thermal conductivity of micro/nano filler filled polymeric composites

Cite this: RSC Advances, 2013, 3,6417

Thermal conductivity of micro/nano filler filledpolymeric composites

Received 11th October 2012,Accepted 4th February 2013

DOI: 10.1039/c3ra22482a

www.rsc.org/advances

Zhiguo Li,*ab Wenjing Wu,a Hong Chen,b Zhenhua Zhu,b Youshan Wangc

and Yong Zhanga

The thermal conductivity of emulsion-polymerized styrene–butadiene rubber (ESBR) composites filled with

carbon nanotubes (CNTs), zinc oxide (ZnO) and alumina (Al2O3) was predicted using the finite element

method (FEM). Two-dimensional (2D) FEM models, which involved the effects of aspect ratio (AR), shape,

orientation and thermal conductivity anisotropy (TCA) of the CNTs, and interfacial thermal resistance (ITR),

were used to simulate the microstructure of CNT filled ESBR composites. Also, 2D and three-dimensional

(3D) FEM models were developed to simulate the microstructure of Al2O3 or ZnO filled ESBR composites.

An increase in the thermal conductivity with increasing Al2O3 or ZnO loadings was predicted by the FEM.

The orientation angle (OA) of the CNTs and the ITR strongly affect the thermal conductivity as predicted by

the FEM. The TCA of the CNTs also has a prominent effect on the thermal conductivity when CNTs have a

relatively small OA. At a given filler loading, the thermal conductivity increased with the increasing intrinsic

thermal conductivity of the filler over a certain range for a particular shape of filler. The thermal

conductivities predicted by the FEM were compared with those predicted by Agari’s models and the

experimental results. The trends of the thermal conductivity predicted by the FEM agreed with the

experimental data. The thermal conductivity of the ESBR composites predicted by 2D and 3D spherical

particle filler (SPF) FEM models as a function of ZnO and Al2O3 loading showed that the 3D SPF FEM model

agreed well with the experimental results at low loadings (not higher than 20 phr), while the 2D SPF FEM

model agreed well with the experimental results at high loadings (higher than 80 phr). In addition to

being used for the analysis of existing composites, the proposed FEM models are useful for the design and

optimization of new composite materials, and are expected to provide a more insightful understanding

into the thermal conductivity of polymeric composites.

Introduction

Currently, the thermal conductivity of rubber composites is amajor concern. It is especially important for applications inthe aerospace industry and for use as electronics packagingmaterials,1,2 where effective heat dissipation is a key factor.Recently, in the tire industry, with the increasing demand fortires that show a high performance, such as high speed andlong service life, there are a number of requirements for tirerubber composites. Among these requirements, high thermalconductivity is urgently needed, because good heat dissipationin tires can guarantee the normal performance of the tires andprolong their service life. Due to the restrictions of cost andtime, the tire industry now is faced with the issue of producinga good quality tire in a short time period. Contemporary tireengineers should be able to apply numerical techniques fordesign, qualification and verification during the development

of a prototype, as numerical simulations, such as the finiteelement method (FEM), can shorten the product design cycle,decrease the design and trial-product cost and remarkablyimprove the product quality.3 However, tire rubber compositesgenerally have a low thermal conductivity, which essentiallylimits their utilization in high performance tires, such as foraircraft and as racing tires. An understanding of the relation-ship between the structure and the thermal conductivity iscrucial for designing and fabricating tire rubber compositeswith a high thermal conductivity.4,5

ESBR is widely used in car tire treads because of itsadvantage over solution-polymerized styrene–butadiene rub-ber in lowering the cost of the product. ESBR composites canbe tailored to have diverse dynamic mechanical properties tosuit specific tire applications by various means, such as theintroduction of liquid isoprene rubber.6 However, their use inhigh performance tires is considerably limited due to their lowthermal conductivity and high heat generation.7,8 ESBRcomposites are multi-component systems, and their heattransfer is quite complicated. Although many papers existconcerning the mechanical properties of ESBR composite

aState Key Lab of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai

200240, China. E-mail: [email protected] Zhongce Rubber Co., Ltd., Hangzhou 310008, ChinacHarbin Institute of Technology, Harbin 150080, China

RSC Advances

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This journal is � The Royal Society of Chemistry 2013 RSC Adv., 2013, 3, 6417–6428 | 6417

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materials, only limited information is available on theirthermal conductivity.9–13 There are few comprehensive meth-ods that can be utilized either for fabricating ESBR compositeswith a certain thermal conductivity or for carrying out ‘what if’types of simulations to assess the effects of certain factors,14

such as the content, orientation and thermal conductivityanisotropy (TCA) of the filler and interfacial thermal resistance(ITR), on the thermal conductivity of ESBR composites.

FEM modelling is a predictive tool in the development ofnew composite materials directed towards improving theirthermal performance. Optimum matrix and filler propertiessuch as shape, size, size distribution and thermal conductivitycould be predicted, thereby reducing the development timeand improving the product performance.3,15,16 The FEM canbe used to study heat transfer in composites.17,18 Ramaniet al.19 studied the effects of filler dispersion, ITR and fiberaspect ratio (AR) on the thermal conductivity of compositesusing the FEM. Bakker20 calculated the thermal conductivity ofporous materials using the FEM and studied the relationshipbetween the two-dimensional (2D) values and the threedimensional (3D) values. We have recently studied the effectsof the aspect ratio, shape, particle size and mass ratio ofsilicon carbide on the thermal conductivity of ESBR compo-sites using a 2D FEM model.21 A literature survey reveals thatonly a few finite element analyses have so far been used tostudy how the microstructural characteristics of composites,such as the interactions, the AR of the filler and the ITR, effectthe thermal conductivity.

The filler AR affects the dispersion of the filler and theformation of conductive chains, which consequently affectsthe thermal conductivity. It determines the packing efficiencyof the filler in the composite. With higher ARs, conductivechains tend to form at lower filler loadings. So fillers with ahigh AR are usually effective in improving heat transferthrough the composite. Since carbon nanotubes (CNTs) havevery large ARs (approximately 2000),22 they can improve thethermal conductivity of ESBR composites. The thermalconductivity of polymers can be increased when they are filledwith CNTs.23,24 A prominent issue related to the preparation ofCNT nanocomposites is the alignment of the CNTs in thematrix, which is directly related to their thermal performances.Fillers oriented with a certain angle would be beneficial for theenhancement of the thermal conductivity of polymer compo-sites.25,26 Han et al.25 achieved the orientation of boron nitride(BN) particles along an electric field. The electric field assistedthermal curing had a significant effect on the thermalconductivity of the composites due to the shape anisotropyand the TCA of the filler particle. Wang et al.26 prepared 25kinds of epoxy/BN composites. An appropriate method used toobtain a high thermal conductivity involved orientating flakyh-BN in the vertical direction to the sample surface. Huanget al.27 prepared an aligned CNT composite film that had ahigher thermal conductivity than that of randomly dispersedCNT composites. Xu et al.28 synthesized poly(methyl metha-crylate) (PMMA)/aligned carbon nanotube (ACNT) compositeswith a thermal conductivity that was 12.64 times higher than

that of PMMA. The alignment of the CNTs in a rubber matrixresulted in a significant improvement in the elastic modulusand the thermal and electrical conductivities.29 The thermalconductivity of the aligned carbon nanotube/carbon (ACNT/C)nanocomposite is about 3 times higher than that of the carbonfiber reinforced carbon matrix (C/C) composite, even thoughthe fraction of ACNTs in the ACNT/C nanocomposite is abouthalf the amount of the carbon fiber in the C/C composite.30 Inconclusion, if the fillers can be oriented at a certainorientation angle (OA), the resultant composite should havea high thermal conductivity.

The thermal conductivity is constrained by the existingthermal contact resistance between the filler particles or thematrix and the filler. The thermal contact resistance dependson both the material property constants and the geometricparameters of the contact area between the particles.3 Oneprobable reason for the marked disparity existing between thepredicted thermal conductivities of the CNT filled compositesand the experimental results is that a high resistance at thenanotube–matrix or nanotube–nanotube interface limits ther-mal transport along the network of CNTs. Huang et al.27 foundthat the enhanced thermal conductivity of the CNT-compositewas far below those predicted using the ‘law of mixtures’. Thepossible reason for this was the existence of a ITR between theoverlaps in the CNT network. The simulation of heat transferbetween the CNTs shows a high thermal resistance. When thenanotubes form a network, the thermal conductivity of thecomposite is mainly controlled by interface thermal conduc-tance.31 Also, related work indicates that improving interfacecontacts between the CNTs and the matrix can reduce the totalthermal resistance.32 Moreover, in a real CNT-composite, thecarbon nanotubes are not uniform in size and shape. They canbe straight, twisted, curled or in the form of ropes and theirdistribution and orientation in the matrix can be nonuniform,unidirectional or random.33 The FEM can help to understandthe relationship between the geometrical characteristic (e.g.CNT orientation) and the thermal conductivity of the CNT-composites. Therefore, simulating the effect of the orientationand TCA of the CNTs and the ITR on the thermal conductivityof the composites would be feasible and have theoretical andpractical meaning.

This paper aimed to study the effects of the micro/nanofillers on the thermal conductivity of the ESBR compositesusing the FEM with the aid of software named ABAQUS. Themodels were based on the finite element solution of thesteady-state heat transfer equation. 2D and 3D FEM models,which were developed using ABAQUS, were used to simulatethe microstructure of the ESBR composites. The effects of type,loading, intrinsic conductivity, orientation and TCA of thefiller and ITR on the thermal conductivity of the ESBRcomposites have been studied by FEM. A main goal of thisstudy was to find out whether the thermal conductivity woulddepend on the above-mentioned factors and to what extent.This paper also aimed to provide theoretical foundations andpractical reference methods for tailoring the thermal con-ductivity of the ESBR composites. Moreover, the thermal

6418 | RSC Adv., 2013, 3, 6417–6428 This journal is � The Royal Society of Chemistry 2013

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conductivities of the ESBR composites predicted by FEM werecompared with those predicted by Agari’s models andavailable experimental results, to confirm the accuracy andvalidity of the proposed FEM models. The proposed FEMmodels can be used as an optimization tool in the develop-ment of new composite materials with different constituents,different types, loadings and orientations of filler, anddifferent microstructures.

2 Finite element simulation

FEM is a widely used numerical tool for analyzing thermal andstructural problems. Assumptions in geometry and physicalproperties have to be made before solving problems. In orderto simulate the thermal properties of the ESBR composites, thefollowing assumptions were made in the present work:

1. The microstructures of the ESBR composites are createdby a representative cubic unit cell containing filler particles.

2. The thermal conductivity of both the matrix and the filler(Al2O3, ZnO) are isotropic.

3. The temperature is assumed to be constant in the ESBRcomposites at any moment. The thermal properties of thematrix and filler are temperature independent over thetemperature range of 25–55 uC, which is used in the FEMmodels.

Based on the above assumptions, FEM models for calculat-ing the thermal conductivity of the ESBR composites wereestablished. Thermal analysis of the heat transfer in the ESBRcomposites was carried out using ABAQUS. 2D FEM models ofa rectangular filler with an AR (length/width) of 125 randomly-dispersed in a cubic region were developed for the CNT filledESBR composites. A 2D FEM model (randomly-dispersedspherical filler) and a 3D FEM model (uniformly-dispersedspherical, cubic or three mutually orthogonal intersectingcylinder-based filler (TMOICF)) were developed for the Al2O3 orZnO filled ESBR composites, respectively. To describe themicrostructure of the ESBR composites, the FEM modelsinvolved the AR, shape and particle size of the filler, and theTCA, orientation and ITR of the CNTs. The physical propertiesof the ESBR, Al2O3, ZnO and the CNTs are listed in Table 1.

2.1 Finite element modeling

2D model. The 2D finite element model consisted of a cubic(foursquare for two-dimensional) matrix region with sphericalor rectangular fillers (AR of 125) dispersed within this region.

It was modeled using a representative cubic unit cell with aside length of a = 176 mm for ZnO filled ESBR composites, a =520 mm for Al2O3 filled ESBR composites, and a = 2 mm for CNTfilled ESBR composites (kept constant). The diameter of thespherical particle in the simulation is about 100 mm for Al2O3

and about 45 mm for ZnO. The rectangular CNT particle has alength of 1.5 mm and a width of 0.012 mm. Examples of thesemodels (with a spherical or rectangular filler) and correspond-ing meshing of these unit cells are all shown in Fig. 1. Torepresent different filler loadings, the filler particles wererandomly added to the cubic region, and the correspondingregions of the ESBR matrix were removed. For a given fillerloading, the filler volume fraction can be calculated.Considering the 2D FEM model, we take the filler volumefraction to the power of two-thirds as the filler area fraction. Inorder to obtain stable predicted thermal conductivities usingthe FEM models, each model was calculated with three

Table 1 Physical properties of the ESBR and conductive fillers

Material Density (g cm23) Diameter (mm) Particle shape Thermal conductivity (W m21 K21)

Matrix ESBR compound 0.93 — — 0.2Filler Al2O3 3.95 75–150 Irregular 10CNTa 1.30 0.004b/0.012c Tubulous 2400/20d

ZnO 5.61 45 Irregular 25

a The average length of the CNT is 1.5 mm. b The average inner diameter of the CNT. c The average outer diameter of the CNT. d Thermalconductivity in the direction vertical to the axial direction of the CNT.

Fig. 1 2D FEM models of the ESBR composites : (a) the microstructure of theESBR composite filled with spherical Al2O3 particles; (b) the corresponding meshfor the spherical filler; (c) the microstructure of the CNT-filled ESBR compositewith a rectangular CNT filler; (d) the corresponding mesh for the rectangularfiller


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randomly dispersed patterns. In this study, the thermalconductivity predicted by the FEM models takes the averagevalue from three calculated data sets that come from the threekinds of filler particle dispersion patterns.

3D model. The 3D finite element model consisted of a cubicmatrix region with a spherical or cubic filler or a TMOICFdispersed within this region. TMOICF was modeled usingeither a representative cubic unit cell with a side length of a =200 mm, which contained TMOICF with a fixed-length of 140mm for Al2O3; or using a representative cubic unit cell with aside length of a = 60 mm, which contained TMOICF particleswith a fixed-length of 40 mm for ZnO. The diameter of thecylindrical filler varied according to the filler loadings. Thespherical and cubic fillers were modeled using a representativecubic unit cell containing a fixed diameter (for the sphericalfiller) or side length (for the cubic filler) of 75 mm for Al2O3 and45 mm for ZnO. The side length of the cubic unit cell variedaccording to the filler loadings. Examples of these models(spherical, cubic or TMOICF) and the corresponding meshingof the unit cells are all shown in Fig. 2. In the simulation, thefiller loading was varied to understand its effect on thethermal conductivity of the ESBR composites.

The way we mesh the FEM models has a great impact on theprecision, solution time, and calculation quantity.2 To getprecise results and save time, we have meshed the FEMmodels with average side length of almost 1 mm for each meshfor ZnO or Al2O3 filled ESBR composites and almost 0.01 mmfor each mesh for the CNT filled ESBR composites.

2.2 Thermal conductivity determination

In this study, FEM models were developed to represent a unitcell in the ESBR composites. A homogenization scheme can beused to define the thermal conductivity of the ESBRcomposites. To quantitatively study the effect of ITR on thethermal conductivity of the ESBR composite, in our FEMmodel, a very thin layer between the CNT and the ESBR matrixwith a thermal conductivity of 0.01 W m21 K21 is used torepresent ITR.

The heat flux (q) through a unit cell is defined by16

q~

ðqidF~{k

LT

Lx(1)

where x denotes the Cartesian coordinate system, T thetemperature, k the thermal conductivity and F the thermalconductive area. The numerical procedure involves solving thesteady-state heat transfer equation.

+?(2 k+T) = 0 (2)

The one-direction heat transfer problem is required to have azero heat flux through the sides parallel to the flux as theboundary conditions. Adiabatic boundary conditions are usedfor the side surfaces and isothermal boundary conditions areused for the top and bottom surfaces in the finite elementmodels, as shown in Fig. 3. The steady-state heat transferproblem is solved using ABAQUS. The heat flux (q) across thetop and bottom surfaces, is calculated by averaging the heatflux at the nodes on the respective surfaces.19

Fig. 2 3D FEM models of the ZnO-filled ESBR composites at the filler loading of 100 phr: (a) the scheme showing a TMOICF particle; (b) the corresponding mesh forthe TMOICF particle; (c) the scheme showing a spherical particle; (d) the corresponding mesh for the spherical particle filler; (e) the scheme showing a cubic particle;(f) the corresponding mesh for the cubic particle filler.


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An adiabatic boundary condition is applied to the sidesurfaces and therefore,

q~{kLT

Lx~0 at x~{

a

2and

a

2mmð Þ for ESBR composites (3)

The temperature is constant at the top and bottom surfaces.Thus,

T~T0~25 0C at y~a


T~T1~55 0C at y~{a


T0 and T1 are constant temperatures imposed on the top andbottom surfaces of the unit cells. FEM was used to solve eqn(2) with boundary conditions shown in eqn (3), (4) and (5). Thethermal conductivity of the ESBR composites can then becalculated using eqn (1). Finite element analysis of the ESBRcomposites was conducted using ABAQUS. The filler and ESBRmatrix were simulated using three-node triangular heattransfer elements for the 2D FEM models and ten-nodequadratic tetrahedron heat transfer elements for the 3D FEMmodels.

3 Results and discussion

3.1 The effect of filler loading on the thermal conductivity ofthe ESBR composites

A theoretical analysis of the thermal conductivity for particu-late composites was conducted using Agari’s model.34,35 Thethermal conductivity of a composite can be expressed as afunction of the properties of its components according to eqn(6):

log kc = V(X2C2 log k2 + X3C3 log k3 + …) + (12V) log(C1k1) (6)

where k1, k2, k3, are the thermal conductivities of the polymerand particles; X2, X3, are the mixing ratios of the particles, andV is the volume content of the particles. Parameters C1, C2 andC3 are experimentally determined constants of order unity. C1

is a measure of the effect of the particles on the secondarystructure of the polymer, such as the crystallinity and crystalsize of the polymer, whereas C2 and C3 measure the ease withwhich the particles form conductive chains.35,36

In Fig. 4 and 5, the thermal conductivities of the ESBRcomposites filled with Al2O3 or ZnO were shown as functionsof the filler loading, which were predicted by several FEMmodels (TMOICF, 2D and 3D spherical particle filler (SPF),cubic particle filler (CPF)) and compared with the experi-

Fig. 3 Boundary conditions used for the FEM models of the ESBR composites: (a) 2D; (b) 3D.

Fig. 4 Thermal conductivity versus filler loading for the ESBR composites filledwith Al2O3.


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mental data and the semi-empirical Agari’s model. Thethermal conductivities increased with an increase in fillerloading in all FEM models, Agari’s model and in theexperimental data. The closest prediction to the experimentalresults was achieved using Agari’s model. In contrast, at lowfiller loadings (¡20 phr), the thermal conductivities of theESBR composites predicted by the TMOICF FEM model werehigher than the experimental data, while at high filler loadings(¢80 phr), the thermal conductivities predicted by theTMOICF FEM model were very close to the experimental data.On the other hand, at low loadings (¡20 phr), the thermalconductivities predicted by the CPF FEM model agreed wellwith the experimental data, while at high loadings (¢80 phr),the thermal conductivities predicted by the CPF FEM modelwere lower than the experimental data. A comparison of thethermal conductivities predicted by the 2D and 3D SPF FEMmodels as a function of the filler loading showed that the 3DSPF FEM model agreed well with the experimental data at lowloadings (¡20 phr), while the 2D SPF FEM model agreed wellwith the experimental data at high loadings (¢80 phr).

The above phenomena could be explained by the followingreasons: in the dispersion system with a low filler loading, fewparticles contributed to form conductive chains, and underthese conditions the matrix polymer was almost continuous.Thus, the fillers’ contribution to the thermal conductivity of acomposite seemed to be less than that of the matrix, and theESBR composites showed a low thermal conductivity. 3D SPFor CPF FEM models were established with a spherical or cubicfiller located in the center of a cubic matrix. The assumptionwas made that the representative unit cells were uniformlydistributed in the ESBR composites. At a low filler loading, thefiller particles could not touch each other to form conductivechains, so the two kinds of FEM model might accurately reflectthe real microstructure of the ESBR composites. At a high fillerloading, there are a large number of filler particles, whichenables the formation of conductive chains and thus greatlycontribute to the thermal conductivity of the ESBR composites.The 2D SPF FEM model and the 3D TMOICF FEM model,

involving the filler–filler interactions and the possible forma-tion of conductive chains of filler, would be better than the 3DSPF or the CPF FEM models for accurately predicting thethermal conductivities of the ESBR composites. At a low fillerloading, the TMOICF and 2D SPF FEM models mightoverestimate the formation of thermally conductive paths. Ingeneral, the thermal conductivities of the ESBR composites atrelatively low filler loadings predicted by the FEM models weresimilar to the experimental data, implying the effectiveness ofFEM.

3.2 The effect of the intrinsic conductivity of the filler on thethermal conductivity of the ESBR composites

In order to provide an insight for designing thermallyconductive ESBR composites, and especially for tailoring theirthermal conductivity by selecting fillers with appropriatethermal conductivity, FEM models were developed in whichthe thermal conductivity assigned to the filler was varied from0.01 to 12 times the initial value, so that the effects of thisparameter on the thermal conductivity of ESBR compositescould be studies.

Fig. 6 shows the effect of the intrinsic thermal conductivityof the filler on the thermal conductivity of the ESBRcomposites. A plateau was reached when the thermalconductivity of the filler is greater than 40 W m21 K21, andthis is shown even at a high filler loading of 100 phr.Therefore, for the ESBR matrix, it is not necessary to use a fillerwith a thermal conductivity that is higher than 40 W m21 K21,as the FEM model predicts that the maximum thermalconductivity of the filler required for the ESBR matrix is about40 W m21 K21. However, when very high filler loadings, suchas 300 phr or more, are required (which are beyond the scopeof the present work), fillers may start to create conductivechains via agglomeration. In those cases, the use of fillers withvery high thermal conductivity would be also meaningful.

Fig. 6 shows that the thermal conductivity of the ESBRcomposites increases when the thermal conductivity of thefiller is increased from 0.1 to 120 W m21 K21. Furthermore,the higher the filler loading, the higher the thermalconductivity of the filler, when the thermal conductivity ofthe ESBR composites reaches its plateau value (Fig. 6a, b, c).For spherical or cubic particle fillers, the plateau value of thethermal conductivity is reached at a low filler loading of 10phr, when the thermal conductivity of filler is greater than 10W m21 K21. Above this value, the intrinsic conductivity of fillerhas an insignificant effect on the thermal conductivity. At ahigh filler loading of 100 phr, only when the thermalconductivity of filler is greater than 40 W m21 K21, is theplateau value of the thermal conductivity reached (Fig. 6d, e).However, for the TMOIC filler, the above trend disappeared(Fig. 6f).

At a relatively high level of thermal conductivity of the filler(.20 W m21 K21), the thermal conductivity of the ESBRcomposites shows a fast increase when the filler loading isincreased. The reason for this may be due to the fact that forthe ESBR composites, heat is transferred through theconductive paths which are mainly formed by filler particles.On increasing the filler loading, more conductive paths areformed, so most of the heat is transferred faster along the

Fig. 5 Thermal conductivity versus filler loading for the ESBR composites filledwith ZnO.


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conductive paths, and thus the thermal conductivity of theESBR composite increases rapidly. However, over a relativelylow range of thermal conductivity of the filler (¡20 W m21

K21), with increasing filler loading, the thermal conductivity ofthe ESBR composites increases more slowly compared with thesamples containing a filler with a high thermal conductivity(Fig. 6d, e, f). The reason for this may be due to the fact that

the relatively low thermal conductivity of the fillers limited theability of heat transferring across the ESBR composite. At thesame filler loading, the thermal conductivity of the ESBRcomposites predicted by the CPF FEM model was higher thanthat predicted by the SPF FEM model. The reason for this isdue to the fact that the cubic particle has a larger surface areathan the spherical particle of the same volume. Therefore, the

Fig. 6 The effect of the intrinsic thermal conductivity of the fillers on the thermal conductivity of the ESBR composites filled with fillers of different shapes at threedifferent filler loadings: (a) 10 phr; (b) 40 phr; (c) 100 phr; (d) cubic; (e) spherical; (f) TMOICF. a Thermal conductivity of ESBR composite. b Thermal conductivity of filler.c See ref. 13.


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cubic particle has a larger contact area with the ESBR matrixcompared with the spherical particle, promoting the increasein the thermal conductivity of the ESBR composites. Accordingto the above trends predicted by the FEM models, it should benoted that the thermal conductivity of the ESBR compositescould not increase infinitely when increasing the thermalconductivity of the filler.

3.3 The effect of the orientation of the filler on the thermalconductivity of the CNT-filled ESBR composites

The orientation of the filler as a result of alignment is expectedto have a significant effect on the conductivity of thecomposites.18 It should be of great significance and value tostudy the effect of the orientation of the filler on the thermalconductivity of the ESBR composites, which not only deepensour understanding of the thermal conductivity mechanism,but also provides good solutions and ideas for developingcomposite materials with high thermal conductivity.

An example of the FEM models for the ESBR compositesfilled with CNTs oriented with a 10 degree deviation from theheat flow direction is shown in Fig. 7. As a comparison, therandomly oriented case is also shown in the figure.

The thermal conductivity of the ESBR composites filled with0.4 vol% (0.7 phr) and 1.5 vol% (3 phr) CNT particles (with anAR of 125) predicted by the FEM models is shown in Fig. 8.With an increasing OA of the CNTs, the thermal conductivityshowed an obvious decrease. At a CNT loading of 0.7 phr, byincreasing the OA from 0 degrees to 90 degrees, the thermalconductivity decreased from 0.64 W m21 K21 to 0.215 W m21

K21. The reason for this may be due to the fact that longerconductive paths could be produced for heat transport whenthe OA increased.

Fig. 8 shows that when the OA is small, such as 10 degrees,the addition of a very small amount of CNTs (0.4 vol%) canlead to an obvious increase in the thermal conductivity.Compared with reported data from other similar rubbercomposite systems, which showed an increase of 0.65 Wm21 K2127 at the same CNT loading, the thermal conductivity

predicted by our FEM model with an OA of 0 degrees is a littlelow. The reason for this may be due to the fact that the AR ofthe CNTs in our FEM model is 125, which is lower than in thereal case (approximately 2000).22 We can also find that at acertain OA, increasing the CNT loading from 0.4 vol% to 1.5vol%, only led to a relatively small increase in the thermalconductivity. Moreover, when increasing the OA of the CNT,the enhanced value of the thermal conductivity was smaller. Itshould be concluded that with a relatively low filler loading,the primary factor in tuning the thermal conductivity is theorientation of the CNTs. In contrast, the amount of CNTs is aminor factor.

Our previous work on the thermal conductivity of the CNTfilled ESBR composites showed that at a CNT loading of 3 phr,the thermal conductivity was relatively low (0.216 W m21

Fig. 7 FEM models for the ESBR composites filled with 0.4 vol% CNT particles: (a) randomly oriented; (b) oriented with a 10 degree deviation from the heat flowdirection (the heat flow direction is along the y-axis; the white parts represent the voids (when considering ITR); the yellow parts represent the CNTs; the black partsrepresent the ESBR matrix).

Fig. 8 The effect of the orientation of the CNT on the thermal conductivity ofthe ESBR composites at different filler loadings (ITR is neglected). a See ref. 13,27.


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K21),13 which was even lower than the value predicted by theFEM model with an OA of 90 degrees. The reason for this isprobably due to either the existence of ITR between the CNTand the ESBR matrix, the bending, twisting, fracture andagglomeration of the CNTs, or being coated by the ESBRmatrix. So it is necessary to improve interfacial adhesion bysome experimental measures to enhance the thermal con-ductivity without increasing the amount of CNTs. We can alsosee that the thermal conductivity of the ESBR composite filledwith randomly oriented CNTs was relatively high. This mightbe attributed to the high AR of the CNTs, which is helpful forthe conductive chain formation.

3.4 The effect of the ITR on the thermal conductivity of theESBR composites

It is known that the ITR between different constituent phasesin a composite can arise from the combination of poormechanical or chemical adhesion at the interface of the fillerand the matrix and a thermal expansion mismatch. Manyexperiments on the thermal conductivity of various compositesystems have shown that the ITR has a dramatic effect on thethermal conductivity of the composites.38–40 The thermalresistance between the CNTs and the polymer matrix interfaceremains a problem when applying a CNT composite in thermalmanagement. Reducing the ITR between the CNTs and thematrix is important to promote the applications of CNTs inthermal management.32,41,42 Therefore, studying the effect ofthe ITR on the thermal conductivity of the CNT-filled polymercomposites might have theoretical and practical significance.

Fig. 9 shows the effect of the ITR on the thermalconductivity of the ESBR composites filled with 0.7 phr and3 phr CNTs with various OAs. From the figure, when the OA issmall (not more than 10 degrees), the ITR has a very slighteffect on the thermal conductivity with the addition of 0.7 phror 3 phr CNT. However, when increasing the OA, the effect ofthe ITR on the thermal conductivity becomes more prominent.When the OA is 90 degrees, i.e., the orientation of the CNT isperpendicular to the heat flow direction, the effect of the ITRwas at its highest, which led to a relatively low thermalconductivity of 0.156 W m21 K21 at the CNT loading of 0.7 phr,and an even lower value of 0.129 W m21 K21 at the CNTloading of 3 phr. These values are much lower than thethermal conductivity of pure ESBR. When the OA is relativelylarge, the ITR becomes the most critical factor influencingthermal conductivity.

We can also find that at relatively large OAs, a higher CNTloading has a greater effect on the ITR, which effects thethermal conductivity. This might be due to the fact that whenthe CNT loading is increased from 0.7 phr to 3 phr, the volumefraction of the voids (representing the ITR) is also increasedfrom 0.5 vol% to 2.1 vol%, which leads to an increase in ITR.For a randomly dispersed and oriented CNT filled ESBRcomposite, without considering the ITR, the thermal con-ductivity is not as low as expected, and this might be becauseof the high AR of CNTs. In a randomly dispersed and orientedCNT filled ESBR composite, the thermally conductive chainscould form more easily than in a composite with CNTsoriented in one direction (Fig. 7), and therefore, the thermalconductivity is relatively high. However, an enormous effect of

the ITR on the thermal conductivity can also be found. Inparticular, with a CNT loading of 3 phr, the thermalconductivity decreased by 46.4% from 0.694 W m21 K21

(when not considering the ITR) to 0.372 W m21 K21 (whenconsidering ITR). Therefore, the ITR has a great effect on thethermal conductivity of randomly dispersed and oriented CNTfilled ESBR composites as well as on the ESBR compositesfilled with CNT with a large OA.

From the above analyses, the ITR can strongly affect thermalconductivity since different values were predicted at the sameCNT filler loading. Therefore, we should take effective surfacetreatment measures for the CNTs, reducing the ITR which willincrease the thermal conductivity.

Fig. 9 The effect of the ITR on the thermal conductivity of the CNT filled ESBRcomposites at different filler loadings: (a) 0.7 phr; (b) 3 phr. a See ref. 27 and 37.b See ref. 13 and 23.


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3.5 The effect of the TCA of the CNT on the thermalconductivity of the ESBR composites

CNTs are actually a kind of filler with TCA.43–45 Thermalanisotropy is a direct result of the anisotropy in thenanostructure of the CNTs. Studying the effect of theiranisotropy on the thermal conductivity of the ESBR compo-sites by FEM models has very important theoretical andpractical significance for understanding the thermal conduc-tivity mechanism of the ESBR composites filled with this kindof filler, and for taking effective measures to tailor the thermalconductivity.

Fig. 10 shows the effect of the TCA of the CNTs on thethermal conductivity of the ESBR composites with varied OAs(0 degrees, 45 degrees, 90 degrees and randomly oriented).Whether considering the ITR or not, for the ESBR compositesfilled with CNTs with different OAs, when the thermalconductivity of the CNTs in their axis direction remains at aconstant of 2400 W m21 K21, we changed the thermalconductivity of the CNTs in the direction vertical to their axis

from 2400 W m21 K21 to 20 W m21 K21, the thermalconductivity changed very slightly. However, after weexchanged the thermal conductivities of the CNTs in bothdirections (that is, the thermal conductivity of the CNTs in thedirection vertical to their axis remains at a constant of 2400 Wm21 K21, the thermal conductivity of the CNTs in the axisdirection is varied), we were surprised to find that the thermalconductivity showed an obvious change when the thermalconductivity of the CNTs in the axis direction is lower than 20W m21 K21.

The general trend was that when the thermal conductivity ofthe CNT was decreased in the axis direction, the thermalconductivity also decreased. The decrease in the thermalconductivity was even more obvious for OAs of 0 degrees andrandomly oriented CNTs. Therefore, the effect of the TCA ofthe CNT on the thermal conductivity is constrained by the sizeand particular range of thermal conductivity in their axisdirection, as well as their OA. The TCA of the CNT can strongly

Fig. 10 The effect of the TCA of the CNT on the thermal conductivity of the ESBR composites with varied OAs at the filler loading of 0.7 phr: (a) randomly oriented; (b)0 degrees; (c) 45 degrees; (d) 90 degrees. a See ref. 37. b See ref. 27.


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affect the thermal conductivity since different values arepredicted at the same CNT loading of 0.7 phr.

When ITR is considered, the general trend in the effect ofthe TCA of the CNT on the thermal conductivity shows adecrease in the thermal conductivity with the decreasingthermal conductivity of CNT in the axis direction. This trend isalso seen in cases when the ITR is not considered. However,with different OAs of CNTs, the results were different.Specifically the thermal conductivity of the ESBR compositesfilled with CNT with an OA of 0 degrees (Fig. 10b) has thesmallest reduction with ITR, whereas, the thermal conductivityof the ESBR composites filled with randomly dispersed ororiented CNTs with an OA of 90 degrees (Fig. 10a,d) has thegreatest reduction with ITR. As an exception, the thermalconductivity of the ESBR composites filled with CNTs with anOA of 90 degrees remained almost unchanged with variousthermal conductivities of the CNTs. The TCA of the CNT has avery slight effect on the thermal conductivity. The reason forthis might be that for the CNT with an OA of 90 degrees, theadvantage of thermal conductivity in their axis directioncannot affect the thermal conductivity of the ESBR compositesbecause the axis direction is perpendicular to the heat flow.Also, the various thermal conductivities of the CNT in thedirection perpendicular to their axis direction cannot have anotable effect on the thermal conductivity due to thermalconductive paths that are too short, even though the directionis parallel to the heat flow. This proved that the effect of theOA, AR and the TCA of the CNT on the thermal conductivityare interdependent.

It should be concluded that the effects of the TCA of theCNT on the thermal conductivity are the results of their highAR and the particular range of thermal conductivity in theiraxis direction. Specifically, for fillers with high ARs (such asCNTs), the thermal conductivity in their axis direction is acritical factor which strongly affects the resultant composite.However, when thermal conductivity in their axis direction ishigher than a certain value, this effect becomes unclear.Moreover, because of thermal conductive paths that are tooshort in the direction perpendicular to their axis direction, it isdifficult for the various thermal conductivities of the CNTs inthis direction to have notable effect on the thermal con-ductivity of the ESBR composites. The above understandingmight be instructive and would have a great significance for usto use appropriate methods to tailor the thermal conductivityof ESBR composites filled with fillers which have character-istics like CNTs.

Conclusions

In the present work, 2D and 3D FEM models were developed topredict the thermal conductivity of ESBR composites filledwith Al2O3, ZnO and CNTs. The effects of loading, intrinsicconductivity, orientation and TCA of the filler, and ITR on thethermal conductivity were studied. An increase in the thermalconductivity with increasing Al2O3 or ZnO loadings waspredicted by FEM models. The OA of the CNT and the ITRstrongly affects the thermal conductivity as predicted by FEM

models. The TCA of the CNTs also has a prominent effect onthe thermal conductivity at relatively small OAs of CNTs. At agiven filler loading, the thermal conductivity increased withthe increasing intrinsic thermal conductivity of the filler over acertain range for different shapes of filler. Furthermore, thethermal conductivities predicted by FEM models were com-pared with those predicted by Agari’s models and theexperimental results. The trends of the thermal conductivitypredicted by FEM models agreed with the experimental data.The thermal conductivity predicted by the 2D and 3D SPF FEMmodels as a function of ZnO and Al2O3 loadings showed thatthe 3D FEM model agreed well with the experimental results atlow loadings (not higher than 20 phr), while the 2D SPF FEMmodel agreed well with the experimental results at highloadings (higher than 80 phr). It should be feasible to fabricatepolymeric composites with a high thermal conductivity bythese measures (such as controlling appropriate filler OAs,reducing the ITR, etc.), which are suggested by the predictedresults of the proposed FEM models.

List of abbreviations

(According to their order of appearance in the paper.)ESBR emulsion-polymerized styrene–butadiene

rubberFEM finite element methodTCA thermal conductivity anisotropyITR interfacial thermal resistanceAR aspect ratioCNT carbon nanotubesACNT aligned carbon nanotubesACNT/C aligned carbon nanotube/carbonC/C carbon fiber reinforced carbon matrixOA orientation angle2D two-dimensional3D three-dimensionalTMOICF three mutually orthogonal intersecting

cylinder-based fillerSPF spherical particle fillerCPF cubic particle filler

Acknowledgements

This work was supported by the National Natural ScienceFoundation of China (grant no. 51073092).

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thermal conductivity of micro/nano filler filled polymeric composites

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