Composites Science and Technology 69 (2009) 1016–1021

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Composites Science and Technology

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Dramatic effect of multiwalled carbon nanotubes on the electrical propertiesof alumina based ceramic nanocomposites

Kaleem Ahmad *, Wei PanState Key Laboratory of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, PR China

a r t i c l e i n f o a b s t r a c t

Article history:Received 3 November 2008Received in revised form 10 January 2009Accepted 14 January 2009Available online 23 January 2009

Keywords:A. Carbon nanotubesA. NanocompositesB. Electrical propertiesB. Transport properties

0266-3538/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.compscitech.2009.01.015

* Corresponding author. Tel.: +86 10 62795496; faxE-mail addresses: amd04@mails.tsinghua.edu.cn

tsinghua.edu.cn (W. Pan).

We report recent work on electrical properties of multiwalled carbon nanotubes (MWNTs)/alumina com-posites. The composites with different contents of MWNTs were consolidated by spark plasma sinteringand their temperature dependence dc conductivity was scrutinized in the temperature range from 5 to300 K. The analysis of the temperature dependence of the conductivity suggests that for temperatureshigher than 50 K, conduction can be ascribed to thermal fluctuation induced tunneling of the charge car-riers through insulating barriers between MWNTs, while at temperatures below 50 K, the conduction canbe attributed to three dimensional variable range hopping through MWNTs network in the aluminamatrix. The frequency dependence of the conductivity was studied from 5 to 1.3 � 107 Hz. The universal-ity of the ac conduction in MWNT/alumina composites was examined by construction of master curve.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Carbon nanotubes (CNTs) are promising additive due to theiroutstanding electrical, mechanical, and thermal properties andhave spurred considerable activity in the development of multi-functional value-added ceramic nanocomposites [1]. In particular,multiwalled carbon nanotubes (MWNTs) are getting more atten-tion due to their amazing electrical properties. Novel experimentsuggests multichannel quasiballistic conducting behavior of indi-vidual MWNT which is attributed to participation of multiple wallsin the electrical transport and the large diameter [2]. Furthermore,MWNTs possess high electrical conductivity �1.85 � 103 S/cm, andhuge current density �107 A/cm2 along the long axis [3]. In singlewall carbon nanotube (SWNT), the conductivity depends on thechirality of the graphene sheet [4], while MWNTs are reported tobe always electrically conductive and their large external diameterimplies the existence of a very small band gap for the semiconduc-tor variety. Additionally, cost effective mass production, high as-pect ratio, nanosize, and low density make them the idealcandidate for development of advanced engineering compositematerials. On the other hand alumina is a typical electrically insu-lator and a key engineering material for its structural applicationsin various fields. There are numerous instances, when alumina canbe used as a functional material and increased conductivity of it iswarranted. The present organic electroconductive materials suffersignificant shortfalls in their mechanical properties, heat resis-

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: +86 10 62771160.(K. Ahmad), panw@mail.

tance, and chemical resistance that limit their usefulness while,the electroconductive metal ceramic composites possess poormechanical properties due to high loadings of imbedded metallicparticles and may not retain refractoriness, stiffness, and hardness.In contrast to the numerous available conventional conductive fill-ers, MWNTs provide the lowest possible percolation threshold andimprove the electrical properties of alumina, while keeping itsintrinsic properties further enhancing instead of worsening [5].The addition of low weight fractions of MWNTs in alumina resultsin a unique combination of structural integrity and improved con-ductivity. Their resistance to chemical, corrosion and, generally, tosevere weather conditions, including extreme radiation and ultra-violet exposure makes them suitable for a wide range of possibleapplications. This includes applications that require electrostaticdissipation (antistatic materials) components for aerospace indus-try, electrically conductive guide articles, electromagnetic radia-tion shielded components for bus compartment enclosures,packages, and substrates for electronic applications, heating ele-ments, electrical igniters, electromagnetic and antistatic shieldingof electronic components, electrodes for fuel cells, crucible for vac-uum induction furnaces, and electrical feed through [6–9]. Pres-ently, a lot of studies have been focused to investigate theelectrical properties of CNTs/polymer composites, while in caseof ceramics, most of the efforts have been exerted to improvemechanical properties specially, the fracture toughness. The workon electrical properties of CNT/alumina composites remained a lessfocused area and only a few studies have been published on roomtemperature dc conductivity of the composites [10,11]. However,no work has yet been reported on ac conductivity and lowtemperature dc conductivity behavior of MWNT/alumina

K. Ahmad, W. Pan / Composites Science and Technology 69 (2009) 1016–1021 1017

composites. In order to tailor and optimize the electrical propertiesof insulating alumina as a functional material it is necessary tostudy the effect of different contents of MWNTs on the electricaltransport properties of the composites [12,13]. The present studyfocused on the room temperature dc conductivity, ac conductivity,and low temperature electronic transport behavior of MWNT/alu-mina composites.

2. Experimental

MWNTs were provided by Green Chemical Reaction Engineer-ing and Technology, Tsinghua University, PR China. They were pro-duced by the catalytic decomposition of propylene on Fe/Al2O3

catalyst and having outer diameter around 10 nm and severalmicrometers in length. Special care was taken to disperse MWNTshomogenously in the matrix using the process described elsewhere[5]. In brief, the different (0.3, 0.4, 0.5, 1, 2, 3, 5, and 6) weight frac-tions of MWNTs were mixed ultrasonically with alumina (99.9% inpurity, PR China) in ethanol. Further mixing by ball milling wascarried out for 24 h. After drying, powder mixtures were sparkplasma sintered (Dr. Sinter 1050, Sumitomo Coal Mining Co., Ja-pan) at 1400 �C in vacuum under a pressure of 50 MPa in a20 mm inner diameter cylindrical graphite mold. The dc electricalconductivities were measured by standard four point probe meth-od. The low temperature dc conductivities were measured usingQuantum Design SQUID magnetometer (MPMS-XL7) in the tem-perature range from �5 to �300 K. For AC conductivities, diskshaped samples were prepared of thickness �1 mm and silverpaint were pasted on both sides. Ac conductivity was measuredby the impedance analyzer HP 4192A in the frequency range from5 to 13 MHz at room temperature.

3. Results and discussion

3.1. DC conductivity

The dc conductivity of the composites increases with the in-crease of MWNTs weight fractions (Fig. 1), and exhibits a typicalinsulator–conductor transition between 0.4 and 0.5 wt.% ofMWNTs. The composites display a dramatic increase of aroundeight orders of magnitude in the conductivity for 0.5 wt.% ofMWNTs. More addition of MWNTs up to 1 wt.% increases the con-ductivity further and then it approximately levels off for higher

Fig. 1. DC conductivity of MWNT/alumina composites as a function of MWNTcontents. Inset shows the log–log plot of DC conductivity with (PMWNT � Pc) forPMWNT > Pc.

concentrations of carbon nanotubes. Further detail of room tem-perature dc conductivity of MWNT/alumina composites has beendescribed in our previous investigation [11]. The conductivity(Fig. 1) follows the power law [14] as described below

rdc ¼ rcðPMWNT � PcÞt; for PMWNT > Pc ð1Þ

where rdc and rc are the dc conductivities of the composite andconducting component, respectively. PMWNT is the weight fractionof the MWNT, and Pc is the critical weight fraction or percolationthreshold. The fit to Eq. (1) is shown in the inset of Fig. 1. We findPc = 0.45 ± 0.01 wt.% and t = 1.82 ± 0.02. The exponent t reflectsthe dimensionality of the system and value of t has been found�1.33 and �2.0 corresponding to two and three dimensions, respec-tively. It has been reported that the smaller value of t at room tem-perature arises from thermally induced hopping transport betweendisconnected or weakly connected parts of the conducting network[15]. Furthermore, in carbon nanotube/alumina composites the tun-neling resistance caused by the internanotube connections or insu-lating barrier between nanotubes or their aggregates play adominant role in the effective electrical conductivity of the compos-ites [16] which in turn suggest that conductivity in these compos-ites is controlled by the fluctuation induced tunneling mechanism.Therefore the value of t lower than �2.0 in the present study maynot be the sign of a two dimensional network but can be interpretedas associated to fluctuation induced tunneling mechanism[12,13,17], where thermally induced hopping transport betweenthe CNTs separated by insulating barrier dominates the conductiv-ity behavior. In order to get full insight in the charge transportmechanisms of CNTs/alumina composites and to assess conclu-sively, what mechanism dominates the conduction in different tem-perature regimes, the low temperature dependent dc conductivityanalysis is the appropriate technique. Fig. 2 shows the scanningelectron microscopy image of fracture surface of three weight per-cent (wt.%) of MWNT/alumina composite. The carbon nanotubeslook well dispersed in the alumina matrix by making intertwiningnetwork structure at the grain boundaries. Two conduction pro-cesses maybe proposed, firstly, the conduction between tube–tubewithin a nanotube bundle/rope and secondly, between ropes thatare making interlinked network in the composites.

The low temperature dependent dc electrical conductivities ofthe composites have been investigated above percolation thresh-old for 1, 3, and 5 wt.% of MWNT/alumina composites in the tem-perature range from �5 to �300 K. The results of conductivity as afunction of temperature are plotted in Fig. 3. All the three compos-ites show similar behavior with temperature and their conductiv-

Fig. 2. Uniform distribution of MWNTs in the composite.

Table 1Fitting parameters of T1, T0, and T3DH for the MWNTs/alumina composites.

wt.% of MWNT T1 (K) T0 (K) T3DH (K)

1 226.81 548.87 0.0523 173.54 315.29 1.3935 314.60 458.91 0.632

Fig. 3. Temperature dependence of dc conductivity for 1, 3, and 5 wt.% of MWNT/alumina composites. Insets show variable range hopping from �5 to �50 K, while�51 to �300 K show FIT.

1018 K. Ahmad, W. Pan / Composites Science and Technology 69 (2009) 1016–1021

ity value increases with the increase in weight fractions of MWNTs.The increase in the MWNTs wt.% results in the enhanced number ofinternanotube connections, consequently numerous conductivepaths become available. The conductivity value increases due toavailability of substantial number of charge carriers travelingthrough the entire network. The conductivity of the composites

also increases with temperature. This is an indication of semicon-ductor like behavior and suggests that the carrier mobility as wellas thermally generated carrier formation reduces as the tempera-ture decreases.

Various transport models have been proposed to explain thelow temperature conductivity behavior. Sheng describes a mecha-nism for tunneling of electrons through a barrier whose heightchanges depending on the fluctuation of the thermal voltage acrossthe barrier [18]. This is known as fluctuation induced tunneling(FIT) model. Many of the composites system obey this mechanism.In this model the temperature dependence of the sample conduc-tivity is governed by the equation [19]

rdc / exp�T1

ðT þ T0Þ

� �ð2Þ

where

T1 ¼wAe2

0

8pkBð2aÞ

T0 ¼2T1

pwv ð2bÞ

T is the absolute temperature, kB is the Boltzman’s constant,v = (2 mV0/h2)1/2, e0 = 4 V0/ew, m is the electron mass, e is thecharge, V0 is the potential barrier height, w is the insulating layerwidth, and A the area of capacitance formed at the junction. Physi-cally T1 is energy required for an electron to cross the insulatingbarrier between conducting particles and T0 determines the lowtemperature, temperature independent resistivity. This model isbased on the assumption that sample consisting of large intercon-nected conducting regions separated by insulating barriers. A directconsequence of large interconnected conducting regions is that to-tal capacitance (C0) is high and the charging energy e2/2C0, requiredto transfer electron across insulating layer is negligible than ther-mal fluctuation voltage produce at the junction [18]. Therefore,the tunneling probability across the insulating barrier is controlledby the thermal fluctuations produced across the junction. For thepresent studied system, the internanotube resistance between mul-tiwalled carbon nanotubes or tunneling resistance between MWNTaggregates/ropes may act as a potential barrier to electron hopping.Fittings of the FIT model Eq. (2), gives a good description of conduc-tivity data variation with temperature above 50 K (Fig. 3). The val-ues of T1 and T0 for each curve are listed in Table 1. These values aremuch larger than those reported by Sichel and co-workers [20,21].The difference in the values may arise due to the fact that Sichelet al. had studied relatively high content (15–45 wt.%) of carbonblack, in contrast we have used low content (0.3–6 wt.%) of MWNTs.In addition, the values of T0, and T1 also depend on the nature of thehost insulating matrix, the structure of the conductive filler, and itsloading. The low wt.% of CNTs used in this study and the low perco-lation threshold due to large aspect ratio of MWNTs may be attrib-uted to the high values of T1 and T0 observed in this present work.

Below 50 K the FIT model does not describe the experimentaldata accurately due to complex nature of charge transport. A pos-sible explanation is that at temperatures lower than 50 K, the ther-mally induced barrier height fluctuations, ETB = (kBT/C)1/2, becomestoo small and FIT does not determine the conduction mechanismanymore, where C is the capacitance formed by the junction. Alter-

K. Ahmad, W. Pan / Composites Science and Technology 69 (2009) 1016–1021 1019

natively, the effect of charging energy may become more impor-tant, which may lead to deviation from FIT at temperatures below50 K.

It can be easily concluded from Eqs. (2a) and (2b) that ratio ofT1:T0 is proportional to the gap width ‘w’ between conducting par-ticles which is approximately proportional to P�1=3

MWNT [22,23]. Therelationship between T1/T0 and P�1=3

MWNT is almost linear (Fig. 4a)which suggests that fluctuation induced tunneling is appropriateto describe the temperature dependence of conductivity of thesamples above 50 K.

Additionally, several researchers have reported that a linear fitbetween logrdc as a function of P�1=3

MWNT may be used to supportthe fluctuation induced tunneling mechanisms [12,13,24]. It caneasily be seen that for constant temperature Eq. (2) can be writtenin the form [22]

logrdc / �w ð3Þ

This is based on the idea that for homogeneous distribution ofcarbon nanotubes in the alumina, the composite conductivity ata constant given temperature can be described by the behaviorof a single tunnel junction, where the insulating gap width (w)can be assumed to be proportional to P�1=3

MWNT [22] which inturn sug-gest that logrdc/ P�1=3

MWNT i.e. linear relationship between logrdc and

Fig. 4. (a) Plot of T1/T0 vs. MWNT weight fractions P�1=3MWNT and (b) linear variation of

log rdc as a function of P�1=3MWNT .

P�1=3MWNT . The plot between P�1=3

MWNT and logrdc for the present studygives an acceptable linear behavior (Fig. 4b). This further corrobo-rates that the fluctuation induced tunneling mechanism exist inthe composites in the temperature range from 300 to 50 K.

Recently, Skakalova et al. [25] have studied the temperaturedependent electrical conductivity of carbon nanotubes. They dem-onstrated that fluctuation induced tunneling is dominant in indi-vidual MWNT above 40 K and suggested that thermally assistedinter shell transfer of charge carriers occur between concentricshells of MWNT. They further showed that in case of thick SWNTnetwork, the temperature dependent conductivity is consistentwith fluctuation induced tunneling through thin barriers separat-ing metallic regions. Additionally, they observed reduction of theconductivity at higher temperatures as backscattering by phononsincreases. In the present study, the highly elongated MWNTs makeinterconnected network above the percolation threshold and showfluctuation induced tunneling in accordance to Skakalova et al.[25]. However, at higher temperatures due to larger diameter ofMWNTs and intershell transfer of charge carriers, the conductivityhas not been reduced as observed in case of thick SWNT network.Gruner [26] has also emphasized the importance of carbon nano-tube networks due to their numerous applications that rely ontheir conductivity and supported the idea of temperature drivencharge transport across the random barriers in carbon nanotubeinterconnects.

Variable range hopping has been reported as main conductionmechanism in carbon nanotubes at temperature below �50 K[27,28]. This law describes the temperature dependent conductiv-ity behavior of disordered semiconductor materials through vari-able range hopping (VRH) conduction mechanism [29]. Indisordered semiconductors with localized states in the band gap,conduction occurs through phonon-assisted tunneling betweenelectronic localized states centered at different positions, thismechanism of conduction is called VRH. As the thermal energykBT decreases with temperature, there is lesser number of nearbystates with accessible energies. Therefore, the mean range of hop-ping increases, which leads to the following expression for theconductivity

rdc ¼ r0 exp � T3DH

T

� �c� �ð4Þ

where, T is the temperature and T3DH is the characteristic tempera-ture, which generally depends on the electronic structure and theenergy distribution of localized states. For hopping in three dimen-sions, the exponent ‘c’ has the value c = 1/4. The randomly distrib-uted multiwalled carbon nanotubes in alumina matrix are making athree dimensional (3D) network along the grain boundaries (Fig. 2)that suggests a 3D VRH conduction process. The insets in Fig. 3show qualitatively that 3D VRH conduction mechanism is appropri-ate to describe the conductivity behavior below 50 K for c = 1/4.This type of conductivity behavior is a signature of localized carriershopping. In order to verify it further nonlinear curve fitting was per-formed in the temperature range 5–50 K. The solid lines show bestfit to the data with c = 0.25 for temperature below 50 K as shown inthe Fig. 3. The values of the parameter T3DH, derived from the fittingcurves are listed in Table 1. The exponent c = 1/4 instead of c = 1/2suggests that the Coulomb blockade effect may be negligible for allthe samples in the measured temperature range. The value ofc = 1/4 has been widely reported in the literature for CNTs or theircomposite [27,30,31]. While, Benoit et al. [32] have reported the va-lue of c = 1/2 in describing the electrical transport behavior ofSWNT/polymer composites. They suggest that Coulomb interac-tions are effective in dilute SWNT systems and these Coulomb inter-actions arise from the charging energy, limit the transport at lowtemperature. Yosida et al. [27,31] also reported 3D VRH conduction

1020 K. Ahmad, W. Pan / Composites Science and Technology 69 (2009) 1016–1021

in MWNTs below 50 K and suggest that a steep decrease in the con-ductivity at low temperature is characteristic of weekly localizedsystem. The values of T3DH listed in Table 1 are close to the valuesreported by Yosida et al. [31] for MWNTs in the same temperaturerange (below �50 K).

3.2. AC conductivity

Fig. 5a shows a log–log plot of the frequency dependent conduc-tivity of the nanocomposites containing different weight fractionsof multiwalled carbon nanotubes at room temperature. The changein ac conductivity with frequency provides information about theoverall connectivity of the conducting network in the compositesand allows distinguishing clearly between conducting samplesand dielectric samples. For samples above the percolation thresh-old Pc, the conductivity is initially constant and then starts to in-crease at higher frequencies. For 6 wt.% of MWNTs/aluminacomposites, the conductivity becomes frequency independent overthe entire frequency range investigated, indicating a nondielectricbehavior. Below Pc, for 0.4 wt.% of MWNTs/alumina composite theac conductivity increases almost linearly with frequency and theslope of the conductivity curve is close to unity which is commonlyobserved for a wide range of highly resistive materials. The

Fig. 5. (a) Frequency dependent conductivity of the composites and (b) mastercurve showing the ac conductivity for MWNT/alumina composites. The solid line isa fit to the extended pair approximation model.

observed slope is in good agreement with the expressionr ¼ 2pf e

0e0 valid for dielectric materials, where r is the conductiv-

ity, e0

is the imaginary term of the dielectric constant, and e0 is thevacuum permittivity.

3.3. Master curve

It is well established through several studies that universality ofac conduction is common in many disordered materials [33]. It hasbeen observed that the shape of the ac conductivity curves is inde-pendent of PMWNT and that only the value of dc conductivity andthe critical frequency fc depend on PMWNT [12,13]. Therefore, it ispossible to construct a master curve independent of PMWNT onthe normalized conductivity r/r0 and as a function of aSF. f, whereaSF is the shift factor depending on PMWNT [22]. The shift factor canbe defined as

aSF ¼fc�ref

fcð5Þ

where, fc�ref is the critical frequency of the reference composite ofMWNT concentration of Pref�r/r0 versus aSF. f is plotted in Fig. 5busing Pref = 5 wt.% of MWNTs as a reference concentration andfc�ref = 3.174 � 106 Hz as reference frequency. The experimentaldefinition of critical frequency ‘fc’ as reported by Kilbride et al.[13] was applied to the frequency dependent conductivity curves.The value of the dc conductivity r0, critical frequency fc, and shiftfactor aSF for the other curves are listed in Table 2. We can see thatall scaled curves follow the similar behavior and formed a singlemaster curve (Fig. 5b). The master curve demonstrates a frequencyrelated conductivity behavior of specific conductor–insulator com-posites over a frequency range much larger than the frequencyrange experimentally available [22]. It has been reported that theextended pair approximation model can be used to describe mastercurve behavior using the following equation [13,34].

rðf Þr0¼ 1þ C

ffc

� �x

ð6Þ

The solid curve in Fig. 5b is a fit to the Eq. (6). The exponent x of themaster curve is �0.80 ± 0.02 indicative of the universality in the acconduction. It has been reported that an approximate power law ofthis form with exponent value in the range 0.7 6 x 6 1.0 is charac-teristic of hopping in a disordered material where, the hoppingcharge carriers are subject to spatially randomly varying energybarriers [35]. This agrees well with the fluctuation induced tunnel-ing model where the barrier height varies due to local random tem-perature fluctuations.

4. Conclusions

Alumina composites mixed by different contents of MWNTsranging from 0.3 to 6 wt.% were consolidated by spark plasma sin-tering. DC electrical transport phenomenon of the composites aredescribed in terms of fluctuation induced tunneling and Motts’slaw for 3D VRH. From room temperature down to 50 K, the con-duction is governed by quantum mechanical tunneling of thecharge carriers through thermally activated fluctuating potential

Table 2Values of r0, fc, and aSF for different weight fractions of MWNTs.

wt.% of MWNT r0 (S/m) fc (Hz) aSF

0.5 1.6 � 10�4 1.519 � 103 2089.531.0 0.112 2.363 � 105 13.433.0 1.245 1.403 � 106 2.265.0 3.545 3.174 � 106 1.00

K. Ahmad, W. Pan / Composites Science and Technology 69 (2009) 1016–1021 1021

barriers formed across the insulating barriers separating twoneighboring conductive MWNTs/aggregates. For temperature low-er than 50 K, the conduction can be best described by the Motts’s3D VRH through tri-dimensional intertwining network of MWNTsin the matrix. The frequency dependence of measured conductivi-ties showed a typical characteristic of the universal dynamic re-sponse curve, which followed a power law with exponent0.7 6 x 6 1, an indication of hopping conductivity.

Acknowledgments

We thank National Natural Science Foundation of China (GrantNos. 50232020 and 50572024) and HEC for financial support.

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