Multifunctional carbon nanotube–epoxy composites for thermal energy management

Abstract

This paper reports development and thermal characterization of tin-capped vertically aligned multiwalled carbon nanotube array composites for thermal energy management in load-bearing structural applications. Three-omega voltage measurements are used to characterize thermal conductivity in the vertically aligned multiwalled carbon nanotube-epoxy composites as well as in its individual constituents, i.e. bulk epon-862 (matrix) and tin thin film in the temperature range 240 K–300 K, and in individual multiwalled carbon nanotubes at room temperature taken from the same vertically aligned multiwalled carbon nanotube batch as the one used to fabricate the carbon nanotube-epoxy composites. A 1-D multilayer thermal model that includes effects of thermal interface resistance is developed to interpret the experimental results. The thermal conductivity of the carbon nanotube-epoxy composite is estimated to be ∼5.8 W/m-K and exhibits a slight increase in the temperature range of 240 K to 300 K. The study suggests that morphological structure/quality of the individual multiwalled carbon nanotubes as well as thin tin capping layer are dominating factors that control the overall thermal conductivity of the thermal interface materials. These results are encouraging in light of the fact that thermal conductivity of a vertically aligned multiwalled carbon nanotube array can be increased by an order of magnitude by using a standard high-temperature post-annealing step. In this way, multifunctional (load bearing) thermal interface materials with effective through-thickness thermal conductivities as high as 25 W/m-K can potentially be fabricated.

Keywords

Thermal interface materials multiwalled carbon nanotube epoxy composites three omega thermal conductivity measurements

Introduction

Thermal management in high thermal environments as those commonly experienced in supersonic and hypersonic air and space vehicles have initiated a demand for high-performance load-bearing thermal interface materials (TIMs). When two nominally flat surfaces come in contact to form a material interface, due to surface asperities the solid–solid contact area is limited to 1–2% of the apparent contact area.¹ As a consequence, the contact junctions as well as the surrounding non-contact area provide parallel paths for heat flow. Ideally, TIMs are designed to have a high thermal conductivity, be as thin as possible, and at the same time effectively “wet” the bounding surfaces. However, real TIMs have a finite thickness (called the bond-line thickness, BLT), and do not completely wet the surfaces, resulting in gaps with contact resistances at the two bounding surfaces.

For a typical TIM with a BLT, and an effective thermal conductivity, k_TIM, the total thermal resistance across an interface can be written in terms of the thermal contact resistances with the bounding surfaces on either side of the TIM, i.e. R_c1 and R_c2, as

R_{Total} = R_{c 1} + \frac{BLT}{k_{TIM}} + R_{c 2} .

(1)

In order to make the TIM effective, the broader goal of the present study is to minimize the total thermal interface resistance across the TIM by reducing BLT and increasing k_TIM, and at the same time minimizing the interfacial contact resistances R_c1 and R_c2, at the bounding surfaces to the TIM.

To date, particle-laden polymers have been one of the most prominent TIMs used in the industry. As described by equation (1), the total thermal contact resistance for a typical TIM is not only dependent on its thermal conductivity but also on the BLT. In this regard, Prasher² introduced a rheology-based semi-empirical model for the prediction of BLT in particle-laden TIMs. The BLT was modeled to depend on the yield stress of the particle-laden polymer and the applied normal pressure. The model was then combined with a thermal conductivity model to estimate the total thermal resistance of the particle-laden polymer TIMs that includes factors, such as, base polymer (matrix) viscosity, particle volume faction and shape, and particle-matrix interfacial resistance, etc. The analysis showed that there exists an optimal filler (particle) volume fraction at which the total thermal resistance of the particle-laden TIM becomes a minimum.

Recent studies indicating relatively high intrinsic thermal conductivities in single-walled and multiwalled carbon nanotubes (SWCNTs and MWCNTs) as well as other graphite materials^3–11 suggest that nanostructured materials and their combinations are promising candidate materials for the development of high-performance TIMs. For example, using effective medium theory (EMT)^12,13 a factor of 500 enhancement in thermal conductivity was predicted when 10% randomly oriented MWCNTs (k_CNT∼3000 W/m-K) were added to an epoxy (k_matrix ∼ 0.2 W/m-K). However, early attempts of using CNT additives have yielded only modest increases in the thermal conductivity of polymers compared to theoretical predictions. The use of randomly orientated SWCNTs as filler materials in oil suspensions¹⁴ reportedly increased the effective thermal conductivity of nanotube-in-oil suspensions by 2.5 times over that of the base fluid (matrix) with only 1% volume fraction of CNTs. Another study¹⁵ involving randomly orientated SWCNT in an epoxy matrix reported enhancements in thermal conductivity of nearly twice the value of the epoxy, while the vapor-grown carbon-fiber (VGCF)-epoxy composites exhibited an enhancement of 45% in thermal conductivity when compared to neat epoxy for the same loading (1 wt%). However, the maximum thermal conductivity achieved by randomly orientated CNT composites was still less than 1 W/m-K. This surprisingly low value has been attributed to several factors including (a) the substantially weak thermal cross-linking between contacting nanotubes,¹⁶ (b) modification of phonon conduction within the individual nanotubes by the polymer matrix,¹⁷ (c) impurities and lattice defects within individual nanotubes,^18,19 and (d) formation of voids in the CNT-polymer composites^20,21 during composite processing.

In recent years, vertically aligned multiwalled carbon nanotube (VA-MWCNT) arrays have generated much interest. By placing CNTs perpendicular to and spanning the system components there are lesser number of CNT/epoxy interfaces in the through-thickness direction, thus minimizing the effective thermal interfacial resistance in the direction of heat flow. Indeed, thermal transport in VA-MWCNT arrays²² has been observed to be highly anisotropic. The longitudinal diffusivity has been reported to be 72 times that of the in-plane value, signifying their importance as 1-D heat pipes between the two contacting surfaces. A similar study, but over a wider temperature range (180 K–300 K),^21,23 reported thermal diffusivity measurements along the axial (cross plane) direction in a VA-MWCNT array (20–50 nm diameter, 1.64 mm long) to be 25 times higher than that in the in-plane direction. Choi et al.¹⁶ reported enhancements in thermal conductivity of SWCNT-epoxy composites of nearly 300% at 3 wt% loading of randomly dispersed SWCNTs, and an additional 10% enhancement in thermal conductivity after applying a magnetic field during processing to improve nanotube alignment. The maximum room temperature thermal conductivity obtained after magnetic alignment during processing was about 6.5 W/m-K, which was higher than those reported in previous studies involving aligned SWCNTs. These results indicate that vertically aligned CNTs in isolation from each other are promising candidate materials as TIMs.

With regard to VA-MWCNTs, Ivanov et al.²² reported a thermal conductivity of 5.5 ± 0.7 W/m-K for an epoxy-infiltrated VA-MWCNT array (8 ± 1 vol%, 2 mm long) and 6.4 ± 0.8 W/m-K for the same array in air. Borca-Tasciuc et al.²¹ reported a maximum thermal conductivity of 3.8 W/m-K in a VA MWCNT-polymer composite along the alignment direction at room temperature with 2% volume fraction of MWCNTs. Xuejiao et al.²⁴ and Tong et al.²⁵ proposed the use of vertically oriented CNTs on both the contacting surfaces of a typical material interface with a CNT-CNT interface in between. The thermal interface resistance of CNT-CNT interface was obtained by Hu et al.²⁶ using diffraction limited infrared microscopy to be much lower than expectations at 3.8 × 10⁻⁴ K-m²/W. Xu and Fisher²⁷ reported a thermal resistance of 2 × 10⁻⁵ km²/W for a dry Cu-VA-MWCNT-Si interface. However, incorporating a phase change material (PCM) into the VA-MWCNT array yielded a lower thermal resistance of 5.2 × 10⁻⁶ km²/W. More recently, Cola et al.²⁸ measured the thermal resistance across (a) a Si-MWCNTs-Ag interface, wherein CNTs are grown on one of the bounding surfaces and (b) Si-CNT-CNT-Cu MWCNT arrays. For the first interface, the total interfacial thermal resistance was found to be dominated by the thermal resistance at the CNT-Ag interface and was measured to be 1.4 × 10⁻⁵ km²/W, while the thermal resistance of the second configuration was dominated by the interface resistance between the tips of the mating CNT arrays and was measured to be an order of magnitude lower at 2 × 10⁻⁶ km²/W. A potentially promising variation of the two-sided CNT interface was the introduction of a thin deformable foil at the interface formed by the nanotube ends of the CNT-CNT arrays, such that the foil could adjust to the deformation of CNTs with far field pressure. In this way, using a 10 µm thick Cu foil (with MWCNT on both sides) the thermal interfacial resistance of a rough Cu-Ag interface was observed to be greatly reduced.²⁹

Recent works^28,30 have explored through-thickness thermal conductance in systems comprising of CNTs on glass, copper, and silicon substrates. In these systems, it was hoped that the weld-contacts made via the catalyst during synthesis of vertical aligned MWCNT arrays would be better than simple van der Waals type bonds. However, it was found that even in the best case scenario the CNT-substrate contact resistance was still quite high. Tao et al.³¹ and Sihn et al.³² used a combination of MWCNT array with thin gold and indium capping layers to improve the thermal conductance between the MWCNT array and the bounding surfaces. Thermal conductivity of the joint (device) was observed to increase by more than 1–2 orders of magnitude compared to the absence of the capping layers.

Encouraged by these findings, in the present paper we report the development of VA-MWCNT array composites for thermal management in load-bearing structural applications. Unlike the majority of previous studies on the use of VA-MWCNT-based thermal interface materials for essentially non-load bearing thermal management applications, the TIMs of interest here involve the use of VA-MWCNTs in an epoxy matrix. The epoxy matrix is expected to impart mechanical strength to these systems while the VACNTs provide avenues for high thru-thickness thermal conductivity across the material interface. In this regard, this paper builds upon previous work to characterize the mechanical properties of these aligned MWCNT composites (up to 20 vol% CNTs),^33–35 which showed promise for use in multifunctional applications with a factor of three enhancements in elastic modulus at 17 vol% CNTs. Furthermore, we introduce a transition zone (TZ) comprising of a tin thin film at the interface between the MWCNTs and the surrounding material (SiO₂) to minimize thermal resistance at the CNT tips-SiO₂ layer interface.

Figure 1 shows a schematic of the Sn-VA-MWCNT/epoxy TIM system investigated in the present study. The overall thermal resistance of the TIM is expected to be governed by the interfacial thermal contact resistance between the bounding solids and the mating surfaces of the Sn VA-MWCNT/epoxy layer. These interfaces are generally neither fully conforming nor smooth, and thus may lead to a significant increment in the total thermal contact resistance.

Figure 1.

Schematic of vertically aligned multiwalled carbon nanotube (VA-MWCNT) thermal interface materials (TIM). The TIM facilitates heat transport between bounding solids (solid 1 and solid 2). A low melting point (Sn) thin film (green) fills the transition zones between the CNT–polymer/solid interfaces.

In particular, in the present study we obtain the thermal conductivity of the Sn-coated VA-MWCNT epoxy composite (device) over a temperature range 240–300 K using the three omega method. In order to estimate the thermal conductivity of the VA MWCNT epoxy composite as well as the thermal interfacial resistance at the various material interfaces in the cross-plane direction, we characterize the thermal conductivity in individual constituents of the VA-MWCNT composite, namely (1) individual free-standing nanotubes selected from the same VA-MWCNT array as that used in the fabrication of the VA-MWCNT-epoxy composite; (2) the epoxy matrix; and (3) Sn thin films (capping layer) of ∼500 nm thickness. A 1-D multilayer thermal model based on Feldman’s notation³⁶ is developed and used in conjunction with the measurements to estimate the thermal conductivity of the CNT-epoxy composite as well as the thermal interfacial resistance between the material layers.

The organization of the paper is as follows: First, a brief description on the processing of the VA-MWCNT composite samples is provide; this is followed by the methods employed in the characterization of thermal transport in its individual constituents, and finally the results and discussion of the study are presented.

Materials and methods

Sample processing

The VA-MWCNT arrays used (Figure 2(a) and (b)) in the present investigation were procured from the laboratory of Prof Shanov at the University of Cincinnati. The CNT arrays were synthesized using water-assisted chemical vapor deposition (CVD).^37–39 The nanotube diameter varied from 15 to 45 nm.

Figure 2.

Scanning electron microscope (SEM) micrographs of vertically aligned multiwalled carbon nanotube (VA-MWCNT) arrays prepared by thermal chemical vapor deposition (CVD) taken at two different magnifications (a) ×740 and (b) ×6200 showing the region near CNT tips.

The Epon 862 resin has been chosen due to its higher working temperature which is important for aerospace applications and low viscosity so that it infiltrates the array and provides sufficient adhesion with the embedded CNTs. Moreover, the resin is known to impart good stiffness and toughness, as well as excellent chemical, electrical and thermal resistance, making it a promising matrix for advanced multifunctional composites.^40,41 For example, carbon-filler composites with EPON-862 as matrix⁴¹ have been shown to exhibit enhanced flexural and compression modulus and strength and high glass-transition temperatures.

The epoxy-based CNT composites were fabricated by immersing the MWCNT array into a solution of Epon 862 epoxy, EPICURE curing agent W, and an acetone solvent. Prior to immersion of the VA-MWCNT array, the Epon 862 epoxy is ultrasonicated for approximately 8 min. The solution is poured onto the VA-MWCNT array and then spin-coated to allow the epoxy to infiltrate the array. Degassing is performed under high vacuum (30 in of Hg) to remove the bubbles generated during mixing. After casting the MWCNT/epoxy composite, both surfaces are cut and lapped. The surfaces are then sequentially polished at 100–150 rpm with 15, 6, 1, and 0.1 µm diamond abrasives while applying a 5 N constant force.

The sample, as observed under an environmental SEM, mostly comprised of nanotubes having outer diameters 35–45 nm with a number density of ∼10⁹–10¹⁰ nanotubes/cm². Using this information and by measuring the sample dimensions, the estimated average volume fraction of CNTs in the composite is estimated to be approximately 8%. This value is also supported by the weight measurements of VACNT arrays from the same batch in air using density of air of 1.2 kg/m³, and an average density of VACNT array samples of approximately 0.05 g/cm³. Moreover, the amount of polymer infiltration is estimated by comparing the measured density of a composite sample to the density predicted for the case in which the polymer had fully infiltrated the space between the nanotubes. In the present study, polymer infiltration is estimated to be 60–65% of the available spacing.

Atomic force microscopy (AFM) topology measurements (Figure 3(d)–(f)) indicate that the polishing process reduces the roughness of the samples from nearly 1 µm to 100 nm or less. Following polishing, the samples are ethanol-washed and air-dried. The MWCNT tips are exposed from the epoxy by reactive ion etching (RIE) using O₂ plasma with 13.5 MHz 125 W RF power for 6–8 min. Once the tips are exposed, a thin layer of tin of thickness ∼500 ± 50 nm is deposited using RF sputtering at 2 × 10⁻⁷ Torr. Besides promoting the transport of phonons from the CNTs to the tin film, the relatively soft tin layer helps in reducing the roughness (and/or gaps) between the CNT tips and the SiO₂ layer, thus reducing the thermal interface resistance at the CNT-SiO₂ interface.

Figure 3.

(a) Atomic force microscopy (AFM) phase imaging of vertically aligned multiwalled carbon nanotube (MWCNT)–epoxy composite before plasma-etching; (b) tapping mode AFM reveals CNT tips exposed after plasma-etching on composite; (c) three-dimensional (3D) view of roughness characteristic on top surface of epoxy before polishing using AFM; (d) surface topology of epoxy composite before polishing indicating roughness 600 nm–1 µm; (e) surface topology traced by AFM tip on composite sample after polishing indicating roughness of the order ∼100 nm.

Thermal conductivity measurements in individual MWCNTs

In the present study, the thermal conductivity of individual MWCNTs is measured using a three-omega-based Wollaston T-Type probe inside a high-resolution scanning electron microscope (SEM). Details of the technique and measurements are provided in Bifano et al.⁴² Figure 4 depicts the Wollaston probe wire’s temperature profile (a) before the specimen is placed in contact and (b) following contact with the specimen. The drop in spatially averaged temperature causes a reduction in electrical resistance, and thus a measureable voltage decrease. The thermal resistance of the probe wire is then determined from the voltage response since the heating current amplitude is known.

Figure 4.

Schematic of the Wollaston probe wire. The probe wire is Joule-heated with a power of Q_RMS, by the low frequency current, I_1ω_RMS. θ _A (x) is the temperature response of the probe wire prior to making contact with the sample of unknown thermal conductivity. Following contact with the sample, the temperature response of the probe wire is θ _B (x). The measured third harmonic voltage, V_3ω_RMS, is a function of the probe wire’s thermal resistance, zero current electrical resistance R_eo, Q_RMS, and the thermal resistance of the sample. The sample’s thermal conductivity is determined by measuring the sample’s thermal resistance and dimensions.

In the method, the relationship between the probe wire’s temperature and its electrical resistivity is first calibrated by measuring the electrical resistance versus power input in the absence of the sample. Once the sample is attached to the probe/heater wire, the change in the measured electrical resistance versus power input of the probe wire is correlated to the decrease in the probe wire’s average temperature rise due to heat flux into the sample. Since the opposing ends of the sample is maintained at the base (ambient) temperature, in effect, the temperature drop and heat flux into the sample can be estimated, and the sample’s thermal resistance determined with sufficient accuracy.

Instead of DC Joule heating and voltage measurements, the probe wire is Joule-heated with a low frequency sinusoidal AC current, I(t) = I_1ωsin(ωt), where I_1ω is the current amplitude. The initial electrical resistance of the probe wire is R_eo. Joule heating at 2ω, Q(t), drives in phase temperature oscillations, $\bar{θ} (t)$ , which are proportional to Q(t), by a thermal transfer function Z_o. The 2ω temperature oscillations create oscillations in electrical resistance given by $R_{e} (t) = R_{eo} big [1 + α \bar{θ} (t)]$ , where α is the measurable temperature coefficient of resistance of the probe wire. Since the heating current is I(t) = I_1ωsin(ωt), the voltage response of the probe wire is expected to be a combination of both the 1ω and 3ω frequency harmonics of the initial heating current and is given by,

\begin{matrix} V (t) = I (t) R_{e} (t) = \\ big [I_{1 ω} R_{eo} + \frac{3}{4} α Z_{o} R_{eo}^{2} I_{1 ω}^{3}] \sin ω t \\ - \\ big [\frac{1}{4} α Z_{o} I_{1 ω}^{3} R_{eo}^{2}] \sin 3 ω t . \end{matrix}

(2)

A Lock-in amplifier is used to measure the specific RMS value of the three-omega component. The measurable 3ω RMS voltage response from equation (2) may be re-written as

V_{3 ω, RMS} = \frac{1}{2} α Z_{o} I_{1 ω, RMS} R_{eo} Q_{RMS},

(3)

where

Q_{RMS} \equiv I_{1 ω, RMS}^{2} R_{eo}

If R_e_3ω,RMS ≡ V_3ω,RMS/I_1ω,RMS, Z_o is determined from the measured slope of $δ R_{e 3 ω, RMS} / δ Q_{RMS}$ . The thermal resistance ratio of probe to the sample, R_th,P/R_th,S, is embedded inside the thermal transfer function Z_o. By modeling the temperature response of the probe wire as a function of R_th,P/R_th,S, a theoretical value of Z_o is compared to the experimental value. Initial calibration in the absence of the sample is used to first determine R_th_,_P, and a subsequent measurement in the presence of the probe wire is used to determine R_th_,_S The samples thermal conductivity is calculated by k_S = L_S/R_th_,_S A_S, where the sample cross-sectional area A_s and length L_s are measured using the SEM beam.

The three omega for thermal conductivity measurements in Sn thin films, bulk epoxy and MWCNT-epoxy composite

In the present study, an approach similar to the differential three-omega method^43–45 was utilized to measure the thermal conductivity of a ∼500 nm thick Sn film, bulk EPON-862 epoxy, and VA-MWCNT-epoxy composite samples. In general, the 3ω method is performed on these samples by passing a current with angular frequency ω through a heater/sensor microfabricated on the sample surface, as shown in Figure 5(c) and (d). The current leads to Joule heating and thus a temperature oscillation at a frequency 2ω in the heater/sensor wire. Subsequently, the metal heater/sensor wire’s electrical resistance also oscillates at 2ω causing a measureable 3ω voltage oscillation detected using a lock-in amplifier. The 3ω voltage measurements are then used to determine the sample’s thermal properties.^46,47 The frequency range for the experiments is chosen by examining the relationship between the film (sample) thickness, the thermal penetration depth of interest, and the heater width. Large heater widths (when compared to sample thickness) produce a one-dimensional heating profile, thereby providing information about the cross-plane thermal conductivity.

The main components for the 3ω set-up (see Figure 5(a)) used in the present work are (1) a cryostat (Janis Research Model: CCS-400H/204); (2) a temperature controller that serves to regulate the sample temperature; and (3) a lock-in amplifier to detect the voltage response of the heater (Figure 5). The cryostat as shown in Figure 5(b) is capable of operating in the temperature range from 10 K to 500 K. An RV-8 rotary vane pump capable of developing a vacuum of 10⁻⁴ torr or less is utilized. A silicon shadow mask is batch fabricated using the conventional lithography technique. Using this microfabricated shadow mask an aluminum metal heater/sensor line is magnetron sputtered on the sample surface. The temperature coefficient of resistance of the heater/sensor line is measured prior to every experiment. The set-up has been automated using LabVIEW 8.5. The bits of the multiplying DAC (AD 7541 KN) are set ‘on’ and ‘off’ to balance the first harmonic signals from the sample and reference resistor. Moreover, the LabVIEW program helps in balancing the first harmonic voltage at the reference resistor and the sample resistor to a greater degree of precision and subsequently extract third harmonic voltage signals in order to determine the temperature rise in the heater/sensor.

Figure 5.

(a) Schematic of Cryostat Setup@ Nanomechanics Lab, Case Western; (b) microfabricated 25-µm wide heater with 250 µm × 250 µm pads attached for wire-bonding; (c) schematic of the conventional 3-Omega set-up used in measurement of the cross-plane thermal conductivity of the samples using the thin film on a substrate configuration (refer corresponding scanning electron microscope [SEM] images, Figure 7).

For electrically conductive samples, a thin insulating film must be deposited prior to the metal line deposition to provide electrical isolation. In the present work, approximately 350 nm thick SiO₂ films were deposited using a low temperature plasma enhanced chemical vapor deposition (PECVD) process. The SiO₂ layer serves as an insulator for all thin films and composite samples evaluated in the present study. Moreover, in all cases, the same heater material (aluminum) and heater dimensions (width) are used. In order to minimize errors due to various approximations of the exact thermal solution for the case of a thin film on a substrate, a numerical procedure in conjunction with the exact solution, as described by Kim,⁴⁸ Borca-Tasciuc et al.,⁴³ and more recently by Tong,⁴⁵ is employed. The analysis of the three omega experiments was based on the work by Cahill and Pohl⁴⁹ and requires the assumption that the heater wire is of infinite length and that the sample dimensions be semi-infinite. Additionally, the method requires the heat penetration depth into the sample to be greater than the heater width, thus satisfying the approximation of an infinite line heat source. Additional details about the three omega technique can be found from various references^43–49 and are therefore not discussed in detail here.

In the present study, the aforementioned three omega method was employed to investigate the thermal conductivity of a 3-mm thick epoxy (EPON-862) sample using the analytical solution discussed in Cahill⁴⁶ for a narrow line source on a semi-infinite substrate. On the other hand, the thermal conductivity of ∼500 nm thin tin films was measured by comparing the total amplitude and phase signal of temperature oscillations with a theoretically obtained solution in the thin layer limit using Tong’s⁴⁵ two-layer model. For the case of the VA-MWCNT composites, a three-layer model based on Feldman’s algorithm³⁶ was derived and used to interpret the experimental results.

Results and discussion

In the present study, we present results of thermal conductivity measurements in individual components of the VA MWCNT epoxy composites including individual free-standing MWCNTs, epoxy matrix, and the tin capping layer. Wherever possible, the thermal measurements were performed at room and lower than room temperatures so as to investigate the effects of increased phonon mean free path lengths on thermal conductivity.

Thermal conductivity in individual carbon nanotube

In the present study, thermal conductivity of individual MWCNTs taken from the same sample batch array UC01 are measured at room temperature. The average thermal conductivity of an individual nanotube from the UC01 batch was found to be ∼60 W/m-K based on the slope change in measured third harmonic resistance versus power input to sensor with and without sample (Figure 6(c) and using equation 3). In a recent study,⁴² the authors’ have also measured the thermal conductivity of individual multiwalled nanotubes from both heat-treated and non-heat-treated sample groups, showing an approximate five-fold increase in thermal conductivity with heat treatment. Heat-treatment was performed at 3000°C for 20 h in an argon gas atmosphere. Moreover, for one of the heat-treated samples, thermal conductivity as high as 730 ± 153 W/m-K was obtained.

Figure 6.

(a) Scanning electron microscope (SEM) micrograph of thermal conductivity experiment on an individual multiwalled carbon nanotube (MWCNT) selected from the UC01 sample group. (b) Raman intensity with excitation wave number for D/G Raman ratio of the UC01 nonheat-treated sample. (c) Measured third harmonic resistance vs power input to sensor with and without sample for an individual nanotube (UC sample).

Qualitative assessments of residual amorphous carbon and defects were made by observing the Raman peak intensities of the D and G-bands. The D band (defect band) is known to be activated by both carbonaceous impurities with sp³ bonding and fragmented sp² bonds,^50,51 both being features of MWCNT defects. The G band is activated by contiguous sp² bonding, i.e., a high degree of crystallinity.^50,51 Therefore, when comparing the two sample groups, a smaller D/G band ratio is representative of a sample with fewer defects and a higher degree of graphitization. The authors have shown that significant increase in thermal conductivity had a strong correlation to the reduced D/G Raman peaks. The average Raman D/G ratio for heat-treated samples was 0.21 ± 0.04, while the non-heat-treated group had an average D/G ratio equal to 0.69 ± 0.15. Note that the UC01 samples are not heat-treated and Raman scattering reveals a D/G ratio of 0.84 (Figure 6(b)). The reduced value of thermal conductivity measured in the UC01 sample correlates well with the non-heat-treated sample group with higher D/G Raman ratios.

Thermal conductivity is undoubtedly expected to improve with increased crystallinity and a decreased density of phonon scattering sites. Andrews et al. (2001)⁵² had observed marked structural and chemical improvements in MWCNT sample quality with heat-treatment. It was observed that annealing temperatures reduced the residual Fe catalyst (essential for CVD growth of MWCNT’s) from 7.1% by wt. to 0.1%. Moreover, it was reported that the temperatures as high as 3000°C healed the sidewall defects evident from the reduced inter-layer spacing between grapheme shells confirmed by x-ray diffraction (XRD) and transmission electron microscope (TEM).

Thermal transport in 500 nm thick Sn thin film

In the present study, a TZ (capping layer) comprising of a Sn thin film is introduced at the interface between the MWCNTs and the bounding surfaces to minimize scattering of the phonons at the interface due to mismatch in phonon spectra as well as thermal interface resistance due to interfacial roughness including the effects not all CNTs making contact at the interface due to unequal length of CNTs. The Sn capping layer, with a relatively high thermal conductivity and low yield strength (46 W/m-K and melting point of 230°C), aids in filling the surface asperities at the two mating surfaces, thereby reducing the interface thermal resistance between the CNT-epoxy composite and the bounding surfaces. Considering diffuse interfaces, even in the regions where the Sn layer wets the CNT tips completely (no air gaps), phonons from the CNT tips are expected to be readily transferred to the Sn layer because of the relatively wide phonon spectrum available to the phonons in Sn when compared to the CNTs (phonon spectra in a material is proportional to the density of states, which is proportional to the inverse of the cube of the sound speed in the material). Additionally, the capping layer is kept relatively thin to help minimize the boundary layer thickness and hence its thermal resistance. As previously mentioned, the top surface of the composite is polished down to ∼100 nm, as verified by AFM. Therefore, a 500-nm thick tin layer should be sufficient to fill the asperities. The thin layer of tin is deposited on the composite sample using sputtering. The sample is then placed in a vacuum oven at near melting point of tin so that it forms a weld contact with the exposed CNT tips on the top surface. Recent work by Prasher⁵³ has confirmed that the weld contact formed by Sn-like soft (and compliant) metals tend to increase the thermal conductance by an order of magnitude compared to more common Van der Waal contacts at the interfaces.

In order to obtain the cross-plane thermal conductivity of the Sn thin film specimens, the differential three-omega method was applied with the Sn thin film specimens deposited on a Si substrate. The Sn film is assumed to be thin enough such that one-dimensional Fourier conduction model can be applied for the analysis and interpretation of the experimental data. Specific conditions that must hold to ensure accurate analysis are given by $d_{f} > 2 b >> L_{f}$ , i.e., the thermal penetration depth d_f must be greater than the heater width and be much larger than the film thickness, L_f. For the experimental investigation discussed herein, the thermal penetration depth and the heater width are greater by at least an order of magnitude of the film thickness to ensure validity of these approximations. Additionally, the thickness of the underlying Si substrate L_s is taken to be such that the validity of the line source as well as the semi-infinite substrate approximation holds. Figure 7 shows SEM pictures of the microfabricated heater and sensor wires on the SiO₂ film, and the Sn thin film specimen, on the Si substrate. Table 1 provides details of the heat and sensor wire dimensions, the thickness of the SiO₂ insulating film, the thickness of the tin thin film specimen, and the Si substrate thickness.

Figure 7.

Scanning electron microscope (SEM) images of heater/sensor wire deposited using shadow mask on (a) SiO₂ 350 nm thin film and Sn 500 nm thin film (with an insulating layer) on silicon substrate.

Table 1.

Experimental parameters for thin film measurement

Heater width	Thickness			Penetration depth (f = 10 Hz)
Heater width	SiO₂ film	Sn film	Si substrate	SiO₂ film	Sn film
25 µm	350 nm	500 nm	500 µm	80 µm	520 µm

From these experiments,⁵⁴ the thermal conductivity of the 500 ± 50 nm tin film was determined to be 46 ± 4 W/m-K at room temperature. The thermal conductivity was found to remain nearly constant in the temperature range of 240 K–300 K (Figure 8). This is understood to be due to the specific heat being constant in the temperature range with the Dulong-Petit limit being at 210 K. Moreover, the phonon and electron mean free paths at room temperature are relatively small, 50 nm and <5 nm, respectively, compared to the boundary dimensions.⁵⁴ Therefore, boundary scattering is not expected to play a role in the thermal conductivity of the sample. Furthermore, even though the reduction in thermal conductivity in metals is known to occur at elevated temperatures due to the increased phonon-phonon inelastic scattering, the test temperatures in our present case are not high enough for inelastic phonon-phonon (Umklapp) interactions to be important, and thermal conduction continues to be dominated by the specific heat. The estimated thermal resistance of the Sn thin film over the measured temperature range is nearly constant at 1.09 × 10⁻⁸ K-m²/W.

Thermal transport in epoxy polymer

The thermal conductivity of EPON-862 epoxy is also measured using the three-omega method at temperatures in the range 100 K to 340 K (Figure 9). The measured thermal conductivity of EPON-862 at room temperature is 0.224 ± 0.02 W/m-K. The slight increase in thermal conductivity with temperature is understood to be a result of the increase in specific heat with test temperature. The thermal transport in amorphous polymers (Reese⁵⁵) is phonon-dominated with the mean free path of phonons remaining a constant due to scattering by the amorphous disordered regions. For the case of EPON-862, the phonon mean free path is estimated to be 0.32 nm based on the sound velocity (dilatational wave velocity) of 1949 m/s (corresponding to the elastic modulus value of 2.58 GPa⁴¹ and Poisson’s ratio of 0.35) and specific heat equal to 1060 J/Kg-K.⁵⁶ The glass transition temperature of EPON-862 is 408 K,⁴¹ and the thermal conductivity of Epon-862 is expected to increase continuously until it reaches the transition point. A small jog in the temperature dependence of thermal conductivity is observed at around 225 K, which is consistent with the observations made earlier in many polymers for specific heat dependency with temperature, and can be attributed to the transition of the local amorphous regions within the polymer from glassy to the rubbery state. The rotational and vibrational motions of atomic groups associated with the polymer chains in the rubbery state require a lesser amount of energy for reorganization and mobility when compared to the glassy state.

Figure 8.

Thermal conductivity of 500 nm Sn thin film (Replotted from Reference [54]).

Figure 9.

(a) Third harmonic voltage measurements vs frequency for epoxy EPON-862 (bulk) at different temperatures; (b) thermal conductivity vs temperature of epoxy EPON-862 from 100 K–340 K.

Thermal transport in the vertically aligned MWCNT–epoxy composite

In order to characterize the thermal conductivity of the VA MWCNT-epoxy composite, the three-omega method outlined earlier is employed. A thin layer (∼500 nm) of tin with a SiO₂ insulating layer on top is deposited on the composite substrate (Figure 10) to prevent direct contact with the aluminum heater line and contact pads. The estimation of both thermal conductivity and thermal interface resistance between the layers is important to obtain the through-thickness thermal conductivity of the VA MWCNT-epoxy composite. Tong in an earlier work⁴⁵ derived a two-layer model (based on Feldman’s notation³⁶). A three-layer 1-D model including the finite interface resistance between layers has been derived in this work (Figure 11).

Figure 10.

Scanning electron microscope (SEM) images of (a) cross-section of multiwalled carbon nanotube (MWCNT) array; (b) cross-section of vertically aligned MWCNT array composite from one of its edges in backscattering mode, on a 45° sample holder with 35° tilt; (c) line heater deposited on top of MWCNTA–composite sample; (d) top cross-section of the measured sample after slicing showing SiO₂–Sn interface and Sn–MWCNT composite interface; (e) bottom cross-section showing vertically aligned multiwalled carbon nanotube (VA-MWCNT) array on silicon wafer; and (f) schematic of 3-omega configuration utilized for measuring VA-MWCNT composite.

Figure 11.

Schematic representation of one-dimensional (1D) thermal transport model for a three-layered structure with a heater on top.

The main steps of the 1-D thermal-model are provided below. The heat equation for a 1-D multilayer problem can be written as,

k_{y, j} \frac{\partial^{2} T_{j} (y, t)}{\partial y^{2}} = ρ_{j} C_{p_{j}} \frac{\partial T_{j} (y, t)}{\partial t},

(4)

where j = 1, 2 and 3 represent the individual layers (1 = SiO₂, 2 = Sn, 3 = CNT-epoxy composite); T_j is the temperature at a point y_j in an individual layer; and

k_{y, j}

ρ_{j}

and

C_{p_{j}}

represent the through-thickness thermal conductivity, density, and the specific heat of the individual layers.

Under periodic excitation with angular time frequency, ω, the general solution to equation (4) can be expressed as

T_{j} (y_{j}, t) = A \cdot e^{(η_{j} y_{j} - 1 ω t)} + B \cdot e^{(- η_{j} y_{j} - i ω t)}

(5)

where

η_{j} = \sqrt{- \frac{i ω ρ_{j} C_{pj}}{k_{y, j}}}

is the inverse of the penetration depth. The two parts of the solution represent thermal waves propagating to the positive and negative directions with two complex coefficients, A and B, to be determined by boundary conditions.

Let us assume for this 1-D material, a periodic heat flux with amplitude q₀ and frequency ω is injected at the surface y₁ = 0

q big (y_{1} = 0, t) = q_{0} e^{- i ω t} .

(6)

Following Feldman’s notation,³⁶ we can express the temperature at any position y as a vector,

T_{j} (y_{j}, t) = big (\begin{matrix} A \cdot e^{(η_{j} y_{j} - i ω t)} \\ B \cdot e^{(- η_{j} y_{j} - i ω t)} \end{matrix}) .

(7)

The matrix formulation aids in finding the correlation between the temperatures at two different locations within the medium as well as that across the interface between the layers. The boundary condition is based on the assumption that with no heat generated or absorbed at the interfaces, the heat flux is continuous across the interfaces, and there is discontinuity in temperature across a j and j+1 interface due to a finite interface thermal resistance R_j,_j+1 _.

\begin{matrix} big . - k_{y, j} \frac{\partial T_{j}}{\partial y_{j}} |_{y_{j} = L_{j}} = \\ big . - k_{y, j + 1} \frac{\partial T_{j + 1}}{\partial y_{j + 1}} |_{y_{j + 1} = 0} \\ = R_{j, j + 1} \\ big [T_{j + 1} big (y_{j + 1} = 0) - T_{J} big (y_{j} = L_{j})] \\ big . \frac{\partial T_{1}}{\partial y_{1}} |_{y_{1} = 0} = 0; \\ big . \frac{\partial T_{3}}{\partial y_{3}} |_{y_{3} = L_{3}} = 0 \end{matrix}

(8)

where L_j is the thickness of the jth layer.

The total thermal impedance Z of the three-layered structure neglecting the interface thermal resistance can be obtained as

Z = \frac{T_{1} (0)}{q_{0}} = \frac{1}{γ_{1}} big [\frac{big (1 + \frac{γ_{3}}{γ_{2}} η_{2} L_{2}) + big (\frac{γ_{3}}{γ_{1}} + \frac{γ_{2}}{γ_{1}} η_{2} L_{2}) η_{1} L_{1}}{big (1 + \frac{γ_{3}}{γ_{2}} η_{2} L_{2}) η_{1} L_{1} + big (\frac{γ_{3}}{γ_{1}} + \frac{γ_{2}}{γ_{1}} η_{2} L_{2})}]

(9)

where

γ_{j} = k_{y, j} η_{j}

and q₀ are the amplitude of the input heat flux. Note that the exponential terms in the solution above have been simplified using Taylor expansion assuming the films are very thin compared to the penetration depth. Since the SiO₂ and Sn films deposited on top of the composite are very thin (on the nanometer scale) compared to the penetration depth of heat, i.e.

big | η_{1} L_{1} | << 1

big | η_{2} L_{2} | << 1

and

big | η_{3} L_{3} | ~ 1

for the range of frequencies used, makes this approximation valid.

Similarly, the total thermal impedance Z for the three-layered structure with interface resistances R₁ = R_1,2 (between SiO₂ and Sn) and R₂ = R_2,3 (between Sn and MWCNT) can be expressed as

\frac{v^{o} (ω)}{a_{b} e^{j ω t}} = \frac{j ω θ^{o}^{T}^{r}}{j ω C_{p}^{o} + \frac{1}{Z^{o}}} (- ω^{2} M + j ω C + K + \frac{- j ω θ^{o} θ^{o}^{T}^{r}}{j ω C_{p}^{o} + \frac{1}{Z^{o}}})^{- 1} M

(10)

The model is verified by comparing them with the results obtained for the two-layer model as described by Tong.⁴⁵ Moreover, using the condition, $γ_{3} = 0$ in the absence of a third layer, and $big | η_{2} L_{2} | ~ 1$ , such that, the heat wave dies down within the second layer (that now acts as a substrate), we get the same result as in Tong et al.,⁴⁵ i.e.

Z = \frac{1}{γ_{2}} + R_{1} + \frac{L_{1}}{k_{1}} big [1 - \frac{γ_{1}^{2}}{γ_{2}^{2}} - \frac{2 γ_{1}^{2}}{γ_{2}} R_{1} - γ_{1}^{2} R_{1}^{2}] .

(11)

The experimental data on temperature oscillations and phase are compared with the predictions of the thermal model with and without thermal interface resistance between the layers. The thermal model is based on several parameters (shown in Table 2), e.g., thermal properties of the various layers, and the unknown thermal interface resistances. An iterative algorithm, as described in Tong et al.,³¹ was employed to obtain the best fit values for the unknowns. The comparison of the experimental results and model predictions based on the best fit values for the unknown parameters is shown in Figure 12. From these comparisons, the thermal conductivity of the CNT-epoxy composite is estimated to be 5.8 ± 0.64 W/m-K at room temperature. The measured amplitude as well as the phase of the temperature oscillations are found to be sensitive to the thermal conductivities of tin, MWCNT-epoxy composite, and the thermal interface resistances. A ±20% uncertainty in thermal conductivity of either tin or the MWCNT-epoxy composite results in a corresponding ±5–10% shift in the amplitude of the temperature oscillations from the measured values. The thermal conductivity of the composite exhibits a slight increase with temperature between 240 K and 300 K (Figure 13) and is understood to be dominated by the specific heat dependence with temperature of the Epon-862 epoxy.^9,57

Figure 12.

Comparison of thermal model with and without interface resistances with experimental data: (a) temperature oscillations vs frequency and (b) phase of oscillations vs frequency.

Figure 13.

Thermal conductivity vs temperature of vertically aligned multiwalled carbon nanotube (VA-MWCNTA)–epoxy (EPON-862) nanocomposite from 240 K–300 K.

Table 2.

Model parameters that fit the experimental amplitude and phase of temperature oscillations

Sample	Thickness	Thermal diffusivity (m²/s)	Thermal conductivity (W/m-K)	Interface thermal resistance (m² K/W)
SiO₂ thin film	350 nm	8.1 × 10⁻⁷	1.2
Tin thin film	500 nm	3.5 × 10⁻⁵	46
Epoxy (EPON-862)	3 mm	1.76 × 10⁻⁷	0.224
VA-MWCNT–epoxy composite	2.1 mm		5.8
interface resistance oxide-tin, R₁				5 × 10⁻⁵
interface resistance tin–MWCNT array, R₂				8 × 10⁻⁶–8.5 × 10⁻⁷

VA-MWCNT: vertically aligned multiwalled carbon nanotube.

The best fit estimates for the interface thermal resistances R_1-2 (between SiO₂ and Sn) and R_2-3 (between Sn and MWCNT) are 5 × 10⁻⁵ m²-K/W and 8 × 10⁻⁶ − 8.5 × 10⁻⁷ m²-K/W, respectively. The amplitude or phase of temperature oscillations is especially sensitive to the thermal resistance of the rougher interface, i.e. the SiO₂–Sn interface. However, it is relatively less sensitive to the interface thermal resistance of the relatively smooth Sn-MWCNT interface, and therefore by keeping all other parameters constant we can estimate the interface resistance of the smooth Sn-MWCNT interface to within an order of magnitude range. The interface resistance between the layers is a combination of Kapitza resistance based on diffuse mismatch model (DMM) and constriction resistance at the contacts of CNTs with the Sn layer. Recently, Prasher^58,59 suggested that for nanosized constrictions (which the vertically aligned MWCNTs make with the layer above it), the effects of mismatch in acoustic properties are more dominant than due to constriction of the heat flux lines. Therefore, vibrational spectra mismatch between Sn, a soft metal with relatively low sound speed, and VA MWCNTs is expected to restrict the thermal conductance through the MWCNT composite. The Debye temperature of Sn is 170 K, while the Debye temperature for multi-MWCNTs is much higher, 960–2500 K, indicating a large mismatch in vibrational spectra of the two materials. Interface thermal resistance between two highly dissimilar materials with large differences in phonon spectra, e.g., interfaces involving metal and dielectric solids, as pointed out by Lyeo and Cahill⁶⁰ is not only due to the coupling of electrons in a metal and phonons in a dielectric substrate but also by anharmonic processes (namely three-phonon processes) that can contribute a significant additional channel for transport of heat by altering (increasing) the phonon frequency by inelastic scattering processes. These higher frequency phonons are expected to be readily accommodated by the much broader phonon spectra available for Sn. For these reasons, CNTs may be particularly attractive for exchange of thermal energy with Sn across the CNT-Sn interfaces involving both phonons and electrons.

Interestingly, even after a spate of research on VA MWCNT composites, there are only few published works in the literature that reported thermal conductivities greater than 1 W/m-K (Figure 14). Sihn et al.³² have reported the highest thermal conductivity so far for a 30 µm VA MWCNT-epoxy composite. Using a simple 1-D thermal resistance network model, we estimate the room temperature thermal conductivity of their VA MWCNT-epoxy composite to be 137 W/m-K. Considering a 10 vol % of MWCNTs in their composite, the thermal conductivity of individual MWCNTs is estimated to be in excess of 1000 W/m-K.

Figure 14.

Thermal conductivity vs volume fraction of nanowires and nanotubes.

The primary reasons for a less than 1 W/m-K thermal conductivity of the MWCNT polymer composites reported in the literature may be due to the low volume fraction of CNTs used in the composites as well as their defect state and purity. In a parallel study,⁴² the authors investigated thermal conductivity in annealed and as-received thermal CVD grown individual multi-MWCNTs. They reported a five-fold increase in thermal conductivity of the MWCNTs from the annealed batch (Figure 15), conforming that the defect state of the CNTs play an important role in controlling the thermal conductivity in individual CNTs. In addition, high-resolution SEM micrographs of CNT arrays (Figure 16) from the same batch as the array that was used in the fabrication of the composite indicate physical deformities, including entanglement of CNTs and fused contacts, that are understood to be the reason for reduced thermal conductivity of the composites. These contact regions between nanotubes occur even in the best-aligned CNT films and serve as scattering sites for phonons propagating along contacting nanotubes. In fact Prasher et al.⁶¹ have shown that the thermal conductivity of a randomly oriented bed of MWCNTs is primarily controlled by the CNT-CNT thermal contact resistance, which is an order of magnitude larger than the intrinsic thermal resistance of a CNT.

Another reason for the relatively low thermal conductivity of the individual CNTs may be because the phonon modes within CNTs can be damped and scattered by the polymer matrix reducing the thermal conductivity of the CNTs themselves. Indeed, Gojny et al.¹⁷ have shown that damping of phonon modes within the outer shells of the nanotube may be a possible reason for the reduction of the thermal conductivity of the nanotubes.

Figure 15.

Thermal conductivity vs Raman ratio of individual multiwalled nanotubes (replotted from Reference [42]).

Figure 16.

Scanning electron microscope (SEM) micrographs (9 kV, 3.5 mm working distance, and spot size, 2.5) of multiwalled carbon nanotube (MWCNT) array batch of which the composite was made and tested: (a) entanglements of individual nanotubes (×87,000) and (b) individual samples are often attached as if they are fused together (×100,000).

Additionally, in order to improve their performance as TIM, thermal conductance at CNT-capping layer interfaces need to be addressed. One of the main advantages of the composites studied in this work is that CNTs themselves are well aligned and span the entire thickness of the polymer in the axial direction, providing direct pathways for heat transport across the composite. However, if some CNTs fail to extend to the surface of the polymer, the CNT-polymer thermal boundary resistance can negatively impact the axial conduction. In this regard, in the present study we initially start with a polished CNT-polymer surface and then plasma-etch it to expose the CNT tips on the surface. These tips are then coated with a low-yield point (Sn) metal to fill the region in between the CNT tips. The results of the present study suggest that the thermal interface resistance for such relatively smooth CNT-metal interfaces may contribute to only second-order effects in the thermal performance of the TIMs at room temperature.

It is to be noted that most previous works reported in the literature on VA-MWCNT-polymer composites^21,22,32,62 show room-temperature thermal conductivity as high as metal nanowire array-polymer composites^63,64 and the semiconductor nanowire array-polymer composites^65,66 with nanowire volume fractions in the same range as the CNTs. Nevertheless, the five-fold increase in thermal conductivity in the post-annealed MWCNTs suggests that the thermal conductivity of VA-MWCNT-epoxy composites can be designed to be as high as 25 W/m-K, which can potentially have a major impact in the design of multifunctional, load-bearing, high-thermal performance structural interfaces for a variety of thermal-management applications.

Summary

This paper reports development of VA-MWCNT array composites for thermal energy management in load-bearing structural applications. Unlike previous studies on the characterization of VA-MWCNT-based TIMs for primarily non-load bearing applications, the material systems of interest here involve the use of VA MWCNTs in an epoxy matrix. The epoxy matrix imparts mechanical strength to these systems while the VACNTs provide avenues for high through-thickness thermal conductivity across a typical material interface. In order to obtain the thermal characteristics of these multifunctional TIMs, we report measurements of thermal conductivity in the Sn-capped VA-MWCNT-epoxy composites as well as in its individual constituents, i.e., bulk EPON-862 (matrix material) and Sn thin film, in the temperature range 240 K to 300 K, and individual multiwall CNTs at room temperature taken from the same VA-MWCNT batch as the one used to fabricate the CNT-epoxy TIM. The thermal conductivity of the epoxy and Sn thin film was obtained as a function of temperature by using a cryostat in conjunction with the three-omega method. The thermal conductivity of individual free-standing MWCNT samples was obtained by employing the Wollaston T-type three-omega probe method inside a high-resolution SEM equipped with nanomanipulators and a gas injection system for electron beam-induced platinum deposition. The thermal conductivity of bulk EPON-862 epoxy was observed to increase gradually from 0.1 W/m-K at 100 K to 0.24 W/m-K at 340 K and is understood to be dominated by the heat capacity of the epoxy. The thermal conductivity of Sn capping layer (500 micron film thickness) was observed to remain nearly constant at about 46 W/m-K over the above-mentioned temperature range. The thermal conductivity of individual free-standing CNTs was measured to be about 60 W/m-K at room temperature. A 1-D multilayer thermal model that includes effects of thermal interface resistance and the thermal conductivity of the CNT-epoxy composite and its constituents was used to interpret the experimental results. The thermal conductivity of the CNT-epoxy composite was estimated to be about 5.8 W/m-K and exhibits a slight increase with temperature in the range of 240 K to 300 K. The best fit estimates for the interface thermal resistances between SiO₂ and Sn and between Sn and MWCNT were 5 × 10⁻⁵ m²-K/W and 8 × 10⁻⁶ − 8.5 × 10⁻⁷ m²-K/W, respectively. The results of this study suggest that the inclusion of an Sn thin layer on the VA-MWCNT array as well as the morphological structure of the individual MWCNTs are dominating factors that control the overall thermal conductivity of the TIM. These results are encouraging in light of the fact that the thermal conductivity of a VA-MWCNT array can be increased by an order of magnitude by using a standard high-temperature post-annealing step. In this way, multifunctional (load bearing) TIMs with effective through-thickness thermal conductivities as high as 25 W/m-K can be potentially fabricated.

Footnotes

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Acknowledgments

The authors would like to acknowledge the support of the Air Force Office of Scientific Research (AFOSR) grant FA9550-08-1-0372 (Program manager Dr. Byung-Lip Lee) and the National Science Foundation Major Research Instrumentation grants CMMI-0521364 and CMMI-0922968 to Vikas Prakash.

Conflict of interest

None declared.

References

Greenwood

Williamson

JBP

. Contact of nominally flat surfaces. Proc Roy Soc London Ser A Math Phys Sci 1966; 295(1442): 300–319.

Prasher

. Thermal interface materials: historical perspective, status, and future directions. Proc IEEE 2006; 94(8): 1571–1586.

Berber

Kwon

Y-K

Tománek

. Unusually high thermal conductivity of carbon nanotubes. Phys Rev Lett 2000; 84(20): 4613–4613.

Hone

Whitney

Piskoti

. Thermal conductivity of single-walled carbon nanotubes. Phys Rev B 1999; 59(4): R2514–R2514.

Hone

. Electrical and thermal transport properties of magnetically aligned single wall carbon nanotube films. Appl Phys Lett 2000; 77(5): 666–666.

Kim

Shi

Majumdar

. Thermal transport measurements of individual multiwalled nanotubes. Phys Rev Lett 2001; 87(21): 215502–215502.

Baughman

. Carbon nanotubes—the route toward applications. Science 2002; 297(5582): 787–792.

Hone

Llaguno

Biercuk

. Thermal properties of carbon nanotubes and nanotube-based materials. Appl Phys A: Mater Sci Process 2002; 74(3): 339–343.

Shi

. Measuring thermal and thermoelectric properties of one-dimensional nanostructures using a microfabricated device. J Heat Transfer 2003; 125(5): 881–888.

10.

Shi

Yao

. Thermal conductance and thermopower of an individual single-wall carbon nanotube. Nano Lett 2005; 5(9): 1842–1846.

11.

Pop

Mann

Wang

. Thermal conductance of an individual single-wall carbon nanotube above room temperature. Nano Lett 2005; 6(1): 96–100.

12.

Nan

C-W

Birringer

Clarke

. Effective thermal conductivity of particulate composites with interfacial thermal resistance. J Appl Phys 1997; 81(10): 6692–6699.

13.

Nan

Shi

Lin

. A simple model for thermal conductivity of carbon nanotube-based composites. Chem Phys Lett 2003; 375(5–6): 666–669.

14.

Choi

SUS

Zhang

. Anomalous thermal conductivity enhancement in nanotube suspensions. Appl Phys Lett 2001; 79(14): 2252–2252.

15.

Biercuk

Llaguno

Radosavljevic

. Carbon nanotube composites for thermal management. Appl Phys Lett 2002; 80(15): 2767–2767.

16.

Choi

Brooks

Eaton

. Enhancement of thermal and electrical properties of carbon nanotube polymer composites by magnetic field processing. J Appl Phys 2003; 94(9): 6034–6034.

17.

Gojny

Wichmann

MHG

Fiedler

. Evaluation and identification of electrical and thermal conduction mechanisms in carbon nanotube/epoxy composites. Polymer 2006; 47(6): 2036–2045.

18.

Itkis

Bekyarova

. Effect of single-walled carbon nanotube purity on the thermal conductivity of carbon nanotube-based composites. Appl Phys Lett 2006; 89(13): 133102–3.

19.

Liu

Fan

. Effects of chemical modifications on the thermal conductivity of carbon nanotube composites. Appl Phys Lett 2005; 86(12): 123106–3.

20.

Grunlan

Kim

Y-S

Ziaee

. Thermal and mechanical behavior of carbon-nanotube-filled latex. Macromol Mater Eng 2006; 291(9): 1035–1043.

21.

Borca-Tasciuc

Mazumder

Son

. Anisotropic thermal diffusivity characterization of aligned carbon nanotube-polymer composites. J Nanosci Nanotechnol 2007; 7(4–5): 1581–1588.

22.

Ivanov

Puretzky

Eres

. Fast and highly anisotropic thermal transport through vertically aligned carbon nanotube arrays. Appl Phys Lett 2006; 89(22): 223110–223110.

23.

Borca-Tasciuc

. Anisotropic thermal diffusivity of aligned multiwall carbon nanotube arrays. J Appl Phys 2005; 98(5): 054309–054309.

24.

Xuejiao H, Linan J and Goodson KE, eds. Thermal conductance enhancement of particle-filled thermal interface materials using carbon nanotube inclusions. In: Thermal and thermomechanical phenomena in electronic systems, 2004 ITHERM ‘04 the ninth intersociety conference, Las Vegas, NV, 1--4 June 2004, pp. 63--69.

25.

Tong

Zhao

Delzeit

. Multiwalled carbon nanotube/nanofiber arrays as conductive and dry adhesive interface materials. ASME Conf Proc 2004; 2004(41774): 7–12.

26.

Panzer

Goodson

. Infrared microscopy thermal characterization of opposing carbon nanotube arrays. J Heat Transfer 2007; 129(1): 91–91.

27.

Fisher

. Enhancement of thermal interface materials with carbon nanotube arrays. Int J Heat Mass Transfer 2006; 49(9–10): 1658–1666.

28.

Cola

Cheng

. Photoacoustic characterization of carbon nanotube array thermal interfaces. J Appl Phys 2007; 101(5): 054313–054313.

29.

Cola

Fisher

. Increased real contact in thermal interfaces: a carbon nanotube/foil material. Appl Phys Lett 2007; 90(9): 093513–093513.

30.

Shaikh

Lafdi

. Thermal conductivity of an aligned carbon nanotube array. Carbon 2007; 45(13): 2608–2613.

31.

Tao

Yang

Delzeit

. Dense vertically aligned multiwalled carbon nanotube arrays as thermal interface materials. Compon Packag Technol, IEEE Transact on 2007; 30(1): 92–100.

32.

Sihn

Ganguli

Roy

. Enhancement of through-thickness thermal conductivity in adhesively bonded joints using aligned carbon nanotubes. Compos Sci Technol 2008; 68(3–4): 658–665.

33.

García

Hart

Wardle

. Fabrication and nanocompression testing of aligned carbon-nanotube–polymer nanocomposites. Adv Mater 2007; 19(16): 2151–2156.

34.

Wardle

Saito

García

. Fabrication and characterization of ultrahigh-volume fraction aligned carbon nanotube–polymer composites. Adv Mater 2008; 20(14): 2707–2714.

35.

Cebeci

Villoria

RGD

Hart

. Multifunctional properties of high volume fraction aligned carbon nanotube polymer composites with controlled morphology. Compos Sci Technol 2009; 69(15–16): 2649–2656.

36.

Feldman

. Algorithm for solutions of the thermal diffusion equation in a stratified medium with a modulated heating source. High Temp High Press 1999; 31(3): 293–298.

37.

Hata

Futaba

Mizuno

. Water-assisted highly efficient synthesis of impurity-free single-walled carbon nanotubes. Science 2004; 306: 1362–1364.

38.

Shanov

Yun

Y-H

Schulz

. Synthesis and characterization of carbon nanotube materials. J Univ Chem Tech Metall 2006; 41(4): 377–390.

39.

Yun

Y-H

Shanov

. Growth mechanism of long aligned multi-wall carbon nanotube arrays by water-assisted chemical vapor deposition. J Phys Chem B 2006; 110: 23920–5.

40.

Yun

Shanov

Schulz

. High sensitivity carbon nanotube tower electrodes. Sensor Actuator B: Chem 2006; 120(1): 298–304.

41.

Rangari

Bhuyan

Jeelani

. Microwave curing of CNFs/EPON-862 nanocomposites and their thermal and mechanical properties. Compos Pt A: Appl Sci Manuf 2011; 42(7): 849–858.

42.

Bifano MFP, Park J, Kaul PB, Roy AK and Prakash V. Effects of heat treatment and contact resistance on the thermal conductivity of individual multiwalled carbon nanotubes using a Wollaston wire thermal probe. Journal of Applied Physics 2012; 111(5): 054321.

43.

Borca-Tasciuc

. Data reduction in 3-omega method for thin-film thermal conductivity determination. Rev Sci Instrum 2001; 72(4): 2139–2139.

44.

Olson

. A practical extension of the 3-omega method to multilayer structures. Rev Sci Instrum 2005; 76(5): 053901–053901.

45.

Tong

Majumdar

. Reexamining the 3-omega technique for thin film thermal characterization. Rev Sci Instrum 2006; 77(10): 104902–104902.

46.

Cahill

. Thermal conductivity measurement from 30 to 750 K: the 3 omega method. Rev Sci Instrum 1990; 61(2): 802–808.

47.

Lee

Cahill

. Heat transport in thin dielectric films. J Appl Phys 1997; 81(6): 2590–2595.

48.

Kim

. Application of the three omega thermal conductivity measurement method to a film on a substrate of finite thickness. J Appl Phys 1999; 86(7): 3959–3959.

49.

Cahill

Pohl

. Thermal conductivity of amorphous solids above the plateau. Phys Rev B 1987; 35(8): 4067–4067.

50.

DiLeo

Landi

Raffaelle

. Purity assessment of multiwalled carbon nanotubes by Raman spectroscopy. J Appl Phys 2007; 101(6): 064307–5.

51.

Dresselhaus

Jorio

Hofmann

. Perspectives on carbon nanotubes and graphene Raman spectroscopy. Nano Lett 2010; 10(3): 751–758.

52.

Andrews

Jacques

Qian

. Purification and structural annealing of multiwalled carbon nanotubes at graphitization temperatures. Carbon 2001; 39(11): 1681–1687.

53.

Prasher

. Acoustic mismatch model for thermal contact resistance of van der Waals contacts. Appl Phys Lett 2009; 94(4): 041905–041905.

54.

Kaul PB and Prakash V. Thickness and temperature dependent thermal conductivity of nanoscale tin films. In: Proceedings of the ASME 2011-65576 International Mechanical Engineering Congress & Exposition IMECE2011, Denver, Colorado, USA, 11--17 November 2011.

55.

Reese

. Temperature dependence of the thermal conductivity of amorphous polymers: polymethyl methacrylate. J Appl Phys 1966; 37(8): 3227–3227.

56.

Ganguli

Roy

Anderson

. Improved thermal conductivity for chemically functionalized exfoliated graphite/epoxy composites. Carbon 2008; 46(5): 806–817.

57.

Pradhan

Duan

Liang

. The specific heat and effective thermal conductivity of composites containing single-wall and multi-wall carbon nanotubes. Nanotechnology 2009; 20(24): 245705–245705.

58.

Prasher

. Predicting the thermal resistance of nanosized constrictions. Nano Lett 2005; 5(11): 2155–2159.

59.

Prasher

. Thermal boundary resistance and thermal conductivity of multiwalled carbon nanotubes. Phys Rev B 2008; 77(7): 075424–075424.

60.

Lyeo

H-K

Cahill

. Thermal conductance of interfaces between highly dissimilar materials. Phys Rev B 2006; 73(14): 144301–144301.

61.

Prasher

Chalopin

. Turning carbon nanotubes from exceptional heat conductors into insulators. Phys Rev Lett 2009; 102(10): 105901–105901.

62.

Marconnet

Yamamoto

Panzer

. Thermal conduction in aligned carbon nanotube–polymer nanocomposites with high packing density. ACS Nano 2011; 5(6): 4818–4825.

63.

. Silver nanowire array-polymer composite as thermal interface material. J Appl Phys 2009; 106(12): 124310–124310.

64.

Zeng

Cao

Yang

. Thermal conductivity enhancement of Ag nanowires on an organic phase change material. J Therm Anal Calorim 2010; 101(1): 385–389.

65.

Abramson

Woo Chul

Huxtable

. Fabrication and characterization of a nanowire/polymer-based nanocomposite for a prototype thermoelectric device. J Microelectromech Sys 2004; 13(3): 505–513.

66.

Biswas

. Thermal conductivity of bismuth telluride nanowire array-epoxy composite. Appl Phys Lett 2009; 94(22): 223116–223116.