NANO LETTERS
Thermal Boundary Resistances of Carbon Nanotubes in Contact with Metals and Polymers
2009 Vol. 9, No. 11 3805-3809
Qingwei Li, Changhong Liu,* and Shoushan Fan Tsinghua-Foxconn Nanotechnology Research Center and Department of Physics, Tsinghua UniVersity, Beijing 100084, People’s Republic of China Received June 22, 2009; Revised Manuscript Received September 27, 2009
ABSTRACT In recent years carbon-nanotube-based thermal interface materials have shown great potential for solving the thermal management problem of integrated circuits and nanodevices. For a long time, the exceptionally high thermal boundary resistances (TBRs) between carbon nanotubes (CNTs) and their surroundings have been suspected as a major factor to restraining their performance. But so far, there are few or no reported work to determine or compare the TBRs between CNTs and various materials. In this paper, we carefully design and carry out the TBR measurements of CNTs in contact with metal and polymer materials, and we present a conclusion that the CNT/polymer generally gives a lower TBR compared to the CNT/metal, which seems a little counterintuitive. We further suggest that the larger CNT-metal TBRs arise from the smaller phonon-mode overlapping between the CNT and the metals at low frequencies, and the low phonon transmission coefficient at the metal-CNT interface in the intermediate and high frequency range. This work may inspire deeper understanding of the TBR and shed light on related theoretical and applied research.
Theoretical and experimental works have shown that the carbon nanotube (CNT) has very high thermal conductivity (κ) along its axial direction.1-4 CNTs have been employed in thermal interface materials to enhance thermal transport properties.5-7 CNT arrays have also been directly used for interfacial thermal conduction (ITC).8-10 Nevertheless, a key puzzle is the heat transfer at the interface between CNTs and target materials.11 It is known that there is a temperature drop, ∆T, at the interface between two materials when a heat flux J (W m-2) flows through the boundary. This phenomenon was first reported by Kapitza in 1941.12 The thermal boundary resistance (TBR), also called the Kapitza resistance, is defined as RK ) ∆T/J. In applications, it is an interface problem that restrains the heat transfer capability of the CNTs into full play. Therefore, we wonder which material generates the lower TBR with CNTs. But so far, there are few works to determine or compare the TBRs between the CNTs and different materials. In this Letter, we introduce a method to measure the relative TBR values between the CNTs and a series of materials, including polymers and metals. The results are quite different from our intuition. The lowest TBR was observed at the CNT-PMMA interface. The TBRs between the polymers and CNTs are obviously lower than those * Corresponding author: e-mail,
[email protected]; telephone, 86 10 62796011. 10.1021/nl901988t CCC: $40.75 Published on Web 10/09/2009
2009 American Chemical Society
between the metals and CNTs, although the thermal resistivities of the polymers are much larger. The CNTs used in our experiment are the continuous single-layer CNT sheets which were drawn out from the superaligned CNT array.13,14 The CNTs used in this work are all multiwalled CNTs with diameters of 10-20 nm, and generally these tubes are metallic. The CNT array was cut into a 4-mm-wide strip by high-power focused laser to guarantee that the drawn sheets had nearly the same width, thickness, density, absorbance, and thermal resistivity. Since the intertube TBRs are large,15,16 a single layer of the ultrathin CNT sheet was employed to lessen the tube-tube TBR effect on the measuring results. Twelve typical materials (six metals and six polymers) were compared in the TBR measurements. The metals included the polished sheets of aurum (Au), argentine (Ag), cuprum (Cu), aluminum (Al), nickel (Ni), and titanium (Ti). The polymers embraced the thin sheets of polyethylene (PE), poly(ethylene terephthalate) (PET), poly(vinyl chloride) (PVC), poly(methyl methacrylate) (PMMA), epoxy resin (EP), and silicone elastomer (S.E.). Twin sheets for each material (thickness ∼50 µm) were adhered to two Al substrates by the high-thermal-conductance grease and made into pairs of “thermal electrodes”. Then all the thermal electrode pairs were equidistantly placed on a plate surface and each pair became a device. The CNT sheet was drawn out and spread on each device (the middle part of the CNT sheet was suspended). We dripped a ethanol drop on each
Table 1. The Relative TBRs between the CNTs and Various Metals ∆Tb ∆TCNT ratio
Au
Ag
Cu
Al
Ni
Ti
3.3 3.1 1.06
4.1 4 1.03
3.2 5 0.64
2.1 2.6 0.81
2.2 3.6 0.61
2.8 3.8 0.74
Table 2. The Relative TBRs between the CNTs and Various Polymers ∆Tb ∆TCNT ratio
Figure 1. The relative TBR measurements. (a) The schematic graphics of the measurement. A near-infrared (NIR) laser was employed to heat the suspended CNT sheet. The temperatures of the points L, M, A, and B are measured by the Optris LS infrared thermometer. (b) The optical photograph of the measurement. The laser head is in the middle which emits the near-infrared laser and the probe light (red spot). The arrow points at the infrared thermometer. (c, d) The optical photograph and the scanning electron microscope image of the CNT sheet which was spread on the polished surface of Ni and Au, respectively.
joint between the CNT sheet and the measuring material. Then the ends of the CNT sheet stuck on the material’s surfaces owing to the very large specific surface area of the CNT sheet and the surface tension of the ethanol.17 By this process, most CNTs sufficiently contacted the surface of the measuring material. In virtue of high-resolution scanning electron microscope observations, we found that the contact states and contact area of the CNTs on the polymer and metal surfaces are almost the same. The steady-state heat flow method was applied in the measurement. A near-infrared (NIR) laser (wavelength 960 nm, generated by a laser diode) was employed to heat the CNT sheet mildly as shown in Figure 1a,b. Then a steady heat flux JCNT was conducted along the aligned CNT sheet to the substrates when the system reached the thermal equilibrium. First, we consider heat conduction across the fixed-length L-M segment of the suspended CNT sheet. The fixed points L and M were 7 mm apart along the sheets’ central axis, as shown in Figure 1a, and the equidistant CNT sheet segments for all the samples had the same thermal resistanceRCNT. The heat flux JCNT caused a temperature drop ∆TCNT across points L and M, that is JCNT ) ∆TCNT /RCNT
(1)
Meanwhile, there would be also a temperature drop ∆Tb at the interface between the CNTs and the counterpart material, when there is a heat flux Jb passing through the boundary. The heat flow which passes through the CNT sheet and through the boundary is the same, so the heat flux Jb can be denoted as Jb ) JCNT/σ, where σ is the ratio of the contact area between the CNT sheet and target materials to 3806
PMMA
EP
S. E.
PE
PET
PVC
0.8 3.2 0.25
1.3 3.2 0.41
1.2 2.6 0.46
1.1 2.3 0.48
1.4 2.9 0.48
1.4 3.5 0.4
the cross-sectional area of the CNT sheet (σ is constant to all the samples). So the TBR is RK )
∆Tb ∆Tb ) σ Jb JCNT
(2)
There would be an energy loss for the heat flux along the L-M segment owing to the infrared radiation and convection. But then the contrast of the average temperatures on the segments for different samples was rather small. The energy loss rate for the different measurements could be roughly figured as the same for a qualitative study. From eqs 1 and 2, we get RK )
∆Tb ∆Tb ) (R σ) Jb ∆TCNT CNT
(3)
where (RCNTσ) is an invariant. So the relative TBR could be determined by the ratio of ∆Tb to ∆TCNT. In the experiment, we used a noncontact method to measure the temperatures of the points L, M, A, and B (through which we get ∆TCNT and ∆Tb) by means of an Optris LS infrared thermometer. The spatial and temperature resolution of the thermometer were 1 mm and 0.1 K, respectively. A high-precision translation-and-lift stage was used to ensure the precise position control. Considering the measuring difficulties, we determined the temperature difference between point A and point B (∆Tb1) as the substitute of ∆Tb (shown in Figure 1a). The temperature change on the materials around the CNT sheet is rather small (within 0.1 K) and negligible compared with the suspended sheet. The measured relative TBR results, represented by the ratio of ∆Tb1 to ∆TCNT, are shown in Table 1, Table 2, and Figure 2. Among the 12 samples, the CNT-PMMA TBR is the lowest, whereas the CNT-Au and CNT-Ag TBRs are the largest. We find that the relative TBRs between the CNTs and polymers are obviously lower than those between the CNTs and metals, that is, there is a gap between CNT-polymer TBR values and CNT-metal TBR values. Seriously ∆Tb ) ∆Tb1 - ∆TA - ∆TB
(4)
where ∆TA is the temperature difference between point A Nano Lett., Vol. 9, No. 11, 2009
Figure 2. The measured relative TBR values at ambient temperature. TBRs between the CNTs and polymers are obviously lower than those between the CNTs and metals, although the thermal conductivities of the polymers are much smaller than those of the metals.
and the nether surface of the CNT sheet which was basically the same for all the samples. ∆TB is the temperature difference between the upper surface of the counterpart material and point B, which was proportional to the thermal resistivity of the material. That is, ∆TB is larger for polymers. Thus the actual relative TBR values are smaller than the measuring values, and the decrements are larger for polymers. So, in reality, the TBR gaps between the polymers and metals are even larger than the measured results in Figure 2 (for detailed discussions see Supporting Information). On the basis of this novel phenomenon, we would like to herein give a further discussion on the origin of the TBR and the factors that affect the TBR between the CNTs and other materials. For phonon-mediated thermal transport, the TBR (Kapitza resistance) arises from the scattering of phonons at the interface,18 in other words, the mismatch of the acoustic properties of the two contacted materials. Specifically, the TBR is determined by the number of the carriers (phonons) incident on the interface, the energy carried by each phonon, and the probability of each phonon transmitting across the interface,19-22 and the Kapitza conductance G can be written as G)
1 ) RK
∫
ωm
0
∂n(ω, T) D1(ω)pω〈Vz〉R1f2(ω) dω ∂T
(5)
where n(ω,T) is the Bose-Einstein distribution function for phonons with frequency ω at temperature T, D1(ω) is the density of phonon states in the material 1 (with higher temperature), R1f2(ω) is the transmission coefficient (TC) of the phonon with frequency ω (i.e., the ratio of the transmitted energy into material 2 to the incident energy from material 1), 〈Vz〉 is the average value of the z component of the phonon group velocity, ωm is the cutoff frequency. From the equation, apparently, the TC R1f2(ω) is the most important term for predicting TBR, for the other terms are determinate for a specific material. There are two representative theoretical frameworks for predicting R1f2(ω) and TBR, i.e., the acoustic mismatch model (AMM) and the diffuse mismatch model (DMM).19,23 But both models are usually in poor agreement with the experiments, especially at high temperature.20 In addition, Nano Lett., Vol. 9, No. 11, 2009
neither model describes the TC dependence of phonon scattering on the phonon frequency and the boundary structure. In recent years, molecular dynamics (MD) simulations are emerging as a powerful tool for the calculations of thermal transport and phonon dynamics.24 In virtue of the phononwave packet simulations, the TC is found to decrease with the increase of the phonon frequency,18,25 that is, because the wavelength of the high-frequency phonon is comparable to the lattice parameter and the interfacial irregularity (which leads to much stronger phonon scatterings), more higherfrequency energy is reflected back. Low-frequency phonons (with long wavelength) can propagate through the interface easily, as the mediums can be seen as continua and the characteristic length of the interface disorder or defect is far less than the wavelength of the phonons. Besides frequency, R1f2(ω) also depends on the matching degree between the vibration modes of the two materials. In the radiation limit, i.e., there are only harmonic processes,20,26 R1f2(ω) is zero when the two materials have no vibration-mode overlapping at frequency ω. Therefore, in low frequency range where few anharmonic scatterings take place, if the two materials have little vibration-mode overlapping, there will be less energy transferred through the boundary in this frequency range. The low-frequency contribution to the overall Kapitza conductance can be estimated with27 G)
1 ∝ RK
∫
ωL
0
D1(ω)D2(ω) dω
(6)
where D2(ω) is the density of phonon states in material 2 and ωL represents the cutoff associated with the half-height of the low-frequency peak. On the basis of the above analysis, the novel phenomenon that the CNT-polymer TBRs are less than the CNT-metal TBRs can be interpreted as follows. (A) For CNT-Polymer Interface. The polymers have abundant low-frequency vibration modes,28-30 and the CNTs also have a certain amount of low-frequency modes.31 A few simulations have shown that the couplings of the lowfrequency vibration modes between the CNTs and polymers (or organic liquid) play a key role in the ITC.27,32 Referring to eq 6, we suggest that it is the larger overlapping of the low-frequency vibration modes, as well as the higher TC in low frequency range, that results in the lower TBRs between the CNTs and polymers (we know that the metals have less low-frequency modes compared to polymers). (B) For CNT-Metal Interface. As we all know, electrons dominate the heat conduction in metals, whereas in the CNTs phonons do. When heat flows through the CNT--metal interface, there must be energy transmission between the electrons of metals and the phonons of CNTs. There are two possible pathways for the metal-nonmetal ITC suggested by Majumdar,33 namely: (i) coupling between electrons and phonons within the metal, and then subsequently interfacial coupling between phonons of the metal and phonons of the nonmetal, and (ii) direct coupling 3807
between electrons of the metal and phonons of the nonmetal at the interface. Experiments validated that path I contributes significantly to the ITC compared to path ii.20,26 Hence we consider that the total CNT-metal TBR is the summation of the intrinsic thermal resistance coming from electron-phonon coupling within the metal (Re-p) and the TBR arising from phonon-phonon coupling at the interface (Rp-p), that is, RK ) Re-p + Rp-p. The value of Re-p is in the magnitude of 10-9 m2 kW-1,34 which is several times less than Rp-p. Therefore the interfacial phonon-phonon mismatch forms the principal part of the total TBR. Further analyses follow. The low-frequency phonon modes and higher frequency modes (i.e., intermediate and high frequency) affect the CNT-metal ITC in different ways. In the low frequency range (1THz), R1f2(ω) decreases fast with the increase of the phonon frequency, which limits the ITC greatly. Hu et al.37 simulated the CNT-silicon interfacial heat transport and found that the R1f2(ω) has fallen below 3% at 1 THz. On the one hand, the wavelength of high frequency phonon is comparable to the lattice parameter and interfacial irregularity (defect, disorder, imperfect contact), which lead to stronger interfacial phonon scatterings and the low R1f2(ω). On the other hand, the CNTs and metals are connected only with physical bonding (van der Waals) rather than chemical bonding (covalent bonding), thus the weak connections fail to allow the intermediate and high frequency phonons to transfer through the interface efficiently, which is confirmed by some calculations.37,38 We know that the intermediate-frequency phonons are the main thermal energy carriers for ITC (for they are abundant both in CNTs and in metals), but the irregular (defects, imperfect contacts) and weak connections at the interface greatly restrict these phonons from transmitting through the boundary. In summary, due to the insignificant low frequency contribution to the ITC, as well as the greatly depressed TC in intermediate and high frequency range, the TBRs between the CNTs and metals are obviously larger than those between the CNTs and polymers. Since the CNT is an electronic conductor or semiconductor,39 there may be the third heat transfer mechanism for the CNT-metal interface, which is different from (i) and (ii). We present it as: (iii) electron coupling at the metal-CNT interface first, then the coupling between the electrons and phonons within the CNTs. Although the metal-metal interfacial heat conduction via the electron coupling has been studied,40 the CNT-metal ITC associated with path iii is still to be discussed in future work. 3808
Some researchers investigated the TBRs between the CNTs and some specific materials theoretically or experimentally in different ways. We collect the related and representative works in the Supporting Information as references for other researchers. In conclusion, this work has introduced a method to measure the relative TBRs between the CNTs and a series of metals andpolymers.Amongtheinvestigatedmaterials,theCNT-PMMA TBR is the lowest, whereas the CNT-Au and CNT-Ag TBRs are the largest. Moreover, the measured relative TBRs between the CNTs and polymers are obviously lower than those between the CNTs and metals, although the thermal conductivities of the polymers (less than 1 W m-1 K-1) are much lower than those of the metals (15-400 W m-1 K-1). Two factors lead to the larger CNT-metal TBRs. One is the small phonon-mode overlapping between the CNTs and the metals in the low frequency range. The other is the low phonon TC in the intermediate and high frequency range, which is caused by the stronger phonon scattering and the weak bonding at the interface. The result may bring us a deeper understanding of the TBRs between the CNTs and various materials and give us new research and application directions for the thermal transport of the CNT. Acknowledgment. This work was supported by National Basic Research Program of China (2005CB623606) and the National Natural Science Foundation of China (50673049, 10721404). Supporting Information Available: A detailed error discussion on the temperature measuring, and the reported TBR values between the CNTs and some specific materials. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Berber, S.; Kwon, Y. K.; Tomanek, D. Phys. ReV. Lett. 2000, 84, 4613– 4616. (2) Kim, P.; Shi, L.; Majumdar, A.; McEuen, P. L. Phys. ReV. Lett. 2001, 87, 215502. (3) Fujii, M.; Zhang, X.; Xie, H. Q.; Ago, H.; Takahashi, K.; Ikuta, T.; Abe, H.; Shimizu, T. Phys. ReV. Lett. 2005, 95, 065502. (4) Li, Q. W.; Liu, C. H.; Wang, X. S.; Fan, S. S. Nanotechnology 2009, 20, 145702. (5) Biercuk, M. J.; Llaguno, M. C.; Radosavljevic, M.; Hyun, J. K.; Johnson, A. T.; Fischer, J. E. Appl. Phys. Lett. 2002, 80, 2767–2769. (6) Liu, C. H.; Huang, H.; Wu, Y.; Fan, S. S. Appl. Phys. Lett. 2004, 84, 4248–4250. (7) Huang, H.; Liu, C. H.; Wu, Y.; Fan, S. S. AdV. Mater. 2005, 17, 1652– 1656. (8) Xu, J.; Fisher, T. S. IEEE Trans. Compon. Packag. Technol. 2006, 29, 261–267. (9) Tong, T.; Zhao, Y.; Delzeit, L.; Kashani, A.; Meyyappan, M.; Majumdar, A. IEEE Trans. Compon. Packag. Technol. 2007, 30, 92– 100. (10) Panzer, M. A.; Zhang, G.; Mann, D.; Hu, X.; Pop, E.; Dai, H.; Goodson, K. E. J. Heat Transfer 2008, 130, 052401. (11) Hu, X. J.; Padilla, A. A.; Xu, J.; Fisher, T. S.; Goodson, K. E. J. Heat Transfer 2006, 128, 1109–1113. (12) Kapitza, P. L. J. Phys. (Paris) 1941, 4, 181. (13) Jiang, K. L.; Li, Q. Q.; Fan, S. S. Nature 2002, 419, 801–801. (14) Zhang, M.; Fang, S. L.; Zakhidov, A. A.; Lee, S. B.; Aliev, A. E.; Williams, C. D.; Atkinson, K. R.; Baughman, R. H. Science 2005, 309, 1215–1219. (15) Zhong, H. L.; Lukes, J. R. Phys. ReV. B 2006, 74, 125403. (16) Maruyama, S.; Igarashi, Y.; Taniguchi, Y.; Shiomi, J. J. Therm. Sci. Technol. 2006, 1, 138–148. Nano Lett., Vol. 9, No. 11, 2009
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NL901988T
3809
