Synergistic electrical and thermal transport properties of ......Synergistic electrical and thermal...

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Synergistic electrical and thermal transport properties of hybrid polymeric nanocomposites based on carbon nanotubes and graphite nanoplatelets Masoud Safdari, Marwan S. Al-Haik * Engineering Science and Mechanics, MC 0219, 333-M Norris Hall, Virginia Tech, Blacksburg, VA 24061, USA ARTICLE INFO Article history: Received 6 May 2013 Accepted 15 July 2013 Available online 18 July 2013 ABSTRACT In this study hybrid ternary polymeric nanocomposites based on carbon nanotubes (CNTs) and graphite nanoplatelets (GNPs) are examined for their enhanced transport properties, over mono-nanofiller composite systems, originated via a synergy mechanism. Using an epoxy as the host matrix, a number of CNTs/epoxy, GNPs/epoxy and hybrid CNTs/GNPs/ epoxy specimens are processed and their electrical and thermal properties are character- ized. Furthermore, these transport properties are also estimated using a set of recently developed computational models based on percolation analysis and statistical continuum mechanics. Results suggest that the models, in agreement with the experimental observa- tions, confirm the presence of the synergy effect for both the electrical and thermal trans- port properties. Both the computational and experimental studies suggest incorporating miniscule amount of auxiliary nanofiller (ex. 10%wt CNTs compared to GNPs), boosts the electricalconductivity of the hybrid composites by several orders of magnitudes. Furthermore, the experimental measurements and the strong contrast computational models suggest that, owing to the formation of the hybrid CNT/GNP network, the hybrid CNT/GNP/polymer nanocomposites outperform their single-nanofiller counterpart config- urations. The investigation affirms that the particle agglomeration severely affects the transport properties of the hybrid nanocomposites and it is the root cause for the conflict- ing results in the literature. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Polymeric nanocomposites comprise a polymeric host matrix and at least one nanostructured filler phase with enhanced physical properties. Among the most utilized nanofillers are carbon nanotubes (CNTs) and graphite nanoplatelets (GNPs) due to their exceptional mechanical, electrical and thermal properties. Nanocomposites based on CNTs are widely employed as electro conductive materials [1,2]. The advancement of integrated circuits (ICs) and high power den- sity communication devices is tied to the evolution of high performance thermal interface materials (TIMs). Common TIMs are composite materials comprising a host matrix and a highly conductive filler phase. In this regard, GNPs are very promising nanofillers for TIMs [3]. To further enhance the transport performance of carbon- nanofillers based composites, ternary hybrid CNT/GNP/poly- mer nanocomposites were pondered. For example, single wall and multiwall CNTs combined with GNPs in variety of forms like graphene nanosheets (GNSs), exfoliated graphite (EG) and reduced graphite oxide (rGO) have shown extraordinarily enhanced thermal conductivities [4–7]. Hybrid porous 0008-6223/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.carbon.2013.07.042 * Corresponding author: Fax: +1 540 23 4574. E-mail addresses: [email protected], [email protected] (M.S. Al-Haik). CARBON 64 (2013) 111 121 Available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/carbon

Transcript of Synergistic electrical and thermal transport properties of ......Synergistic electrical and thermal...

Page 1: Synergistic electrical and thermal transport properties of ......Synergistic electrical and thermal transport properties of hybrid polymeric nanocomposites based on carbon nanotubes

C A R B O N 6 4 ( 2 0 1 3 ) 1 1 1 – 1 2 1

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Avai lab le a t www

journal homepage: www.elsevier .com/ locate /carbon

Synergistic electrical and thermal transportproperties of hybrid polymeric nanocompositesbased on carbon nanotubes and graphitenanoplatelets

0008-6223/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.carbon.2013.07.042

* Corresponding author: Fax: +1 540 23 4574.E-mail addresses: [email protected], [email protected] (M.S. Al-Haik).

Masoud Safdari, Marwan S. Al-Haik *

Engineering Science and Mechanics, MC 0219, 333-M Norris Hall, Virginia Tech, Blacksburg, VA 24061, USA

A R T I C L E I N F O A B S T R A C T

Article history:

Received 6 May 2013

Accepted 15 July 2013

Available online 18 July 2013

In this study hybrid ternary polymeric nanocomposites based on carbon nanotubes (CNTs)

and graphite nanoplatelets (GNPs) are examined for their enhanced transport properties,

over mono-nanofiller composite systems, originated via a synergy mechanism. Using an

epoxy as the host matrix, a number of CNTs/epoxy, GNPs/epoxy and hybrid CNTs/GNPs/

epoxy specimens are processed and their electrical and thermal properties are character-

ized. Furthermore, these transport properties are also estimated using a set of recently

developed computational models based on percolation analysis and statistical continuum

mechanics. Results suggest that the models, in agreement with the experimental observa-

tions, confirm the presence of the synergy effect for both the electrical and thermal trans-

port properties. Both the computational and experimental studies suggest incorporating

miniscule amount of auxiliary nanofiller (ex. 10%wt CNTs compared to GNPs), boosts the

electricalconductivity of the hybrid composites by several orders of magnitudes.

Furthermore, the experimental measurements and the strong contrast computational

models suggest that, owing to the formation of the hybrid CNT/GNP network, the hybrid

CNT/GNP/polymer nanocomposites outperform their single-nanofiller counterpart config-

urations. The investigation affirms that the particle agglomeration severely affects the

transport properties of the hybrid nanocomposites and it is the root cause for the conflict-

ing results in the literature.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction performance thermal interface materials (TIMs). Common

Polymeric nanocomposites comprise a polymeric host matrix

and at least one nanostructured filler phase with enhanced

physical properties. Among the most utilized nanofillers are

carbon nanotubes (CNTs) and graphite nanoplatelets (GNPs)

due to their exceptional mechanical, electrical and thermal

properties. Nanocomposites based on CNTs are widely

employed as electro conductive materials [1,2]. The

advancement of integrated circuits (ICs) and high power den-

sity communication devices is tied to the evolution of high

TIMs are composite materials comprising a host matrix and

a highly conductive filler phase. In this regard, GNPs are very

promising nanofillers for TIMs [3].

To further enhance the transport performance of carbon-

nanofillers based composites, ternary hybrid CNT/GNP/poly-

mer nanocomposites were pondered. For example, single wall

and multiwall CNTs combined with GNPs in variety of forms

like graphene nanosheets (GNSs), exfoliated graphite (EG) and

reduced graphite oxide (rGO) have shown extraordinarily

enhanced thermal conductivities [4–7]. Hybrid porous

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112 C A R B O N 6 4 ( 2 0 1 3 ) 1 1 1 – 1 2 1

electrodes made from CNTs and reduced graphite oxide (rGO)

were deemed very feasible for the new generation of high en-

ergy density super capacitors [8,9]. Furthermore, hybrid CNT/

GNP nanocomposites have been employed in dye-sensitized

solar cells (DSSCs) to boost the power generation performance

by enhancing the dye adsorption and charge recombination

processes [10]. Other hybridnanocomposites have been uti-

lized as thin films in the solar cells to tailor their electrical

conductivity and optical transparency [11]. Beyond the

enhancement of the transport properties, hybrid CNT/GNP/

polymer composites exhibit enhanced storage and loss

moduli [12], static mechanical properties [13] and dielectric

properties [14].

Despite the several envisioned applications for the hybrid

CNT/GNP polymer nanocomposites, the early attempts to

optimize their electrical conductivities were not successful

[7]. Actually, several studies reported inconsistent levels of

the electrical conductivity improvement upon hybridization

[6,15–19].

In an attempt to probe these inconclusive and conflicting

experimental results, the electrical and thermal properties

of binary polymeric nanocomposites were investigated com-

putationally [20].

Geometrical concepts like the excluded volume and the

interparticle distance (IPD) provided the basis for several

models in investigating the effects of the filler’s shape, size,

aspect ratio [2,21–23] and its state of dispersion and agglom-

eration [24,25] on the electrical percolation threshold. In the

vicinity of the percolation threshold, the electrical conductiv-

ities of these single-nanofiller systems have been predicted by

the classical percolation law [26]. More rigorous models have

been developed to explain the electrical conductivity of these

nanocomposites below the percolation threshold; the so-

called dielectric region, to right above it [27,28]. According to

these studies the electrical conductivity in randomly distrib-

uted particulate-based nanocomposites are mainly governed

by the electrical tunneling mechanism, first introduced by

van Beek [29] and Frenkel [30].

Similarly, the thermal conductivity of binary polymeric

nanocomposites based on CNTs or GNPs have been investi-

gated computationally. In an early study, the effective med-

ium approach was utilized to compare the viability of GNPs

and CNTs to enhance the effective thermal conductivity of a

polymeric host [31]. Other approaches were utilized to inves-

tigate the thermal conductivity of ordered heterogeneous

nanocomposites based on the classical homogenization tech-

niques [32].

Most of the computational investigations of the electrical

and thermal properties of polymer nanocomposites are

strictly limited to binary nanocomposites systems with ideal

microstructures. These ideal assumptions restrain the feasi-

bility of these models since particulate nanocomposites are

prone to uneven distribution and poor dispersion of the

nanofillers. The conflicting reported results of several experi-

mental studies of the electrical and thermal properties of the

hybrid CNT/GNP/polymer systems could be contingent to

these difficulties.

Alternatively, for randomly disordered composite systems,

the transport properties can be evaluated computationally

using statistical continuum approaches [33,34]. On this basis,

to investigate the effective electrical and thermal conductivi-

ties of a hybrid ternary nanocomposite, two computational

models were recently developed by the authors [35–37]. These

models assume a general and more realistic random distribu-

tion of the nanofillers within the polymeric matrix, which ex-

tends their applicability to the composites with nanofiller’s

shape imperfections, deformations and agglomerations.

In the current study, these models are employed to esti-

mate the electrical and thermal conductivities of hybrid

CNT/GNP/epoxy nanocomposites by taking into account the

particle aggregation and deformation defects. To scrutinize

the validity of the models and to probe the basis of the syn-

ergy effect between the two nanofillers, a number of CNT/

GNP/epoxy nanocomposite configurations are also processed

and their morphologies together with their thermal and elec-

trical properties are characterized. The state of deformation

and agglomeration of the embedded CNTs and GNPs is quan-

tified and utilized later in the computational study. Finally,

the model predictions of the electrical and thermal conduc-

tivities are compared to the experimental measurements to

explore the prospects of the synergy mechanism and its driv-

ing forces.

2. Experimental study

2.1. Samples preparation

A number of CNT/polymer, GNP/polymer and hybrid CNT/

GNP/polymer nanocomposites specimens were processed.

For the CNT/polymer and the GNP/polymer specimens, five

different configurations were prepared comprising 1.0–

5.0%wt of the CNTs and the GNPs, respectively. For the hybrid

CNT/GNP polymer specimens five different configurations

were selected as well; each comprising (X)%wt GNP and (X/

10)%wt CNT were X = 1.0–5.0.

Exfoliated graphite nanoplatelets (x-GNPs) were supplied

by XG-Sciences, Inc., with average particle diameter of 5.0 mi-

crons and thickness of 6.0–8.0 nm (i.e., nominal aspect ra-

tio = 650–850). Short length multiwall carbon nanotubes

(MWCNTs) were supplied by Cheap Tubes, Inc., with outer

diameters of approximately 8.0 nm and lengths in the range

0.5–2.0 lm (chemical purity >95.0%). The hosting polymeric

matrix is a bisphenol-A epoxy vinyl ester resin (Derakane

411–350) supplied by Ashland, Inc., along with suitable hard-

ener (Norox MEKP-925H) and promoter (Cobalt Naphtenate-

6.0%) according to the supplier’s recommendation. The high

purity non-ionic surfactant Triton X-100 was supplied by Sig-

ma–Aldrich, Inc.

In order to eliminate, or at least reduce, the metallic impu-

rities (mainly catalytic metals and amorphous carbon) which

can subsequently affect the properties of the nanocomposites

and to add some functional groups to facilitate the dispersion,

the required amount of CNTs was weighed and then soaked

in a 1.0 M nitric acid solution for three hours within ultrason-

ication bath at 40 �C. Afterward the CNTs were neutralized

and washed with deionized (DI) water three times. Every time

the CNT conglomerates and sediments were re-dispersed into

the DI water and bath-ultrasonicated for 2 min and then cen-

trifuged, using a tabletop high speed centrifuge device, at 13 K

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C A R B O N 6 4 ( 2 0 1 3 ) 1 1 1 – 1 2 1 113

rpm. Finally, the neutralized CNTs were dried in an oven fur-

nace at 70 �C. The dried CNTs were crushed carefully with a

ceramic mortar into a fine powder. For each specimen, the

needed amount of the as-prepared CNTs were weighed and

then mixed with 3.0 ml of Acetone followed by 5 min of tip

sonication (using a Vibra-Cell VCX 500 tip-sonicator) in 20%

amplitude at room temperature. After 1 min of tip-sonication,

1.0 ml Triton X-100 was added to the solution to enhance the

dispersion and to prevent the re-aggregation. In order to pre-

vent the CNT–Acetone mixture from conglomeration and sed-

imentation prior to its usage, the suspension was placed in a

bath sonicator and after every 1 min it was tip-sonicated for

10 s. The required amounts of GNPs were also weighed and

gradually added directly to the resin while employing high

speed dispersion (IKA Ultra-Turrax T-18 basic high speed dis-

persion unit) under 100% rotation speed. The mixing process

was followed up by another 30 min of homogenization inside

a water bath at room temperature. After then, the dispersed

CNTs were added drop-wise to the as-prepared resin/GNPs

suspension and the mix was high-speed dispersed for an-

other 30 min. Finally, to improve the dispersion and distribu-

tion, the as-prepared mixture was tip-sonicated for another

30 min in a water bath. Whenever it was needed, disposable

wooden sticks were utilized to mechanically mix the ingredi-

ents. To ensure proper gelling time, after a number of trials

and errors, the proper amounts of curing agent and promoter

were weighed and added to the mixture and mechanically

stirred followed by one minute homogenization. The CNT/

GNP/resin suspension was poured into glass tubes and stored

under vacuum in a desiccator for 3 h for proper degassing and

to ensure initial curing at room temperature. Finally, the

nanocomposite specimens were post-cured in a convention

oven for 24 h at 75 �C and were cut into 2.5 mm thick disks

using a high precision low-speed diamond saw. Identical

processing protocols were carried out for f the mono-filler

composites (i.e., CNT/epoxy and GNP/epoxy) specimens.

2.2. Samples characterization

For each composite configuration prepared, a 0.1 mm disk

sample was sliced and the morphology of the cryofractured

cross section was investigated using a LEO (Zeiss) 1550 field

effect scanning electron microscope (FESEM). Several micro-

graphs were generated at different locations on the cross-sec-

tion under different magnifications.

The electrical conductivities were measured using a 4-

point probe station equipped with a Keithley 2001 digital mul-

timeter. The surface resistance was measured at 20 different

sites on both sides of each specimen. The averaged value is

reported as the electric resistance. The thermal conductivities

of the specimens were measured utilizing a Hot disk AB de-

vice. For each composite configuration, a Kepton hot-disk

probe was sandwiched in-between the flat surfaces of two

cleaned disk-shaped specimens. Using a mechanical fixture,

the stack was loaded uniformly to ensure proper contact

and to minimize the air gap and then the thermal conductiv-

ity was measured. For each configuration, the thermal con-

ductivity was averaged over five measurements.

3. Computational study

3.1. Nanofillers aggregation model

Ideally, computational studies treat CNTs and GNPs as perfect

straight cylindrical-shaped and disk-shaped particles, respec-

tively, with uniform dimensions. However, in the bulk powder

forms, both CNTs and GNPs are typically clustered into large

aggregates formed by several nanoparticles entangled to-

gether (e.g., CNTs) or stacked on top of each other (e.g., GNPs).

Sonication and dispersing processes, to a certain extent, as-

sist in disentangling these aggregates to uniformly distrib-

ute/disperse them into the host polymeric matrix. However,

even under highly engineered processing protocols, some

aggregates are retained in the final nanocomposite. Prolonged

homogenization processes could enhance the dispersion of

the nanofillers, however this enhancement comes with the

caveat of fracturing and deforming the individual particles.

Consequently, this will reduce the effective aspect ratios of

these nanofillers leading to poor transport properties [25].

Hence, in order to account for these geometric imperfections

in the simulations, in the current study the nanofillers are

treated as cylindrical aggregates each comprising an average

of �n individual particle. The number of particles in the aggre-

gate is assumed to vary based on a normal distribution with

an average value and a standard deviation estimated from

the experimental observations. Furthermore, the aspect ratio

of each cylindrical aggregate is selected based on the simple

geometric aggregation model defined by

k0 ¼ n1�3ak ð1Þ

In this equation, k is the nominal aspect ratio of the parti-

cles, k 0 is the effective aspect ratio of the aggregates and a rep-

resents the diminution factor that governs the variation of the

aspect ratio of the aggregates and it should be estimated from

the morphological studies. The parameter a is best defined by

a distribution with some average value and standard devia-

tion. This equation is simply constructed by assuming that

the total volume of the nanofillers is always conserved.

Based on the experimental observations, detailed later,

and by using image-processing algorithms, the distribution

of geometrical dimensions of nanoparticles aggregates were

evaluated. Subsequently, the model parameters were selected

by fitting the virtual distributions against the experimentally

developed ones. In the following computational study for

the GNPs the number of particles in each aggregate is selected

to follow a normal distribution with �n ¼ 5 and a standard

deviation rn = 3 (i.e., aggregates comprising 2–8 GNPs) and

the aspect ratio is selected to be normally distributed

�r ¼ �0:1 and ra = 0.05 (i.e., an aggregate possesses reduced

diameter due to the deformation and increased thickness

due to aggregation). Based on the experimental study, the

CNTs form aggregates much easier than the GNPs especially

for the high volume fraction configurations (>2.0%wt). In or-

der to ensure the formation of low aspect ratio aggregates

for CNTs, the average number of particles in the aggregate

was selected to be �n ¼ 1000 with rn = 500 (i.e., a wide distribu-

tion of large aggregates and small ones) and the aspect ratio

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114 C A R B O N 6 4 ( 2 0 1 3 ) 1 1 1 – 1 2 1

was selected to be normally distributed with �r ¼ 0:51 and

ra = 0.01 (i.e., reduced length and increased diameter).

3.2. Electrical conductivity model

According to classical Monte Carlo analysis (referred to as MC

model onward) [35], the electrical conductivity of the polymer

nanocomposites re can be evaluated by

re ¼ rpreexp � 2dc

� �ð2Þ

In this equation, e is the tunneling distance, dc represents

the statistically averaged interparticle half distance for which

the electrons should tunnel through the polymeric matrix to

establish the electrical conductivity and rpre is a prefactor pro-

portional to the contact conductance. The electrical conduc-

tivities of the CNT/epoxy, GNP/epoxy and CNT/GNP/epoxy

polymer nanocomposites, with nanofillers loadings concur-

ring with the experimental values, were estimated by this

model. For this purpose, each time a random distribution of

the nanofiller was generated via Monte Carlo simulation algo-

rithm and the model parameter dc was calculated and substi-

tuted into Eq. (2) to estimate the corresponding effective

electrical conductivity. The Monte Carlo simulations, details-

eliminated here for brevity, were carried out following the

technique explained in our previous work [35,37]. For each

configuration, the simulations were repeated twenty times

to report the average electrical conductivity. In each simula-

tion the tunneling distance was taken to be a constant value

e = 10 nm and for the CNT/epoxy and the GNP/epoxy configu-

ration, rpre was adopted from the values reported in Table 1;

for GNPs we used the parallel to the surface value, and for

CNTs we utilized the axial value. For the hybrid nanocompos-

ite cases, rpre corresponding to the CNTs was selected assum-

ing that the weakest element in the percolation network

dominates the effective electricalconductivity. Furthermore,

in each simulation, the state of the nanofillers agglomeration

and geometric imperfections was considered during the par-

ticle generation step through the nanofiller’s aggregation

model described earlier. For this purpose, the numeral values

of the corresponding parameters were estimated from the

microscopic observations that will be reported later. Further

details about the model and simulation steps can be found

elsewhere [35].

3.3. Modified strong-contrast (SC) model for thermalconductivity

Per our proposed model [36], the effective thermal conductiv-

ity tensor rt for the nanocomposite comprises up to three

phases (CNTs, GNPs and epoxy), where each phase occupies

Table 1 – Relevant physical and geometrical properties of the CNTsupplier’s datasheet.

Materials Designation Dimensions Density [gr c

CNTs Short MWCNT 8 nm · (0.5–2) lm 2.1GNPs xGNP-M 5 lm · (6–8) nm 2.2Epoxy Derakane 411–350 N/A 1.1a Value adopted from the literature [38].

a volume fraction /aða ¼ 1;2;3Þ. The thermal conductivity

for each of the constituent phases is depicted by isotropic sca-

lar ra. Hence, the effective conductivity can be evaluated

through

1r0

rt � 1

� ��1

¼ 13

1X3

a¼1

/aba0

� 1

0BBBB@

1CCCCAI�A2 � A3 ð3Þ

where r0 is the thermal conductivity of the isotropic refer-

ence phase and the second-order terms A2 and the third-or-

der terms A3 are defined by Eq. (4) and (5) and they

epitomize the microstructural information in the solution uti-

lizing one, two and three-point correlation functions

(Sa1;S

ab2 and Sabc

3 ; a;b; c ¼ 1::::3), scalar phase polarizabilities

(b0a, a = 1–3) and double gradient tensors H(0). To minimize

the estimation error, the reference phase property r0 was cho-

sen based on prescribed method[36].

A2 ¼r0X3

a¼1

/aba0

!2

Z X3

a¼1

X3

b¼1

ðb0ab0b½Sab2 ð1;2Þ

� Sa1ð1ÞS

b1ð2Þ�ÞHð0Þð1;2Þd2 ð4Þ

A3 ¼3r0X3

a¼1

/aba0

!2

Z Z

�X3

a¼1

X3

b¼1

X3

c¼1

b0ab0bb0cSabc3 ð1; 2;3Þ

� 1P3a¼1/aba0

X3

a¼1

X3

b¼1

X3

c¼1

X3

d¼1

b0ab0bb0cb0dSab2 ð1;2ÞS

cd2 ð2;3Þ

!

�Hð0Þð1; 2ÞHð0Þð2;3Þd2d3 ð5Þ

The thermal conductivities of the three systems CNT/epoxy,

GNP/epoxy and CNT/GNP/epoxy nanocomposites with nano-

filler loadings corresponding to the experimental values were

evaluated by this model using the material parameters listed

in Table 1. For each nanofiller/epoxy configuration five random

nanofiller distributions were generated and the average value

of the thermal conductivity was reported. Again, the nanofiller

deformation and agglomeration conditions were replicated in

the simulation using the nanofiller aggregation model. One

and two-point correlation functions (Sa1 and Sab

2 ) were directly

evaluated from the simulated nanoparticle distributions. The

three-point correlation functions (Sabc3 ) were approximated

from the one and two-point correlation functions following

elaborated procedures established elsewhere [39].

s, GNPs and Epoxy utilized in the simulations gathered from

m�3] Resistivity [X cm] Thermal conductivity [Wm�1 K�1]

�1 �1000 a

5 · 10–5 k, 1? 3000 k, 6?�1015 0.2

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C A R B O N 6 4 ( 2 0 1 3 ) 1 1 1 – 1 2 1 115

3.4. Estimating the thermal conductivity by finite elementanalysis

To validate the strong-contrast model’s predictions, the effec-

tive thermal conductivities were also evaluated by the finite

element method using the commercial finite element code

ABAQUS 6.10-EF. For each nanocomposite configuration the

generated random microstructure was simulated and meshed

with tetrahedral DC3D4 elements by assuming perfect bound-

ing between the particulate inclusions and the epoxy matrix.

The FEM solution converged through progressive local and

global mesh refinements. For each direction, the boundary

conditions were chosen to comprise a constant temperature

distributed over the mesh grids on two opposing sides along

that direction of the simulation cuboid and the heat equation

was solved under steady state conditions. Finally, the effec-

tive thermal conductivity was calculated from the tempera-

ture difference and the volume averaged heat-flux vector

over the entire simulated cuboid. For each specimen, this pro-

cess was repeated five times with fivedifferent representative

random microstructures and the average thermal conductiv-

ity was reported. Further details about the adopted FEM solu-

tion including some samples of the simulation results are

provided in the next sections.

4. Results and discussions

4.1. Nanocomposites morphologies

The morphologies of the CNTs and GNPs embedded in the

epoxy matrix were explored via scanning electron microscopy

(SEM). Some of the SEM micrographs are shown in Fig. 1.

Graphite nanoplatelets can be distinguished by their thin

crack-shaped morphology. The low magnification micrograph

(Fig. 1a) shows that the GNPs are reasonably distributed with-

in the epoxy matrix. Higher magnification micrographs

(Fig. 1b and c) reveal how the GNP particles interlocate to form

a local percolation network. This figure also confirms that the

Fig. 1 – Random scanning electron microscopy micrographs from

matrix of 1%wt GNP/epoxy specimens at different magnification

distribution in the 1%wt CNT/epoxy specimen, (e) Shows an ag

specimens, (f) Shows fully exfoliated GNP and an agglomerated

each other in a 1.0%wt GNP/epoxy specimen.

GNPs are not perfect disk-shaped nanoparticles; shear-mix-

ing forces (e.g., tip-sonication process) can break them into

smaller fragments and distort their shapes.

From Fig. 1d, it can be observed that the utilized mixing

technique disperses CNTs well within the specimens with

lower loading of CNTs. However, at higher loadings of CNTs

(>2.0%wt), the practiced method generated CNTs aggregates.

According to Fig. 1e and similar SEM images, the formation

of CNT aggregates is more prominent for the composites con-

figuration with high CNTs loadings. From experimental per-

spective, perfect mixing of samples with high CNT loading

(>2.0%wt) is rather a more challenging task. In these speci-

mens, microscale voids and microbubbles are also apparent.

Similarly, close inspection of the well-distributed GNPs

(Fig. 1f) revealed that usually 2–8 GNPs remained stacked de-

spite the practiced dispersion method.

In Fig. 2a, it can be observed that CNTs play the role of

interconnects to form a percolation network between the

GNPs planes. For the CNT/GNP/epoxy nanocomposite, CNTs

act as conductive flexible pathways spanning in-between

the larger high-surface area GNPs. These two species syner-

gistically cooperate to form a hybrid percolation network

and, consequently, are expected to enhance the electrical

and thermal conductivities of the specimen. The measure-

ments of the diameter and the length of these flexible path-

ways reveal that even when highly dispersed, a number of

CNTs are bundled as nanofilaments. Similarly, Fig. 2b shows

that CNT aggregates are also exist in the hybrid nanocompos-

ite configurations with low CNT loadings. However, it is rela-

tively harder to locate them in these specimens. While the

formation of such CNT aggregates is not desirable; these

aggregates can still contribute to the formation of the perco-

lation network as shown in this figure.

4.2. Electrical conductivity results

The average electrical conductivities of the specimens were

measured via the four-point probe method are reported in

different specimens. (a–c) GNPs embedded in the epoxy

s shows uniform distribution, (d) Shows the CNTs

glomerated CNT cluster formed in the 5% wt CNT/epoxy

GNP cluster consisting 2–8 layers of GNPs stacked on top of

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Fig. 2 – Scanning electron microscopy micrographs from hybrid nanocomposite specimen with 5.0%wt GNPs and 0.5%wt

CNTs. (a) Flexible CNTs connecting large two-dimensional GNPs (b) A CNT cluster connecting three GNPs.

116 C A R B O N 6 4 ( 2 0 1 3 ) 1 1 1 – 1 2 1

Fig. 3a. The electrical conductivity for GNP/epoxy samples

with 1.0–3.0%wt GNP are not reported in this figure since

the minimum possible reading by the utilized equipment

was 10�7 S/m which was higher than the conductivity of

these specimens. In the current study, the electrical conduc-

tivity equivalent to 10�7 S/m is also selected as the percola-

tion threshold criterion which corresponds to six orders of

magnitudes enhancement in the electrical conductivity over

that for the base epoxy host matrix.

Fig. 3b depicts the predicted electrical conductivities. By

taking the reference threshold for the electrical conductivity

to be 10�7 S/m, the predicted percolation thresholds were

found to be 0.6%wt for CNT/epoxy, 0.8%wt for CNT/GNP/

epoxy and 1.9%wt for GNP/epoxy configurations, respectively.

The corresponding experimentally measured values were

0.6%wt for CNT/epoxy specimens, 0.9%wt for CNT/GNP/epoxy

specimens and 3.6%wt for the GNP/epoxy specimens, respec-

tively. It can be observed that the model predictions are in

good agreement with the experiments; expect for the GNP/

epoxy configuration in which the experimental results are

not reliable due to the measurement instrument limitation.

In contrast to the CNT/epoxy configurations, the GNP/epoxy

configurations attained the lowest electrical conductivities.

This is mainly because the randomly distributed more rigid

two-dimensional GNPs particles,are unable to form a percola-

tion network as effective as the more flexible one-dimen-

sional CNTs.

In Fig. 4a, the experimentally measured electrical conduc-

tivity of the CNT/epoxy specimens are compared with the

Fig. 3 – (a) The electrical conductivity of CNT/epoxy, GNP/epoxy

the four point probe technique. (b) The predicted values for the

model predictions. Upto 2.0%wt CNT, good agreement is ob-

served between the measurements and the model predic-

tions. For higher loadings of CNT, both the experimental

measurements and the model capture the saturation of the

electrical conductivity, however, the model overestimates

the electrical conductivity. This discrepancy between the

model predictions and the experimental measurements

stems from the incapability of the aggregation model to prop-

erly introduce larger aggregate of CNTs into the simulations

to reflect the aggregate formation in samples with high CNT

loadings. Similarly, Fig. 4b compares the measured electrical

conductivity of CNT/GNP/epoxy specimens together with

the model predictions. It can be observed that the model pre-

dicts the same trend for the electrical conductivity enhance-

ment and the saturation at higher loadings. However, there

is still a discrepancy between the predicted values and the

experimental measurements. This can be ascribed to the

modeling simplifications as well as the assumptions of con-

stant tunneling length and isotropic electrical conductivity

for the nanofillers and also to the inherent inaccuracy of the

simple geometric nanoparticle aggregation model utilized.

It can be concluded that both the percolation model and

experimental measurements suggest that by adding minute

amounts of the CNTs (10% compared to GNPs) as the auxiliary

conductive phase, the percolation threshold diminishes at

least by 50% and the electrical conductivity increases by sev-

eral orders of magnitudes. This substantial improvement can

be attributed primarily to the formation of the highly effective

hybrid CNT/GNP networks.

and CNT/GNP/epoxy specimen measured experimentally by

electrical conductivities.

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Fig. 4 – The predicted values for the electrical conductivities of (a) CNT/epoxy specimens and (b) CNT/GNP/epoxy specimens

compared to the experimentally measured values. Exp.: experimental measurements, MC: Monte Carlo percolation model

predictions.

C A R B O N 6 4 ( 2 0 1 3 ) 1 1 1 – 1 2 1 117

4.3. Thermal conductivity results

The thermal conductivities of the specimens measured by the

hot disk method are depicted in Fig. 5a. It can be observed

that the CNT/epoxy specimens attain minimal thermal con-

ductivity compared to the two other nanocomposite configu-

rations. The thermal conductivity curve for the CNT

nanocomposite specimens reaches a plateau around 1.0%wt

CNT with insignificant enhancement in the thermal conduc-

tivity. Three sources can contribute to this observation. First,

CNTs are more flexible than GNPs and, therefore, are more

prone to bending during mixing into the polymer matrix

and, in return, their effective aspect ratio is reduced. Second,

the formation of the CNT aggregates at higher loadings hin-

ders further enhancement of the thermal conductivity and fi-

nally, the high CNT/polymer interface resistance could

restrict the effective thermal conductivity of the percolated

nanofillers networkin these specimens. However, for identical

nanofiller weight%, the GNP/epoxy specimens exhibit better

thermal conductivity owed to their higher surface area, com-

pared to the CNTs, their more rigid structure and their lower

interface resistance.

Finally, it can be observed that the hybrid CNT/GNP/epoxy

specimens outperform the two single nanofiller configura-

Fig. 5 – The thermal conductivity of CNT/epoxy, GNP/epoxy and

technique and (b) predicted by the modified strong-contrast (SC

tions. More than two-fold enhancement in the thermal con-

ductivity was observed for the hybrid nanocomposite

configuration comprising 5.0%wt CNT/GNP/epoxy in contrast

to the neat epoxy specimen. This enhancement is ascribed to

the formation of a more efficient hybrid CNT/GNP networks in

these specimens, as observed by SEM micrographs, which re-

duces the undesirable particle/polymer interfacial resistance

effects.

The strong-contrast model predictions of the thermal con-

ductivity of each configuration are represented in Fig. 5b. In

agreement with the experimental observation, the hybrid

CNT/GNP/epoxy nanocomposite configurations attain the

best thermal conductivity compared to the CNT/epoxy and

the GNP/epoxy configurations with a single type of nanoinclu-

sions. Similarly, for the assumed nanofiller loadings, the GNP/

epoxy specimens are predicted to attain better thermal con-

ductivity in comparison to the CNT/epoxy specimens. The

experimental measurements (Fig. 5a) are assertive of these

findings.

Both the model and experimental results confirm that for

unique filler loadings, the GNP/epoxy nanocomposites exhib-

its 10–90% higher thermal conductivities in comparison to the

CNT/epoxy specimens with identical nanofiller weight per-

centages. This can be ascribed to the higher surface area

CNT/GNP/epoxy specimen (a) measured by the hot disk

) model.

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118 C A R B O N 6 4 ( 2 0 1 3 ) 1 1 1 – 1 2 1

and the more robust structure of GNPs compared to CNTs,

which is desirable for the phonon transport process. Further-

more, the good agreement between the model and the exper-

imental measurements also implies that there is a lower

thermal resistance in the GNP/matrix interface than the

CNT/matrix interface which is also reported by other stud-

ies[40]. Finally, it can be observed that the hybrid CNT/GNP/

epoxy specimens preform up to 15% better than the corre-

sponding GNP/epoxy and up to almost 100% better than their

CNT/epoxy counterpart specimens. Nevertheless, it should be

emphasized that this synergy effect is more noticeable atlow-

er filler content ranges (<4.0%wt) as increasing the GNP con-

tent will increase the GNP/GNP connection density to a

degree that suppresses the complementary effect of additive

CNTs interconnects in between the GNPs.

The effective thermal conductivities for the different

nanocomposite configurations were predicted by both the fi-

nite element model and the strong-contrast model and were

compared together with the experimental measurements as

illustrated in Fig. 6. The models predictions are compared

with the experimental measurements of the thermal conduc-

tivity of GNP/epoxy specimens in Fig. 6a. Perfect agreement

between the model predictions and the experimental mea-

surements can be observed. An acceptable agreement be-

tween the SC model prediction and the FEM results can be

observed for the GNP/epoxy specimen as well. The predic-

tions of the two models and the experimental measurements

of the thermal conductivity for the CNT/epoxy specimens are

Fig. 6 – The predicted values for the thermal conductivities of (a

specimens compared to the experimentally measured values. E

contrast predictions and FEM: finite element predictions.

provided by Fig. 6b. A good agreement is onlynoticeable for

samples with lower loadings of CNTs (<2.0%wt) For CNT/

epoxy samples with higher loadings of CNTs, both the strong

contrast and the FE models overestimate the thermal conduc-

tivity compared to the experimental measurements. In anal-

ogy to the electrical conductivity study described earlier,

this observation can be attributed to the high tendency of

the CNT/epoxy specimens to form large aggregates and the

failure of the geometric nanoparticle aggregation model to

properly simulate these conditions. Another contributing

source for this discrepancy is the high CNT/polymer interfa-

cial resistance and its effect on the performance of the CNT

percolation network, which was not considered in both the

modified strong-contrast and finite element models (perfect

bonding was assumed).

Finally, the predicted values for the thermal conductivity

of the hybrid CNT/GNP/epoxy specimens with their corre-

sponding experimentally measured values are depicted in

Fig. 6c. A good agreement between the strong-contrast model

predictions and the corresponding experimental values can

be observed. An acceptable agreement between the SC model

prediction and the FEM results is also established.

To provide a better insight into the root differences be-

tween the heat conduction mechanisms in different configu-

ration some sample FEM simulation results are provided here.

Fig. 7 illustrates finite element predictions of the distribution

of the actual heat flux in the simulation cuboids representing

two different configurations. Fig. 7a, b are illustrating the

) GNP/epoxy (b) CNT/epoxy and (c) hybrid CNT/GNP/epoxy

xp.: experimental measurements, SC: modified strong-

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Fig. 7 – Finite element calculation of the actual heat flux (W/m2) distribution in the representative simulation cuboid. (a, b)

show the external and internal distribution of the heat flux for the hybrid configuration with 5%wt GNPs and 0.5%wt CNT, (c,

d) show corresponding result for the binary configuration with 5%wt CNTs.

C A R B O N 6 4 ( 2 0 1 3 ) 1 1 1 – 1 2 1 119

distribution of the heat flux in a sample simulation cuboid

representing hybrid configuration with nanofiller loading of

5%wt GNPs and 0.5%wt CNTs. Fig. 7c, d illustrate correspond-

ing result for the binary configuration with 5%wt CNTs. A

comparison between these different configurations provided

implies that in the hybrid configuration a more uniform dis-

tribution for the heat flux can be expected. However for the

binary configuration based on CNTs, the heat flux distribution

is characterized with local concentrations and lower unifor-

mity. This observation reveals the physics behind better ther-

mal conductivity of the hybrid configuration.

5. Conclusions

The transport electrical and thermal properties of polymer

nanocomposites based on CNTs and GNPs were investigated.

A number of polymer nanocomposites comprising 1.0–5.0%wt

of CNTs, GNPs and a combination of both were processed and

characterized. The electrical and thermal conductivities of

the processed specimens were evaluated utilizing newly

developed computational models. The computational models

estimate the transport properties of each configuration by

taking into account the physical properties of its constituents

and their state of dispersion and distribution. In an attempt to

account for nanofillers agglomeration morphology a geomet-

ric model was proposed and implemented in the

computations.

The electrical percolation thresholds of each configuration

were successfully predicted by the proposed MC percolation

model. In agreement with the experimental findings, the

MC model predictions suggested that the CNT/epoxy speci-

mens attain lower percolation threshold and higher electrical

conductivity than the GNP/epoxy specimens. These findings

were attributed to the more facile formation of percolation

network compared for CNTs compared to GNPs. However,

the experimental study showed that the inevitable formation

of agglomeration in high CNT loadings (>2.0%wt) suppresses

further enhancement in the electrical conductivity. The MC

percolation threshold simulation failed to capture this exper-

imental finding as a consequence of the simplified nanoparti-

cle aggregation model. Both the computational and

experimental studies suggest that by incorporating minute

amounts of auxiliary CNTs (10% compared to GNPs), the elec-

trical conductivity enhances drastically by several orders of

magnitudes and the percolation threshold is lowered by

50%. In light of the SEM micrographs, this finding was attrib-

uted to the formation of a hybrid CNT/GNP network with nat-

urally enhanced properties.

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120 C A R B O N 6 4 ( 2 0 1 3 ) 1 1 1 – 1 2 1

The strong contrast and finite element models were em-

ployed to predict the thermal conductivities of the different

nanocomposites. For unique loadings, using the SC model,

the CNT/epoxy specimens were observed to exhibit lower

thermal conductivity compared to the GNP/epoxy specimens.

Finite element simulations confirmed that under ideal inter-

facial properties, the higher surface area of GNPs compared

to CNTs better facilitates phonon transform mechanism. This

computational prediction was also substantiated by the

experimental measurements and is attributed to the more ro-

bust structure of the GNPs and their possible lower particle/

matrix interfacial resistance. Furthermore, the experimental

measurements and computational models suggested that

owing to the formation of the hybrid CNT/GNP network, the

hybrid nanocomposites outperform their counterpart mono-

filler nanocomposites. Finally, this study also confirmed the

synergistic nature of the thermal properties of the hybrid

CNT/GNP/polymer nanocomposites.

The tools developed in this study provide basis for further

development of future multifunctional nanocomposites

based on CNTs and GNPs with tailored electrical and thermal

properties to oblige many applications in the microelectron-

ics, energy and automotive industries.

Acknowledgements

This work has been supported by the Office of Naval Research

(ONR) Grant# 10960991 and the National Science Foundation

(NSF) award CMMI: CAREER-0846589. The authors gratefully

acknowledge this support.

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