654
2008, 112, 654-658 Published on Web 12/23/2007
Thermal Conductivity of Single-Wall Carbon Nanotube Dispersions: Role of Interfacial Effects Jagjit Nanda,* Clay Maranville, Shannon C. Bollin, Dustyn Sawall, Hiroko Ohtani, Jeffrey T. Remillard, and J. M. Ginder Research and AdVanced Engineering, Ford Motor Co. Dearborn, Michigan 48121 ReceiVed: NoVember 25, 2007; In Final Form: December 5, 2007
We report measurements of the effective thermal conductivity of dispersions of single-wall carbon nanotubes in technologically important fluids: (poly)-alpha olefins and ethylene glycol. The morphology of this dispersion was studied using rheology, AFM, and light scattering techniques. The enhancement of thermal conductivity was analyzed using a Maxwell-Garnett effective medium theory including the interfacial thermal-resistance layer between the nanotube and the fluid. The results were compared with previously reported results on multiwall carbon nanotubes in similar dispersion media and point to the critical role of the nanotube-fluid interfacial thermal resistance.
Colloidal dispersions of nanoparticles commonly referred to as “nanofluids” have been studied extensively over the past decade because of their potential applications in the area of heat transfer and thermal management.1-7 One area of controversy in this work has been the reported variability in the measured thermal conductivity (κ) of similarly prepared nanofluids, which has led to a debate over the relevant mechanisms responsible for the enhancement of κ observed in some nanoparticle dispersions. Recent literature reports suggest that any realistic explanation for the enhancement of κ should encompass such key aspects as (i) the thermal resistance (or conductance) of the nanoparticle-fluid interface,8 (ii) the nanoparticle aspect ratio, and (iii) the aggregation/agglomeration structure of the suspended nanoparticles.9,10 Individual carbon nanotubes are known to have significantly higher thermal conductivity values as reported in a few reports.11-13 However, dispersions of nanotube bundles/ropes in fluid media can have a range of κ that depends on a number of factors such as the volume fraction of the nanotube, the thermal boundary layer properties of the nanotube/fluid interface, and the synthetic method and processes that determine the material purity of the tubes or nanotube bundles.14,15 With respect to carbon nanostructures, the first experimental observation of an enhancement of κ was reported by Choi et al.16 for the case of multiwall carbon nanotubes (MWCNT) dispersed in (poly) alpha-olefins (PAO) with the aid of an oil solubilizing dispersant. They reported a 160% enhancement of κ at ∼1 volume percent nanotube loading and termed this effect as anomalous; that is, the observed increase in κ exceeded what is predicted from effective media theory. Similar or even larger enhancements in the value of κ for multiwall carbon nanotubebased dispersions (made using the same base fluid and dispersants) have been reported by other groups.17 In this letter, we report κ measurements of nanofluids comprised of single-wall carbon nanotubes (SWCNT) dispersed * Corresponding author. E-mail:
[email protected].
10.1021/jp711164h CCC: $40.75
in two base fluids; ethylene glycol (EG) and (poly)-alpha olefins (PAO). Compared to the base fluids, the values of κ for the nanofluids were found to be larger and consistent with a modified effective medium approximation (EMA) that accounts for the interfacial resistance between the nanotubes and the surrounding matrix, the nanotube aspect ratio, and the tube diameter. The purified SWCNT samples were procured from two suppliers: Carbon Solutions (CS-SWCNT) and Carbon Nanotechnologies Inc. (CNI-SWCNT). The selection of these particular SWCNTs was based on the choice of base fluids. The CS-SWCNT sample was synthesized using the electric-arc method and purified using acid treatment leaving functional carboxylic groups (-COOH) at the end-cap region of the nanotubes. These functionalized nanotubes form a stable dispersion in EG without need for a separate dispersant. The CNISWCNT sample was suspended in PAO with the aid of a dispersant. Details of the sample preparation, dispersion process, and experimental methods are discussed in the Supporting Information. To predict the nanofluid thermal conductivity correctly, it is important to characterize the morphology of the nanotubes after they are dispersed in their respective base fluids. This was accomplished using a variety of techniques including light scattering, atomic force microscopy (AFM), transmission electron microscopy (TEM), and fluid rheology measurements. It is important to note that the light scattering and microscopy measurements require the nanofluid samples to be diluted by several orders of magnitude (using an appropriate solvent) or evaporated in order to deposit the nanoparticles onto substrate or grid. These procedures can cause the nanoparticles to agglomerate and thus potentially yield inaccurate information about their real morphology in the dispersion state of the nanofluids. Rheological experiments provide a more conclusive (though indirect) picture of the nanotube morphology at higher weight loadings. © 2008 American Chemical Society
Letters
Figure 1. Viscosity vs shear rate of 1 wt % CS-SWCNT (blue solid star) and CNI-SWCNT (green square) in EG and PAO, respectively. The Newtonian behavior of the base fluid (6 cSt PAO) plus dispersant is shown as open dot-circles (red).
Figure 1 shows the steady shear viscosity (at 25 °C) results for the base fluid and the CNI-SWCNT in PAO + dispersant and CS-SWCNT in EG. The carbon nanotube loading was ∼1 wt % in both dispersions. The PAO + dispersant sample showed typical Newtonian behavior up to shear rates 1000) the effective thermal conductivity, Ke, of the dispersion is given by the expression
2(Kc11 - Km) Kc11 + Km
and βz )
Kc33 -1 Km
(2)
f is the volume fraction of the nanotubes, and Kc11 and Kc33 are the thermal conductivities along the transverse and longitudinal axes of the tube. Nan and co-workers modified eq 2 to include the effects of interfacial thermal resistance by considering an equivalent thermal conductivity evaluated using a series model.26 For the case of low volume fraction ( f ∼ 0.001) the expression for the ratio of the thermal conductivity enhancement is given by
Ke fp )1+ Km 3
Kc/Km 2ak Kc p+ d Km
(3)
In the above expression, ak is the Kapitza radius defined as ak ) RkKm and Rk is the interfacial resistance between the nanotube and fluid. Kc and Km are the thermal conductivities of the carbon nanotube and the medium, respectively, p is the nanotube aspect ratio, and d is the nanotube diameter. Before applying eq 3 to our experiments, we note the following. First, the expression assumes a dispersion of individual nanotubes, a condition that does not hold for our samples based on the rheological and AFM measurements. Also, in the case of the CNI-SWCNT in PAO, a surfactant was used to form the dispersion. Thus, for this sample, there are ideally two interfaces: one between the nanotube and surfactant and another between the surfactant and PAO. In what follows, we will calculate the thermal conductivities of the nanofluid samples using eq 3 assuming dispersions consisting of individual
Figure 4. Experimental and calculated thermal conductivity ratios for SWCNT dispersion in ethylene glycol (squares) and (poly)-alpha olefin (circles) at room temperature. The solid line shows the theoretical values in the absence of interfacial resistance between the nanotube and the medium. The dotted lines are theoretical thermal conductivity ratios predicted with the effective medium approximation including interfacial resistance.
Letters nanoparticles that have a single interface with the suspending media. Figure 4 shows a comparison of the theoretical model to the experimental thermal conductivity values for both fluids. The solid line shows the theoretical values of κ in the absence of any interfacial resistance, which in this case follows a simple sum of mixture rule. Under this simplified scenario, the κ enhancement depends only on the volume fraction of the particles and the contrast ratio, Kc/Km. For our calculation, we have used the interfacial resistance value, Rk ) 8 × 10-8 m2K/ W. This value was determined experimentally by Huxtable et al. for SWCNT stabilized using a surfactant sodium dodecyl sulfonate (SDS) in D2O and is expected to be similar for the nanotube-EG and nanotube-PAO interfaces.8 Km was measured to be 0.26 W/m K and 0.16 W/m K for EG and PAO plus the dispersant, respectively. The values for the Kapitza radius calculated from the above values were 20.8 and 13 nm for CS-SWCNT-EG and CNI-SWCNT-PAO, respectively. Knowing that the nanotubes used in this experiment have limited purity (∼85%), the thermal conductivity of the SWCNTs was chosen to be 2000 W/m K; we note that higher values have been reported in the literature for individual SWCNTs.11,12 The diameter of the individual SWCNT determined from highresolution TEM (not shown here) is typically between 1 and 1.4 nm. The aspect ratio was taken to be 2000 for the CS-SWCNT and 1000 for the CNI-SWCNT (from data provided by suppliers and independent measurements as described in the earlier section). As shown in Figure 4, we obtain good agreement between the calculated κ and the experimental values for different nanotube loadings in both fluids. We emphasize that the theoretical curves were obtained using only a combination of measured nanotube and fluid parameters and reasonable choices for the remaining constants; that is, none of the parameters were determined by fitting. The modified EMA theory, which includes the interfacial thermal resistance, therefore provides a good estimate for predicting the κ enhancement in the case of SWCNT dispersions. A better description of the observed experimental behavior of carbon nanotubes dispersed in fluids could be possible using more sophisticated theoretical models such as including the effect of aggregation kinetics9,10 or percolative-based theory,27 which has been shown to explain the unusually large thermal conductivity increase as noticed in multiwall carbon nanotubes (MWCNT) dispersed in PAO (ref 16). In the present work we, however, see only a modest increase in the κ enhancement for the case of SWCNTs dispersed in similar fluids and surfactants. As emphasized in the earlier section, the measurements of κ in liquid or fluid medium (dispersions) requires avoiding contribution from factors such as convection and correct input of specific heat capacity of the medium. Finally, Figure 5 compares the values of κ measured in the current study with those reported by other research groups working with suspensions of single- and multiple-wall carbon nanotubes. The results show significant differences in κ enhancement; suspensions of SWCNT consistently show a smaller enhancement in κ than those made from multiwall carbon nanotubes. This observation is consistent with the modified M-G expression given in eq 3, which predicts a higher κ enhancement for suspensions that are made from largediameter nanotubes. In all of the cases demonstrated above, the nanotube quality (purity) also determines the extent of the thermal conductivity increase for a particular volume fraction as reported recently by Haddon and co-workers for nanotubeepoxy composites.28
J. Phys. Chem. C, Vol. 112, No. 3, 2008 657
Figure 5. Thermal conductivity enhancement of SWCNT and MWCNT suspensions at room temperature from literature and the present work. The blue dashed lines are for the MWCNT dispersions, and the black dashed lines are for the SWCNT dispersions.
In conclusion, our experimental results show enhancement of the effective thermal conductivity of PAO and ethylene glycol containing dispersed SWCNTs and further shows the role of the interfacial thermal boundary layer. Morphological investigation of the nanotubes at higher loading shows the formation of random aggregated networks. The κ enhancement can be explained in terms of a simple M-G-type theory incorporating the effects of a thermal interface layer and the morphology/ aspect ratio of the nanotubes. The observed increase was lower than the multiwall carbon nanotubes for a similar loading factor as indicated by the theory. Acknowledgment. We acknowledge the help of James Mueller for help in sample dispersion and characterization. J.N. thanks Abhishek Shetty of University of Michigan, Ann Arbor for the rheology measurements. We also thank BASF Corporation for providing the succinimide based dispersant “Kerrocom PIBSI”. Supporting Information Available: Details of the dispersion of the carbon nanotubes and measurements. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Eastman, J. A.; Phillpot, S. R.; Choi, S. U. S.; Keblinski, P. Annu. ReV. Mater. Res. 2004, 34, 219. (2) Cahill, D. G.; Ford, W. K.; Goodson, K. E.; Mahan, G. D.; Majumdar, A.; Maris, H. J.; Merlin, R.; Phillpot, S. R. J. Appl. Phys. 2003, 93, 793. (3) Vadasz, J. J.; Govender, S.; Vadasz, P. Int. J. Heat Mass Transfer 2005, 48, 2673. (4) Yu, A.; Ramesh, P.; Itkis, M. E.; Bekyarova, E.; Haddon, R. C. J. Phys. Chem C 2007, 111, 7565. (5) Moniruzzaman, M.; Winey, K. I. Macromolecules 2006, 39, 5194. (6) Itkis, M. E.; Borondics, F.; Yu, A.; Haddon, R. C. Nano Lett. 2007, 7, 900. (7) Biercuk, M. J.; Llaguno, M. C.; Radosavljevic, M.; Hyun, J. K.; Johnson, A. T.; Fischer, J. E. Appl. Phys. Lett. 2002, 80, 2767. (8) Huxtable, S. T.; Cahill, D. G.; Shenogin, S.; Xue, L.; Ozisik, R.; Barone, P.; Usrey, M.; Strano, M. S.; Siddons, G.; Shim, M.; Keblinski, P. Nat. Mater. 2003, 2, 731. (9) Prasher, R.; Phelan, P.; Bhattacharya, P. Nano Lett. 2006, 6, 1529. (10) Prasher, R.; Evans, W.; Meakin, P.; FIsh, J.; Phelan, P.; Keblinski, P. Appl. Phys. Lett. 2006, 89, 143119. (11) Yu, C.; Shi, L.; Yao, Z.; Li, D.; Majumdar, A. Nano Lett. 2005, 5, 1842. (12) Pop, E.; Mann, D.; Wang, Q.; Goodson, K. E.; Dai, H. Nano Lett. 2006, 6, 96.
658 J. Phys. Chem. C, Vol. 112, No. 3, 2008 (13) Che, J.; Cagin, T.; Goddard, W. A., III Nanotechnology 2000, 11, 65. (14) Terrones, M.; Jorio, A.; Endo, M.; Rao, A. M.; Kim, Y. A.; Hayashi, T.; Terrones, H.; Charlier, J.-C.; Dresselhaus, G.; Dresselhaus, M. S. Mater. Today 2004, 30. (15) Rinzler, A. G.; Liu, J.; Dai, H.; Nikolaev, P.; Huffman, C. B.; Rodriguez-Marcias, F. J.; Boul, P. J.; Lu, A. H.; Heymann, D.; Colbert, D. T.; Lee, R. S.; Fischer, J. E.; Rao, A. M.; Eklund, P. C.; Smalley, R. E. Appl. Phys. A 1998, 67, 29. (16) Choi, S. U. S.; Zhang, Z. G.; Yu, W.; Lockwood, F. E.; Grulke, E. A. Appl. Phys. Lett. 2001, 79, 2252. (17) Yang, Y. Ph.D. Thesis, University of Kentucky, 2006. (18) Rahatekar, S. S.; Koziol, K. K. K.; Butler, S. A.; Elliott, J. A.; Shaffer, M. S. P.; Mackley, M. R.; Windle, A. H. J. Rheol. 2006, 50, 599. (19) Shetty, A.; Wilkins, G.; Nanda, J.; Solomon, M. J. Unpublished results, 2007.
Letters (20) Zhou, W.; Islam, M. F.; Wang, H.; Ho, D. L.; Yodh, A. G.; Winey, K. I.; Fischer, J. E. Chem. Phys. Lett. 2004, 384, 185. (21) Hough, L. A.; Islam, M. F.; Hammouda, B.; Yodh, A. G.; Heiney, P. A. Nano Lett. 2006, 6, 313. (22) Bohac, V.; Gustavsson, M. K.; Kubicar, L., Gustafsson, S. E. ReV. Sci. Instrum. 2000, 71, 2452. (23) Maranville, C. W.; Ohtani, H.; Sawall, D. D.; Remillard, J. T.; Ginder, J. M. In SAE World Congress; SAE: Detroit, MI, 2006. (24) Nan, C.-W.; Birringer, R.; Clarke, D. R.; Gleiter, H. J. Appl. Phys. 1997, 81, 6692. (25) Nan, C.-W.; Shi, Z.; Lin, Y. Chem. Phys. Lett. 2003, 375, 666. (26) Nan, C.-W.; Liu, G.; Lin, Y.; Li, M. Appl. Phys. Lett. 2004, 85, 3549. (27) Foygel, M.; Morris, R. D.; Anez, D.; French, S.; Sobolev, V. L. Phys. ReV. B 2005, 71, 104201. (28) Yu, A.; Itkis, M. E.; Bekyarova, E.; Haddon, R. C. Appl. Phys. Lett. 2006, 89, 133102.
