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Dependence of Thermal Conductivity of Carbon Nanopeapods on Filling Ratios of Fullerene Molecules Liu Cui,† Yanhui Feng,*,†,‡ and Xinxin Zhang†,‡ †

School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China Beijing Key Laboratory of Energy Saving and Emission Reduction for Metallurgical Industry, University of Science and Technology Beijing, Beijing 100083, China

‡

S Supporting Information *

ABSTRACT: Focusing on carbon nanopeapods (CNPs), i.e., carbon nanotubes (CNTs) filled with fullerene C60 molecules, the thermal conductivity and its dependence on the filling ratio of C60 molecules have been investigated by equilibrium molecular dynamics simulations. It turns out that the CNP thermal conductivity increases first, reaches its maximum value at filling ratio of 50%, and then decreases with increasing filling ratio. The heat transfer mechanisms were analyzed by the motion of C60 molecules, the mass transfer contribution, the phonon vibrational density of states, and the relative contributions of tube and C60 molecules to the total heat flux. The mass transfer in CNPs is mainly attributed to the rotational and translational motion of C60 molecules in tubes. As the filling ratio is larger than 50%, the axially translational motion of C60 molecules gets more and more restricted with increasing filling ratio. For either the mass transfer contribution to heat transfer or the phonon coupling between the tube wall and C60, the peaking behavior occurs at a filling ratio of 50%, which confirms the corresponding maximum thermal conductivity of CNP. With the filling ratio increasing, the dominating contribution to heat transfer changes from tube-wall atoms to fullerene atoms. Their relative contributions almost keep stable when the filling ratio is larger than 50% until it reaches 100%, where the contribution from fullerene atoms suddenly drops because of strong confinement of translational motion of C60 molecules. This work may offer valuable routes for probing heat transport in CNT hybrid structures, and possible device applications.

1. INTRODUCTION Carbon nanotubes (CNTs) can serve as a container for encapsulating atoms or molecules into their vacant cavities, thus forming a quasi one-dimensional CNT hybrid structure. To date, various materials, such as fullerenes,1 metals,2,3 carbides,4 oxides,5 or even proteins6 have been introduced into CNT cavities. In particular, a novel hybrid structure usually named carbon nanopeapod (CNP),1 consisting of fullerene C60 molecules enclosed in a single-walled CNT, has received much attention. There are some theoretical and experimental researches have been reported on the CNP properties. Ni et al.7 predicted that the buckling force of CNPs can be larger than that of empty CNTs, and the increase magnitude depends on the density of filling C60. CNPs may find their applications in functional nanoscale devices, such as nanopistons, nanobearings, etc. Kuo et al.8 calculated the interfacial energy, adhesive strength, and adhesive friction of CNPs by performing MD simulations. Their results claimed that CNPs have lower interfacial binding energy but better adhesion strength, compared with doublewalled CNTs. CNPs can potentially be applied to bioinspired synthetic adhesives. Li et al.9 measured the electron transport properties of CNPs and CNTs. It was found that CNPs possess an enhanced p-type transport property compared with those for © 2015 American Chemical Society

bare CNTs, due to the charge transfer effect from C60. In addition, the photoinduced electron transfer phenomenon was found in CNPs under light illumination. CNPs could be used as photosensitive wires and photodetectors in the future. Recently, it has been found that excellent properties are restricted to not only CNPs but also their similar structures. Kwon et al.10 investigated the internal dynamics of an encapsulation of a K@ C60 endohedral complex inside a carbon nanocapsule. They expected that the structure has potential applications as a nonvolatile memory element, where transitions between two states are induced by an applied electric field between two endcaps of nanocapsule. Simon et al.11 reported the preparation of CNPs containing a derivative of the azafullerene C59N. The material might find their applications in nanoelectronic devices as the sizable electric dipole moment of the molecule allows us to tune the CNT properties. However, the thermal properties of CNPs have been rarely explored. Vavro et al.12 measured the thermal conductivity on bucky papers of highly C60-filled CNPs. Their results claimed that C60 molecules have little or no contribution to the thermal Received: August 17, 2015 Revised: October 14, 2015 Published: October 20, 2015 11226

DOI: 10.1021/acs.jpca.5b07995 J. Phys. Chem. A 2015, 119, 11226−11232

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The Journal of Physical Chemistry A

Figure 1. Models of CNPs (length 7.87 nm) with filling ratios of (a) σ = 0, (b) σ = 50%, and (c) σ = 100%.

transport of filled tubes. In addition, they noted, single tube experiments and more accurate data are necessary. Nevertheless, it is difficult to measure the thermal conductivity of an individual CNP due to high costs and technological limitations related to the nano size. Consequently, the molecular dynamics (MD) simulation presents an attractive alternative. Noya et al.13 and Kawamura et al.14 calculated the thermal conductivity of an individual CNP fully filled with C60 molecules using MD methods. Both of them found that CNPs have larger thermal conductivities compared with those of CNTs. Kawamura et al.14 further investigated the effects of the C60 filling ratio, and it turned out that the CNP thermal conductivity increases with the increment in filling ratio. However, to make the simulation of thermal conductivity converge easily, Kawamura et al. set momentum limitation on each C60 molecule in the CNP so that C60 molecules only have rotational motion. Actually, C60 molecules have both rotational and translational motion in not fully filled CNPs. In our previous study,15 the thermal conductivity of infinite-length CNPs fully filled with C60 has been investigated. The results showed that filled C60 can increase the CNT thermal conductivity significantly. The coupling of phonon modes between the CNT and C60 in the range 0−20 THz and the increase in mass transfer are primarily responsible for the thermal conductivity increment. To date, the impacts of the C60 filling ratio on CNP thermal conductivity still remains unclear. The thermal transport mechanisms in CNPs need to be further investigated. In this work, the thermal transport of CNPs was investigated by using equilibrium molecular dynamics (EMD) simulations. The effects of filling ratio of C60 molecules were discussed on the thermal conductivity. The motion of C60 molecules, the mass transfer contribution, the phonon vibrational density of states, and the relative contributions of tube and C60 molecules to the total heat flux were analyzed to explain the thermal transport mechanisms in CNPs. The exploration of this work paves the way for design and application of the relevant devices that could benefit from the extreme high and tunable thermal conductivity of CNPs, such as the components for thermal transport management in ultra large-integration chips.

2. MODEL STRUCTURES AND CALCULATION METHODS The models of CNPs were built using the HYPERCHEM program. CNTs with chirality (10, 10) are encapsulated with C60 molecules uniformly. The lengths of CNPs are about 19.68 nm. The diameters of C60 molecules and CNTs are 0.72 and 1.34 nm, respectively. We defined the filling ratio σ as m , when l − ⌊l ⌋ ≥ 0.72 ⌈l ⌉ m , when l − ⌊l ⌋ < 0.72 σ= ⌊l ⌋ σ=

(1)

where m is the number of C60, l (nm) is the length of CNP, ⌈ ⌉ and ⌊ ⌋ are used to round the length l up and down to an integer, respectively. There are no C60 molecules filled in CNTs as the filling ratio is zero, i.e., the bare CNTs. When the filling ratio is 100%, CNTs are uniformly filled with C60 molecules along the tube axis with 1 nm interval or so. Parts a−c of Figure 1 depict examples of 7.87 nm length CNPs with filling ratios of 0, 50%, and 100%, respectively. To obtain the thermal conductivity, the equilibrium molecular dynamics (EMD) was employed. EMD is a reliable method to predict thermal conductivity of nanoscale materials.16−19 All MD simulations were performed using LAMMPS,20 and the time step is 0.5 fs. The adaptive intermolecular reactive empirical bond order (AIREBO) potential21 was used to describe the interactions between carbon atoms of CNTs and CNPs. This potential not only accurately computes the bond−bond interactions of carbon atoms but also reproduces the van der Waals interactions precisely.7 It consists of three terms E=

1 2

∑ ∑ [EijREBO + EijLJ + ∑ ∑ i

j≠i

k≠i ,j l≠i ,j,k

TORSION Ekijl ]

(2)

where EREBO is the REBO potential function, ELj ij ij adds longerrepresents dihedral angle ranged interactions, and ETORSION kijl preferences and has been turned off in this work. The thermal conductivity λ is the integral of heat current autocorrelation function (HCACF) over the correlation time t. The axial (z-direction) thermal conductivity λz is given by 11227


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The Journal of Physical Chemistry A λz =

V kBT 2

∫0

∞

⟨Jz (0) Jz (t )⟩ dt

Generally, the HCACF clearly consists of two stages, an initial rapid decay followed by a gradual exponential decay over a very long time. The initial fast decay corresponds to the contribution from high-frequency optical modes to thermal conductivity, whereas the gradual decay corresponds to the contribution from low-frequency acoustic modes, which is the dominating part in thermal conductivity.27,28 Figure 2 also shows that the HCACF decays to approximately 0 within 150 ps, so the correlation time of 1500 ps is long enough for the calculation of thermal conductivity.

(3)

where V and T are the system volume and temperature, respectively. kB is Boltzmann’s constant. Angular brackets denote the ensemble average. The axial heat flux Jz(t) can be computed as Jz (t ) =

⎡ 1⎢ ∑ vi⃗ ,zεi + 1 V ⎢⎣ i 2 +

∑ i ,j,k

∑

⎯ ⇀ ⇀ ⎯⇀ rij , z( fij · vj )

i ,j,i≠j

3. RESULTS AND DISCUSSION 3.1. Effects of C60 Filling Ratios on CNP Thermal Conductivity. The thermal conductivities of CNPs with different filling ratios are summarized in Figure 3, together with

⎤ ⎯ ⇀ ⎯⇀ ⇀ rij , z( fj (ijk) · vj )⎥ ⎥⎦

(4)

where the subscript “z” indicates a quantity in the axial direction. V is the volume of selected region to calculate the heat flux. εi and vi are the local site energy and velocity of atom ⎯⇀ ⎯

⎯⇀ ⎯

i. rij,z is the distance between atom i and j, and fij and fj (ijk) are the two-body and three-body interactions, respectively. In eq 4, the first term on the right-hand side represents local particle shifts showing the contribution of mass transfer, whereas the other terms describe the thermal energy dissipated between groups of atoms.22 In the first stage of MD simulations, the system ran under the NPT ensemble for 1 ns, followed by NVT ensemble for additional 1 ns. The atom positions and velocities were generated by perfroming the time integration on nonHamiltonian equations of motion.23 The Nosé−Hoover thermostat24 was applied. After that, the system was transferred to the NVE ensemble for 8 ns. The heat current can be calculated and outputted for every time step. Because the periodic boundary condition has limitations in the track of realistic positions of particles, the free boundary conditions were implemented in all three directions. C60 molecules can freely rotate and translate throughout the whole simulation. To obtain good converged thermal conductivity of CNPs, the HCACF integrations from six uncorrelated NVE ensembles (1500 ps for each ensemble) were averaged. We took the mean value as the final thermal conductivity. This treatment for thermal conductivity calculation has been used in literatures for zeolitic imidazolate framework-825 and graphene.26 The standard deviation was estimated from the averaged thermal conductivity curves in the correlation time between 900 and 1500 ps. Figure 2 shows the normalized HCACFs of CNPs, i.e., ⟨Jz(0) Jz(t)⟩/⟨Jz(0) Jz(0)⟩, under a temperature of 300 K.

Figure 3. Thermal conductivity of CNPs versus filling ratio under temperature of 300 K.

the results reported by Kawamura et al.14 We first notice that the thermal conductivity of CNPs (0 < σ ≤ 100%) is always higher than that of bare CNTs (σ = 0). A similar qualitative conclusion has been reported by Noya et al.13 and Kawamura et al.14 A more interesting feature in Figure 3 is the thermal conductivity of fully filled CNP (σ = 100%) is lower than the incompletely filled CNP (σ < 100%). Besides the above features, Figure 3 also indicates the nonmonotonic dependence of CNP thermal conductivity on the filling ratio of C60 molecules. The CNP thermal conductivity increases first, reaches a peak at σ = 50%, and then decreases with the increasing filling ratio. This tendency is different from the EMD result of Kawamura et al.,14 which exhibits a monotonically increasing trend as the increment in filling ratio. This discrepancy may be partially caused by the different semiempirical potentials and simulation parameters we used. Especially, Kawamura’s models are under periodic boundaries in the tube axial direction whereas ours are with free boundary conditions. Moreover, Kawamura simplified their CNP simulation to easily obtain the convergence results. They set momentum limitation on all C60 molecules so that the C60 could not move along the tube axis. However, C60 molecules have both rotational and translational motion in CNPs. In addition, the computational value of 19.68 nm length CNT thermal conductivity is in the same order as that reproted by other literatures.29,30 However, the CNP thermal conductivity is much less than that given by Noya et al.,13 using NEMD with periodic boundary conditions to calculate thermal conductivity. It can be attributed to the following reasons: (1) Stress in the nanotubes affects the thermal conductivity.

Figure 2. Normalized heat current autocorrelation functions (HCACFs) of CNPs at temperature of 300 K. 11228


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Figure 4. Motion of C60 molecules in CNPs with different filling ratios. Top panel: angular velocity versus simulation time. Bottom panel: axial position versus simulation time.

finding of the nonmonotonic dependence of CNP thermal conductivity on the filling ratios can inspire others to adopt various methods to pursue more exact values of CNP thermal conductivities with different filling ratios, such as ab initio based anharmonic lattice dynamics simulation coupled with the Boltzmann transport equation. 3.2. Motion of C60 Molecules. To elucidate the underlying mechanism for the thermal transport in CNPs, the motion of C60 molecules was investigated first. The axial positions of each C60 molecule in CNPs were recorded and shown in the bottom panel of Figure 4 for the last 500 ps simulation time. It is interesting to find C60 molecules are always inside the tube no matter what the filling ratio is. In addition, C60 molecules remain in their original positions in a completely filled CNP (σ = 100%). Differently, when the filling ratio is less than 100%, the C60 keeps moving randomly along the longitudinal axis of tube. As the filling ratio is larger than 50%, the axially translational motion of C60 molecules gets more and more restricted with the increasing filling ratio. The top panel of Figure 4 shows the angular velocities of a certain C60 molecule as a function of time. Evidently, the C60 molecule has random rotation in all three directions no matter what the filling ratio is. The motion of C60 molecules impacts the mass transfer and phonon coupling in CNPs as discussed in the following sections, which affects the heat transfer in CNPs. 3.3. Contributions of Mass Transfer. The filling ratio dependence of thermal conductivity can be analyzed by quantifying the mass transfer contributions to the overall heat transport. We mainly attribute the mass transfer in CNPs to the motion of C60 molecules mentioned above. The calculation was based on nonequilibrium molecular dynamics (NEMD), which can generate a constant heat flux between hot and cold bath regions defined in the CNP (simulation details of NEMD are given in the Supporting Information). The mass transfer portion of the heat flux, i.e., the first term on the right-hand side of eq 4, and the total heat flux were evaluated and averaged over 3 ns. Their ratio denotes the contribution of mass transfer to the overall heat flux. Figure 5 illustrates the enhancement of mass transfer contribution of CNP compared with that for bare CNT, i.e., the percentage of mass transfer contribution in CNP minus that in CNT. It is clearly seen that the enhancement of mass transfer contribution first increases, up to maximal 30.3% at the filling ratio of 50%, and then falls at larger filling ratios with increasing restriction of axially translational motion of C60

Moreland et al.31 calculated the tube length under zero pressure by applying free boundary conditions in the axial direction to allow for longitudinal contraction or expansion and then applied periodic boundaries for the remaining simulations. They got much lower thermal conductivity than either experimental data or some other simulation results only under periodic boundary conditions. Because the efforts to mitigate stress by relaxing the CNT structure were not mentioned in the paper of Noya et al., we think that their high calculated values are possibly caused by the tube compression. (2) The thermal conductivity predicted by MD is sensitive to the choice of interatomic potential. Salaway et al.32 found a correlation between the interatomic potential type employed in a simulation and the predicted values of thermal conductivity: the simulated thermal conductivity tends to increase following the order from AIREBO21 and BrennerII33+LJ, to Brenner34/Brenner-II, to Tersoff,35 and to an optimized version of the Tersoff potential.36 To date, it is still not clear which kind of potential is better for simulating CNT or CNP. The Brenner potential was used by Noya et al., whereas our simulations were based on the AIREBO potential. To some extent, Salaway’s study helps to explain why the simulation result of Noya et al. is higher than ours. It should be noted that the thermal conductivity values of CNTs predicted by the MD method are possibly unable to be quantitatively coincident, due to their sensitivity to the choices for system length, boundary condition, interatomic potential, and method employed for calculations.32 Nevertheless, the qualitative conclusions revealed in the simulations are still consistent across studies undertaken with different simulation details. For instance for different system lengths, Lukes and Zhong29 explored the temperature effect on the thermal conductivity of CNT. They found that the temperature dependences of thermal conductivity are consistent among studies undertaken with different CNT lengths. Zhang and Li37 and Fthenakis et al.38 computed the isotope impurity effect on the thermal conductivity of CNTs with length of 6 and 2.46 nm, respectively. They got a consistent conclusion that the CNT thermal conductivity decreases with an increment in the percentage of isotope impurity. These qualitative conclusions provide some insights into the mechanisms of nanoscale thermal transport in CNTs and pave the way for the design of CNT materials with thermal transport properties tailored for particular practical applications. In addition, we expect that our 11229


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Figure 5. Enhancement of mass transfer contribution (percentage) to total heat flux versus filling ratio.

molecules. This mechanism offers a proof for the nonmonotonic dependence of CNP thermal conductivity on filling ratios. 3.4. Vibrational Density of States. To obtain more physical insight into the mechanism of filling ratio effects on the CNP thermal conductivity, the normalized vibrational density of states (VDOS) for CNP was calculated by performing a fast Fourier transform of the velocity autocorrelation function (VACF)39,40 +∞

VDOS(v) =

∫−∞

VACF(t )e−2πivt dt

Figure 6. (a) Vibrational density of states for tube-wall and fullerene atoms and their overlap at filling ratio of 100%. (b) Overlap energy between tube-wall and fullerene atoms versus filling ratio.

(5)

where ν is the phonon frequency, i the is imaginary unit, and the VACF can be calculated as N ⇀

VACF(t ) =

where go(ν) indicates the overlap region, ν is phonon frequency, h is the Planck constant, 1/(exp(hν/kBT) − 1) is the Bose−Einstein distribution function, T is the absolute temperature, and kB is the Boltzmann’s constant. Figure 6b shows the Eoverlap between tube-wall and fullerene atoms as a function of filling ratio under temperature of 300 K. The Eoverlap first increases, reaches a peak, and then decreases as the filling ratio increases, finally rises again at σ = 100%. For incompletely filled CNPs (σ < 100%), the vibrational match between the tube wall and fullerene first enhances and then decreases with the increasing filling ratio; that is, the phonon coupling becomes strong first and then becomes weak. This confirms the nonmonotonic dependence of CNP thermal conductivity on filling ratios. Interestingly, the Eoverlap increases abruptly for the fully filled CNP, which indicates a relatively strong phonon coupling and benefits heat transport. However, it is noted that there is no such jump, but a drop happening on the thermal conductivity for fully filled CNP, as illustrated in Figure 3. Detailed mechanisms responsible for this point are still unclear and require more study. In addition, the Eoverlap has a largest value about 0.001 51 eV at the filling ratio of 50%, as shown in Figure 6b. It also helps to explain why the thermal conductivity of CNP reached the maximum at σ = 50%. 3.5. Contributions of Tube-Wall and Fullerene Atoms. We further analyzed the relative contributions of tube-wall and fullerene atoms, to the overall heat transport. This was implemented by estimating the local heat flux onto a single atom based on the NEMD, which describes the contribution of every atom to each term in eq 4 of heat flux.47 The result on each atom was averaged over 3 ns. Figure 7 shows the relative contributions of tube-wall and fullerene atoms as a function of filling ratio. It is seen that the overall heat transfer is dominated by tube-wall atoms when the filling ratio is small. As the filling ratio increases, the tube-wall contribution gradually decreases

⇀

⟨∑i = 1 vi (t0) · vi (t0+t )⟩ N ⇀

⇀

⟨∑i = 1 vi (t0) · vi (t0)⟩

(6) ⇀ vi (t0)

where N is the number of carbon atoms, is the velocity of atom i at time t0, and the angular brackets indicate the ensemble average. Figure 6a shows the VDOSs for two parts constituting the whole CNP with filling ratio 100%, i.e., the tube-wall and fullerene atoms, respectively. Evidently, the VDOS either for tube-wall atoms or for fullerene atoms disperses widely within the frequency range 0−60 THz. A mismatch in the two VDOSs is the primary mechanism of interface scattering,41 i.e., the CNT and fullerene in our paper. The phonons inside the overlap area of two VODSs can participate in the elastic scattering process. Any phonon interactions outside the overlap region are attributed to the inelastic phonon scattering process, which is in smaller probability and contributes less to the overall heat conduction across the interface,42,43 in comparison with the elastic process. The bigger the overlap area of VDOSs, the better the interface heat transfer. The overlap area of VDOSs has been used in the literature to analyze the interfacial phonon scattering.25,44−46 Figure 6a shows a large overlap area of two VDOSs and indicates a small vibrational mismatch or a strong phonon coupling between the tube wall and C60, which benefits heat transfer. To quantitatively analyze the overlap area of VDOS, the overlap energy Eoverlap under different filling ratios was calculated. It was given by25 Eoverlap =

∫ go(ν) exp(hν/hkν T ) − 1 dν B

(7) 11230


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NEMD simulation details for calculations of “contributions of mass transfer” in section 3.3 and “contributions of tube-wall and fullerene atoms” in section 3.5. (PDF)

AUTHOR INFORMATION

Corresponding Author

*Y. Feng. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Basic Research Program of China (2012CB720404), National Natural Science Foundation of China (51176011 and 51422601), and National Key Technology R&D Program of China (2013BAJ01B03).

Figure 7. Relative contribution (percentage) of vibrations from the tube-wall and fullerene atoms to total heat flux versus filling ratio.

■

while the contribution from fullerene atoms increases, indicating that the heat flux is mostly localized to the carbon atoms of fullerene at larger filling ratios. It is attributed to the fact that filled C60 provides additional ways for heat transfer. The fullerene contribution suppresses the tube-wall contribution, as the filling ratio is larger than 35%, and the relative contributions from the tube wall and fullerene almost remain stable when the filling ratio is roughly larger than 50%. As evidenced by the Eoverlap shown in Figure 6b, the thermal energy transport between the tube wall and fullerene is inefficient within the filling ratio range 50−100%, due to the weak phonon coupling between tube-wall and fullerene atoms. Thus, it yields a decreasing trend in the CNP thermal conductivity with the increasing filling ratio larger than 50%. Note that, when the filling ratio reaches 100%, the contribution from fullerene atoms suddenly drops due to restrictions of axially translational motion of C60 molecules. The relative contributions from tubewall and fullerene atoms are nearly identical for fully filled CNPs.

(1) Smith, B. W.; Monthioux, M.; Luzzi, D. E. Encapsulated C60 in Carbon Nanotubes. Nature 1998, 396, 323−324. (2) Borowiak-Palen, E.; Mendoza, E.; Bachmatiuk, A.; Rummeli, M. H.; Gemming, T.; Nogues, J.; Skumryev, V.; Kalenczuk, R. J.; Pichler, T.; Silva, S. R. P. Iron Filled Single-Wall Carbon Nanotubes−a Novel Ferromagnetic Medium. Chem. Phys. Lett. 2006, 421, 129−133. (3) Kumar, T. P.; Ramesh, R.; Lin, Y. Y.; Fey, G. T. K. Tin-Filled Carbon Nanotubes as Insertion Anode Materials for Lithium-Ion Batteries. Electrochem. Commun. 2004, 6, 520−525. (4) Seraphin, S.; Zhou, D.; Jiao, J.; Withers, J. C.; Loutfy, R. Selective Encapsulation of the Carbides of Yttrium and Titanium into Carbon Nanoclusters. Appl. Phys. Lett. 1993, 63, 2073−2075. (5) Hang, B. T.; Hayashi, H.; Yoon, S. H.; Okada, S.; Yamaki, J. I. Fe 2 O 3-Filled Carbon Nanotubes as a Negative Electrode for an Fe−Air Battery. J. Power Sources 2008, 178, 393−401. (6) Davis, J. J.; Green, M. L.; Hill, H. A. O.; Leung, Y. C.; Sadler, P. J.; Sloan, J.; Xavier, A. V.; Tsang, S. C. The Immobilisation of Proteins in Carbon Nanotubes. Inorg. Chim. Acta 1998, 272, 261−266. (7) Ni, B.; Sinnott, S. B.; Mikulski, P. T.; Harrison, J. A. Compression of Carbon Nanotubes Filled with C 60, Ch 4, or Ne: Predictions from Molecular Dynamics Simulations. Phys. Rev. Lett. 2002, 88, 205505. (8) Kuo, J. K.; Huang, P. H.; Wu, W. T.; Hsu, Y. C. Molecular Dynamics Investigations on the Interfacial Energy and Adhesive Strength between C 60-Filled Carbon Nanotubes and Metallic Surface. Mater. Chem. Phys. 2014, 143, 873−880. (9) Li, Y. F.; Kaneko, T.; Hatakeyama, R. Electrical Transport Properties of Fullerene Peapods Interacting with Light. Nanotechnology 2008, 19, 415201. (10) Kwon, Y. K.; Tománek, D.; Iijima, S. ″Bucky Shuttle″ Memory Device: Synthetic Approach and Molecular Dynamics Simulations. Phys. Rev. Lett. 1999, 82, 1470−1473. (11) Simon, F.; Kuzmany, H.; Bernardi, J.; Hauke, F.; Hirsch, A. Encapsulating C59n Azafullerene Derivatives inside Single-Wall Carbon Nanotubes. Carbon 2006, 44, 1958−1962. (12) Vavro, J.; Llaguno, M.; Satishkumar, B.; Luzzi, D.; Fischer, J. Electrical and Thermal Properties of C60-Filled Single-Wall Carbon Nanotubes. Appl. Phys. Lett. 2002, 80, 1450−1452. (13) Noya, E. G.; Srivastava, D.; Chernozatonskii, L. A.; Menon, M. Thermal Conductivity of Carbon Nanotube Peapods. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 70, 115416. (14) Kawamura, T.; Kangawa, Y.; Kakimoto, K. Investigation of the Thermal Conductivity of a Fullerene Peapod by Molecular Dynamics Simulation. J. Cryst. Growth 2008, 310, 2301−2305. (15) Cui, L.; Feng, Y.; Zhang, X. Enhancement of Heat Conduction in Carbon Nanotubes with Filled Fullerene Molecules. Phys. Chem. Chem. Phys. 2015, 17, 27520. (16) Zhang, X. L.; Jiang, J. W. Thermal Conductivity of Zeolitic Imidazolate Framework-8: A Molecular Simulation Study. J. Phys. Chem. C 2013, 117, 18441−18447.

4. CONCLUSIONS The thermal conductivity of carbon nanopeapods (CNPs) was investigated with different filling ratios of fullerene C60 molecules, by equilibrium molecular dynamics simulations. The result shows the thermal conductivity of CNPs increases first, reaches a peak at the filling ratio of 50%, and then decreases as the filling ratio increasing. The heat transfer mechanisms were analyzed by the motion of C60 molecules, the mass transfer contribution, the phonon vibrational density of states and the relative contributions of tube and C60 molecules to the total heat flux. The rotational and translational motion of C60 molecules have impacts on the mass transfer and phonon coupling in CNPs. The nonmonotonic filling-ratio dependence of CNP thermal conductivity stems from the peaking behaviors both in mass transfer and in phonon coupling between the tube wall and C60. The fullerene contribution suppresses the tubewall contribution as the filling ratio is larger than 35%, which means the heat flux becomes largely localized to the carbon atoms of fullerene. When the filling ratio reaches 100%, the contribution from fullerene atoms drops due to the strong limitation in the translational motion of C60 molecules.

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REFERENCES

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b07995. 11231


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Dependence of Thermal Conductivity of Carbon ... - ACS Publications

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