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Wonchang Park

Kyungwho Choi

Department of Mechanical Engineering,

Texas A&M University,

College Station, TX 77843

Khalid LafdiCarbon Research Laboratory,

University of Dayton,

Dayton, OH 45469

Choongho Yu1

Department of Mechanical Engineering,

Texas A&M Universiity,

College Station, TX 77843;

Materials Science and Engineering

Interdisciplinary Program,

Texas A&M University,

College Station, TX 77843

e-mail: [email protected]

Influence of Nanomaterials inPolymer Composites on ThermalConductivity

Carbon nanotube- or/and graphite-filled polymer composites were synthesized by usingsimple mixing and drying methods, and their thermal conductivities and structures werecharacterized by using a steady-state method (ASTM D5470) and scanning and transmis-sion electron microscopies. In order to investigate the influence of synthesis conditionson the thermal conductivity of composites, various concentrations of multiwall carbonnanotubes, graphites, surfactants, and polymer matrix materials as well as two differentnanoparticles and solvents were tested. Our composites containing both nanotubes(25 wt. %) and graphites (25 wt. %) with sodium dodecyl benzene sulfonate (SDBS) as adispersant showed the highest thermal conductivity, $1.8 W/m-K at room temperature.The highest conductivity from nanotube/graphite mixtures would be from good adhesionand less voids between nanotubes and polymers as well as excellent thermal conductionfrom graphite sheets. The thermal conductivities of the composites have been calculatedas a function of carbon nanotube concentrations by using a model based on the Max-wells effective medium theory, and the most effective method of improving thermal con-ductivity was suggested. [DOI: 10.1115/1.4005201]

Keywords: thermal interface material, carbon nanotube, graphite, effective mediumtheory

1 Introduction

Heat dissipation in electronic devices becomes very importantbecause the power density of the state-of-the-art electronic devi-ces is extremely high due to their highly integrated circuits andsmall sizes. Effective heat dissipation is also crucial in maintain-ing the performance of electronic devices [1]. One of the mostlimiting factors in heat dissipation is thermal contact resistancebetween different parts. In order to reduce the contact resistance,various materials have been synthesized and tested for a widevariety of applications including microprocessors, optoelectronics,and power electronics [24]. These are typically called thermalinterface materials (TIMs) [3,5,6].

The thermal contact resistance is mainly from the surface asper-ity that prohibits a full contact, which leaves voids betweenobjects in contact. The actual contact area is often only a fractionof apparent contact areas [3]. The void is typically filled with airor vacuum whose thermal conductivity is significantly lower thanthose of solid materials. In general, polymeric materials are flexi-ble, and thereby suitable for filling highly irregular spacesbetween surfaces. However, typical polymers have very low ther-mal conductivity ($0.2W/m-K [79]), which has been one of thekey parameters in the efforts for improving the performance ofTIMs [912]. In order to improve the thermal conductivity, carbonnanotubes (CNTs), and graphites have been used because of their

high thermal conductivities. The thermal conductivities ofan individual nanotube and graphite (in-plane) can reach over103 W/m-K at room temperature [1315]. For example, verticallyaligned nanotube arrays without using a polymer matrix havebeen synthesized for TIM [11] but they are often inadequate toaccommodate highly irregular surfaces for increasing actual con-tact areas. It is also necessary to use a high temperature synthesisprocess, prohibiting a direct integration on heat dissipating

devices or structures. These drawbacks could be alleviated bysynthesizing free-standing polymer composites made of combin-ing polymers, nanotubes, and graphites.

Polymer composites with nanomaterials can be synthesized bysolution mixing, melt blending, and polymerization [16]. Hu et al.made composites by mixing Ni metal particles and multiwallcarbon nanotubes (MWCNTs) in silicone oil [9]. They found thatthe thermal conductivity of the composites with a large amount ofNi particles (3040 vol. %, $13.5lm in diameter) and 23 vol. %

of MWCNTs enhanced thermal conductivity. However, a highconcentration of Ni particles often makes it difficult to form asolid material with good adhesion and strength. Huang et al. [17]synthesized CNT-polymer composites by injecting polymers intoaligned nanotube arrays. Their thermal conductivities wereimproved due to aligned CNTs perpendicular to the substrate. Thethermal conductivity was increased from 0.56 W/m-K up to1.21 W/m-K. The alignment process is complicated, but yieldedonly marginal conductivity increments. Moreover, high process-ing temperatures of the chemical vapor deposition for the directdeposition of nanotubes on a substrate can damage devices/partssuch as electronic chips and heat sinks. On the other hand, graph-ite additives have resulted in better thermal conductivity than car-bon nanotubes [8,12]. The higher conductivity may be from theexcellent conduction along the in-plane direction of graphite

sheets whose lengths are much longer than those of nanotubes.However, the sheet structure often causes void formations andpoor mechanical strength, which generally require high pressurepressing or high temperature curing steps. These limitations arenot desirable for TIM applications [18].

This work presents simple fabrication methods and thermalconductivities of nanotube- or/and graphite-filled polymer compo-sites. Both nanotubes and graphites were also mixed together inorder to seek synergistic effects from two dissimilar shape materi-als. In addition, metallic nanoparticles were incorporated intonanotubes to study the influence of the nanoparticles on thermaltransport behaviors. Two different polymer matrix materials, Vin-napas 401 and Epon 862 were used in this study. In these compo-sites, nanotube/graphite dispersion is crucial in obtaining good

1Corresponding author.Contributed by the Heat Transfer Division of ASME for publication in the

JOURNAL OF HEAT TRANSFER. Manuscript received July 22, 2010; final manuscriptreceived September 27, 2011; published online February 13, 2012. Assoc. Editor:Pamela M. Norris.

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thermal and mechanical properties of composites. For better disper-sion of nanotubes/graphites in water, sodium dodecyl sulfate (SDS,or sodium lauryl sulfate), or sodium dodecyl benzene sulfonate(SDBS) was employed as a stabilizer [19]. The influence of the sur-factant on thermal conductivity was also investigated by stabilizingnanotubes/graphites in dimethylformamide (DMF) or 1-methyl-2-pyrrolidinone (NMP) without using SDS or SDBS. Samples weresimply dried at room temperature or relatively low temperature($80 C) without applying any external pressure. Our experimen-tal results show that composites containing nanotube/graphite mix-

tures dispersed with SDBS have the highest thermal conductivity($1.85W/m-K at room temperature). The mixture provides betterstructural integrity from good adhesion between nanotubes andpolymers as well as higher thermal conduction from graphites. Inaddition, nanotubes fill voids between graphites, making compositesless porous. The optimum ratio between nanotubes and graphiteswas also studied in this work. The following describe the detailprocedures of sample preparation and characterization as well as theanalyses of thermal conductivity measurement results.

2 Experimental Procedures

Total 20 different composites were synthesized with MWCNTs,exfoliated graphites, metal nanoparticles, and polymer matrixmaterials, as listed in Table 1. Vinnapas 401 (Wacker chemical)consists of a vinyl acetateethylene copolymer emulsion [7,20]and Epon 862 (Miller Stephenson chemical) diglycidyl ether ofBisphenol F) [21]. The samples made of Vinnapas is flexible dueto a low glass transition temperature as opposed to stiff Epon sam-ples. A typical synthesis process with a surfactant and MWCNT/graphite is the following. MWCNTs (Cheaptubes, 95%), exfoli-ated graphites [8], SDS (Fisher scientific), and SDBS (Acrosorganics, 88%) with the weight ratios in Table 1 were mixed withdeionized (DI) water of 1520 ml. The total weights of the nano-tubes/graphites and surfactants ranged from 0.06 to 0.375 g. Theconcentrations of MWCNTs were varied from 10 wt. % to 40 wt. %except the metal-decorated nanotubes, and the concentrations ofgraphites from 10 wt. % to 80 wt. %. The weight ratio of conductivefillers to surfactants was selected from 3:1, 2:1, and 1:1 except themetal-decorated nanotubes. It should be noted that SDS and SDBS

are necessary to effectively disperse/stabilize nanotubes in water[7,19,20,22,23]. The mixture was sonicated with an ultrasonic ho-mogenizer (Misonix XL-2000) for 2030 min until nanotubes/graphites were well dispersed in water. Water was added to themixture during the sonication for better dispersion. At the end ofthe sonication, the total volume of solidliquid mixtures was$40 ml. Then, the polymer matrix material, Vinnapas 401 or Epon862 was added to the solution followed by another sonication pro-cess for 2$ 3 minutes. The weight of the polymers ranged from0.08 to 0.4 g. The mixture thickened by the sonication was poured

into a plastic container (5.4 cm 5.4 cm 1.7 cm). Subsequently,the mixture was dried in a fume hood at room temperature for 23days. Finally, the composite was completely dried in an oven at80 C for$ 1 h in order to remove residual water.

For decorating metals on MWCNT surfaces, nanotubes wererefluxed in 70% nitric acid with stirring for 20 h at the boilingtemperature. The solution was diluted with DI water and subse-quently filtered with polytetrafluoroethylene (PTFE) membranes(pore diameter:$ 0.45lm). The nanotubes were thoroughlywashed with DI water and dried in a fume hood for 2 days atroom temperature. The acid treated nanotubes (0.15 g) were dis-persed in 100 ml of DMF (Fisher scientific, 99.9%) at 60 C bystirring. After 30 min, 100 ml of 0.02 M iron nitrate (Acros organ-ics, 99%) in water was added into the mixture of nanotube andDMF. The solution was stirred for 16 h at 60 C. Finally, the nano-tubes were filtered and washed with DI water, and then fully dried

at room temperature in a fume hood for 23 days. In order to dec-orate nickel particles on nanotubes, hydrogen reduction was used[24,25]. First, 0.1 g of acid treated nanotubes was mixed with100 ml of 0.05 M nickel nitrate (Fisher scientific, 99.0%) inwater. The mixture was sonicated in an ultrasonic bath (Branson1510 R-MT) for$5 min and then stirred at room temperature for20 h. The mixture was filtered and dried at $120C on a hot plateuntil the tubes were completely dried. The nanotubes were thenannealed at 450 C for 2h with a 4 C/min ramping rate in 2030sccm Ar in a tube furnace of 23-mm inside diameter. Subsequently,temperature was raised to 500 C and the sample was reduced with2030 sccm H2 gas for 3 h. Polymer composites with iron- or nickel-incorporated nanotubes were synthesized by using the methoddescribed above. Due to the high density of the metals compared to

Table 1 The concentrations of filler, surfactant, and matrix materials, and the thicknesses of polymer composites

Filler (wt. %)

Graphite MWCNTs Surfactant (wt. %) Polymer Matrix (wt. %) Thickness (lm)

1 15 SDS 5 Vinnapas 401 80 109.36 2.32 15 SDBS 5 Vinnapas 401 80 122.26 5.03 30 SDS 10 Vinnapas 401 60 126.26 2.24 27.2 (Fe: 12.9)

[CNT: 9.3 vol. %(Fe: 2.2 vol. %)]

SDBS 36.4[46.8 vol. %]

Vinnapas 401 36.4[41.7 vol. %]

68.56 1.2

5 41 (Ni: 20.5)[CNT: 15.3 vol. %

(Ni: 3.6 vol. %)]

SDS 20.5%[30.3 vol. %]

Vinnapas 401 38.5[50.7 vol. %]

94.36 16.2

6 30 SDBS 30 Vinnapas 401 40 72.46 8.0

7 50 SDBS 25 Vinnapas 401 25 176.86 9.08 60 SDBS 20 Vinnapas 401 20 221.96 6.99 40 10 SDBS 25 Vinnapas 401 25 158.46 7.110 25 25 SDBS 25 Vinnapas 401 25 250.46 5.111 10 40 SDBS 25 Vinnapas 401 25 1556 3.412 60 DMF Vinnapas 401 40 46.66 1.713 30 30 DMF Vinnapas 401 40 194.66 15.814 80 DMF Vinnapas 401 20 615.56 2.515 40 40 DMF Vinnapas 401 20 216.26 4.616 80 NMP Vinnapas 401 20 192.76 5.017 64 16 NMP Vinnapas 401 20 304.56 0.518 40 40 NMP Vinnapas 401 20 441.46 18.919 50 - SDBS 25 EPON 862 25 285.76 5.320 25 25 SDBS 25 EPON 862 25 76.66 2.7

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other carbon-based materials, the volume fractions were also listed inTable 1. Note that the densities of nickel and iron are, respectively,8.908 and 7.874g/cm3 [26].

Composites were also synthesized without using any surfactant.This requires solvents such as DMF or NMP (Alfa aesar, 99%)for better nanotube and/or graphite dispersion [27]. MWCNTs(0.060.112 g) were sonicated in the solvent (5 ml) with a pentype sonicator until they were well dispersed. Subsequently, Vin-napas or Epon was added and then sonicated for additional10 min. Samples were dried at 50 C for$ 4 h in a vacuum (better

than 1Torr).The structure of the samples was analyzed with scanning elec-tron micrographs (SEMs, taken by using JEOL JSM-7500 F) afterthe samples were cold-fractured in liquid nitrogen to expose theircross sections. The cross-sectional surfaces were highly unevendue to many graphite particles pulled out from the compositesbecause the sample was too flexible to easily fracture the sample(The samples were rather torn apart). Transmission electronmicrographs (TEMs, taken by using JEOL 1200 EX) were alsotaken to inspect the morphology of metal particle-decorated nano-tubes. The nickel-decorated nanotubes were also scanned in anX-ray diffractometer (Bruker-AXS D8 VARIO). Thermal conduc-tivities were obtained by using a steady-state measurement(ASTM D5470) setup. The thickness measurements were per-formed at ten different locations for each sample. The largesterrors came from the variation of the thickness, and uncertainty

analyses were performed with 95% confidence.

3 Results and Discussion

The thermal conductivity of the nanocomposite is expected tobe increased as a function of MWCNT/graphite concentrationssince polymers such as Vinnapas 401 typically have relativelylow thermal conductivity ($ 0.2W/m-K) [7,20,22,23]. The poly-mers are necessary to bind the fillers, providing enhanced me-chanical strength and thermal conduction. However, the sampleswith moderate filler ratios only showed conductivities close tothose of polymers. For example, the thermal conductivities of15-wt. % MWCNT composites were measured to be$ 0.2W/m-Kat room temperature (sample 1 and 2; see Fig. 1). This is some-what surprising because the thermal conductivity of an individual

MWCNT was reported to be$ 3000 W/m-K at room temperature[14]. For instance, when a nanotube concentration is$ 10 vol. %,the thermal conductivity of a composite is estimated to be

$102 W/m-K using a parallel resistor model [7]. This implies thatphonons do not effectively travel through junctions between thenanotubes as well as across the nanotubes and polymer matrixmaterials [7,20,23]. The surfactants, SDS and SDBS, which arenecessary for dispersing nanotubes in water, did not make signifi-cant differences (samples 1 and 2). SDBS is similar to SDS, buthas an additional benzene ring that may slightly reduce conductiv-ity. An increase of the MWCNT concentration to 30 wt. % (sam-ple 3) doubled thermal conductivity ($0.4 W/m-K), but theconductivity is still much lower than expected values. The current

recipe, however, was not adequate to synthesize samples with ananotube concentration higher than 30 wt. % when graphites werenot added. Samples with higher nanotube concentrations werecracked into pieces during the drying process. Strongly bundledand/or aggregated nanotubes are likely to inhibit nanotube-network structures that are necessary to form composites.

We have explored the influence of the metal nanoparticles onthe thermal conductivity of the composites. Iron particles are afew nanometers in size, much smaller than nickel particles whoseparticles range from several to tens of nanometers, as shown inFig. 2. The particles in samples 4 and 5 were identified as iron andnickel, respectively, by using energy dispersive spectroscopy. TheX-ray diffraction result shown in the inset of Fig. 1 confirmed thepresence of nickel. Iron was not identified by the X-ray diffrac-tion. We believe this is because of small particle quantity or/andamorphous structures. The conductivities of the composites are

more or less similar to those of other samples without nanopar-ticles. Nevertheless, the iron-incorporated sample (sample 4)shows a higher conductivity compared to the nickel sample (sam-ple 5). The thermal conductivities of nickel and iron are, respec-tively, 90.9 and 80.4 W/m-K at 300 K [26]. The relatively highconductivities of the metals compared to polymers ($0.2 W/m-K)may enhance the overall conductivity of composites. Neverthe-less, our results indicate that the metal incorporation does not con-siderably change the conductivity. The density of metal particlesis very different from those of nanotubes and polymers, whichmay impede phonon transport due to their mass differences. Inaddition, the metal decoration makes nanotubes aggregated duringthe composite synthesis process, which is likely to reduce thermalconductivity significantly.

When graphites were used instead of nanotubes, high graphite

loadings up to 80 wt. % were possible. Such high loadings werefeasible when DMF or NMP was used instead of SDS or SDBS.The DMF and NMP solvents were removed by the drying process,

Fig. 1 The thermal conductivities of samples 18 at room temperature. MW, Vin,and Gra represent MWCNT, Vinnapas 401, and graphite, respectively. The insetshows X-ray diffraction of nickel-decorated nanotubes.

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but SDS and SDBS cannot be eliminated from the composites.The composite with 30-wt. % graphite (sample 6) exhibits higherconductivity than those of the nanotube-filled samples. As graph-ite concentrations were increased to 50 wt. % (sample 7) and60 wt. % (sample 8), the thermal conductivity was raised to$ 0.84and $1.1W/m-K, respectively. The improved conductivity islikely to come from less thermally resistive paths along graphitesheets than those across tubetube junctions in the nanotube-filledcomposites. Nevertheless, thermal transport across contactsbetween the sheets is still not good enough to obtain a graphite-like conductivity.

While the polymer matrix can accommodate high-concentrationgraphites, their anisotropic thermal conductivities (in- and out-of-plane directions) are disadvantageous. When graphite sheets arestacked together, the conduction along the direction perpendicularto the graphite plane is limited. In addition, their sheet structurestend to make voids between the sheets, making composites po-rous. These could be at least partially overcome by introducingsmaller particles such as MWCNTs. Nanotubes may thermallybridge graphite sheets and fill the voids. In this study, MWCNTswere mixed together with three different weight ratios ofMWCNTs to graphite (4:1, 1:1, and 1:4). Figure 3 shows thereplacement of graphites with MWCNTs increases thermal con-ductivity, reaching $1.5W/m-K with 25-wt. % graphites and

25-wt. % nanotubes (sample 10). However, excess MWCNTssuch as 10-wt. % graphites and 40-wt. % nanotubes (sample 11)decreased thermal conductivity. Figures 4(a) and 4(b), respec-

tively, show the fractured cross-sections of the composites withand without nanotubes. Graphite sheets are relatively loose fromthe polymer matrix in the graphite only sample (sample 7, Fig.4(a)) compared to sample 10 (Fig. 4(b)) that contains both graph-ites and nanotubes. The inset of Fig. 4(b) also shows nanotubesbridged between graphite sheets.

These samples contain a surfactant such as SDBS or SDS thatis necessary for dispersing graphites and nanotubes in water. Thesurfactants do not have high conductivities close to those ofgraphites and nanotubes. In addition, they typically wrap around

the conductive fillers, preventing direct contacts between them.The different vibration spectra between the fillers and surfactantsmay also hamper phonon transport. In order to avoid any adverseinfluence from the surfactants, solvents (DMF and NMP) wereused for the dispersion without adding any additional surfactants.When Vinnapas with DMF was used instead of 20-wt. % SDBS insample 8, the conductivity was decreased to $0.85 W/m-K (60 wt.% graphite; sample 12) compared to sample 8 ($1.1 W/m-K), asshown in Fig. 5. Replacing 30-wt. % graphites with nanotubes(sample 13) showed a similar conductivity. The composites madeof 80-wt. % graphites (sample 14) or a mixture of 40-wt. % graph-ites and 40-wt. % nanotubes (sample 15) exhibited similar con-ductivities in comparison to the composite made of 60-wt. %graphites dispersed by 20-wt. % SDBS (sample 8). On the otherhand, the conductivity was raised when NMP was used instead of

DMF (samples 17 and 18), as shown in Fig. 5. The mixture ofgraphites and nanotubes (40 wt. % each; 80 wt. % total conductivefillers) improved conductivity from $1.1W/m-K (sample 16) to$1.7 W/m-K (sample 18). The thermal conductivity difference

Fig. 3 Room temperature thermal conductivities (samples 7and 911) as a function of four different weight ratios (1:0, 4:1,1:1, and 1:4) of graphites to MWCNTs. The composites containtotal 50-wt. % fillers and 25-wt. % surfactant.

Fig. 4 The cold-fractured cross-sectional surfaces of (a) sam-

ple 7 (50-wt. % graphites) and (b) sample 10 (25-wt. % graphitesand 25-wt. % MWCNTs). The inset show a nanotube bundlebetween graphite sheets. Scale bars indicate 5 lm except theinset scale bar (2lm).

Fig. 5 The thermal conductivities of samples 8 and 1218 atroom temperature. For samples 1218, nanotubes and graph-ites were dispersed in DMF or NMP without using any stabil-izers such as SDBS or SDS.

Fig. 2 (a) Iron-incorporated nanotubes and (b) nickel-incorporated nanotubes before they were mixed into polymers.Black circular shape objects are the metal nanoparticles. Bothscale bars indicate 100 nm.



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between samples dispersed by DMF and NMP can be inferredfrom SEMs in Fig. 6. Sample 15 (dispersed in DMF) shows poly-mers coated on graphite sheets, which may prevent direct contactsbetween nanotubes and graphites.

The matrix material for these samples are Vinnapas 401, whichhas a relatively low glass transition temperature (Tg15

C). LowTg polymers typically show lower thermal conductivity than high Tgpolymers due to loose interatomic bondings. High Tg polymers, how-ever, are often brittle and tend to break by external impact. Here, ther-mal transport performance of composites made of Epon 862(T

g 135C) [28] was compared to the samples containing Vinnapas

as shown in Fig. 7. The matrix replacement from Vinnapas to Eponincreased the conductivity of sample 7 (50 wt. %-graphite and 25 wt.%-SDBS with Vinnapas) by$ 180% ($ 1.5W/m-K, sample 19). Bymixing 25-wt. % nanotubes as a substitute for 25-wt. % graphite withthe Epon matrix material, the highest conductivity of$ 1.85W/m-Kwas obtained (sample 20). However, when Vinnapas was used instead of Epon (sample 10), the conductivity was similar to that ofsample 19 (50wt. %-graphite and 25 wt. %-SDBS with Epon). Thebrittle and rigid characteristics of Epon is shown in the inset of Fig. 7.The fractured surface of the Epon sample (sample 20) shows sharpedges, which are different from the samples made of Vinnapas.

In order to investigate the influence of the graphite, CNT, andpolymer matrix on the thermal conductivity of the composite, weemployed a model based on the Maxwells effective mediumtheory [29]. When the interactions between constituents in the

composites are negligible (e.g., low concentration fillers), thefollowing Maxwells model is considered to be valid [9,30]:

ke kmke 2km

fpkp km

kp 2km

(1)

where ke, kp, and km, respectively, represent thermal conductivitiesfor the composite, the particles (i.e., graphite or CNT), and thematrix. Here, fp is the volume fraction of the particles. When acomposite has high concentration fillers whose thermal conductiv-ity is much higher than that of the matrix, the percolated networksof the fillers need to be considered. In this case, the Maxwellsmodel underestimates the thermal conductivity of the composite

since the model does not take the interaction between the particlesinto account. In particular, it should be considered for the compo-sites with high aspect-ratio fillers like CNTs and graphites ratherthan spheres (or cubes) since they are easier to make percolatednetworks. In order to consider the influence of the filler interac-tions, the Maxwell model has been modified to a simplified formwith different v (a factor that varies depending on literatures)[9,3133]

ke

km 1 vfp (2)

For example, v 3 underestimated the thermal conductivity ofCNT-filled composites [31]. In our study, we modified theMaxwells model under the assumption ofkp) km since our com-

posites contain graphites and CNTs whose thermal conductivitiesare much higher than the polymer matrix

ke

km

1 afp1 fp

(3)

where a is a coefficient that accounts for the effectiveness of con-ductive fillers on altering the composite thermal conductivity. Thecoefficient, a is 2 for the Maxwells model. In our study, a islarger than 2 due to the high concentration and high aspect ratiosof the fillers. It also depends on the dispersion and connections ofthe fillers in the matrix. It is likely that the factor is a strong func-tion of the filler type (i.e., graphite and CNT) at a filler concentra-tion well above the percolation threshold due to their very

different morphologies. Here, we used experimental data for sam-ples 68 to find a since they contain only graphites as a filler withthe same Vinnapas matrix. The graphite concentrations are,respectively, 18.7, 34.8, and 44.5 vol. % (i.e., 30, 50, and 60 wt.%). Note that fp is the volume fraction but Table 1 lists weightratios since weight is the actual measurable quantity. Therefore,weight percentage was converted into volume percentage. Thevolume fraction of each constituent (fi) was calculated using thefollowing relation:

fi mi

qi

Xj

mj

qj(4)

where m and q indicate mass and density of the indexed (i orj) material. The densities of MWCNTs, graphites, SDBS,

Vinnapas, and Epon are, respectively, selected as 2.1 g/cm

3

[9],2.1g/cm3 [34,35], 1.06g/cm3 [36], 1.19g/cm3 [7], and1.19 g/cm3 [21,28], respectively. The a values for samples 68were, respectively, calculated to be 5.52, 5.09, and 4.30 byusing Eq. (3). The thermal conductivity of Vinnapas, km, wasassumed to be 0.2 W/m K [7]. Figure 8(a) shows the experi-mental data for samples 68 (black hollow symbols) as a func-tion of graphite vol. % as well as the fitting curve with theaverage value, a 4.97 in Eq. (3).

In order to consider the interactions between the conductivematerials in the composites with additional CNTs (samples 911)or with a different matrix material (Epon in sample 20), weemployed a full-correlation model to calculate the thermal con-ductivity of the composite, k(fGraphite, fCNT) [9].

Fig. 6 The cold-fractured cross-sectional surfaces of (a) sample

15 (dispersant: DMF) and (b) sample 16 (dispersant: NMP). Theinset in (a) shows nanotube bundles between graphite sheets.Scale bars indicate 5lm except the inset scale bar (2 lm).

Fig. 7 Room temperature thermal conductivities of samples 7,19, 10, and 20 to find the influence of polymer matrices (EPONvs Vinnapas) on the thermal conductivity of the composites.The inset shows a fractured surface of sample 20. The scale barindicates 5lm.



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kfGraphite;fCNT kefGraphite1

1 fCNT

b(5)

where ke(fGraphite) denotes the effective thermal conductivity with-

out containing CNTs, which can be calculated by using Eq. (3),and the coefficient b accounts for the effectiveness of improvingcomposite thermal conductivity by the fillers. A larger b valueindicates more effective additives on increasing the thermal con-ductivity of composites. Here, we first found ke(fGraphite) by usingEq. (3) at 27.8, 17.4, and 7.00 vol. % (40, 25, and 10 graphite wt.% for the use in sample 9, 10, 11) when only graphite fillers wereconsidered, as shown in the filled symbols of Fig. 8(a). Then, thethermal conductivity behaviors of the composites (samples 911)were calculated as a function of the CNT concentration by usingEq. (5), as depicted in Fig. 8(b). Here, the maximum CNT con-centration was calculated for the plot because there are limitedspaces available for the filler, surfactant, and polymer matrix. Theminimum concentration of the polymer matrix required for

synthesizing continuous solid samples without cracks was esti-mated to be 26 vol. %, and the maximum concentration of the fill-ers was 44 vol. % with minimum 30 vol. % surfactant from thecondition of sample 8. Note that the surfactant (SDBS) is neces-sary to disperse the graphite and CNT in water. Otherwise, theystrongly aggregate and result in very low thermal conductivity.Therefore, the maximum CNT concentrations were calculated tobe 16, 27, 37, and 27 vol. % (22, 36, 50, and 36 wt. %) for samples911 and 20, respectively. From the calculation results, when theratio of CNTs to graphites is slightly higher than unity, the highest

thermal conductivity over 3 W/m-K may be achievable (see theplots for samples 10 and 20). The effectiveness of adding CNTs,which can also be identified by the coefficient b, for sample 10 isthe highest (b 6.28). The additional CNTs might thermallybridge the graphite sheets, resulting in the conductivity increase.Sample 9 also show relatively large b of 5.76. Nevertheless, theCNT loading is limited, and thereby the maximum achievableconductivity is estimated to be less than 2 W/m-K. On the otherhand, when the concentration of the graphite is low (sample 11,graphite:CNT 1:4), the effectiveness of adding CNTs is moder-ate (b 4.59), as depicted in the slope. The plots for samples 10and 20 were selected to identify the role of the polymer matrix(Vinnapas and Epon). In order to find the thermal conductivity ofthe Epon polymer, we used the experimental result of sample 19.For the given ke in Eq. (3), the matrix conductivity, km was calcu-lated to be 0.346 W/m-K. This value is close to or higher than

those of other experiments [8,37]. The polymer made of Epon,which is stiffer than that of Vinnapas, is likely to have higher ther-mal conductivity than the Vinnapas matrix. It is also possible thatEpon may have better thermal contacts with graphites and CNTsthan Vinnapas. It has been found that the thermal conductivity canbe dramatically improved by adding them into Epon [8,38] ratherthan Vinnapas matrices [7,20,22,23]. With the Epon thermal con-ductivity, ke was calculated to be 0.782 for sample 20 fromEq. (3) with a 4.97. Note that we used the same a since the coef-ficient considers the interactions between the fillers, which governthe thermal conductivity of the composites. Then, the model fromEq. (5) was plotted with a matching coefficient b of 4.50. The rel-atively high conductivity for sample 20 may be attributed to thematrix whose thermal performance in the composite is superior toVinnapas.

4 Conclusions

This study presents thermal transport behaviors of polymernanocomposites as a function of various synthesis conditions andconcentrations, different polymer matrix materials, and differentsurfactants. Carbon nanotube- or/and graphite-filled polymer com-posites were synthesized by using simple mixing and drying meth-ods, and their thermal conductivities were measured by using asteady-state technique. Nanoparticle-decorated nanotubes werealso incorporated into polymer matrices for investigating theirinfluence on thermal conductivity. Two different surfactants, SDSor SDBS was used for stabilizing nanotubes/graphites in water.DMF or NMP was also utilized for nanotube/graphite dispersionwithout using any surfactants. For the matrix materials, flexible

Vinnapas or stiff Epon was employed. The conductive filler con-centrations were varied to find the optimum synthesis conditionfor improving thermal conductivity.

The experimental results show that the composite containing amixture of nanotube and graphite fillers with the Epon matrix hasthe highest thermal conductivity, $1.85 W/m-K at room tempera-ture. The composite contain 25-wt. % nanotubes and 25-wt. %graphites with the SDBS surfactant. The nanotube-filled compo-sites are more flexible and less porous than graphite-filled sampleswhereas the graphite-filled composites are stiffer with higher ther-mal conductivities. The mixture of nanotubes and graphites pro-vides better structural integrity from good adhesion betweennanotubes and polymers as well as higher thermal conductionfrom graphites. In addition, nanotubes fill voids between

Fig. 8 (a) Calculated thermal conductivities for the graphite-filled composites. The solid line represents calculated thermalconductivities from Eq. (3) with a54.97. The experimental ther-mal conductivities for sample 6 (hollow circle), sample 7 (hol-low triangle), and sample 8 (hollow square) were used for

finding a. ke(fgraphite) in Eq. (5) for sample 9 (green filled dia-mond), sample 10 (red filled circle), and sample 11 (blue filledtriangle) were obtained from Eq. (3). (b) Calculated thermal con-ductivities for sample 9 (green dash line), 10 (red solid line), 11(blue dashed-dotted line), and 20 (black dotted line) obtained byusing Eq. (5). Experimental data for sample 9 (green filled dia-mond), sample 10 (red filled circle), sample 11 (blue filled trian-gle), and sample 20 (black hexagon) were plotted together andused for finding b.



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graphites, making the sample less porous. When solvents (DMFand NMP) were used as a surfactant, conductive filler concentra-tions can be raised to 80wt. % (40 wt. %-nanotubes and 40 wt. %-graphite; or 80 wt. % graphite), resulting in $1.7 W/m-K at roomtemperature. The thermal conductivity of the composite was alsopredicted by using a model based on the Maxwells effective me-dium theory. The most effective method of improving the com-posite thermal conductivity is to use both graphites and CNTswith a ratio of CNTs to graphites slightly higher than unity. TheCNTs may thermally bridge the graphite sheets and improve ther-

mal transport behaviors in the composites.

Acknowledgment

The authors (W.P., K.C., C.Y.) gratefully acknowledge finan-cial supports from the U.S. Air Force Office of Scientific Research(Grant No. FA9550-09-1-0609), the U.S. National Science Foun-dation (Award No. 1030958 and 0854467), and the PioneerResearch Center Program through the National Research Founda-tion of Korea (2011-0001645) funded by the Ministry of Educa-tion, Science and Technology (MEST). The FE-SEM acquisitionin the microscopy imaging center at Texas A&M Univ. was sup-ported in part by the National Science Foundation under GrantNo. DBI-0116835. The authors thank H. Yangs assistance inacquiring XRD data.

Nomenclature

f volume fractionk thermal conductivity (W/m-K)

m mass (g)

Greek Symbols

a a coefficient that account for the effectiveness ofconductive fillers on altering the thermal conductiv-ity of a composite (with one kind filler)

b a coefficient that account for the effectiveness ofconductive fillers on altering the thermal conductiv-ity of a composite (with two different kinds of fillers)

q density (g/cm3)v fitting parameter

Subscripts

e effective propertym matrixp particle

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