Effect of chemical functionalization on thermal transport of carbon nanotube composites S. Shenogin, A. Bodapati, L. Xue, R. Ozisik, and P. Keblinski Citation: Applied Physics Letters 85, 2229 (2004); doi: 10.1063/1.1794370 View online: http://dx.doi.org/10.1063/1.1794370 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/85/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Thermal conductivity of carbon nanotube—polyamide-6,6 nanocomposites: Reverse non-equilibrium molecular dynamics simulations J. Chem. Phys. 135, 184905 (2011); 10.1063/1.3660348 Contact thermal resistance between individual multiwall carbon nanotubes Appl. Phys. Lett. 96, 023109 (2010); 10.1063/1.3292203 Thermal conductivity and interfacial resistance in single-wall carbon nanotube epoxy composites Appl. Phys. Lett. 87, 161909 (2005); 10.1063/1.2103398 Effects of chemical modifications on the thermal conductivity of carbon nanotube composites Appl. Phys. Lett. 86, 123106 (2005); 10.1063/1.1887839 Interface effect on thermal conductivity of carbon nanotube composites Appl. Phys. Lett. 85, 3549 (2004); 10.1063/1.1808874 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 58.211.88.98 On: Sat, 26 Mar 2016 06:55:38 Effect of chemical functionalization on thermal transport of carbon nanotube composites S. Shenogin, A. Bodapati, L. Xue, R. Ozisik, and P. Keblinski a) Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180 (Received 19 March 2004; accepted 17 July 2004) We use molecular dynamics simulations to analyze the role of chemical bonding between the matrix and the fiber on thermal transport in carbon nanotube organic matrix composites. We find that chemical bonding significantly reduces tube-matrix thermal boundary resistance, but at the same time decreases intrinsic tube conductivity. Estimates based on the effective medium theory predict increase, by about a factor of two, of the composite conductivity due to functionalization of single-walled nanotubes with aspect ratios within 100–1000 range. Interestingly, at high degree of chemical functionalization, intrinsic tube conductivity becomes independent of the bond density. © 2004 American Institute of Physics. [DOI: 10.1063/1.1794370] Due to their unique properties carbon nanotubes are can- didates for applications as fillers in composite materials to enhance mechanical behavior, 1,2 electrical transport, 1,3,4 and thermal transport. 5,6 In the case of thermal conductivity, re- cent experiments report more than doubling of the thermal conductivity of organic fluids or polymers when filled with 1% by volume of carbon nanotubes. 5,6 These increases were attributed to the high thermal conductivity of the nanotubes, 7,8 and to the high aspect ratio of the nanotubes. They are, however, well below increases predicted by engi- neering rule of mixtures. 9,10 These lower than expected en- hancements might be attributed to lower intrinsic tube con- ductivity, possibly due to scattering of heat carrying phonons by interactions with the surroundings 8 or from defects. An alternative explanation explored recently by a com- bination of experimental and molecular modeling studies is high nanotube-matrix interfacial thermal resistance. 9 One key reason for the high value of interfacial resistance is weak bonding between various matrix materials with (unfunction- alized) nanotube walls. To alleviate this problem, one can consider introduction of stronger chemical bonds (such as covalent bonds) between the tube and the matrix molecules. However, such bonds will act as scattering centers for phonons propagating along the tube axis, thus reducing in- trinsic tube conductivity. In this letter, we will use classical molecular dynamics (MD) simulations to determine the dependence of interfacial resistance and intrinsic carbon nanotube conductivity on the degree of chemical functionalization, and estimate within the effective medium theory the net effect on composite thermal conductivity. To study the effect of functionalization on tube-matrix interfacial resistance, we used the same model as in our re- cent studies; 9 a (5,5) single-walled nanotube with a diameter of 7 Å immersed in octane melt. Octane melt, from the ther- mal transport point of view, is representative of amorphous (solid) or liquid polymer material. It has similar thermal con- ductivity and strength of matrix–nanotube interactions. Therefore, conclusions of our studies apply to a wide range of organic matrix based carbon nanotube composites, while they will not necessarily apply to inorganic matrix compos- ites, which are characterized by much larger matrix conduc- tivity and stiffness. The carbon nanotube consisted of 460 atoms, corre- sponding to a nanotube length of 5.4 nm, and was sur- rounded by 282 octane molecules. For functionalized tubes a given number (from1to32) of octane molecules were co- valently bonded to randomly selected tube carbon atoms, which are sp 3 hybridized, since they form four covalent bonds. Both carbon and hydrogen atoms are modeled explic- itly. Periodic boundary conditions are applied in all direc- tions. The interatomic forces were described by the PCFF force field. 11 The pressure and temperature were set to 1 atm and 298 K, respectively. To evaluate the interfacial resistance, the nanotube was heated instantaneously to a predetermined temperature and then the system was allowed to relax. We observed that the difference between the nanotube and the liquid temperature followed an exponential decay, 9 which is the result of heat flow being limited by thermal resistance at the interface. Un- der such conditions, the time constant, t, of the decay de- pends on the nanotube heat capacity, c T , and the thermal resistance of the nanotube-liquid interface, R K : t = R K · c T A T , s1d where A T is the area of the nanotube. The relaxation times ranged from ,70 ps for unfunctionalized tubes to ,20 ps for the highest density of covalent bonding, demonstrating significant decrease of the interfacial resistance with func- tionalization. To illustrate the importance of the interface on heat flow, R K can be given in equivalent matrix thickness units, which corresponds to the thickness of the matrix material (in our case octane) over which the temperature drop is the same as that across the interface in the planar geometry. For the un- functionalized tube, R K is equivalent to about 7 nm of matrix material, which is 10 times more than a typical radius of a single walled nanotube. With functionalization, the interfa- cial resistance decreases (see Fig. 1), and is reduced by more than three times when an octane molecule is attached to one out of 15 tube carbon atoms. This should increase the com- a) Electronic mail:

[email protected] APPLIED PHYSICS LETTERS VOLUME 85, NUMBER 12 20 SEPTEMBER 2004 0003-6951/2004/85(12)/2229/3/$22.00 © 2004 American Institute of Physics2229 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 58.211.88.98 On: Sat, 26 Mar 2016 06:55:38 posite conductivity. However, tube carbon atoms that are co- valently attached to matrix molecules have different bonding strength and geometry ssp 3 d than the remaining tube carbon atoms ssp 2 d. They will therefore act as scattering centers for the heat carrying wave packages (phonons) and reduce tube thermal conductivity. Recent MD simulations of single- walled nanotubes demonstrated this effect and showed that the introduction of vacancies or 5–7 ring defects led to sharp reduction in thermal conductivity. 12 To study the effects of sp 3 hybridized carbon atoms on conductivity and explore larger concentration of defects than previously considered, we evaluated thermal conductivity of sp 3 defected nanotubes with the use of equilibrium MD simulations. Use of nonequilibrium approaches with heat sinks and sources is limited by the fact that in highly con- ductive nanotubes mean free path of phonons is several hun- dred nanometers, 12 which requires significantly larger system size to avoid finite length effects. 13 In the equilibrium simulation, fluctuations of the thermal current, J Q , are monitored and the conductivity, k,isob- tained from the Green–Kubo fluctuation-dissipation relationships 14 k = 1 k B T 2 V E 0 ‘ dtkJ Q s0dJ Q stdl, s2d where V is volume, k B is the Boltzmann constant, T is tem- perature and kJ Q s0dJ Q stdl is the time-averaged correlation between heat flux at time t 1 and t 2 =t 1 +t. For computation efficiency and comparison with litera- ture data, we used a (10,10), 1.4 nm diameter nanotube in vacuum, and the atomic interactions were described by the Tersoff force field. 15 The pristine tube consisted of 2000 at- oms with a corresponding length of 12.5 nm. In functional- ized tubes, randomly selected atoms were covalently bonded with additional carbon atoms residing just outside the tube wall. This leads to sp 3 hybridized “defects” in the tube wall analogous to those in the functionalized tubes embedded in the octane matrix. The thermal conductivity of such model tubes is ob- tained from Eq. (2) where we use a volume corresponding to that occupied by a tube in a nanotube bundle. 12 To obtain satisfactory statistics for the heat current autocorrelation function, and thus the convergence of the integral in Eq. (2), we preformed three independent simulations of 20 million MD time steps with Dt=1.8310 −16 s for each case. All simulations were performed at T=300 K. The calculated thermal conductivity for the pristine tube is 6000±500 W m −1 K −1 , which is in good agreement with previously reported values for the same model system. 8 As shown in Fig. 2, with increasing degree of functionalization, the conductivity drops significantly. 12 However, once about 1% of carbon atoms are functionalized, further increase in defect density does not affect thermal conductivity, which remains essentially constant at ,1700 W m −1 K −1 level. The above result can be understood from the kinetic theory of thermal conductivity according to which, 16 k = 1 3 E C q v q L q dq, s3d where the integral is over all phonons, q, v q , and L q are phonon wave vector, group velocity, and mean free path, respectively, and C q , is the spectral heat capacity. As defects are introduced, the mean free path of phonons is reduced, thus conductivity decreases. However, long wavelength phonons are only weakly scattered by local defects and they are likely responsible for the plateau value for the conduc- tivity at high defect concentration. To get an estimate of the net effect of functionalization on the composite thermal conductivity, we used effective medium theory analytical formulas 10 with tube conductivity and interfacial resistance parameters given by our simula- tions. According to Fig. 3 for aspect ratios below 100, there is little benefit of conductive fibers. In the 100–1000 aspect ratio range, use of functionalized tubes leads to larger ther- mal conductivity values by approximately factor of two. This magnitude of composite thermal conductivity increase is consistent with about factor of 3–4 decrease of interfacial resistance, however, accompanied with lower tube conduc- tivity. For larger aspect ratios, composites with unfunction- alized tubes are better conductors. This behavior can be understood via an estimate of the “critical” nanotube length, L c , over which the heat flown in to the fiber is dissipated to the matrix, given by 17 L c ˛ rk tube R K , s4d where k tube and r are the tube conductivity and radius, re- spectively. Assuming k tube =3000 W m −1 K −1 and r=0.7 nm, FIG. 1. Interfacial resistance in units of equivalent matrix thickness vs frac- tion of tube carbon atoms with covalently attached octane molecules. FIG. 2. Carbon nanotube conductivity vs fraction of functionalized tube carbon atoms. 2230 Appl. Phys. Lett., Vol. 85, No. 12, 20 September 2004 Shenogin et al. Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 58.211.88.98 On: Sat, 26 Mar 2016 06:55:38 Eq. (5) yields an aspect ratio of L c /2r200 for unfunction- alized tube and L c /2r100 for highly functionalized tube. Parameter L c is an estimate of the size of “contact zone” required for effective heat exchange between the conductive fiber and the matrix. The functionalization can improve the heat exchange only for fibers with lengths comparable to L c . For fibers much longer then L c the interfacial resistance plays less significant role since their large surface area allows for effective exchange of the thermal energy with the matrix. In this case it is advantageous to preserve high intrinsic fiber conductivity, rather than reduce interfacial resistance. This work was supported by DOE Grant No. DE-FG02- 04ER46104, NSF Grant No. DMR 134725, and funding from Phillip Morris, USA. The authors are also grateful for the helpful comments of Dr. David Cahill. 1 P. M. Ajayan, L. S. Schadler, C. Giannaris, and A. Rubio, Adv. Mater. (Weinheim, Ger.) 12, 750 (2000). 2 A. Allaoui, S. Bai, H. M. Cheng, and J. B. Bai, Compos. Sci. Technol. 62, 1993 (2002). 3 B. E. Kilbride, J. N. Coleman, J. Fraysse, P. 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