechnol 2008, 3: 491–495. 10.1038/nnano.2008.199View Article
              11. Lee C, Wei X, Kysar JW, Hone J: Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 2008, 321: 385–388. 10.1126/science.1157996View Article
              12. Kim H, Abdala AA, Macosko CW: Graphene/polymer nanocomposites. Macromolecules 2010, 43: 6515–6530. 10.1021/ma100572eView Article
              13. Verdejo R, Bernal MM, Romasanta LJ, Lopez-Manchado MA: Graphene filled polymer nanocomposites. J Mater Chem 2011, 21: 3301–3310. 10.1039/c0jm02708aView Article
              14. Eatsman JA, Choi SUS, Li S, Yu W, Thompson LJ: Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Appl Phys Lett 2001, 78: 718–720. 10.1063/1.1341218View Article
              15. Kleinstreuer C, Feng Y: Experimental and theoretical studies of nanofluid thermal conductivity enhancement: a review. Nanoscale Res Lett 2011, 6: 439. 10.1186/1556-276X-6-439View Article
              16. Verdejo R, Lamoriniere S, Cottam B, Bismarck A, Shaffer MSP: Removal of oxidation debris from multi-walled carbon nanotubes. Chem Commun 2007, 5: 513–515.View Article
              17. Verdejo R, Barroso-Bujans F, Rodriguez-Perez MA, Saja JA, Lopez-Manchado MA: Functionalized graphene sheet filled silicone foam nanocomposites. J Mater Chem 2008, 18: 2221–2226. 10.1039/b718289aView Article
              18. Pascault JP, Williams RJJ: Epoxy Polymers: New Materials and Innovations. Weinheim: Wiley-VCH Verlag GmbH $ Co. KGaA; 2010.View Article
              19. Maeda T, Horie C: Phonon modes in single-wall nanotubes with a small diameter. Physica B 1999, 263–264: 479–481. 10.1016/S0921-4526(98)01415-XView Article
              20. Popov VN: Theoretical evidence T 1/2 specific behavior in carbon nanotube systems. Carbon 2004, 42: 991–995. 10.1016/j.carbon.2003.12.014View Article
              21. Li Q, Liu C, Wang X, Fan S: Measuring the thermal conductivity of individual carbon nanotubes by the Raman shift method. Nanotechnology 2009, 20: 145702. 10.1088/0957-4484/20/14/145702View Article
              22. Mingo N, Broido DA: Carbon nanotube ballistic thermal conductance and its limits. Phys Rev Lett 2005, 95: 096105–096108.View Article
              23. Dresselhaus MS, Dresselhaus G, Jorio A, Filho AGS, Saito R: Raman spectroscopy on isolated single wall carbon nanotubes. Carbon 2002, 40: 2043–2061. 10.1016/S0008-6223(02)00066-0View Article
              24. Deng F, Zheng QS, Wang LF: Effects of anisotropy, aspect ratio, and nonstraightness of carbon nanotubes on thermal conductivity of carbon nanotube composites. Appl Phys Lett 2007, 90: 021914–021916. 10.1063/1.2430914View Article
              25. Che J, Cagin T, Goddard WA: Thermal conductivity of carbon nanotubes. Nanotechnology 2000, 11: 65–69. 10.1088/0957-4484/11/2/305View Article
              26. Kapitza PL: The study of heat transfer in helium II. J Phys USSR 1941, 4: 181–210.
              27. Gojny FH, Wichmann MHG, Fiedler B, Kinloch IA, Bauhofer W, Windle AH, Schulte K: Evaluation and identification of electrical and thermal conduction mechanisms in carbon nanotube/epoxy composites. Polymer 2006, 47: 2036–2045. 10.1016/j.polymer.2006.01.029View Article
              28. Moisala A, Li Q, Kinloch IA, Windle AH: Thermal and electrical conductivity of single- and multi-walled carbon nanotube-epoxy composites. Compos Sci Technol 2006, 66: 1285–1288. 10.1016/j.compscitech.2005.10.016View Article
              29. Konatham D, Striolo A: Thermal boundary resistance at the graphene-oil interface. Appl Phys Lett 2009, 95: 163105–163107. 10.1063/1.3251794View Article
              30. Hamilton RL, Crosser OK: Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Fundam 1962, 1: 187–191. 10.1021/i160003a005View Article
              31. Thostenson ET, Chou TW: On the elastic properties of carbon nanotube-based composited: modelling and characterization. J Phys D: Appl Phys 2003, 36: 573–582. 10.1088/0022-3727/36/5/323View Article
              32. Choi SUS, Zhang ZG, Yu W, Lockwood FE, Grulke EA: Anomalous thermal conductivity enhancement in nanotube suspensions. Appl Phys Lett 2001, 79: 2252–2254. 10.1063/1.1408272View Article
              33. Peñas JRV, Ortiz de Zárate JM, Khayet M: Measurement of thermal conductivity of nanofluids by the multicurrent hot-wire method. J Appl Phys 2008, 104: 044314–044321. 10.1063/1.2970086View Article
              34. Thostenson ET, Chou T: Processing-structure-multi-functional property relationship in carbon nanotube/epoxy composites. Carbon 2006, 44: 3022–3029. 10.1016/j.carbon.2006.05.014View Article
              35. Debelak B, Lafdi K: Use of exfoliated graphite filler to enhance polymer physical properties. Carbon 2007, 45: 1727–1734. 10.1016/j.carbon.2007.05.010View Article
              36. Yu A, Ramesh P, Itkis PE, Bekyarova E, Haddon RC: Graphite nanoplatelet-epoxy composite thermal interface materials. J Phys Chem C 2007, 111: 7565–7569. 10.1021/jp071761sView Article
              37. Huxtable ST, Cahill DG, Shenogin S, Xue L, Ozisik R, Barone P, Usrey M, Strano MS, Siddons G, Shim M, Keblinski P: Interfacial heat flow in carbon nanotube suspensions. Nat Mater 2003, 2: 731–734. 10.1038/nmat996View Article
              38. Shenogin S, Xue L, Ozisik R, Keblinski P: Role of thermal boundary resistance on the heat flow in carbon-nanotube composites. J Appl Phys 2004, 95: 8136–8144. 10.1063/1.1736328View Article


              © Martin-Gallego et al; licensee Springer. 2011

              This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://​creativecommons.​org/​licenses/​by/​2.​0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.