Nanoscale Azide Polymer Functionalization: A Robust Solution for

Article pubs.acs.org/JPCC

Nanoscale Azide Polymer Functionalization: A Robust Solution for Suppressing the Carbon Nanotube−Polymer Matrix Thermal Interface Resistance Yuxiang Ni,† Haoxue Han,‡ Sebastian Volz,‡ and Traian Dumitricǎ*,† †

Department of Mechanical Engineering, University of Minnesota, 111 Church Street SE, Minneapolis, Minnesota 55455, United States ‡ Laboratoire d’Energétique Moléculaire et Macroscopique, CNRS UPR 288, École Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry, France S Supporting Information *

ABSTRACT: The large thermal resistance across the carbon nanotube (CNT)−polymer matrix interface is a limiting factor for achieving polymer composites with high thermal conductivities. Using equilibrium molecular dynamics simulations we show that an azide-terminated aromatic polymer HLK5 (C22H25O3N3) functionalized onto the CNT sidewall can efficiently decrease the thermal resistance between the nanotube and different types of polymer matrices (polystyrene, epoxy, and polyethylene). The HLK5 functionalization can also significantly decrease the CNT−CNT junction resistance. Compared with hydroxyl and octane functionalizations, the HLK5 one alters less the high intrinsic CNT thermal conductivity at the same surface coverage ratio. By revealing the important role played by the atomistic van der Waals interactions in attaining these key results, our study brings a new perspective in the nanoscale design of advanced CNT−polymer materials. functionalized CNT−epoxy matrix.14 Nevertheless, CNTs are used in combination with a variety of polymers, including polystyrene (PS), epoxy, and polyethylene (PE). When in contact with such different host matrices, it is desirable for a particular functionalization to remain effective in reducing thermal resistance. Unfortunately, chemical functionalization can also be detrimental as it introduces phonons scattering centers, which in turn leads to a decrease of the CNT conductivity.12,15,16 To make progress, what is needed is the identification of a functionalization that optimally addresses the issues delineated above. In this article we investigate the CNT functionalization with the recently synthesized azide-terminated aromatic polymer C22H25O3N3, abbreviated as HLK5.17 By way of equilibrium molecular dynamics (EMD) simulations, we examine the impact of HLK5 on the CNT−polymer and CNT−CNT thermal barriers, as well as its influence on the intrinsic thermal conductivity of the CNT onto which it attaches. In comparison with conventional functionalization, the complex HLK5 molecule presents several attractive features for the problem at hand. First, HLK5 can be attached on the CNT walls

I. INTRODUCTION Polymer composites with high thermal conductivities are of great interest for applications.1 Due to their high and robust intrinsic thermal conductivity, high aspect ratio, and low percolation thresholds,2−5 carbon nanotubes (CNTs) are probably the most researched filler nanofibers for enhancing the polymer properties. In spite of some success,1 the achieved thermal conductivity improvements by CNTs addition are lower than those derived from the properties of the CNTs and of the polymer.6−8 It has been determined that the CNT− polymer interface leads to a large thermal resistance, and this is the principal factor that obstructs the heat flow in CNT− polymer materials.9,10 Conventional thermal characterizations measure temperatures averaged over macroscales.11 Therefore, they cannot provide direct information about the mechanisms governing the thermal transport across the nanoscale CNT−polymer interface. Atomistic modeling provides an alternative way to investigate the nanoscale structure−heat transport relationship. Molecular dynamics (MD) simulations revealed that the CNT functionalization can reduce the nanotube-matrix thermal resistance. For example, enhanced interfacial thermal transport has been reported in octane molecule functionalized CNT− octane matrix,12 linear hydrocarbon chains grafted CNT− poly(ethylene vinyl acetate) matrix,13 and cross-linker DETDA© 2015 American Chemical Society

Received: March 16, 2015 Revised: May 9, 2015 Published: May 18, 2015 12193

DOI: 10.1021/acs.jpcc.5b02551 J. Phys. Chem. C 2015, 119, 12193−12198

Article

The Journal of Physical Chemistry C

Figure 1. (a) Chemical structure of HLK5 and CNT−HLK5 covalent bonding. (b) Relaxed configuration of the proposed HLK5 coating of the CNT: side view (left) and cross-sectional view (right). Color scheme: carbon in CNT and CH2, gray; carbon in benzene, blue; oxygen, red; nitrogen, orange; hydrogen, white. Snapshots of (c) HLK5 coated CNT immersed in polystyrene and (d) bare CNT-polystyrene system. The supercell crosssection dimensions are 3.5 × 3.5 nm.

through strong covalent C−N bonds. Recent experiments18−20 used HLK5 to optimize the thermal paths between vertically aligned CNTs and a copper superstrate. When the tips of CNTs were covalently linked to a thin HLK5 intermediate layer, the total thermal resistance decreased by 1 order of magnitude. Second, the van der Waals interaction between the tail of HLK5 and the CNT could bring in an additional channel of heat transport that will not perturb the CNT axial thermal conductivity. Third, the long tail of HLK5 could enable good interpenetration with the polymer matrix. This could favor efficient interaction with the polymer via long-ranged van der Waals and Coulombic interactions, further promoting heat transfer from the HLK5 to the host polymer. The interaction between the HLK5 tails could also mediate the heat transfer at CNT junctions.

Based on this behavior we proposed the HLK5 coating structure shown in Figure 1b, containing 12 HLK5 monomers linked to the CNT through 12 C−N bonds. With the long chain tails wrapping around the tube wall, we achive a 100% coverage with the combination of covalent and van der Waals bonding. Defining the physical HLK5−polymer interface is difficult due to the interpenetration of matrix chains, visible also in Figure 1c. This ambiguity makes it difficult to employ the direct nonequilibrium molecular dynamics (NEMD) method27 for computing the interface thermal resistance from the temperature profile. Therefore, we employ the EMD method, which relies on averaging the autocorrelation of temperature differences measured on atoms located on the two subsystems in contact.28 This method proved to be robust in calculating interface resistances in various systems.20,29,30 Here it also brings the important advantage of allowing us to separate the thermal resistance of the CNT−HLK5 (RC‑H) and the HLK5− polymer matrix (RH‑M) interfaces. To evidence the role of HLK5, we have also performed EMD calculations for the thermal resistance between the pristine CNT and the polymer matrix (Figure 1d).

II. SIMULATION DETAILS Our MD simulations were performed on a (4,4) CNT supercell of 4.2 nm in length. PS, diglycidyl ether of bisphenol A (DGEBA), and PE were used as host matrices. These three types of polymers have different characteristic functional groups and are currently being used in CNT−polymer composites.8,21−26 As illustrated in Figure 1a, HLK5 forms covalent bonds with CNT through its tail group azide. Our structural relaxations show that the HLK5 tail wraps around the CNT with the benzene rings of HLK5 π-staked above the CNT wall.

III. RESULTS AND DISCUSSION The calculated thermal interface resistances are summarized in Table 1. Remarkably, we find that R of CNT−HLK5/matrix is 12194

DOI: 10.1021/acs.jpcc.5b02551 J. Phys. Chem. C 2015, 119, 12193−12198

Article

The Journal of Physical Chemistry C Table 1. Thermal Interface Resistances in CNT−HLK5/Matrix and Bare CNT/Matrix Systemsa

a

matrix

RC‑H

RH‑M

RC‑M

R(CNT-HLK5/matrix)

R(CNT/matrix)

PS DGEBA PE

4.10 ± 0.78 3.87 ± 0.65 3.43 ± 1.10

3.94 ± 0.50 2.81 ± 0.89 4.13 ± 1.12

12.05 ± 1.23 14.32 ± 1.23 11.54 ± 0.95

4.82 ± 0.62 4.55 ± 0.68 4.56 ± 0.66

11.37 ± 1.50 14.11 ± 1.90 10.70 ± 1.20

The unit of the resistances is 108 K/W.

much smaller, by about 60%, than that in pristine CNT−matrix. In calculating R, we considered two parallel thermal paths between CNT and matrix, one passing through HLK5 and the other from CNT directly to the matrix. Thus, the total interface resistance was estimated as 1/R = 1/(RC‑H + RH‑M) + 1/RC‑M, where RC‑M is the thermal resistance between CNT and matrix. For a broader view, in Table 2 we compare our results to the reported interface resistances in CNT-based composites. The Table 2. Comparison of Thermal Interface Resistances in CNT-Based Composites from Experiments and MD Simulations interface CNT-PS sulfonate surfactant/D2O9 CNT/sodium dodecyl sulfate9 CNT/octane9 CNT/octane10 CNT-octane/octane12 CNT-hydrocabon chains/EVA13 CNT-DETDA/epoxy14 CNT-HLK5/PS (current study) CNT-HLK5/DGEBA (current study) CNT-HLK5/PE (current study)

thermal resistance (×10−8 m2 K/W) 8.3 8.3 4.0 3.49−14.7 1.59−4.93 0.2−9.6 0.77−2.5 0.70 0.66 0.66

exp. exp. MD MD MD MD MD MD MD MD

Figure 2. Normalized vibrational density of states in CNT, functionalized CNTs, and various polymer systems.

The above discussion shows that the reduced R is due to the CNT−matrix coupling enabled by the different types of atomistic interactions promoted by HLK5. We have therefore focused next on understanding the relative contribution of the atomistic interactions responsible for lowering RC‑H and RH‑M. The low RC‑H originates in both the CNT−HLK5 covalent bonds33,34 and the van der Waals interactions between the long tail of HLK5 and CNT. To gain insight into the two contributions, we have performed additional simulation for CNT−HLK5 monomer in which we excluded the CNT− HLK5 van der Waals interactions. This resulted in doubling of the contact resistance, from 2.17 × 109 K/W to 4.92 × 109 K/ W. Thus, for CNT−HLK5, the van der Waals interactions are as important as the covalent ones in suppressing the contact resistance. Furthermore, the thermal resistance due to the van der Waals interaction can be lowered more by increasing the structural length of the molecule attached to the CNT,13 specifically by increasing the length of the side chain (see Supporting Information). We attribute the low RH‑M to the different types of longranged interactions with the polymer matrix promoted by HLK5. For more insight, we have analyzed the relative importance of the van der Waals and Coulombic interactions on the thermal conductance (1/RH‑M) at the HLK5−PS interface. We decoupled these two effects by separately computing thermal resistances in MD simulations in which we excluded the forces caused by the atomic charges located on HLK5 and the attractive van der Waals term in the HLK5−PS Buckingham potential. These simulations obtained that the thermal conductance due to the van der Waals forces of (1.73 ± 0.3) × 10−9 W/K significantly surpasses the one found due to Coulombic forces of (0.85 ± 0.2) × 10−9 W/K. Note that the total conductance 2.58 × 10−9 W/K corresponds to a resistance of 3.87 × 108 K/W, which complies well with the RH‑M value of 3.94 × 108 K/W shown in Table 1.

computed CNT−HLK5/matrix resistances31 are much lower than the direct CNT−matrix contact resistances obtained from experiment and simulation,9,10 and are in general lower than the ones previously calculated with other functionalized CNTs.12−14 We note that in refs 13 and 14, the functional molecule−polymer matrix contact resistances were not incorporated in the reported values. Therefore, the total resistances are likely larger than the values reported in lines 6 and 7 of Table 2. What is the important feature of the HLK5 functionalization that helps lower the interfacial thermal resistance? Previous work32 pointed out that a combination of covalent bonding and good vibrational match is crucial for enhancing thermal transport at interfaces between hard and soft materials. We have therefore performed an analysis of the vibrational density of states (VDOS). In Figure 2 we see a significant mismatch in VDOS between CNT and the investigated matrices. The addition of the HLK5 coating indeed introduces a large range of vibrational frequencies which are common with those of the polymer matrices. Nevertheless, this aspect is not particular to HLK5. For example, there is good vibrational match between CNT covalently bound with octane and the various polymer matrices. In spite of good VDOS match, the lowest total resistance of CNT−octane/octane is 1.59 × 10−8 m2 K/W, more than a factor of 2 larger than that obtained by us for the CNT−HLK5/matrix (Table 2). Since many covalent functionalizations provide VDOS matching, we conclude that this already recognized feature cannot be the cause of the HLK5 advantage. 12195

DOI: 10.1021/acs.jpcc.5b02551 J. Phys. Chem. C 2015, 119, 12193−12198

Article

The Journal of Physical Chemistry C The large thermal resistance at the CNT−CNT contacts is another limiting factor in developing advanced polymer composites.37,38 We have investigated how HLK5 impacts the thermal contact resistance at the junction of two crossed CNTs (Figure 3a). Two mutually perpendicular CNTs each linked

Figure 4. Thermal conductivity of CNT functionalized by HLK5, octane, and hydroxyl at different surface coverage ratios normalized by the pristine CNT thermal conductivity at the same length.

Figure 3. (a) Snapshot of a HLK5 functionalized CNT−CNT junction. The thermal resistances between CNT and its corresponding ′ ) and between the two HLK5 HLK5 monomer (RC‑H and RC‑H monomers (RH‑H) are indicated. Black dashed lines indicate the πstacking of benzene rings. (b) The total thermal contact resistance of ′ + RH‑H HLK5 functionalized CNT−CNT junction RC‑H + RC‑H compared with the bare values RC‑C calculated with EMD35 and NEMD.36

groups are needed to achieve the same coverage. Additionally, an analysis of the bonding of the CNT surface revealed that the honeycombed lattice is disturbed by the OH functionalization. The occurring defects, most often C−C bond breaking, are hindering significantly the phonon transport. By contrast, HLK5 introduced little disturbance in the hexagonal arrangement of the CNT wall. The only defect activated by HLK5 was a 5−7−7−5 defect formed by the 90° rotation of a C−C bond41 located in the vicinity of the C−N bond.

with one HLK5 monomer were released at an intertube distance of 10 Å and were allowed to evolve freely. After equilibration, the intertube distance measured 9.0 Å mm. At this separation, we computed the contact resistance as R = RC‑H + RH‑H + R′C‑H. As indicated in Figure 3a, RC‑H and R′C‑H are the resistances between a CNT and the attached HLK5 and RH‑H is the resistance between the two HLK5 monomers. We have ignored the interactions between each HLK5 monomer and the nanotube to which they are not linked.39 In the comparison shown in Figure 3b, the obtained R of 6.5 × 109 K/W is much lower than the contact resistance of the bare 90° CNTs junction (RC‑C) obtained previously by EMD and atomistic Green’s function method35 (20 × 109 K/W) and NEMD simulation36 (17.4 × 109 K/W). At the microscopic level, the thermal contact is likely enabled by the aromatic stacking between the two HLK5, as indicated in Figure 3a. In our simulations, the average distance between the face-to-face benzene rings is 3.45 Å. Finally, we have investigated how the HLK5 functionalization impacts the intrinsic CNT thermal transport. Our calculations considered different HLK5 coverage ratios. (4,4) CNTs with 8.4 nm in length were used in the calculations. For a comparison, we also considered a pristine CNT and CNTs functionalized by octane and hydroxyl (OH) groups, respectively. Figure 4 plots the obtained thermal conductivity κ values normalized by the pristine CNT thermal conductivity κ0 = 1720 W/mK, function of the surface coverage ratios. Overall, we find that the HLK5 functionalization best preserves κ. For example, at around 7% coverage, HLK5, octane, and OH functionalizations give κ values of 223, 172, and 65 W/mK, respectively.40 The differences in behavior can be understood by considering the different number of carbon atoms involved in the covalent functionalization. For example, one HLK5 monomer covers 20 carbon atoms of the CNT involving one covalent bonding, in contrast, 2 octane and 20 covalent OH

IV. SUMMARY In summary, our EMD investigation suggests that HLK5 functionalization represents a superior solution for reducing the thermal resistance at CNT−polymer matrix interface. The thermal resistance between CNT and the polymer matrix is reduced by almost 60% when the CNT is functionalized with HLK5. Besides reducing the CNT−matrix resistance, HLK5 can also significantly decrease the CNT−CNT junction resistance. We also show that, compared with the OH- and octane functionalizations, the HLK5 one alters less the intrinsic CNT thermal conductivity at the same surface coverage ratio. To understand the origin of thermal resistance lowering, we performed an analysis beyond the already recognized32 generic combination of covalent bonding and VDOS match. This analysis reveals the importance of the van der Waals interactions promoted by the HLK5’s chain structure that incorporates a benzene ring: Specifically, we show that the van der Waals interactions between HLK5 and CNT are as important as the covalent ones in reducing RC‑H. Additionally, the van der Waals interactions represent the main cause of reducing RH‑M. The revealing of the key role played by the van der Waals interactions in lowering the thermal resistances between both CNT−HLK5 and HLK5−polymer matrices is new and has broad implications. This knowledge brings an interesting perspective into the CNT functionalization design and could be useful for understanding similar systems.

■

ASSOCIATED CONTENT

S Supporting Information *

Methods, simulation details, and the effect of HLK5 side chain length and number of monomers on the CNT-HLK5 thermal resistance. The Supporting Information is available free of 12196

DOI: 10.1021/acs.jpcc.5b02551 J. Phys. Chem. C 2015, 119, 12193−12198

Article

The Journal of Physical Chemistry C

(15) Gulotty, R.; Castellino, M.; Jagdale, P.; Tagliaferro, A.; Balandin, A. A. Effects of Functionalization on Thermal Properties of SingleWall and Multi-Wall Carbon Nanotube-Polymer Nanocomposites. ACS Nano 2013, 7, 5114−5121. (16) Padgett, C. W.; Brenner, D. W. Influence of Chemisorption on the Thermal Conductivity of Single-Wall Carbon Nanotubes. Nano Lett. 2004, 4, 1051−1053. (17) Divay, L.; Le Khanh, H.; Le Barny, P. Patent: Thermal Interface Based on a Material Having Low Thermal Resistance and Manufacturing Process. WO2012/126955 A1, 2012. (18) Le Khanh, H.; Divay, L.; Ni, Y.; Le Barny, P.; Leveugle, E.; Chastaing, E.; Wyczisk, F.; Ziaei, A.; Volz, S.; Bai, J. Enhancement of the Thermal Properties of a Vertically Aligned Carbon Nanotube Thermal Interface Material Using a Tailored Polymer. 18th International Workshop on Thermal Investigations of ICs and Systems, Budapest, Hungary, 2012; pp 1−4. (19) Leveugle, E.; Divay, L.; Le Khanh, H.; Daon, J.; Chastaing, E.; Le Barny, P.; Ziaei, A. Free Standing Thermal Interface Material Based on Vertical Arrays Composites. 19th International Workshop on Thermal Investigations of ICs and Systems, Berlin, Germany, 2013; pp 244−247. (20) Ni, Y.; Khanh, H. L.; Chalopin, Y.; Bai, J. B.; Lebarny, P.; Divay, L.; Volz, S. Highly Efficient Thermal Glue for Carbon Nanotubes Based on Azide Polymers. Appl. Phys. Lett. 2012, 100, 193118. (21) Sen, R.; Zhao, B.; Perea, D.; Itkis, M. E.; Hu, H.; Love, J.; Bekyarova, E.; Haddon, R. C. Preparation of Single-Walled Carbon Nanotube Reinforced Polystyrene and Polyurethane Nanofibers and Membranes by Electrospinning. Nano Lett. 2004, 4, 459−464. (22) Mitchell, C. A.; Bahr, J. L.; Arepalli, S.; Tour, J. M.; Krishnamoorti, R. Dispersion of Functionalized Carbon Nanotubes in Polystyrene. Macromolecules 2002, 35, 8825−8830. (23) Liao, K.; Li, S. Interfacial Characteristics of a Carbon Nanotube−Polystyrene Composite System. Appl. Phys. Lett. 2001, 79, 4225−4227. (24) McNally, T.; Pötschke, P.; Halley, P.; Murphy, M.; Martin, D.; Bell, S. E. J.; Brennan, G. P.; Bein, D.; Lemoine, P.; Quinn, J. P. Polyethylene Multiwalled Carbon Nanotube Composites. Polymer 2005, 46, 8222−8232. (25) Bozlar, M.; He, D.; Bai, J.; Chalopin, Y.; Mingo, N.; Volz, S. Carbon Nanotube Microarchitectures for Enhanced Thermal Conduction at Ultralow Mass Fraction in Polymer Composites. Adv. Mater. 2010, 22, 1654−1658. (26) Liu, Y.; Kumar, S. Polymer/Carbon Nanotube Nano Composite FibersA Review. ACS Appl. Mater. Interfaces 2014, 6, 6069−6087. (27) Gill, S. P. In Trends in Computational Nanomechanics: Transcending Length and Time Scales; Dumitricǎ, T., Ed.; Springer: Netherlands, 2010; pp85−134. (28) Rajabpour, A.; Volz, S. Thermal Boundary Resistance from Mode Energy Relaxation Times: Case Study of Argon-Like Crystals by Molecular Dynamics. J. Appl. Phys. 2010, 108, 094324. (29) Ni, Y.; Chalopin, Y.; Volz, S. Significant Thickness Dependence of the Thermal Resistance Between Few-Layer Graphenes. Appl. Phys. Lett. 2013, 103, 061906. (30) Ni, Y.; Chalopin, Y.; Volz, S. Few Layer Graphene Based Superlattices as Efficient Thermal Insulators. Appl. Phys. Lett. 2013, 103, 141905. (31) The HLK5-matrix contact surface 1.46 × 10−17 m2 is used to derive the thermal resistance per unit area. (32) Sun, F.; Zhang, T.; Jobbins, M. M.; Guo, Z.; Zhang, X.; Zheng, Z.; Tang, D.; Ptasinska, S.; Luo, T. Molecular Bridge Enables Anomalous Enhancement in Thermal Transport across Hard-Soft Material Interfaces. Adv. Mater. 2014, 26, 6093−6099. (33) Luo, T.; Lloyd, J. R. Enhancement of Thermal Energy Transport Across Graphene/Graphite and Polymer Interfaces: A Molecular Dynamics Study. Adv. Funct. Mater. 2012, 22, 2495−2502. (34) Liu, J.; Alhashme, M.; Yang, R. Thermal Transport Across Carbon Nanotubes Connected by Molecular Linkers. Carbon 2012, 50, 1063−1070.

charge on the ACS Publications website at DOI: 10.1021/ acs.jpcc.5b02551.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Computations were performed at the Minnesota Supercomputing Institute and École Centrale Paris. Y.N. and T.D. acknowledge support from NSF Grant No. CMMI-1332228. H.H. and S.V. acknowledge the support of the NANOTHERM project cofunded by the European Commission under the “Information and Communication Technologies” and the seventh Framework Programme under the Grant Agreement No. 318117.

■

REFERENCES

(1) Han, Z.; Fina, A. Thermal Conductivity of Carbon Nanotubes and Their Polymer Nanocomposites: A Review. Prog. Polym. Sci. 2011, 36, 914−944. (2) Pop, E.; Mann, D.; Wang, Q.; Goodson, K.; Dai, H. Thermal Conductance of an Individual Single-Wall Carbon Nanotube Above Room Temperature. Nano Lett. 2005, 6, 96−100. (3) Yu, C.; Shi, L.; Yao, Z.; Li, D.; Majumdar, A. Thermal Conductance and Thermopower of an Individual Single-Wall Carbon Nanotube. Nano Lett. 2005, 5, 1842−1846. (4) Sandler, J. K. W.; Kirk, J. E.; Kinloch, I. A.; Shaffer, M. S. P.; Windle, A. H. Ultra-Low Electrical Percolation Threshold in CarbonNanotube-Epoxy Composites. Polymer 2003, 44, 5893−5899. (5) Ma, J.; Ni, Y.; Volz, S.; Dumitricǎ, T. Thermal Transport in Single-Walled Carbon Nanotubes Under Pure Bending. Phys. Rev. Appl. 2015, 3, 024014. (6) Cahill, D. G.; Braun, P. V.; Chen, G.; Clarke, D. R.; Fan, S.; Goodson, E. K.; Keblinski, P.; King, W. P.; Mahan, G. D.; Majumdar, A.; et al. Nanoscale Thermal Transport. II. 2003−2012. Appl. Phys. Rev. 2014, 1, 011305. (7) Gojny, F. H.; Wichmann, M. H. G.; Fiedler, B.; Kinloch, I. A.; Bauhofer, W.; Windle, A. H.; Schulte, K. Evaluation and Identification of Electrical and Thermal Conduction Mechanisms in Carbon Nanotube/Epoxy Composites. Polymer 2006, 47, 2036−2045. (8) Haggenmueller, R.; Guthy, C.; Lukes, J. R.; Fischer, J. E.; Winey, K. I. Single Wall Carbon Nanotube/Polyethylene Nanocomposites: Thermal and Electrical Conductivity. Macromolecules 2007, 40, 2417− 2421. (9) 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. Interfacial Heat Flow in Carbon Nanotube Suspensions. Nat. Mater. 2003, 2, 731−734. (10) Shenogin, S.; Xue, L.; Ozisik, R.; Keblinski, P.; Cahill, D. G. Role of Thermal Boundary Resistance on the Heat Flow in CarbonNanotube Composites. J. Appl. Phys. 2004, 95, 8136−8144. (11) Borca-Tasciuc, T.; Chen, G. In Thermal Conductivity: Theory, Properties, and Applications; Tritt, T. M., Ed.; Kluwer Academic/ Plenum Publishers: New York, 2004; pp 205−237. (12) Shenogin, S.; Bodapati, A.; Xue, L.; Ozisik, R.; Keblinski, P. Effect of Chemical Functionalization on Thermal Transport of Carbon Nanotube Composites. Appl. Phys. Lett. 2004, 85, 2229−2231. (13) Clancy, T. C.; Gates, T. S. Modeling of Interfacial Modification Effects on Thermal Conductivity of Carbon Nanotube Composites. Polymer 2006, 47, 5990−5996. (14) Varshney, V.; Roy, A.; Michalak, T.; Lee, J.; Farmer, B. Effect of Curing and Functionalization on the Interface Thermal Conductance in Carbon Nanotube-Epoxy Composites. JOM 2013, 65, 140−146. 12197

DOI: 10.1021/acs.jpcc.5b02551 J. Phys. Chem. C 2015, 119, 12193−12198

Article

The Journal of Physical Chemistry C (35) Prasher, R. S.; Hu, X. J.; Chalopin, Y.; Mingo, N.; Lofgreen, K.; Volz, S.; Cleri, F.; Keblinski, P. Turning Carbon Nanotubes from Exceptional Heat Conductors into Insulators. Phys. Rev. Lett. 2009, 102, 105901. (36) Evans, W. J.; Shen, M.; Keblinski, P. Inter-tube Thermal Conductance in Carbon Nanotubes Arrays and Bundles: Effects of Contact Area and Pressure. Appl. Phys. Lett. 2012, 100, 261908. (37) Yang, J.; Waltermire, S.; Chen, Y.; Zinn, A. A.; Xu, T. T.; Li, D. Contact Thermal Resistance Between Individual Multiwall Carbon Nanotubes. Appl. Phys. Lett. 2010, 96, 023109. (38) Zhong, H.; Lukes, J. Interfacial Thermal Resistance Between Carbon Nanotubes: Molecular Dynamics Simulations and Analytical Thermal Modeling. Phys. Rev. B 2006, 74, 125403. (39) This is a reasonable assumption because the total force between the HLK5 and nonlinked (linked) CNT is 0.21 eV/Å (11.32 eV/Å). (40) For octane functionalization, κ converges at 7% coverage ratio involving three octane−CNT covalent bonds, which corresponds to a 0.6% fraction of functionalized tube carbon atoms. Our results are consistent with ref 12, where thermal conductivity was found to be constant when the fraction of functionalized carbon atoms located on the CNT reached 0.8% (41) Dumitricǎ, T.; Yakobson, B. I. Rate Theory of Yield in Boron Nitride Nanotubes. Phys. Rev. B 2005, 72, 035418.

12198

DOI: 10.1021/acs.jpcc.5b02551 J. Phys. Chem. C 2015, 119, 12193−12198