Accepted Manuscript

Effectively Decoupling Electrical and Thermal Conductivity of Polymer Com‐

posites

Kun Zhang, Yue Zhang, Shiren Wang

PII: S0008-6223(13)00766-5

DOI: http://dx.doi.org/10.1016/j.carbon.2013.08.005

Reference: CARBON 8284

To appear in: Carbon

Received Date: 22 May 2013

Accepted Date: 7 August 2013

Please cite this article as: Zhang, K., Zhang, Y., Wang, S., Effectively Decoupling Electrical and Thermal

Conductivity of Polymer Composites, Carbon (2013), doi: http://dx.doi.org/10.1016/j.carbon.2013.08.005

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1

Effectively Decoupling Electrical and Thermal Conductivity of Polymer Composites

Kun Zhang, Yue Zhang, Shiren Wang

Department of Industrial Engineering, Whitacre College of Engineering, Texas Tech University,

Lubbock, Texas 79409

Abstract

Hybrid nanocrystals, fullerene-decorated graphene, were incorporated into the epoxy

composites, and their electrical and thermal transport was investigated. The hybrid nanocrystals were

fabricated through a solution process and the resultant hybrid nanostructure was verified by

transmission electron microscopy and X-ray diffraction characterization. After incorporation of

fullerene-functionalized graphene into epoxy resin, the electrical conductivity increased significantly

while the thermal conductivity only increase slightly, resulting in effective decoupling

thermal/electrical conductivity. Through filling fullerene/graphene nanohybrids into the epoxy resins,

the electrical conductivity was increased from 10-14

to 2949 S/m, more than 17 orders of magnitude.

On the other hand, the thermal conductivity was only increased from 0.3 to 0.66 W m-1

K-1

, only two-

fold increments. Further theoretical calculations and comparative experiments indicated that the

synergistic effects of graphene and fullerene nanocrystals resulted in the effective decoupling of

thermal/electrical transport. The electrical transport was improved through graphene sheets while the

lattice thermal transport was impeded through fullerene decorated on the graphene sheets. The de-

coupling of electrical and thermal conductivity of polymer composites opens numerous opportunities

for new materials and systems.

1. Introduction

The de-coupling of thermal and electrical conductivity has attracted a great deal of attentions.

Thermally conductive and electrically insulating materials are important for the powerful miniature

and electronic product due to the heat dissipation. High-performance electronic packaging materials

are thermally conductive electrically insulating materials that permit heat to be effectively dissipated

but do not affect the integrated circuit [1-4]. By de-coupling the thermal conductivity and electrical

conductivity, the thermally conductive electrically insulating materials could be used in the fabrication

of printed circuit boards for dissipating heat to improve electronics reliability [2] or even directly as

printed circuit board (PCB) materials so that heat can be effectively dissipated without shorting the

circuit. On the other hand, materials with low thermal conductivity and high electrical conductivity are

*Corresponding author. Tel: 806 834-8507. E-mail: shiren.wang@ttu.edu (Shiren Wang)

2

desired for thermoelectrics [5-6]. Thermoelectric conversion involves the energy conversion between

heat and electricity. It has attracted a great deal of attentions since it can be used as power generation,

thermal management, as well as fuel efficiency improvement. The performance of thermoelectric

materials is characterized by a dimensionless figure of merit ZT= S2σT/к, where S, σ, к, T represents

the Seebeck coefficient (μV/K), electrical conductivity (S/cm), thermal conductivity (W/m.K), and

absolute temperature (K), respectively [7]. Therefore, an ideal thermoelectric material should have

high power factor (S2σ) and low thermal conductivity.

It is very challenging to decouple thermal and electrical conductivity due to their strong

correlations according to the Wiedemann−Franz law [8]. High electrical conductivity usually coupled

with high thermal conductivity. According to the Wiedemann−Franz law, the thermal conductivity

к=кe+кl=LσT+кl, where кe is the electronic thermal conductivity, which is correlated with the

electrical conductivity, кl is the lattice thermal conductivity. Apparently, only the lattice thermal

conductivity кl is independent of the electrical conductivity. Therefore, it is possible to decouple the

thermal/electrical conductivity through hindering the lattice thermal conductivity while increase the

electrical conductivity.

Some efforts have been made to add various conductive fillers into polymer, but the composites

usually demonstrated high electrical conductivity and high thermal conductivity [9-14]. Epoxy is one

of the most important thermosetting polymers. Due to the high chemical and corrosion resistance, good

mechanical properties and low thermal conductivity, epoxy has been extensively used in various fields

including coating, high-performance adhesives, and composite matrix. Even though many efforts have

made to investigate the conductive epoxy composites [15-18], to the best of our knowledge, there have

been no reports attempting to de-couple electrical and thermal conductivity.

In this work, we innovatively fill the hybrid nanomaterials, fullerene-decorated reduced

graphene oxide (rGO), into epoxy composites for de-coupled electrical and thermal conductivity. rGO

was successfully decorated by fullerene via solution interfacial assembly. The fullerene nanoparticles

was employed to reduce the lattice thermal conductivity by effectively scattering phonons. Fullerene

has been reported with the thermal conductivity of ~0.16 W/m-1

K-1

at 300K [19]. Fullerene has been

used to reduce the thermal conductivity and thus improve their thermoelectric performance [20-24].

Synergistic effect of graphene and fullerene is promising to decouple thermal and electrical transport.

Fullerene/graphene hybrids were filled into the epoxy resins and their electrical/thermal conductivity

was studied.

3

2. Experimental

2.1 Materials

Graphite was provided by Asbury Carbons. The sodium chloride (>99%), N,N-

Dimethylformamide (DMF, anhydrous, 99.8%), isopropyl alcohol (IPA, 99.7%) , phenylhydrazine

(97%), and m-xylene (anhydrous, ≥ 99%) were purchased from Sigma-Aldrich. The nitric acid (fuming,

ACS reagent) was purchased from Acros Organics. The epoxy resin system, Epon 862 (epoxy)/EPI

Cure-W (hardener) was kindly provided by Shell Corporation.

2.2 Preparation of graphite oxide

Graphene was fabricated through chemical reduction of exfoliated graphite oxide. Graphite

oxide was prepared with a modified Brodie’s method [25-26]. Typically, graphite (10 g), fuming nitric

acid (160 mL), and sodium chlorate (85 g) were mixed at room temperature. The mixture was then

stirred for 24 hours, followed by washing, filtration, and cleaning as described by Brodie. Graphite

oxide was collected through a precipitation method and evaporation of the solution at 60 °C.

2.3 Preparation of chemically reduced graphene oxide (rGO)

Graphene nanosheets were produced by reducing graphene oxide with the assistant of

phenylhydrazine. Typically, the dried graphite oxide (200 mg) was dispersed in DMF (20 mL) by tip

sonication at 50 W (Misonix sonicator 3000) for 1 hour, resulting in exfoliated graphene oxide. Then

0.5 mL phenylhydrazine (35 wt %) was added. The mixture was stirred at room temperature for 24

hour, followed by washing with water (500 ml) and ethanol (500 ml), sequently. The materials were

filtrated and annealed in vacuum oven at 270ºC overnight, resulting in reduced graphene.

2.4 Preparation of fullerene/rGO-epoxy nanocomposites

The fullerene/graphene samples were prepared according to a liquid-liquid interfacial

precipitation (LLIP) method [27]. Typically, fullerene and rGO were dispersed in m-xylene and

isopropyl alcohol (IPA) separately through the ultrasonic process. Then the rGO/IPA (900 mg/L)

solution was injected into the fullerne/m-xylene solution (500 mg/L) slowly at a volume ratio of 5:1.

An interfacial was formed between the two solutions. The interfacial solution was removed by a

syringe every 15 minutes and collected for further using. The epoxy and hardener were dissolved

(epoxy: hardener = 100:26.4 in weight ratio) in 5 ml acetone and sonicated for 10 minutes. Then the

solution of fullerene/rGO and the solution of epoxy/hardener were mixed and filtrated, forming the

4

film of fullerene/graphene/epoxy resin. The film was heated in an oven at 177°C for 1 hour. The

samples with 0, 18, 45, 58, 71 wt% fullerene/rGO were named as S1, S2, S3, S4 and S5.

2.5 Characterization

The fullerene/graphene samples were characterized by Powder X-ray diffraction (XRD, Rigaku

Ultima III diffractometer, 40 kV, 44 mA, with Cu KR (λ=1.54 Å)) was used to study the

FULLERENE/graphene samples, and the measurements were taken at a 2θ range of 5º≤2θ ≤ 40º at

room temperature. The sample morphology was characterized by high-resolution transmission electron

microscopy (HRTEM, Hitachi H-7650) with an acceleration voltage of 60 kV. Scanning electron

micrographs (SEM) of the samples were taken with the Shimadzu 4300 electron microscope. Electrical

conductivity measurements were performed on a SRM probe (Bridge Technology Inc.) by a standard

four-point probe method with a Keithley 2400 current source meter and a Keithley 2182A

Nanovoltmeter at the room temperature. Thermal conductivity was measured by LFA 447 Nanoflash

thermal analysis equipment (NETZSCH Instruments).

3. Results and Discussion

Figure 1 shows XRD patterns for fullerene, fullerene/rGO hybrids and rGO. The graphite

flakes showed a (002) peak at 27°, indicating an interlayer spacing of 0.34 nm. The (002) peak of

graphite oxide shifted to 12°, indicating that the interlayer spacing increased to 0.72 nm after

oxidization [28]. After chemical reduction by hydrazine, the sharp (002) peak of graphite oxide

disappeared while another broad peak of around 24° appeared. The disappearance of the sharp peak

can be attributed to the exfoliation of layered structures of graphite oxide. The broad peak may stem

from the partial restacking of exfoliated graphene layers. Fullerene/graphene hybrids show

characteristic peaks of fullerene at 10.8°, 17.7°, 20.8°, 21.7°, 27.5° and 28.2° corresponding to the

(111), (220), (311), (222), (331) and (420) diffraction of fullerene [29]. As shown in the inset, the

broad diffraction of graphene in the range of 22° to 26° disappeared and this might be attributed to the

grafted fullerene clusters, which effectively prevented the restacking of the graphene layers. The XRD

pattern indicates that fullerene had been successfully incorporated onto the surface of graphene and

they worked as spacers to keep the individual graphene sheets from restacking.

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Figure 1. XRD patterns of fullerene, fullerene/rGO hybrid, rGO, graphite oxide, and graphite.

In order to further confirm the fullerene/rGO hybrid structure, as-prepared rGO and

fullerene/rGO hybrid were characterized by TEM. rGO has smooth surface without any defects or

contamination (Figure 2a). As shown in Figure 2b-d, the black dots on the surface of graphene are

fullerene nanoparticles with <100 nm diameter. Smaller fullerene nanoparticles are spherical, while

larger nanoparticles possess variable shapes, which might arise from the agglomeration of small

spheres [30-31]. Moreover, graphene layers without fullerene molecules tend to restack due to

interlayer π-π interaction, forming few-layered graphene (Figure 2a). While the fullerene /rGO samples

showed single or few layered structures, which might stem from the attached fullerene particles

preventing the restacking and agglomeration of graphene layers during processing in solution. TEM

images indicate that the fullerene nanoparticles have been successfully grafted onto graphene layers,

and they work as effective spacers to prevent the restacking of the graphene nanosheets.

6

Figure 2. TEM images of graphene (a) and fullerene/graphene hybrid (b-d). (Scale bar: 100 nm)

Fullerene/rGO hybrid nanocrystals were incorporated into epoxy resin at various fractions. The

electrical conductivity and the thermal conductivity of epoxy composites were measured and plotted in

Figure 3. Neat epoxy resin was insulating with electrical conductivity of 10-14

S/m. With the addition

of 18wt% fullerene/rGO, the electrical conductivity was increased by more than 1015

order to 45.6 S/m

(Figure 3). This might be due to the formation of rGO percolation network in the epoxy composites.

Since graphene is highly electrically conductive and shows high carrier mobility [16], the

incorporation of fullerene-functionalized graphene could increase the electrical conductivity of epoxy

composite. When the rGO fraction in epoxy resin reached the percolation threshold for electronic

transport, continuous electron transport paths could lead to the increase of electrical conductivity. With

further addition of the fullerene /rGO hierarchical nanostructures, the electrical conductivity of the

(a) (b)

(c) (d)

7

composite continued increasing to 2949 S/m. In addition, the incorporation of the fullerene/rGO

hierarchical nanostructure may increase the carrier mobility [16], due to their intimate contact between

rGO and epoxy matrix [33]. The electrical conductivity σ can be approximated by [34]:

Where, e, n and μ are the electron charge, carrier concentration and carrier mobility, respectively.

Obviously, increasing the carrier mobility could help to improve the electrical conductivity.

Figure 3. Electrical conductivity and thermal conductivity of fullerene-functionalized

rGO/epoxy composites.

On the other hand, the thermal conductivities of epoxy composites were also characterized by

LFA 447 instruments. The results ranged from 0.5 W/(m.K) to 0.66 W/(m

.K) dependent on the fraction

of filler loading (see Figure 3). The thermal conductivity of neat epoxy resin was measured to 0.3

W/mK, and thus composite thermal conductivity was increased by only ~2 fold. Since graphene

possesses high thermal conductivity, adding graphene might increase the thermal conductivity of

epoxy composites; however, it seems that the thermal conductivity of epoxy composites increased very

slightly in comparison to the enhancement of electrical conductivity. In addition, rGO/epoxy

composites without fullerene were fabricated and characterized. Their electrical conductivity and

thermal conductivity are shown in Figure S1 (Supplementary Material). The electrical conductivities of

rGO/epoxy composites were comparable to that of the fullerene-functionalized rGO/epoxy composites.

However, rGO/epoxy composites showed much higher thermal conductivity than fullerene-

functionalized rGO/epoxy composites. The thermal conductivity of rGO/epoxy composites was as high

8

as 4.5 W/(m.K) at 22.7 wt% rGO loading, which was well consistent with literatures [35-37]. At

increasing rGO loading, the thermal conductivity of rGO/epoxy composites was above 9 W/(m.K),

more than 30-fold increment in comparison to the epoxy resin. Obviously, integration of fullerene-

functionalized rGO can keep the improvement of electrical conductivity, but significantly diminish the

increment of thermal conductivity. Therefore, fullerene-functionalized rGO could effectively decouple

the thermal/electrical conductivity.

The mechanism should arise from the nanoparticles-moderated thermal transport. It has been

reported that the incorporation of nanoparticles can effectively reduce lattice thermal conductivity by

scattering phonons due to nanoparticles [38]. The thermal conductivity of epoxy composites at room

temperature should be dominated by phonon transport. Low frequency phonons have a long mean free

path (long wavelength), and high frequency phonons have a short one (short wavelength). Phonon

scattering effect was illustrated in Figure 4. Large fullerene particles scattered phonons with middle

wavelengths, small fullerene particles scattered phonons with short wavelengths, while thin epoxy

layers between rGO layers formed interfaces for scattering phonons with long wavelengths. For

phonons that carry most of the heat, an average mean-free-path can be plausibly defined. When the

particle size matches the phonon mean free path in epoxy, effective phonon scattering will occur

according to Casimir regime [39-41]. According to the TEM images of fullerene/rGO in Figure 2, the

fullerene particle size on graphene surfaces ranges from several nanometers to ~100 nm. The fullerene

nanoparticles on the surface of graphene may facilitate scattering phonons with whole wavelengths,

achieving a lower lattice thermal conductivity. Another possible reason might come from the higher

thermal interfacial resistance between epoxy and rGO layers [33]. The neighbored rGO sheets were

separated by 0D fullerene nanoparticles, which might prevent the thermal transport in the filler

network. The presence of thin epoxy layers surrounding rGO might further preclude direct rGO-rGO

heat transfer. Thus the hybridized fullerene/rGO can help scattering phonons to achieve a lower

thermal conductivity.

9

Figure 4. Schematic diagram for phonon scattering in fullerene/rGO-epoxy nanocomposites.

The morphology of fullerene/rGO-filled epoxy composites was also characterized by SEM.

Since the filler fraction was above the percolation threshold, the morphology of the composites looks

very similar. Particularly, the SEM images of composites with 45% filler are shown in Figure 5.

Isolated graphene nanosheets were homogeneously dispersed in the polymer matrix and no big bundles

were observed, indicating the good dispersion of the fullerene/rGO filler in the epoxy matrix. However,

it was not able to observe the fullerene morphology directly. As observed in Figure 2, the size of the

fullerene nanoparticles was at tens of nanometers, which is beyond the capability of the scanning

electron microscope (HITACHI S-4300). Embedding into the resins made it more difficult to see the

fullerene morphology. According to the SEM images, the graphene sheets were coated with thin resins

and formed a good percolation. This kind of morphology verified that good electrical transport was

achieved in the as-fabricated composites. Neighbored fillers were in good contact with each other and

the fullerenes particles may serve as bridges. Particularly, it was observed that thin epoxy layers were

coated to the graphene sheets, confirming our illustration that resin layers preclude direct graphene-

graphene thermal transport. In addition, the composites demonstrated porous nanostructures due to the

curved graphene sheets, and this further help to scatter phonons, resulting in lower thermal

conductivity.

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Figure 5. SEM images of fullerene/rGO-epoxy nanocomposites. (a) Large area of composite

morphology; and (b) local morphology at a higher magnitude

The electronic thermal conductivity кe can be calculated by Weidemann-Franz relation кe=L0σT,

where L0 is Lorentz constant of 2.45˟10-8

V2/K

2, σ is the electrical conductivity, T is room

temperature. However, the contribution of кe to the total thermal conductivity к is very small.

According to the calculation of lattice and electronic thermal conductivity as shown in Figure 6, the

proportion of кe in к is 0.06%, 3.9%, 2.9%, and 9.8% for sample S2 (18 wt%), S3(45 wt%), S4 (58

wt%), S5 (71 wt%), respectively. Moreover, it has been reported that the Lorentz constant could be

reduced to more than 20% when the material possesses low carrier concentration [6]. In epoxy

composites, the increased electrical conductivity mainly stems from the increased carrier mobility,

indicating a low carrier concentration. So the calculated electronic thermal conductivity should be

larger than actual ones, suggesting that the contribution of electronic thermal conductivity could be

much smaller. Therefore, we believe that the thermal conductivity of fullerene/rGO-epoxy

nanocomposites mainly depend on the lattice thermal conductivity кl. However, the lattice thermal

conductivity seems insensitive to the incorporation of fullerene/rGO hybrid fillers, since the lattice

thermal conductivities are all ranged in a relatively stable level close to the measured as-prepared pure

epoxy. Therefore, we could conclude that the phonon scattering stemmed from the decoration of

fullerene on rGO surfaces significantly influence the phonon transport in epoxy nanocomposites,

resulting in effective de-coupling of electrical/thermal transport.

(b) (a)

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Figure 6. Lattice and electronic thermal conductivity of fullerene/rGO-epoxy ncomposites.

To further understand the role of fullerene-functionalized rGO on thermal/electrical decoupling,

fullerenes and rGO were separately added to the epoxy resins through physical mixing, and their

thermal conductivity was compared with that of the composites filled by fullerene-functionalized rGO

hybrids. The fraction of filler was set to 20% by weight. As shown in Figure 7, the composite prepared

through physically mixed fullerene, graphene and epoxy, showed thermal conductivity of 1.11

W/(m.K). While the epoxy composite filled with fullerene-functionalized rGO hybrids showed thermal

conductivity of 0.58 W/(m.K). In the composite prepared by physically mixing three components,

fullerene, graphene, epoxy resins), fullerenes may not break the percolation formed by graphene, and

thus thermal conductivity was high. On the other hand, when composites were prepared by dispersing

fullerene/rGO hybrids into epoxy resins (two component dispersion), fullerene may break the direct

graphene-graphene contact and prevent the heat transfer from graphene to graphene. Therefore,

fullerene decorated on the graphene surface could significantly break the paths of thermal transport

through increasing phonon scattering.

12

Figure 7. Thermal conductivity of epoxy-composite prepared through physically mixing neat epoxy,

and the composites prepared through hybridized fullerene/rGO-filled epoxy

4. Conclusion

In conclusion, fullerene decorated reduced graphene oxide (rGO) was assembled via liquid-liquid

interfacial precipitation (LLIP) by π-π interaction. With the incorporation of fullerene-decorated rGO

as conductive filler, the electrical conductivity dramatically increased from 10-14

to 2949 S/m, while

the thermal conductivity was found to approach only a doubly increase to 0.66 W/m.K in comparison

to the thermal conductivity of neat epoxy (~0.3 W/m.K), which might be due to the involved phonon

scattering by the small molecule fullerene decorated on rGO surfaces. The strategy of integrating rGO

decorated by fullerene into insulated polymers to decouple the electrical and thermal conductivity may

provide potential route towards novel functional materials and systems.

Acknowledge

The authors acknowledge the funding support from National Science Foundation CAREER

Award (0953674) and China Scholarship Council (NO.2009663056).

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