Journal of Composite Materials - Case School of Engineering...reported enhancements in thermal conductivity of nearly twice the value of the epoxy, while the vapor-grown carbon-ﬁber

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DOI: 10.1177/0021998312453750

2013 47: 77Journal of Composite MaterialsPankaj B Kaul, Michael FP Bifano and Vikas Prakash

epoxy composites for thermal energy management−Multifunctional carbon nanotube

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JOURNAL OFC O M P O S I T EM AT E R I A L SArticle

Multifunctional carbon nanotube–epoxycomposites for thermal energymanagement

Pankaj B Kaul, Michael FP Bifano and Vikas Prakash

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 multi-

layer 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 asthose commonly experienced in supersonic and hyper-sonic air and space vehicles have initiated a demand forhigh-performance load-bearing thermal interface mater-ials (TIMs). When two nominally flat surfaces come incontact to form amaterial interface, due to surface aspe-rities the solid–solid contact area is limited to 1–2% ofthe apparent contact area.1 As a consequence, the con-tact junctions as well as the surrounding non-contactarea 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 havea finite thickness (called the bond-line thickness, BLT),and do not completely wet the surfaces, resulting in gapswith contact resistances at the two bounding surfaces.

For a typical TIM with a BLT, and an effective ther-mal conductivity, kTIM, the total thermal resistanceacross an interface can be written in terms of the ther-mal contact resistances with the bounding surfaces oneither side of the TIM, i.e. Rc1 and Rc2, as

RTotal ¼ Rc1 þBLT

kTIMþ Rc2: ð1Þ

In order to make the TIM effective, the broader goalof the present study is to minimize the total thermal

Department of Mechanical and Aerospace Engineering, Case Western

Reserve University, Cleveland, OH, USA

Corresponding author:

Vikas Prakash, Department of Mechanical and Aerospace Engineering,

Case Western Reserve University, Cleveland, OH, USA.

Email: [email protected]

Journal of Composite Materials

47(1) 77–95

! The Author(s) 2012

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DOI: 10.1177/0021998312453750

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interface resistance across the TIM by reducing BLTand increasing kTIM, and at the same time minimizingthe interfacial contact resistances Rc1 and Rc2, at thebounding surfaces to the TIM.

To date, particle-laden polymers have been one ofthe most prominent TIMs used in the industry. Asdescribed by equation (1), the total thermal contactresistance for a typical TIM is not only dependent onits thermal conductivity but also on the BLT. In thisregard, Prasher2 introduced a rheology-based semi-empirical model for the prediction of BLT in particle-laden TIMs. The BLT was modeled to depend on theyield stress of the particle-laden polymer and theapplied normal pressure. The model was then combinedwith a thermal conductivity model to estimate the totalthermal resistance of the particle-laden polymer TIMsthat includes factors, such as, base polymer (matrix)viscosity, particle volume faction and shape, and parti-cle-matrix interfacial resistance, etc. The analysisshowed that there exists an optimal filler (particle)volume fraction at which the total thermal resistanceof the particle-laden TIM becomes a minimum.

Recent studies indicating relatively high intrinsicthermal conductivities in single-walled and multiwalledcarbon nanotubes (SWCNTs and MWCNTs) as well asother graphite materials3–11 suggest that nanostructuredmaterials and their combinations are promising candi-date materials for the development of high-performanceTIMs. For example, using effective medium theory(EMT)12,13 a factor of 500 enhancement in thermal con-ductivity was predicted when 10% randomly orientedMWCNTs (kCNT�3000W/m-K) were added to anepoxy (kmatrix� 0.2W/m-K). However, early attemptsof using CNT additives have yielded only modestincreases in the thermal conductivity of polymers com-pared to theoretical predictions. The use of randomlyorientated SWCNTs as filler materials in oil suspen-sions14 reportedly increased the effective thermal con-ductivity of nanotube-in-oil suspensions by 2.5 timesover that of the base fluid (matrix) with only 1%volume fraction of CNTs. Another study15 involvingrandomly orientated SWCNT in an epoxy matrixreported enhancements in thermal conductivity ofnearly twice the value of the epoxy, while the vapor-grown carbon-fiber (VGCF)-epoxy composites exhib-ited an enhancement of 45% in thermal conductivitywhen compared to neat epoxy for the same loading(1wt%). However, the maximum thermal conductivityachieved by randomly orientated CNT composites wasstill less than 1W/m-K. This surprisingly low value hasbeen attributed to several factors including (a) the sub-stantially weak thermal cross-linking between contact-ing nanotubes,16 (b) modification of phonon conductionwithin the individual nanotubes by the polymermatrix,17 (c) impurities and lattice defects within

individual nanotubes,18,19 and (d) formation of voidsin the CNT-polymer composites20,21 during compositeprocessing.

In recent years, vertically aligned multiwalled carbonnanotube (VA-MWCNT) arrays have generated muchinterest. By placing CNTs perpendicular to and span-ning the system components there are lesser number ofCNT/epoxy interfaces in the through-thickness direc-tion, thus minimizing the effective thermal interfacialresistance in the direction of heat flow. Indeed, thermaltransport in VA-MWCNT arrays22 has been observedto be highly anisotropic. The longitudinal diffusivityhas been reported to be 72 times that of the in-planevalue, signifying their importance as 1-D heat pipesbetween the two contacting surfaces. A similar study,but over a wider temperature range (180 K–300 K),21,23

reported thermal diffusivity measurements along theaxial (cross plane) direction in a VA-MWCNT array(20–50 nm diameter, 1.64mm long) to be 25 timeshigher than that in the in-plane direction. Choiet al.16 reported enhancements in thermal conductivityof SWCNT-epoxy composites of nearly 300% at 3wt%loading of randomly dispersed SWCNTs, and an add-itional 10% enhancement in thermal conductivity afterapplying a magnetic field during processing to improvenanotube alignment. The maximum room temperaturethermal conductivity obtained after magnetic alignmentduring processing was about 6.5W/m-K, which washigher than those reported in previous studies involvingaligned SWCNTs. These results indicate that verticallyaligned CNTs in isolation from each other are promis-ing candidate materials as TIMs.

With regard to VA-MWCNTs, Ivanov et al.22

reported a thermal conductivity of 5.5� 0.7W/m-Kfor an epoxy-infiltrated VA-MWCNT array(8� 1 vol%, 2mm long) and 6.4� 0.8W/m-K for thesame array in air. Borca-Tasciuc et al.21 reported a max-imum thermal conductivity of 3.8 W/m-K in a VAMWCNT-polymer composite along the alignment dir-ection at room temperature with 2% volume fraction ofMWCNTs. Xuejiao et al.24 and Tong et al.25 proposedthe use of vertically oriented CNTs on both the contact-ing surfaces of a typical material interface with a CNT-CNT interface in between. The thermal interface resist-ance of CNT-CNT interface was obtained by Hu et al.26

using diffraction limited infrared microscopy to bemuchlower than expectations at 3.8� 10�4K-m2/W. Xu andFisher27 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 theVA-MWCNT array yielded a lower thermal resistanceof 5.2� 10�6 km2/W. More recently, Cola et al.28 mea-sured the thermal resistance across (a) a Si-MWCNTs-Ag interface, wherein CNTs are grown on one of thebounding surfaces and (b) Si-CNT-CNT-Cu MWCNT

78 Journal of Composite Materials 47(1)



arrays. For the first interface, the total interfacial ther-mal resistance was found to be dominated by the thermalresistance at the CNT-Ag interface and was measured tobe 1.4� 10�5 km2/W, while the thermal resistance of thesecond configuration was dominated by the interfaceresistance between the tips of the mating CNT arraysand was measured to be an order of magnitude lowerat 2� 10�6 km2/W. A potentially promising variation ofthe two-sided CNT interface was the introduction of athin deformable foil at the interface formed by the nano-tube ends of the CNT-CNT arrays, such that the foilcould adjust to the deformation of CNTs with far fieldpressure. In this way, using a 10 mm thick Cu foil (withMWCNT on both sides) the thermal interfacial resist-ance of a rough Cu-Ag interface was observed to begreatly reduced.29

Recent works28,30 have explored through-thicknessthermal conductance in systems comprising of CNTson glass, copper, and silicon substrates. In these systems,it was hoped that the weld-contacts made via the catalystduring synthesis of vertical aligned MWCNT arrayswould be better than simple van der Waals type bonds.However, it was found that even in the best case scenariothe CNT-substrate contact resistance was still quitehigh. Tao et al.31 and Sihn et al.32 used a combinationof MWCNT array with thin gold and indium cappinglayers to improve the thermal conductance between theMWCNT array and the bounding surfaces. Thermalconductivity of the joint (device) was observed toincrease by more than 1–2 orders of magnitude com-pared to the absence of the capping layers.

Encouraged by these findings, in the present paperwe report the development of VA-MWCNT array com-posites for thermal management in load-bearing struc-tural applications. Unlike the majority of previousstudies on the use of VA-MWCNT-based thermalinterface materials for essentially non-load bearingthermal management applications, the TIMs of interesthere involve the use of VA-MWCNTs in an epoxymatrix. The epoxy matrix is expected to impart mech-anical strength to these systems while the VACNTsprovide avenues for high thru-thickness thermal con-ductivity across the material interface. In this regard,this paper builds upon previous work to characterizethe mechanical properties of these aligned MWCNTcomposites (up to 20 vol% CNTs),33–35 which showedpromise for use in multifunctional applications with afactor of three enhancements in elastic modulus at 17vol% CNTs. Furthermore, we introduce a transitionzone (TZ) comprising of a tin thin film at the interfacebetween 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 expectedto be governed by the interfacial thermal contact resist-ance between the bounding solids and the mating sur-faces of the Sn VA-MWCNT/epoxy layer. Theseinterfaces are generally neither fully conforming norsmooth, and thus may lead to a significant incrementin the total thermal contact resistance.

In particular, in the present study we obtain the ther-mal conductivity of the Sn-coated VA-MWCNT epoxycomposite (device) over a temperature range 240–300Kusing the three omega method. In order to estimate thethermal conductivity of the VA MWCNT epoxy com-posite as well as the thermal interfacial resistance at thevarious material interfaces in the cross-plane direction,we characterize the thermal conductivity in individualconstituents of the VA-MWCNT composite, namely (1)individual free-standing nanotubes selected from thesame VA-MWCNT array as that used in the fabrica-tion of the VA-MWCNT-epoxy composite; (2) theepoxy matrix; and (3) Sn thin films (capping layer) of�500 nm thickness. A 1-D multilayer thermal modelbased on Feldman’s notation36 is developed and usedin conjunction with the measurements to estimate thethermal conductivity of the CNT-epoxy composite aswell as the thermal interfacial resistance between thematerial layers.

The organization of the paper is as follows: First, abrief description on the processing of the VA-MWCNTcomposite samples is provide; this is followed by themethods employed in the characterization of thermaltransport in its individual constituents, and finally theresults and discussion of the study are presented.

Materials and methods

Sample processing

The VA-MWCNT arrays used (Figure 2(a) and (b)) inthe present investigation were procured from the

Solid 1

Solid 2

VA MWCNTs inan epoxy matrix

Low meltingpoint metalthin film

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.

Kaul et al. 79



laboratory of Prof Shanov at the University ofCincinnati. The CNT arrays were synthesized usingwater-assisted chemical vapor deposition (CVD).37–39

The nanotube diameter varied from 15 to 45 nm.The Epon 862 resin has been chosen due to its higher

working temperature which is important for aerospaceapplications and low viscosity so that it infiltratesthe array and provides sufficient adhesion with theembedded CNTs. Moreover, the resin is knownto impart good stiffness and toughness, as well asexcellent chemical, electrical and thermal resistance,making it a promising matrix for advanced multi-functional composites.40,41 For example, carbon-fillercomposites with EPON-862 as matrix41 have beenshown to exhibit enhanced flexural and compressionmodulus and strength and high glass-transitiontemperatures.

The epoxy-based CNT composites were fabricatedby immersing the MWCNT array into a solution ofEpon 862 epoxy, EPICURE curing agent W, and anacetone solvent. Prior to immersion of the VA-MWCNT array, the Epon 862 epoxy is ultrasonicatedfor approximately 8min. The solution is poured ontothe VA-MWCNT array and then spin-coated to allowthe epoxy to infiltrate the array. Degassing is performedunder high vacuum (30 in of Hg) to remove the bubblesgenerated during mixing. After casting the MWCNT/epoxy composite, both surfaces are cut and lapped. Thesurfaces are then sequentially polished at 100–150 rpmwith 15, 6, 1, and 0.1 mm diamond abrasives whileapplying a 5N constant force.

The sample, as observed under an environmentalSEM, mostly comprised of nanotubes having outerdiameters 35–45 nm with a number density of �109–1010 nanotubes/cm2. Using this information and bymeasuring the sample dimensions, the estimated aver-age volume fraction of CNTs in the composite is esti-mated to be approximately 8%. This value is also

supported by the weight measurements of VACNTarrays from the same batch in air using density of airof 1.2 kg/m3, and an average density of VACNT arraysamples of approximately 0.05 g/cm3. Moreover, theamount of polymer infiltration is estimated by compar-ing the measured density of a composite sample to thedensity predicted for the case in which the polymer hadfully infiltrated the space between the nanotubes. In thepresent study, polymer infiltration is estimated to be60–65% of the available spacing.

Atomic force microscopy (AFM) topology measure-ments (Figure 3(d)–(f)) indicate that the polishingprocess reduces the roughness of the samples fromnearly 1 mm to 100 nm or less. Following polishing,the samples are ethanol-washed and air-dried. TheMWCNT tips are exposed from the epoxy by reactiveion etching (RIE) using O2 plasma with 13.5MHz 125W RF power for 6–8min. Once the tips are exposed, athin layer of tin of thickness �500� 50 nm is depositedusing RF sputtering at 2� 10�7 Torr. Besides promot-ing the transport of phonons from the CNTs to the tinfilm, the relatively soft tin layer helps in reducing theroughness (and/or gaps) between the CNT tips and theSiO2 layer, thus reducing the thermal interface resist-ance at the CNT-SiO2 interface.

Thermal conductivity measurements in individualMWCNTs

In the present study, the thermal conductivity of indi-vidual MWCNTs is measured using a three-omega-based Wollaston T-Type probe inside a high-resolutionscanning electron microscope (SEM). Details of thetechnique and measurements are provided in Bifanoet al.42 Figure 4 depicts the Wollaston probe wire’stemperature profile (a) before the specimen is placedin contact and (b) following contact with the specimen.The drop in spatially averaged temperature causes a

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.




reduction in electrical resistance, and thus a measure-able voltage decrease. The thermal resistance of theprobe wire is then determined from the voltageresponse since the heating current amplitude is known.

In the method, the relationship between the probewire’s temperature and its electrical resistivity is firstcalibrated by measuring the electrical resistance versuspower input in the absence of the sample. Once the

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–1mm; (e) surface topology traced by AFM tip on composite sample after

polishing indicating roughness of the order �100 nm.

Kaul et al. 81



sample is attached to the probe/heater wire, the changein the measured electrical resistance versus power inputof the probe wire is correlated to the decrease in theprobe wire’s average temperature rise due to heat fluxinto the sample. Since the opposing ends of the sampleis maintained at the base (ambient) temperature, ineffect, the temperature drop and heat flux into thesample can be estimated, and the sample’s thermalresistance determined with sufficient accuracy.

Instead of DC Joule heating and voltage measure-ments, the probe wire is Joule-heated with a low fre-quency sinusoidal AC current, I(t)¼ I1osin(ot), whereI1o is the current amplitude. The initial electrical resist-ance of the probe wire is Reo. Joule heating at 2o, Q(t),drives in phase temperature oscillations, �yðtÞ, which areproportional to Q(t), by a thermal transfer function Zo.The 2o temperature oscillations create oscillations inelectrical resistance given by ReðtÞ ¼ Reo 1þ a�yðtÞ

� �,

where a is the measurable temperature coefficient ofresistance of the probe wire. Since the heating current

is I(t)¼ I1osin(ot), the voltage response of the probewireis expected to be a combination of both the 1o and 3ofrequency harmonics of the initial heating current and isgiven by,

VðtÞ ¼ IðtÞReðtÞ ¼ I1oReo þ3

4aZoR

2eoI

31o

� �sinot

�1

4aZoI

31oR

2eo

� �sin 3ot: ð2Þ

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

V3o,RMS ¼1

2aZoI1o,RMSReoQRMS, ð3Þ

where QRMS � I21o,RMSReo

If Re3o,RMS�V3o,RMS/I1o,RMS, Zo is determinedfrom the measured slope of dRe3o,RMS=dQRMS. The ther-mal resistance ratio of probe to the sample,Rth,P/Rth,S, isembedded inside the thermal transfer function Zo. Bymodeling the temperature response of the probe wireas a function of Rth,P/Rth,S, a theoretical value of Zo iscompared to the experimental value. Initial calibrationin the absence of the sample is used to first determineRth,P, and a subsequent measurement in the presence ofthe probe wire is used to determine Rth,S The samplesthermal conductivity is calculated by kS¼LS/Rth,S AS,where the sample cross-sectional area As and length Ls

are measured using the SEM beam.

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

In the present study, an approach similar to the differ-ential three-omega method43–45 was utilized to measurethe thermal conductivity of a �500 nm thick Sn film,bulk EPON-862 epoxy, and VA-MWCNT-epoxy com-posite samples. In general, the 3o method is performedon these samples by passing a current with angular fre-quency o through a heater/sensor microfabricated onthe sample surface, as shown in Figure 5(c) and (d). Thecurrent leads to Joule heating and thus a temperatureoscillation at a frequency 2o in the heater/sensor wire.Subsequently, the metal heater/sensor wire’s electricalresistance also oscillates at 2o causing a measureable3o voltage oscillation detected using a lock-in amplifier.The 3o voltage measurements are then used to deter-mine the sample’s thermal properties.46,47 The fre-quency range for the experiments is chosen byexamining the relationship between the film (sample)thickness, the thermal penetration depth of interest,

Figure 4. Schematic of the Wollaston probe wire. The probe

wire is Joule-heated with a power of QRMS, by the low frequency

current, I1o RMS. yA(x) is the temperature response of the probe

wire prior to making contact with the sample of unknown ther-

mal conductivity. Following contact with the sample, the tem-

perature response of the probe wire is yB(x). The measured third

harmonic voltage, V3o RMS, is a function of the probe wire’s

thermal resistance, zero current electrical resistance Reo, QRMS,

and the thermal resistance of the sample. The sample’s thermal

conductivity is determined by measuring the sample’s thermal

resistance and dimensions.




and the heater width. Large heater widths (when com-pared to sample thickness) produce a one-dimensionalheating profile, thereby providing information about thecross-plane thermal conductivity.

The main components for the 3o set-up (seeFigure 5(a)) used in the present work are (1) a cryostat(Janis Research Model: CCS-400H/204); (2) a tempera-ture controller that serves to regulate the sample tem-perature; and (3) a lock-in amplifier to detect the voltageresponse of the heater (Figure 5). The cryostat as shownin Figure 5(b) is capable of operating in the temperaturerange from 10K to 500K. An RV-8 rotary vane pumpcapable of developing a vacuum of 10�4 torr or less isutilized. A silicon shadowmask is batch fabricated usingthe conventional lithography technique. Using thismicrofabricated shadow mask an aluminum metalheater/sensor line is magnetron sputtered on the

sample surface. The temperature coefficient of resistanceof the heater/sensor line is measured prior to everyexperiment. The set-up has been automated usingLabVIEW 8.5. The bits of the multiplying DAC (AD7541 KN) are set ‘on’ and ‘off’ to balance the firstharmonic signals from the sample and reference resistor.Moreover, the LabVIEW program helps in balancingthe first harmonic voltage at the reference resistor andthe sample resistor to a greater degree of precision andsubsequently extract third harmonic voltage signals inorder to determine the temperature rise in the heater/sensor.

For electrically conductive samples, a thin insulatingfilm must be deposited prior to the metal line depositionto provide electrical isolation. In the present work,approximately 350 nm thick SiO2 films were depositedusing a low temperature plasma enhanced chemical

Figure 5. (a) Schematic of Cryostat Setup@ Nanomechanics Lab, Case Western; (b) microfabricated 25-mm wide heater with

250 mm� 250 mm 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).

Kaul et al. 83



vapor deposition (PECVD) process. The SiO2 layerserves as an insulator for all thin films and compositesamples evaluated in the present study. Moreover, in allcases, the same heater material (aluminum) and heaterdimensions (width) are used. In order to minimizeerrors due to various approximations of the exact ther-mal solution for the case of a thin film on a substrate, anumerical procedure in conjunction with the exact solu-tion, as described by Kim,48 Borca-Tasciuc et al.,43 andmore recently by Tong,45 is employed. The analysis ofthe three omega experiments was based on the work byCahill and Pohl49 and requires the assumption that theheater wire is of infinite length and that the sampledimensions be semi-infinite. Additionally, the methodrequires the heat penetration depth into the sample tobe greater than the heater width, thus satisfying theapproximation of an infinite line heat source.Additional details about the three omega techniquecan be found from various references43–49 and aretherefore not discussed in detail here.

In the present study, the aforementioned threeomega method was employed to investigate the thermalconductivity of a 3-mm thick epoxy (EPON-862)sample using the analytical solution discussed inCahill46 for a narrow line source on a semi-infinite sub-strate. On the other hand, the thermal conductivity of

�500 nm thin tin films was measured by comparing thetotal amplitude and phase signal of temperature oscil-lations with a theoretically obtained solution in the thinlayer limit using Tong’s45 two-layer model. For the caseof the VA-MWCNT composites, a three-layer modelbased on Feldman’s algorithm36 was derived and usedto interpret the experimental results.

Results and discussion

In the present study, we present results of thermal con-ductivity measurements in individual components ofthe VA MWCNT epoxy composites including individ-ual free-standing MWCNTs, epoxy matrix, and the tincapping layer. Wherever possible, the thermal measure-ments were performed at room and lower than roomtemperatures so as to investigate the effects of increasedphonon mean free path lengths on thermalconductivity.

Thermal conductivity in individual carbon nanotube

In the present study, thermal conductivity of individualMWCNTs taken from the same sample batch arrayUC01 are measured at room temperature. The averagethermal conductivity of an individual nanotube from

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).




the UC01 batch was found to be �60W/m-K based onthe slope change in measured third harmonic resistanceversus 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 conduct-ivity of individual multiwalled nanotubes from bothheat-treated and non-heat-treated sample groups,showing an approximate five-fold increase in thermalconductivity with heat treatment. Heat-treatment wasperformed at 3000�C for 20 h in an argon gas atmos-phere. Moreover, for one of the heat-treated samples,thermal conductivity as high as 730� 153W/m-K wasobtained.

Qualitative assessments of residual amorphouscarbon and defects were made by observing theRaman peak intensities of the D and G-bands. The Dband (defect band) is known to be activated by bothcarbonaceous impurities with sp3 bonding and frag-mented sp2 bonds,50,51 both being features ofMWCNT defects. The G band is activated by contigu-ous sp2 bonding, i.e., a high degree of crystallinity.50,51

Therefore, when comparing the two sample groups, asmaller D/G band ratio is representative of a samplewith fewer defects and a higher degree of graphitiza-tion. The authors have shown that significant increasein thermal conductivity had a strong correlation to thereduced D/G Raman peaks. The average Raman D/Gratio for heat-treated samples was 0.21� 0.04, while thenon-heat-treated group had an average D/G ratio equalto 0.69� 0.15. Note that the UC01 samples are notheat-treated and Raman scattering reveals a D/Gratio of 0.84 (Figure 6(b)). The reduced value of ther-mal conductivity measured in the UC01 sample correl-ates well with the non-heat-treated sample group withhigher D/G Raman ratios.

Thermal conductivity is undoubtedly expected toimprove with increased crystallinity and a decreaseddensity 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 temperaturesreduced the residual Fe catalyst (essential for CVDgrowth of MWCNT’s) from 7.1% by wt. to 0.1%.Moreover, it was reported that the temperatures ashigh as 3000�C healed the sidewall defects evidentfrom the reduced inter-layer spacing between graphemeshells confirmed by x-ray diffraction (XRD) and trans-mission electron microscope (TEM).

Thermal transport in 500 nm thick Sn thin film

In the present study, a TZ (capping layer) comprising ofa Sn thin film is introduced at the interface between theMWCNTs and the bounding surfaces to minimize scat-tering of the phonons at the interface due to mismatchin phonon spectra as well as thermal interface resistancedue to interfacial roughness including the effects not allCNTs making contact at the interface due to unequallength of CNTs. The Sn capping layer, with a relativelyhigh thermal conductivity and low yield strength (46W/m-K and melting point of 230�C), aids in filling thesurface asperities at the two mating surfaces, therebyreducing the interface thermal resistance between theCNT-epoxy composite and the bounding surfaces.Considering diffuse interfaces, even in the regionswhere the Sn layer wets the CNT tips completely (noair gaps), phonons from the CNT tips are expected tobe readily transferred to the Sn layer because of therelatively wide phonon spectrum available to the pho-nons in Sn when compared to the CNTs (phonon spec-tra in a material is proportional to the density of states,which is proportional to the inverse of the cube of thesound speed in the material). Additionally, the cappinglayer is kept relatively thin to help minimize the bound-ary layer thickness and hence its thermal resistance. Aspreviously mentioned, the top surface of the compositeis polished down to �100 nm, as verified by AFM.Therefore, a 500-nm thick tin layer should be sufficient

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.

Kaul et al. 85



to fill the asperities. The thin layer of tin is deposited onthe composite sample using sputtering. The sample isthen placed in a vacuum oven at near melting point oftin so that it forms a weld contact with the exposedCNT tips on the top surface. Recent work byPrasher53 has confirmed that the weld contact formedby Sn-like soft (and compliant) metals tend to increasethe thermal conductance by an order of magnitudecompared to more common Van der Waal contacts atthe interfaces.

In order to obtain the cross-plane thermal conduct-ivity of the Sn thin film specimens, the differential three-omega method was applied with the Sn thin film speci-mens deposited on a Si substrate. The Sn film isassumed to be thin enough such that one-dimensionalFourier conduction model can be applied for the ana-lysis and interpretation of the experimental data.Specific conditions that must hold to ensure accurateanalysis are given by df 4 2b� Lf, i.e., the thermalpenetration depth df must be greater than the heaterwidth and be much larger than the film thickness, Lf.For the experimental investigation discussed herein, thethermal penetration depth and the heater width aregreater by at least an order of magnitude of the filmthickness to ensure validity of these approximations.Additionally, the thickness of the underlying Si sub-strate Ls is taken to be such that the validity of theline source as well as the semi-infinite substrateapproximation holds. Figure 7 shows SEM pictures ofthe 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 wiredimensions, the thickness of the SiO2 insulating film,the thickness of the tin thin film specimen, and the Sisubstrate thickness.

From these experiments,54 the thermal conductivityof the 500� 50 nm tin film was determined to be46� 4W/m-K at room temperature. The thermal con-ductivity was found to remain nearly constant in thetemperature range of 240K–300K (Figure 8). This isunderstood to be due to the specific heat being constantin the temperature range with the Dulong-Petit limitbeing at 210K. Moreover, the phonon and electronmean free paths at room temperature are relativelysmall, 50 nm and <5 nm, respectively, compared tothe boundary dimensions.54 Therefore, boundary

scattering is not expected to play a role in the thermalconductivity of the sample. Furthermore, even thoughthe reduction in thermal conductivity in metals isknown to occur at elevated temperatures due to theincreased phonon-phonon inelastic scattering, the testtemperatures in our present case are not high enoughfor inelastic phonon-phonon (Umklapp) interactions tobe important, and thermal conduction continues to bedominated by the specific heat. The estimated thermalresistance of the Sn thin film over the measured tempera-ture range is nearly constant at 1.09� 10�8K-m2/W.

Thermal transport in epoxy polymer

The thermal conductivity of EPON-862 epoxy is alsomeasured using the three-omega method at tempera-tures in the range 100K to 340K (Figure 9). The mea-sured thermal conductivity of EPON-862 at roomtemperature is 0.224� 0.02W/m-K. The slight increasein thermal conductivity with temperature is understoodto be a result of the increase in specific heat with testtemperature. The thermal transport in amorphouspolymers (Reese55) is phonon-dominated with themean free path of phonons remaining a constant dueto scattering by the amorphous disordered regions. Forthe case of EPON-862, the phonon mean free path isestimated to be 0.32 nm based on the sound velocity(dilatational wave velocity) of 1949m/s (correspondingto the elastic modulus value of 2.58GPa41 andPoisson’s ratio of 0.35) and specific heat equal to1060 J/Kg-K.56 The glass transition temperature ofEPON-862 is 408K,41 and the thermal conductivity ofEpon-862 is expected to increase continuously until itreaches the transition point. A small jog in the tempera-ture dependence of thermal conductivity is observed ataround 225K, which is consistent with the observationsmade earlier in many polymers for specific heat depend-ency with temperature, and can be attributed to the

Figure 8. Thermal conductivity of 500 nm Sn thin film

(Replotted from Reference [54]).

Table 1. Experimental parameters for thin film measurement

Heater

width

Thickness

Penetration

depth (f¼ 10 Hz)

SiO2 film Sn film Si substrate SiO2 film Sn film

25mm 350 nm 500 nm 500mm 80mm 520mm




transition of the local amorphous regions withinthe polymer from glassy to the rubbery state. Therotational and vibrational motions of atomicgroups associated with the polymer chains in therubbery state require a lesser amount of energy forreorganization and mobility when compared to theglassy state.

Thermal transport in the vertically aligned MWCNT–epoxy composite

In order to characterize the thermal conductivity ofthe VA MWCNT-epoxy composite, the three-omegamethod outlined earlier is employed. A thin layer(�500 nm) of tin with a SiO2 insulating layer on topis deposited on the composite substrate (Figure 10) toprevent direct contact with the aluminum heater lineand contact pads. The estimation of both thermal con-ductivity and thermal interface resistance between thelayers is important to obtain the through-thicknessthermal conductivity of the VA MWCNT-epoxy com-posite. Tong in an earlier work45 derived a two-layermodel (based on Feldman’s notation36). A three-layer1-D model including the finite interface resistancebetween layers has been derived in this work(Figure 11).

The main steps of the 1-D thermal-model are pro-vided below. The heat equation for a 1-D multilayerproblem can be written as,

ky,j@2Tj ð y,tÞ

@y2¼ rjCpj

@Tj ð y,tÞ

@t, ð4Þ

where j¼ 1, 2 and 3 represent the individual layers(1¼ SiO2, 2¼ Sn, 3¼CNT-epoxy composite); Tj isthe temperature at a point yj in an individual layer;

and ky,j, rj and Cpj represent the through-thickness ther-mal conductivity, density, and the specific heat of theindividual layers.

Under periodic excitation with angular timefrequency, o, the general solution to equation (4) canbe expressed as

Tj ð yj,tÞ ¼ A eðZjyj�1otÞ þ B eð�Zjyj�iotÞ ð5Þ

where

Zj ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�iorjCpj

ky,j

s

is the inverse of the penetration depth. The two parts ofthe solution represent thermal waves propagating to thepositive and negative directions with two complex coef-ficients, A and B, to be determined by boundaryconditions.

Let us assume for this 1-D material, a periodic heatflux with amplitude q0 and frequency o is injected at thesurface y1¼ 0

q y1 ¼ 0,tð Þ ¼ q0e�iot: ð6Þ

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

Tj ð yj,tÞ ¼A eðZjyj�iotÞ

B eð�Zjyj�iotÞ

� �: ð7Þ

The matrix formulation aids in finding the correl-ation between the temperatures at two different loca-tions within the medium as well as that across theinterface between the layers. The boundary condition

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.

Kaul et al. 87



is based on the assumption that with no heat generatedor absorbed at the interfaces, the heat flux is continuousacross the interfaces, and there is discontinuity in tem-perature across a j and jþ1 interface due to a finiteinterface thermal resistance Rj,jþ1.

�ky,j@Tj

@yj

yj¼Lj

¼ �ky,jþ1@Tjþ1

@yjþ1

yjþ1¼0

¼ Rj,jþ1 Tjþ1 yjþ1 ¼ 0 �

� TJ yj ¼ Lj

� h i@T1

@y1

y1¼0

¼ 0;@T3

@y3

y3¼L3

¼ 0 ð8Þ

where Lj is the thickness of the jth layer.

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 multi-

walled 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 total thermal impedance Z of the three-layeredstructure neglecting the interface thermal resistance canbe obtained as

Z ¼T1ð0Þ

q0¼

1

g1

1þ g3g2Z2L2

� þ

g3g1þ

g2g1Z2L2

� Z1L1

1þ g3g2Z2L2

� Z1L1 þ

g3g1þ

g2g1Z2L2

� 24

35ð9Þ

where gj ¼ ky,jZj and q0 are the amplitude of the inputheat flux. Note that the exponential terms in the solu-tion above have been simplified using Taylor expansionassuming the films are very thin compared to the pene-tration depth. Since the SiO2 and Sn films deposited ontop of the composite are very thin (on the nanometerscale) compared to the penetration depth of heat, i.e.Z1L1

1, Z2L2

1 and Z3L3

� 1 for the range offrequencies used, makes this approximation valid.

Similarly, the total thermal impedance Z for thethree-layered structure with interface resistancesR1¼R1,2 (between SiO2 and Sn) and R2¼R2,3 (betweenSn and MWCNT) can be expressed as

Z¼1

g1

1þg3R1þg3R2

�þ g2R1þ

g3g2þg2g3R1R2

� �Z2L2

24

35

þg3g1þ

g2g1þg2g3g1

Z2L2

� �Z2L2

� �Z1L1

0BBBB@

1CCCCA

1þg3R1þg3R2

�þ g2R1þ

g3g2þg2g3R1R2

� �Z2L2

24

35Z1L1

þg3g1þ

g2g1þg2g3g1

R2

� �Z2L2

� �Z1L1

0BBBB@

1CCCCA

26666666666666664

37777777777777775ð10Þ

The model is verified by comparing them with theresults obtained for the two-layer model as describedby Tong.45 Moreover, using the condition, g3 ¼ 0 in

the absence of a third layer, and Z2L2

� 1, suchthat, the heat wave dies down within the secondlayer (that now acts as a substrate), we get the sameresult as in Tong et al.,45 i.e.

Z ¼1

g2þ R1 þ

L1

k11�

g21g22�2g21g2

R1 � g21R21

� �: ð11Þ

The experimental data on temperature oscillationsand phase are compared with the predictions of the ther-mal model with and without thermal interface resistancebetween the layers. The thermal model is based on sev-eral parameters (shown in Table 2), e.g., thermal proper-ties of the various layers, and the unknown thermalinterface resistances. An iterative algorithm, asdescribed in Tong et al.,31 was employed to obtain thebest fit values for the unknowns. The comparison of theexperimental results and model predictions based on thebest fit values for the unknown parameters is shown inFigure 12. From these comparisons, the thermal con-ductivity of the CNT-epoxy composite is estimated tobe 5.8� 0.64W/m-K at room temperature. The mea-sured amplitude as well as the phase of the temperatureoscillations are found to be sensitive to the thermal con-ductivities of tin, MWCNT-epoxy composite, and thethermal interface resistances. A �20% uncertainty inthermal conductivity of either tin or the MWCNT-epoxy composite results in a corresponding �5–10%shift in the amplitude of the temperature oscillationsfrom the measured values. The thermal conductivity ofthe composite exhibits a slight increase with temperaturebetween 240K and 300K (Figure 13) and is understoodto be dominated by the specific heat dependence withtemperature of the Epon-862 epoxy.9,57

The best fit estimates for the interface thermalresistances R1-2 (between SiO2 and Sn) and R2-3

(between Sn and MWCNT) are 5� 10�5m2-K/W and8� 10�6� 8.5� 10�7m2-K/W, respectively. The ampli-tude or phase of temperature oscillations is especially

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.

Kaul et al. 89



sensitive to the thermal resistance of the rougher inter-face, i.e. the SiO2–Sn interface. However, it is relativelyless sensitive to the interface thermal resistance of therelatively smooth Sn-MWCNT interface, and thereforeby keeping all other parameters constant we canestimate the interface resistance of the smoothSn-MWCNT interface to within an order of magnituderange. The interface resistance between the layers is acombination of Kapitza resistance based on diffuse mis-match model (DMM) and constriction resistance at thecontacts of CNTs with the Sn layer. Recently,Prasher58,59 suggested that for nanosized constrictions(which the vertically aligned MWCNTs make with thelayer above it), the effects of mismatch in acoustic prop-erties are more dominant than due to constriction ofthe heat flux lines. Therefore, vibrational spectra mis-match between Sn, a soft metal with relatively low

sound speed, and VA MWCNTs is expected to restrictthe thermal conductance through the MWCNT com-posite. The Debye temperature of Sn is 170K, while theDebye temperature for multi-MWCNTs is muchhigher, 960–2500K, indicating a large mismatch invibrational spectra of the two materials. Interface ther-mal resistance between two highly dissimilar materialswith large differences in phonon spectra, e.g., interfacesinvolving metal and dielectric solids, as pointed out byLyeo and Cahill60 is not only due to the coupling ofelectrons in a metal and phonons in a dielectric sub-strate but also by anharmonic processes (namely three-phonon processes) that can contribute a significantadditional channel for transport of heat by altering(increasing) the phonon frequency by inelastic scatter-ing processes. These higher frequency phonons areexpected to be readily accommodated by the muchbroader phonon spectra available for Sn. For these rea-sons, CNTs may be particularly attractive for exchangeof thermal energy with Sn across the CNT-Sn interfacesinvolving both phonons and electrons.

Interestingly, even after a spate of research on VAMWCNT composites, there are only few publishedworks in the literature that reported thermal conductiv-ities greater than 1W/m-K (Figure 14). Sihn et al.32

have reported the highest thermal conductivity so farfor a 30 mm VA MWCNT-epoxy composite. Using asimple 1-D thermal resistance network model, we esti-mate the room temperature thermal conductivity oftheir VA MWCNT-epoxy composite to be 137W/m-K. Considering a 10 vol % of MWCNTs in their com-posite, the thermal conductivity of individualMWCNTs is estimated to be in excess of 1000W/m-K.

The primary reasons for a less than 1W/m-K ther-mal conductivity of the MWCNT polymer compositesreported in the literature may be due to the low volume

Figure 12. Comparison of thermal model with and without interface resistances with experimental data: (a) temperature oscilla-

tions 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.




fraction of CNTs used in the composites as well as theirdefect state and purity. In a parallel study,42 theauthors investigated thermal conductivity in annealedand as-received thermal CVD grown individual multi-MWCNTs. They reported a five-fold increase in ther-mal conductivity of the MWCNTs from the annealedbatch (Figure 15), conforming that the defect state ofthe CNTs play an important role in controlling thethermal conductivity in individual CNTs. In addition,high-resolution SEM micrographs of CNT arrays(Figure 16) from the same batch as the array that wasused in the fabrication of the composite indicate physicaldeformities, including entanglement of CNTs and fusedcontacts, that are understood to be the reason forreduced thermal conductivity of the composites. Thesecontact regions between nanotubes occur even in thebest-aligned CNT films and serve as scattering sites forphonons propagating along contacting nanotubes. Infact Prasher et al.61 have shown that the thermal con-ductivity of a randomly oriented bed of MWCNTs isprimarily controlled by the CNT-CNT thermal contactresistance, which is an order of magnitude larger thanthe intrinsic thermal resistance of a CNT.

Another reason for the relatively low thermalconductivity of the individual CNTs may be becausethe phonon modes within CNTs can be damped andscattered by the polymer matrix reducing the thermalconductivity of the CNTs themselves. Indeed, Gojnyet al.17 have shown that damping of phonon modeswithin the outer shells of the nanotube may be a pos-sible reason for the reduction of the thermal conduct-ivity of the nanotubes.

Additionally, in order to improve their performanceas TIM, thermal conductance at CNT-capping layerinterfaces need to be addressed. One of the main advan-tages of the composites studied in this work is thatCNTs themselves are well aligned and span the entirethickness of the polymer in the axial direction, provid-ing direct pathways for heat transport across the com-posite. However, if some CNTs fail to extend to thesurface of the polymer, the CNT-polymer thermalboundary resistance can negatively impact the axialconduction. In this regard, in the present study we ini-tially start with a polished CNT-polymer surface andthen plasma-etch it to expose the CNT tips on the sur-face. 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 thermalinterface resistance for such relatively smooth CNT-metal interfaces may contribute to only second-ordereffects in the thermal performance of the TIMs atroom temperature.

It is to be noted that most previous works reportedin the literature on VA-MWCNT-polymer compos-ites21,22,32,62 show room-temperature thermal conduct-ivity as high as metal nanowire array-polymercomposites63,64 and the semiconductor nanowirearray-polymer composites65,66 with nanowire volumefractions in the same range as the CNTs.Nevertheless, the five-fold increase in thermal conduct-ivity in the post-annealed MWCNTs suggests that thethermal conductivity of VA-MWCNT-epoxy compos-ites can be designed to be as high as 25 W/m-K, whichcan potentially have a major impact in the design of

Figure 14. Thermal conductivity vs volume fraction of nanowires and nanotubes.

Kaul et al. 91



multifunctional, load-bearing, high-thermal perform-ance structural interfaces for a variety of thermal-management applications.

Summary

This paper reports development of VA-MWCNT arraycomposites for thermal energy management in load-bearing structural applications. Unlike previous studieson the characterization of VA-MWCNT-based TIMsfor primarily non-load bearing applications,

the material systems of interest here involve the use ofVA MWCNTs in an epoxy matrix. The epoxy matriximparts mechanical strength to these systems while theVACNTs provide avenues for high through-thicknessthermal conductivity across a typical material interface.In order to obtain the thermal characteristics of thesemultifunctional TIMs, we report measurements of ther-mal conductivity in the Sn-capped VA-MWCNT-epoxycomposites as well as in its individual constituents, i.e.,bulk EPON-862 (matrix material) and Sn thin film, inthe temperature range 240K to 300K, and individual

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).




multiwall CNTs at room temperature taken from thesame VA-MWCNT batch as the one used to fabricatethe CNT-epoxy TIM. The thermal conductivity of theepoxy and Sn thin film was obtained as a function oftemperature by using a cryostat in conjunction with thethree-omega method. The thermal conductivity of indi-vidual free-standing MWCNT samples was obtained byemploying the Wollaston T-type three-omega probemethod inside a high-resolution SEM equipped withnanomanipulators and a gas injection system for elec-tron beam-induced platinum deposition. The thermalconductivity of bulk EPON-862 epoxy was observedto increase gradually from 0.1W/m-K at 100K to0.24W/m-K at 340K and is understood to be domi-nated by the heat capacity of the epoxy. The thermalconductivity of Sn capping layer (500 micron film thick-ness) was observed to remain nearly constant at about46W/m-K over the above-mentioned temperaturerange. The thermal conductivity of individual free-standing CNTs was measured to be about 60W/m-Kat room temperature. A 1-D multilayer thermal modelthat includes effects of thermal interface resistance andthe thermal conductivity of the CNT-epoxy compositeand its constituents was used to interpret the experi-mental results. The thermal conductivity of the CNT-epoxy composite was estimated to be about 5.8W/m-Kand exhibits a slight increase with temperature in therange of 240K to 300K. The best fit estimates for theinterface thermal resistances between SiO2 and Sn andbetween Sn and MWCNT were 5� 10�5m2-K/W and8� 10�6� 8.5� 10�7m2-K/W, respectively. The resultsof this study suggest that the inclusion of an Sn thinlayer on the VA-MWCNT array as well as the morpho-logical structure of the individual MWCNTs are dom-inating factors that control the overall thermalconductivity of the TIM. These results are encouragingin light of the fact that the thermal conductivity of aVA-MWCNT array can be increased by an order ofmagnitude by using a standard high-temperaturepost-annealing step. In this way, multifunctional (loadbearing) TIMs with effective through-thickness thermalconductivities as high as 25W/m-K can be potentiallyfabricated.

Funding

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

Acknowledgments

The authors would like to acknowledge the support of the AirForce Office of Scientific Research (AFOSR) grant FA9550-08-1-0372 (Program manager Dr. Byung-Lip Lee) and theNational Science Foundation Major Research

Instrumentation grants CMMI-0521364 and CMMI-0922968 to Vikas Prakash.

Conflict of interest

None declared.

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Journal of Composite Materials - Case School of Engineering...reported enhancements in thermal conductivity of nearly twice the value of the epoxy, while the vapor-grown carbon-ﬁber

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