Recent Developments in Multifunctional Nanocomposites Using ...

Jacob M. WernikShaker A. Meguid 1e-mail: meguid@mie.utoronto.caDepartment of Mechanical and IndustrialEngineering,Mechanics and Aerospace Design Laboratory,University of Toronto,5 King’s College Road,Toronto, ON, M5S 3G8, CanadaRecent Developments inMultifunctional NanocompositesUsing Carbon NanotubesThis review summarizes the most recent advances in multifunctional polymer nanocompositesreinforced by carbon nanotubes and aims to stimulate further research in thisfield. Experimental and theoretical investigations of the mechanical, thermal, and electricalproperties of carbon nanotubes and their composite counterparts are presented.This review identifies the processing challenges associated with this class of materialsand presents techniques that are currently being adopted to address these challenges andtheir relative merits. This review suggests possible future trends, opportunities, and challengesin the field and introduces the use of these multifunctional nanocomposites instructural health monitoring applications. DOI: 10.1115/1.4003503Keywords: carbon nanotubes, nanocomposites, nanotailoring, nanoreinforcement,multifunctional, structural health monitoring1 IntroductionIt has been recognized for sometime that the mechanical, thermal,and electrical properties of polymeric materials can be engineeredby fabricating composites that are comprised of differentvolume fractions of one or more reinforcing phases. Traditionally,polymeric materials have been reinforced with carbon or glassmicrofibers to improve their mechanical properties and a varietyof metallic and/or organic fillers for electrical and thermal propertyenhancements. These composite materials have been used ina wide variety of applications in automotive, aerospace, masstransit, and nuclear industries. Rarely, however, have traditionalfillers been able to substantially improve a combination of theseproperties. As time has progressed, practical realization of suchcomposites has begun to shift from microscale composites tonanocomposites, taking advantage of the unique combination ofmechanical, electrical, and thermal properties of nanofillers fillerswith a characteristic dimension below 100 nm. There are anumber of advantages associated with dispersing nanofillers inpolymeric materials. While some credit can be attributed to theintrinsic properties of the fillers, most of these advantages stemfrom the extreme reduction in filler size combined with the largeenhancement in the specific surface area and interfacial area theypresent to the matrix phase. In addition, whereas traditional compositesuse over 40 wt % of the reinforcing phase, the dispersionof just a few weight percentages of nanofillers into polymericmatrices could lead to dramatic changes in their mechanical 1,2,thermal 3,4, and electrical 5 properties with added functionalities.Perhaps the most widely used and studied nanofiller is the carbonnanotube CNT. CNTs are highly unusual electrical conductors,the strongest known fibers, and excellent thermal conductors.In fact, some CNTs are stronger than steel, lighter than aluminum,and more conductive than copper 6. Theoretical and experimentalstudies have shown that CNTs exhibit extremely high tensilemodulus 1 TPa and strength 150 GPa. Depending ontheir atomic structure, CNTs can be either metallic or semiconductingwith experimental measurements showing intrinsic electricalconductivities of approximately 10 5 –10 6 S/m for metallicnanotubes and 10 S/m for semiconducting nanotubes. Furthermore,CNTs exhibit large phonon mean free paths that result in1 Corresponding author.Published online February 18, 2011. Transmitted by Editor: J. N. Reddy.high thermal conductivities, which have been theoretically estimatedto be in the range of 6000–3000 W/m K. In addition, CNTsexhibit high flexibility, low density 1.3–1.4 g/cm 3 , and largeaspect ratios 1000 s. Due to this unique combination of physicaland multifunctional properties, CNTs have emerged as excellentcandidates for use as tailoring agents in polymeric materials toyield next generation multifunctional composite materials.The ability to tailor the mechanical, thermal, and electricalproperties of polymeric materials through the dispersion of CNTsdepends on several important factors. The first is the propertybeing tailored. Both mechanical and electrical properties seem tobe more sensitive to the CNT concentrations and geometrical parameterswhen compared with thermal properties. For example,Thostenson et al. 7 studied the influence of nanotube concentrationon the electrical properties of the CNT/vinyl-ester composites.At a concentration of only 0.1 wt % of CNTs, the volumeresistivity decreased by over eight orders of magnitude. The limitthat governs the sudden transition between insulating and conductingbehaviors is known as the percolation threshold, whichwill be given more attention in the coming discussions. Gojny etal. 8 demonstrated that the addition of as little as 0.1 wt % ofCNTs in an epoxy matrix can increase the fracture toughness byupward of 20% with further improvements observed for aminofunctionalizednanotubes. In comparison, the thermal conductivityof cured nanotube-epoxy composites shows a minimal and nearinsignificant increase with nanotube content, less that 0.5% for aconcentration of 0.5 wt % of CNTs 9.A second aspect to consider when tailoring the properties is thechoice of CNT and polymeric medium to which it is dispersed.The enhancement in thermal conductivities appears to be greaterfor single-walled carbon nanotubes SWCNTs than for carbonnanofibers CNFs 10, probably reflecting the intrinsic propertiesof the fillers. Furthermore, the mechanical properties of nanocompositeshave been shown to increase significantly when the CNTsare chemically modified to form reactive bridges with the surroundingpolymer chains 11–14, a process known as functionalization.In this context, the same CNTs can be shown to provide awide range of improvements in the mechanical properties fromthis surface modification process.The addition of CNTs in polymeric materials does not alwaysresult in improved properties. Several important factors relating tothe processing of the nanocomposite also play a significant role.One of the most important aspects to consider is the homogeneousdispersion of the nanofillers in the polymeric matrix. CNTs tend toApplied Mechanics Reviews Copyright © 2010 by ASME SEPTEMBER 2010, Vol. 63 / 050801-1Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

exhibit an enormous surface area being several orders of magnitudelarger than the surface of conventional fillers. The large surfacearea of CNTs leads to two counteracting effects: one desirableoffering increased stress transfer and the other undesirableleading to strong attractive intermolecular and van der Waalsforces between the nanofillers resulting in excessive agglomeration.The resulting aggregates act as defect sites rather than reinforcements,which could lead to a subsequent degradation of thenanocomposite properties. An efficient utilization of CNT propertiesin polymeric materials is therefore directly related to theirhomogeneous dispersion in the matrix. This tendency for thenanofillers to agglomerate also limits the concentration of thenanofillers that can be dispersed in the media. Meguid and Sun15 showed that the homogeneous dispersion of CNTs in an epoxyadhesive can improve the bonding and shear properties ofcomposite interfaces. However, they showed that there was anoptimal CNT concentration above which the properties of thecomposite begin to degrade to below that of the pure epoxy indicativeof the sensitivity of these properties on the nanofillerconcentration.Clearly, there are a number of important factors to consider inthe design and fabrication of nanocomposite materials. It is thereforethe purpose of this review to summarize the latest developmentsin this field and identify the processing challenges associatedwith this class of materials and the techniques currently beingadopted in treating them. The general term nanocomposite can beused to reflect any composite material with a reinforcing phaseexhibiting a characteristic dimension below 100 nm. In fact, nanofillerssuch as carbon blacks, silicas, and clays have widely beenincorporated into a variety of host materials such as polymers,ceramics, and metallic matrices constituting a nanocomposite material.However, the focus of this review is on the nanotailoring ofthe mechanical, thermal, and electrical properties of polymericmaterials through the homogeneous dispersion of CNTs.The layout of this review paper is as follows. Section 2 willdiscuss the structure, mechanical, thermal, and electrical propertiesof CNTs. Section 3 will focus on the experimental and numericalinvestigations of polymer nanocomposites reinforced withCNTs, with attention given to both thermoset and thermoplasticmatrix phases. This section will also address some of the challengesassociated with the design and fabrication of these materials.Section 4 will discuss a fascinating and emerging applicationof these materials that exploits their multifunctional capabilities,namely, structural health monitoring SHM in civil and aerospaceindustries. Finally, Sec. 5 will summarize the current challengesand future outlook of this field.2 Carbon NanotubesCarbon nanotubes exhibit a remarkable combination of mechanical,electrical, and thermal properties. As such, many potentiallyimportant applications have been explored, including the useof nanotubes as nanoprobe tips 16, field emitters 17–20, storageor filtering media 21, and nanoscale electronic devices22–26, just to name a few. Their discovery, together with earliertheoretical predictions of a “nanosupermaterial,” stimulated enormousinterest in the field of nanomaterials. A large percentage ofacademic and popular literature attributes the discovery of CNTsto Iijima in 1991 27. However, there are several papers publishedwell before that time that identified the nanoscale carbonaceousfibers in several controlled experiments 28,29. For example,a paper published in 1976 by Oberlin et al. 28 clearlydepicted an individual CNT synthesized using a hydrocarbon decompositiontechnique, which is reproduced in Fig. 1. However,due to the magnification and resolution limitations of electronmicroscopes at that time, they were unable to resolve the individualgraphene fringes, and it was not claimed by the authors tobe in fact a CNT. It is, however, Iijima 27 who was responsiblefor reporting the structural perfections of CNTs and, hence, impliedthe extraordinary properties that have been realized today. InFig. 1†28‡…this section, we review the mechanical, electrical, and thermalproperties of CNTs, which make them ideal candidates for theabovementioned applications.2.1 Structure. Carbon nanotubes occur in two general forms:SWCNTs and multiwalled carbon nanotubes MWCNTs.SWCNTs can generally be visualized as a single sheet of graphenethat has been rolled into a hollow tubular shape. The orientation ofthe graphene sheet as it is rolled will dictate the resulting structureof the CNT. SWCNTs can have diameters as small as 0.4 nm andnormally no larger than 2 nm. MWCNTs can be viewed as severalconcentric SWCNTs with outside diameters that range between 5nm and 100 nm. The interlayer spacing of MWCNTs is approximately0.34 nm 30,31, and this value is also widely taken as thethickness of individual CNT layers in numerical simulations32–35 and in some experimental investigations 36,37. Figure 2depicts both the SWCNT and MWCNT structures.A schematic illustration of an unrolled graphene sheet is shownin Fig. 3. CNTs are defined by a pair of indices n,m, which areused to identify their atomic structure and size. These indicescorrespond to a lattice vector R=nr 1 +mr 2 on the graphene plane,where r 1 and r 2 are unit vectors in the hexagonal lattice, and n andm are integers. This lattice vector maps onto the circumference ofthe resulting nanotube cylinder. The orientation of the graphitelattice relative to the longitudinal axis defines the chirality or helicityof the nanotube 38. Two main symmetry groups exist:armchair n,n and zigzag n,0 configurations, with all othern,m combinations referred to as chiral nanotubes. The CNT radiusand chiral angle can be determined from the following simpleexpressions:Fig. 2Early bright field SEM image of a MWCNT „from Ref.r CNT = 3r o2 n 2 + mn + m 2Two CNT variants: „a… a SWCNT and „b… a MWCNT1050801-2 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 3Unrolled graphene sheet and the chiral lattice vector = cos −12n + m2 n 2 + mn + m 2where r o is the equilibrium bond length normally taken to be0.1421 nm. A variant of the CNT is the CNF. CNFs differ fromnanotubes in the way the graphene sheet is oriented with respectto the fiber axis. Unlike CNTs, which have the graphene sheetorientated parallel to the fiber axis, CNFs can have a wide rangeof orientations of the graphitic layers. These nanostructures arebest visualized as nanoscale cones or disks stacked atop one another,as shown in Fig. 4. They can also be hollow and typically2have outside diameters in the range of 50–100 nm.A noticeable feature of the graphene sheet is the hexagonalpattern, which is repeated periodically in space. Each carbon atomin the lattice is covalently bonded to three neighboring atoms.This hexagonal structure is attributed to the sp 2 hybridization process.One s-orbital and two p-orbitals of a carbon atom in itsexcited state combine to form three hybrid sp 2 -orbitals at 120 degrelative to each other. This sp 2 hybridization process is illustratedin Fig. 5. The resulting covalent bond, known also as the -bond,is a strong chemical bond, which is largely responsible for theunique properties of CNTs. The other relatively weak out-of-planebond, known as the -bond, is typically exploited in functionalizationprocesses, which involve the grafting of functional groupson the walls of CNTs as a means of improving their interfacialbonding with a surrounding polymer matrix.2.2 Mechanical Properties. Early theoretical and experimentalworks have confirmed that CNTs possess exceptional mechanicalproperties. To date, a number of researchers have employedboth experimental and theoretical techniques to determine the mechanicalproperties of CNTs. However, due to the extremely smallsize of CNTs, the experimental studies are challenging, and theresults normally show significant variability. This could also beattributed to differences in the CNT structure, existing defects,and synthesis techniques. Experimental techniques approximateCNTs as elastic structural members and, in so doing, impose continuumassumptions. As a consequence, the experimental measurementsare faced with the problem of defining the crosssectionalarea of the CNTs. Most approaches approximate thecross-sectional area to be equal to that of a hollow thin walledcylinder, namely, dt, where t is taken as the interlayer spacing ofgraphene 36,37.Although the testing of individual nanotubes is a challengingtask, a number of techniques have been developed to provideFig. 4 TEM images of commercial CNFs, highlighting structural variations in the orientation of the graphiticplanes „from Ref. †347‡…Fig. 5sp 2 hybridization process and the resulting - and -bondsApplied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-3Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 6 SEM images showing a SWCNT rope under direct tensileloading using AFM „from Ref. †37‡…insights into their mechanical behavior and to quantify these properties.The experimental techniques used range from direct tensileloadingmeasurements to techniques based on observing theirfreestanding room temperature vibrations in a transmission electronmicroscope TEM. For example, Lourie and Wagner 39measured the cooling-induced compressive response of CNTs usingmicro-Raman spectroscopy. Young’s moduli of both SWCNTsand MWCNTs were then derived from a concentric cylindermodel involving thermal stresses. In their study, Lourie and Wagnerreported Young’s moduli of 2.8–3.6 TPa and 1.7–2.4 TPa forSWCNT and MWCNT, respectively. In comparison, Yu et al.37,40 determined the Young’s modulus to range from 320 GPato 1470 GPa and from 270 GPa to 950 GPa for SWCNT ropes andindividual MWCNTs, respectively, using atomic force microscopyAFM. Figure 6 shows scanning electron microscope SEM imagesof the SWCNT rope multitudes of entangled CNTs tensileloadingexperiment conducted by Yu et al. where both pre-andpost-loaded CNTs are depicted. Several experimental reports ofYoung’s modulus values for both SWCNTs and MWCNTs areprovided in Table 1 along with their respective references anddetails of their methodology.Experimental measurements of the tensile strengths of CNTshave also been conducted. However, they are limited due to thedifficulties associated with the application of direct tensile loadson individual CNTs. The tensile strengths of SWCNT ropes wereinvestigated by Walter et al. 43 via AFM. They assumed Young’smodulus of 1.25 TPa in their calculations and, in so doing, obtainedtensile strengths of 457 GPa. In the study by Yu et al.40, the tensile strengths of MWCNTs ranged from 11 GPa to 63GPa. The MWCNTs were also shown to fail via a sword-andsheathtype mechanism, where the outer layer first fractured andthe inner layers were subsequently pulled out. Weak load transferwas observed between the inner and outer layers of the MWCNTwith interfacial shear strengths ISSs of 0.08 MPa and 0.3 MPaarising from the weak van der Waals interactions between thesubsequent layers. The weak load transfer between the subsequentlayers was also demonstrated by Cumings and Zettl 44. Theyused a movable nanomanipulator inside a high-resolution TEM towithdraw the inner layer of a MWCNT from its surrounding outerlayer. The measured interfacial shear strength arising from the vander Waals interactions was determined to be in the range of 0.43–0.66 MPa. They also demonstrated controlled and reversible telescopicextension of MWCNTs whereby the inner layer is withdrawnunder direct loading, and upon removal of the load, itretracts back as a result of the attractive van der Waalsinteractions.Researchers have used modeling methods accounting for alllength scales to characterize the behavior of CNTs. First principlequantum mechanical descriptions have been employed to modelthe structural deformation 45, fracture 46, defect nucleation47, chemical reactivity 48,49, and functionalization 50,51 ofindividual CNTs. Classical molecular dynamics MD and molecularmechanic simulations have been shown to play an importantrole in determining the constitutive relations of CNTs underdifferent loading conditions 52–54, CNT growth mechanisms55, oscillatory properties 56, and the effects of chirality andlength on the mechanical properties 57. At the coarser end of thelength scale, continuum mechanical concepts have also been usedin characterizing the CNT behavior. In continuum-based approaches,the CNT is modeled as a continuous shell with a fixedwall thickness and material properties 58–60. However, the onlyway of distinguishing between nanotubes of different chiralitieszigzag, armchair, and chiral is through the radius of the shell.The disadvantages of this approach are that the CNT is drasticallyoversimplified, it cannot be used to study the effect of defects, andthe atomic structure of the CNT has been ignored. Nevertheless,continuum-based approaches have been shown to reasonably predictthe tensile and shear moduli of individual CNTs 61,62 andtheir deformation and stability under different loads 60,63,64.Additionally, a number of multiscale approaches have also beenpursued 65. The theoretical predictions tend to overestimate themechanical properties when compared with experimental findings,which assume that the CNT is a defect-free structure. At the sametime, it is easier to investigate the effect of such parameters astemperature, strain rate, defect nucleation, chirality, size, and differentloading conditions in theoretical approaches. In this context,the elastic properties of CNTs are rarely presented as singlevalues but rather as varying functions of the diameter or chirality.Due to the shear number of theoretical efforts made in this field,the reader is referred to a review by Ruoff et al. 66 for furtherdetails.2.3 Electrical Properties. The electrical properties of CNTshave also attracted a great deal of interest from the research community.Their nanoscale dimensions, coupled with the uniqueelectronic structure of the host graphene sheet, lead to a variety ofunique electrical properties. These properties have been extensivelyinvestigated both theoretically and experimentally 67–83.However, as with the mechanical properties, measurements of theelectronic properties of individual CNTs are challenging. Earlytheoretical studies conducted by Hamada et al. 84, Mintmire etal. 85, and Saito et al. 86 showed that the electronic propertiesof CNTs were heavily dependent on their geometric structure,namely, the diameter and chirality. These theoretical studies basedon tight-binding calculations predicted that CNTs can act either asmetals or as semiconductors with different sized energy bandgaps, which depend on the above parameters. The chiral indicesTable 1Experimental measurements of carbon nanotube Young’s modulusAuthor Technique CNT type Young’s modulus Ref.Lourie and Wagner Micro-Raman spectroscopy SWCNT 2.8–3.6 TPa 39Micro-Raman spectroscopy MWCNT 1.7–2.4 TPa 39Yu et al. AFM SWCNT rope 320–1470 GPa 37,40AFM MWCNT 270–950 GPa 37,40Tombler et al. AFM SWCNT 1.2 TPa 36Krishnan et al. TEM/vibrational theory SWCNT 0.9–1.7 TPa 41Salvetat et al. AFM SWCNT rope 0.810.41 TPa 42050801-4 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 7Metal and semiconducting nanotubes as a function of their chiral indicesn,m can be used to determine whether a CNT will act as a metal,a large band gap semiconductor, or a tiny band gap semiconductor.The general rules are such that all armchair n,n nanotubesare metals, n,m nanotubes with n−m=3j, where j is a nonzerointeger, are small band gap semiconductors, and all others arelarge band gap semiconductors. Accordingly, approximately onethirdof SWCNTs are metals, while the other two-thirds are consideredsemiconductors. This is in agreement with experimentalobservations, which have little or no control on the chirality of thetest specimens. Figure 7 illustrates some of these different possibilitiesas a function of the chiral indices.The CNT size has also been shown to have a significant effecton the electrical properties. As the radius of the nanotube increases,the band gap decreases for both small and large band gapsemiconductors with respective 1/R and 1/R 2 dependence 87.Asimilar observation has been made for CNTs with very small diameters.It was found that strong hybridization effects can occurin these nanotubes, leading to a decrease in the energy band gapsby nearly 50% 87, thus providing them with superconductiveproperties 88. CNTs with such a small diameter distribution areconfined to 3,3, 4,2, and 5,0 configurations. The electricalproperties of these CNTs have already been extensively studiedusing ab initio methods 89–91.The first experimental measurements of individual SWCNTswere carried out by Tans et al. 71. These experiments verifiedthe theoretical predictions and confirmed that CNTs can displayboth metallic and semiconducting properties. The electrical conductivityat room temperature was measured to be approximately10 5 –10 6 S/m for metallic nanotubes and approximately 10 S/mfor semiconducting nanotubes. Furthermore, theoretical predictionswere verified using scanning tunneling microscopy STMexperiments conducted by Odom et al. 92 and Wilder et al. 93.They showed that the electrical properties of CNTs depend upontheir geometrical parameters. In these experimental measurements,the resolution allowed for the identification of individualcarbon rings. The structure of the CNTs was then determined fromthe orientation of the carbon rings and the diameter of the CNTs.In comparison, the conductivity of SWCNT bundles has beenfound to vary between 110 4 S/m 94 and 310 6 S/m95,96 at room temperature. Furthermore, the electrical conductivitiesof individual MWCNTs have also been investigated experimentally.They have been reported to range between 20 S/mand 210 7 S/m 97, depending on the helicities of the outermostshells 98 and the presence of defects 99. Defects such asthe Stone-Wales defect, vacancies, and impurities have all beenfound to affect the electrical properties 100,101. The extent towhich the properties are affected would depend on the number ofdefects, their proximity to each other, and the nanotube structureconsidered. Furthermore, structural deformations such as twistingand bending can also produce variations in the conductivities ofCNTs 102–104. Therefore, the introduction of defects in CNTsand/or deforming CNTs can be viewed as an interesting way ofchanging their electrical properties.2.4 Thermal Properties. The study of the thermal propertiesof CNTs has received considerably less attention in comparison totheir mechanical and electrical properties. However, there existpublications that describe experimental and theoretical investigationsinto such thermal properties as their specific heat, thermalconductivity, and thermal expansion. As with the mechanical andelectrical experiments, the thermal measurements were also madeon a single nanotube. Such measurements are very difficult. Consequently,SWCNT thermal conductivities have primarily beenevaluated theoretically. Experimental results exist only forSWCNT bundles and individual MWCNTs.The unique crystal structure of CNTs, together with their highaspect ratios, led to early speculations that the longitudinal thermalconductivity of CNTs could exceed that of the host materialgraphite 105. Indeed, CNTs do have a very high thermal conductivity,which arises from the strong covalent bonding betweenthe carbon atoms. The theoretical predictions of Berber et al.106 based on molecular dynamics simulations have predictedtheir room temperature thermal conductivities to be as high as6600 W/m K, which surpasses that of diamond 2000 W/m K.Berber et al. also calculated the thermal conductivities ofSWCNTs over a range of temperatures. They found that the conductivitypeaks near 100 K and subsequently decreases with increasingtemperature. The peak value was determined to be37,000 W/m K, which is comparable to the highest thermal conductivityever measured 41,000 W/m K 107. In comparison,the theoretical MD predictions of Osman and Srivastava 108showed that the peak value occurs at around room temperature fora number of SWCNTs with diameters in the range of 1–2 nm anddifferent chiralities. This room temperature conductivity was determinedto be approximately 2500 W/m K. The decrease in thermalconductivity at higher temperatures can be explained by phononscattering events. As the temperature increases, more andmore phonons contribute to the heat flow in the system. However,at high temperatures, phonon-phonon scattering events begin todominate, and the subsequent heat flow decreases, as depicted inApplied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-5Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 8 Molecular dynamics predictions of the thermal conductivityof a „10,10… nanotube. The characteristic peaking behavioroccurs at approximately 100 K „from Ref. †106‡….Fig. 8.The experimental measurements of Li 109 also showed a peakvalue in the thermal conductance occurring at around room temperature310 K for SWCNT bundles. In addition, the experimentalmeasurements of Hone et al. 110 of bulk SWCNT samplesover a temperature range of 0 K to 300 K also indicate an increasein thermal conductivity with increasing temperature. Their measurementsshowed a decrease in the slope occurring at the hightemperature range. However, the characteristic peaking behaviorwas not evident as the temperature range was not extended beyond300 K. It is difficult to determine the intrinsic thermal conductivitiesin these experimental measurements because the numberof SWCNTs contributing to the heat flow cannot bedetermined. These measurements confirm that phonon-phononscattering events become important at near room temperature forSWCNT bundles. In the above experimental measurements, theroom temperature conductivities for the SWCNT bundles rangefrom 2.3 W/m K to 35 W/m K. However, the nanotubes in thesesamples are highly entangled, and the thermal pathway is considerablylonger than the direct distance between the points of measurement.To avoid the irregularities and random distribution inthe above samples, Hone 111 used magnetically alignedSWCNT thin films for his measurements. The measured thermalconductivity of these samples increased with temperature up to400 K, reaching a maximum value of approximately 200 W/m K,which is approximately an order of magnitude higher than thehighest value obtained for the random entangled samples. Thethermal conductivities of MWCNT have also been investigatedexperimentally by Small et al. 112 over a temperature range of 8K to 370 K. Again, the conductivity increases with increasingtemperature up to a maximum value of 3000 W/m K at a temperatureof approximately 300 K. In contrast, bulk samples ofMWCNTs exhibit a thermal conductivity of only 25 W/m K atroom temperature 113. The high thermal conductivities of bothSWCNTs and MWCNTs show tremendous potential for CNTs tobe used in thermal management applications such as heat sinks inelectrical circuitry.The relatively large variation among the different measurementsof thermal conductivity of both MWCNTs and SWCNTsare due to inconsistencies among the CNTs of the experimentalsetups. CNTs can be synthesized using a variety of different techniques,including chemical vapor deposition CVD, arc discharge,and laser ablation, to name a few. Depending on themanufacturing technique used, the nanotubes could have differentstructures, sizes, purities, and, more importantly, defectdistributions/concentrations. As with both the mechanical andelectrical properties, it is expected that the intrinsic thermal conductivityof CNTs will be affected by the abovementioned parameters.For example, defects act as phonon scattering sites, thuslimiting the intrinsic conductivity of the nanotube. Che et al. 114used molecular dynamics simulations to investigate the effect ofboth vacancy and Stone-Wales defects on the intrinsic conductivity.They found that the intrinsic thermal conductivity decreasedsignificantly with increasing defect density with a more severedegradation observed with the vacancy defects. Their results arecomplemented by the recent study of Fan et al. 115. Similarly,Yan et al. 116 developed an analytical model to show that thethermal conductivities of SWCNTs and MWCNTs are in fact bothdiameter and chirality dependent. Their results clearly suggest thatthe thermal conductivity increases with decreasing nanotube diameter.The phonon scattering processes are suppressed in smalldiameter nanotubes, giving rise to high thermal conductivity.This section of the review has introduced the extraordinary mechanical,thermal, and electrical properties of CNTs. It is due tothese properties that researchers are introducing CNTs as tailoringagents in polymeric materials. It presents the opportunity to introduceboth thermally and electrically conductive capabilities to thehost matrix, meanwhile improving its mechanical performance. Amaterial with such multifunctional capabilities can find numerousapplications in a variety of industries. However, composites containingCNTs have not yet realized their full potential. This can beattributed to a number of difficulties associated with the processingof this class of materials. These processing challenges areaddressed in the following section.3 Multifunctional CNT Polymer CompositesNow that the intrinsic mechanical, electrical, and thermal propertiesof CNTs have been explored, we are in a position to discusstheir ability to tailor the properties of polymeric materials to yieldmultifunctional nanocomposites. Recent work in this area showsthat the scientific community is adopting a variety of differentmethods to develop these nanotailored composites with varyinglevels of success. The properties of CNT polymer composites areinfluenced by a number of factors that include the CNT synthesisand purification process, the geometrical and structural propertiesof the CNTs, their alignment in the matrix, the dispersion process,and the fabrication process. In the following sections, we willdiscuss the processing challenges associated with this class ofmaterials and the techniques used by the research community toovercome them. Specifically, emphasis will be placed on the techniquesused to disperse CNTs in polymeric matrices, the differentfunctionalization processes, which ultimately lead to more stableCNT solutions, and the different techniques used to align CNT inthe matrix. The mechanical, electrical, and thermal properties ofCNT polymer nanocomposites and the parameters that influencethem will then be explored both from experimental and theoreticalstandpoints.3.1 Dispersion and Functionalization. One of the most importantaspects to consider in the fabrication of polymer nanocompositesis the homogeneous dispersion of the nanofillers into thepolymeric matrix. The ultimate goal of the dispersion process is tobreak up nanotube agglomerates and homogeneously distributethe individual CNTs throughout the matrix. CNTs tend to exhibitan enormous surface area being several orders of magnitude largerthan the surface of conventional fillers due to their nanoscopicsize and large aspect ratios. The large surface area of CNTs leadsto two counteracting effects: one desirable offering increasedstress transfer and the other undesirable leading to excessive agglomerationdue to intermolecular van der Waals forces. van derWaals forces are the weakest type of intermolecular forces and arecreated by the attraction between induced dipoles in a nonpolarmolecule. The van der Waals interactions between CNTs are notablylarger than van der Waals interactions between polymerchains because of the absence of hydrogen atoms. This attraction,coupled with their nanoscopic size and high aspect ratios, leads toconsiderable aggregation. The resulting aggregates act as defectsites rather than reinforcements, leading to a degradation in theproperties of the nanocomposite 117. An efficient utilization ofthe nanofiller properties in polymeric materials is therefore relatedto their homogeneous dispersion in the matrix. Of equal impor-050801-6 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 9 Ultrasound induced cavitation stages from „a… the nucleation of avoid and „b… its unstable growth to „c… its implosiontance is the stability of the resulting dispersion. It is desirable thatthe CNTs remain in their uniformly dispersed state after processingand not re-agglomerate as a result of their attractiveinteractions.The dispersion, aggregation, agglomeration, and entanglementof CNTs are a subject of current intensive research 118–121.Most strategies combine the use of mechanical and chemicalroutes. The mechanical route includes high shearing techniquesusing mechanical stirring, sonication, microfluidizing, and calendering.These methods involve imposing high shear forces on theCNT/polymer mixture that leads to the homogeneous dispersionof the CNTs. Chemical strategies, on the other hand, typicallyinvolve either a covalent modification of the surface of the CNTor the use of a dispersant or surfactant, being polymeric or supramolecularin nature. The chemical strategies are more effectivein preventing the re-agglomeration of the CNTs after the dispersionprocess has been carried out. A number of factors will determinethe state of the resulting dispersion. However, to date, theonly way of assessing the quality of the dispersion is throughelectron microscopy imaging techniques, which can be fairly limitedin terms of providing a large spatial field of view. Often, onlysmall sections of the sample are examined, which may lead to aninaccurate assessment of the quality of the dispersion. There are,however, some efforts being directed to developing consistentmethods based on ultracentrifuge and absorption spectrum measurements122, absorption and fluorescence spectroscopic techniques123, and a combination of magnetic field and infraredthermographic imaging 124.The mechanical techniques all rely on imposing high shearstresses on the CNT polymer mixture as a means of exfoliating theagglomerates and allowing the polymer molecules to appropriatelywet the CNTs. Mechanical stirring is normally used as ameans of producing a premixture or preliminary dispersion that issubsequently employed in the other techniques. The mechanicalstirring operation is normally carried out using a mixing device atrelatively high revolutions about 2000 rpm. The size and shapeof the propeller and the mixing speed control the resulting dispersion.The resulting premixture is then used with either of the remainingtechniques to further disperse the CNTs.Ultrasonication is a common technique widely used either onits own or in combination with other processes to disperse nanotubesinto polymer matrices. It uses high frequency sound wavesto induce the separation of CNT agglomerates. It operates on theprinciple of inertial cavitation with the rapid formation and violentcollapse of a void or bubble in the liquid producing intense shearingforces. When sonicating liquids at high intensities, the soundwaves that propagate throughout the media result in alternatinghigh-pressure and low-pressure cycles. During the low-pressurecycle, the high-intensity waves form small vacuum bubbles in theliquid. When the bubbles attain a volume at which they can nolonger absorb energy, they implode, producing a shockwave. Thisprocess is schematically illustrated in Fig. 9. The frequency of theultrasound determines the maximum void size. Low frequencies20 kHz produce large voids and high energy forces duringtheir collapse. Increasing the frequency reduces the size of thevoids, and cavitation is reduced. There are two methods for deliveringultrasonic energy into the liquid medium, the ultrasonicbath, and the ultrasonic horn. The ultrasonic bath uses a higherfrequency 50 kHz and does not produce a defined caviationzone as the horn, and the energy is more uniformly distributedthroughout the liquid 125. The ultrasonic horn uses a probe thatoscillates at a fixed frequency. This rapid oscillation of the proberesults in a conical field of high energy where cavitation takesplace. Ultrasonic devices have high impact energy but introducerelatively low shear forces; hence, this method is only suitable forlow viscous matrix materials 126. Furthermore, when an ultrasonichorn is used, the sonication process becomes effective onlyin the immediate region surrounding the probe tip due to the extremereduction of the vibrational energy with increasing distance.Therefore, as sample sizes increase, this method becomes lesseffective. Another adverse effect associated with this method, dueto the local energy input, is the reported fragmentation of theCNTs 127,122 leading to a reduction in their effective length.Both the time and frequency of the sonication process will affectthe resulting dispersion. Ultrasonic instruments using a frequencyof 20 kHz have been shown to homogeneously disperse MWCNTmats 128. Kearns and Shambaugh 129 reported an optimumsonication time of 2hfora1wt%CNTconcentration in a polypropylenesolution. Additionally, care must be taken when processingepoxy samples using this method. In view of the fact thatthe sonication process usually involves localized heating of thesample mixture, this may induce premature curing of the epoxy. Inthis case, it may be appropriate to place the sample in a cold waterbath and avoid prolonged exposure.The calendering or three-roll mill approach relies on processingthe mixture through three horizontally positioned rolls all rotatingat different angular velocities and in opposite directions relative toone another. Figure 10 shows a schematic of the general configurationof this method. The mismatch in the roller velocitiescoupled with a very small gap between the rollers results in highshear stresses. This approach offers nearly pure shearing comparedwith other milling techniques, which also rely on compressivestresses to induce separation. As such, it does not significantlydegrade the nanotubes. This technique has recently beenapplied by a number of research groups reporting excellent dispersions8,124,130,131. In contrast, the microfluidizer approachrelies on forcing the mixture through a very narrow 100 mZ-shaped channel at high speeds 500 m/s to impose the shearstresses 132. This technique has been used in a number ofchemical, medical, pharmaceutical, and cosmetic applications buthas just recently been viewed as an alternative to the existingmechanical dispersion techniques.Some of the above techniques may initially break up the ag-Applied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-7Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 10 Schematic illustration of the calendering dispersion technique. „a…Roller positions and „b… high shear zone between the feed and centerrollers.glomerates but are incapable of creating a stable solution thatprevents the re-agglomeration of the nanofillers especially in lowviscous mediums. Alternatively, the addition of CNTs in a polymericmedium has been shown to affect the rheological propertiesof the polymer through an increase in viscosity 133,134, thusrendering some of these methods incapable of sufficiently dispersingthe CNTs at high concentrations. In other cases, the increase inviscosity can make the removal of trapped air relatively difficult,causing degradation in the composite properties 130. In thesespecific cases, it is desirable to combine the mechanical techniqueswith chemical methods.Chemical strategies improve the stability of the CNT polymersolution and prevent their re-agglomeration, which ultimatelyleads to a better dispersion when coupled with the mechanicaltechniques. Furthermore, these techniques also improve the loadtransfer and interfacial bonding between the CNTs and the surroundingpolymer. Two approaches are generally available whenusing chemical methods to aid in the dispersion of CNTs in apolymeric matrix. The first is noncovalent functionalization,which refers to the adsorption of surfactant molecules or the helicalwrapping of polymer molecules on the CNT walls. This isrealized by using conjugated polymers, which can associate withthe CNTs by means of -a electronic interactions with the CNTlattice. This results in the helical wrapping of polymer chainsaround the CNT, which in turn improves the wetting of the CNTsby the polymer. The helical wrapping of the polymer chain hasbeen observed experimentally 135. This form of functionalizationis particularly attractive because it provides an opportunity toattach a large number of functional groups on the walls of CNTswithout introducing structural defects. These functional groupsprevent the individual CNTs from attracting one another by separatingthem sufficiently such that the van der Waals interactionscannot act between them. Hence, this technique prevents the formationof agglomerates and improves the dispersability of theCNTs 136. When surfactants are used in this approach, theyhave the additional benefit of effectively imposing repulsive electrostaticforces on the neighboring nanotubes aiding their separation.It should be noted, however, that noncovalent functionalizationhas been reported to work poorly for small diameter tubessuch as 0.7–0.8 nm 137.The second approach is called covalent functionalization orchemical cross-linking. In this case, a small percentage of strongcovalent bonds forms from the grafting of functional groups onthe CNT walls. Therefore, unlike noncovalent functionalization,which relies on the wrapping of a polymer chain with functionalgroups mounted on the backbone, covalent functionalization directlygrafts the functional groups on the exterior walls of theCNT.CNTs exist as ropes or bundles, and there are always somecatalyst residuals present, such as bucky onions, spheroidalfullerenes, amorphous carbon, polyhedron graphite nanoparticles,and other forms of impurities. Therefore, the first step in chemicallymodifying the CNTs is the purification process. A number oftechniques can be used to purify CNTs, some of which includeoxidation, centrifugal separation, and intercalation. Once theCNTs have been purified, they undergo a cutting process thatopens up the tubes and provides active sites for functional groupsto react with. The next step is the activation treatment of the CNTswhereby the functional groups react with multifunctional aminesand form bonds. Finally, with the addition of the polymer matrix,the free amino functions react with the polymer molecules, resultingin improved bonding between the CNT and the matrix. In thisway, the functional groups act as intermediary bonding sites betweenthe nanotube and polymer chains. This technique can significantlyimprove the load transfer between the CNT and thepolymer matrix, but it is also possible that this form of functionalizationmay compromise the properties of the nanotube by introducingstructural changes in the graphitic layers of the nanotube138,139 and/or reducing its overall aspect ratio 140.Therefore, short term treatments are normally preferred when covalentlyfunctionalizing CNTs so as not to introduce too manydefects. This technique has also been shown to improve the dispersabilityof CNTs in polymer matrices 14,141. However, largeagglomerates can still exist in the mix because of the relativelyinsufficient coating of the CNT walls by the functional groups thatare attached to the few defects.Due to the significant variability in property measurements ofCNT polymer composites, even for systems with the same constituentmaterials, it becomes evident that the dispersion process isof key importance. There are several techniques available to improvethe dispersion of nanofillers into polymeric matrices, butthere is as of yet no simple and consistent method that can beapplied without fail. Furthermore, the dispersion of CNTs has onlybeen achieved on a laboratory scale and to a limited concentrationof approximately 1–5 wt %. Clearly, much more research workneeds to be done in this area. The literature indicates that techniquesto disperse nanofillers in solutions invariably suffer fromproblems associated with the strong interactions between nanofillersand their tendency to agglomerate. No single method outlinedabove has been found to be successful on its own. However, surfacetreatment methods, used in conjunction with mechanicalshearing techniques, can potentially provide a means of counteractingthese effects.3.2 Nanotube Alignment. As with conventional composites,the mechanical, electrical, and thermal properties of CNT polymercomposites are highly influenced by the degree of CNT alignmentin the matrix. The purpose of aligning CNTs in the matrix isdependent on the desired application of the composite. Some applicationsmight prefer a set of isotropic composite properties asin the case of rotating disks. However, many applications requirea particular set of properties in a preferential direction such ashigh-performance composites with improved damage tolerancecapabilities. Similarly, some applications might call for preferentialheat conduction or electrical conductivity in a particular direction.It has also been shown that randomly oriented CNTs embeddedin a polymer matrix fail to generate composites in which thefull reinforcing potential of the CNTs is fully utilized and exploited.To this end, there are a number of techniques that can beused to align CNTs in both thermoset and thermoplastic polymericmatrices. These include force-, magnetic-, and electric-fieldinducedalignment techniques. Furthermore, some of the force-050801-8 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

field techniques are nanocomposite fabrication methods, whichinherently induce some degree of CNT alignment in the resultingcomposite, while others are post-processing techniques, which canbe used to align nanotubes that have already been dispersed in aliquid matrix prior to curing or polymerization.3.2.1 Force-Field/Shear-Induced Alignment. Force-field/shear-induced alignment methods are relatively simple techniquesthat rely on imposing external mechanical loads to force the alignmentof the nanotubes. The first observation of CNT alignmentwas by Ajayan et al. 142. In their work, MWCNTs were dispersedin an epoxy matrix using a simple mechanical stirring technique.Thin slices, ranging in thickness from 50 nm to 1 m,were cut from the composite block with a diamond knife. Theauthors observed that the nanotubes were preferentially orientedduring the cutting process, which created a state of shear inducingflow of the material. No breakage of the nanotubes was observed,which suggested that the nanotubes were very strong and the interfacebetween them and the matrix was relatively weak. Followingthese observations, de Heer et al. 143 developed a methodologyto create large surfaces of highly aligned and denselypacked CNTs and measured their optical and electrical properties.The process consisted of drawing an ethanol nanotube suspensionthrough a 0.2 m pore ceramic filter, leaving a uniform blackdeposit on the filter. The deposit was then transferred onto a plasticsurface by pressing the tube coated side of the filter onto thepolymer. The filter was then lifted to expose the surface, whichunder SEM appeared to show no evidence of nanotubes, but ratherdomelike structures. Upon rubbing with a Teflon sheet or aluminumfoil, the surface became silver and was shown to have a highdegree of nanotube orientation along the direction of rubbing. Itwas then concluded that the untreated polymer surface had nanotubesorientated perpendicular to the surface, which gave rise tothe domelike objects, and that the mechanical shear force inducedby rubbing aligned them flat on the surface.The above methods focused on the alignment of the CNTs on apolymer substrate or surface and did not give any consideration tothe alignment of CNTs in the bulk composite. The most effectiveway of achieving high shear alignment of CNTs throughout thecomposite is through drawing or stretching of a composite fiber orfilm. The process of spin-drawing or melt-spinning is an exampleof such a technique used to produce highly ordered CNT/polymerfibers. Haggenmueller et al. 144 applied this technique toSWCNTs dispersed in a polymethyl methacrylate PMMA matrix.The composite fibers were melt-spun to achieve draw ratiosbetween 20 and 3600. The elastic modulus and yield strength ofthe SWCNT/PMMA composite fibers increased with nanotubeloading and draw ratio. Polarized resonant Raman spectroscopyindicated that the nanotubes in the fibers were well aligned withmosaic distribution full widths at half-maximum FWHMs assmall as 4 deg. More recently, Perrot et al. 145 applied thistechnique to fabricate MWCNT/PA12 composite fibers and studiedthe influence of several spinning factors, including spinningspeed, extrusion rate, and draw ratio and correlated them to thestructure and properties of the fibers. Similarly, the melt extrusionprocess can be used to fabricate CNT composite fibers that cansubsequently be drawn to their desired ratios to induce preferentialalignment of the CNTs in the fibers 146. Additional shearinducedalignment techniques can be viewed in Refs. 147,148.3.2.2 Electric-Field-Induced Alignment. The application of anelectric field has also been shown to induce alignment of thenanotubes in a polymer matrix. In fact, exposing CNTs to anelectric field during their stage of growth can yield highly orientedCNT forests on the growth substrate 149. Introducing the polymeracross the vertical nanotubes, a well aligned composite can beformed. This process has already been demonstrated by a numberof researchers, and the electric-field-induced alignment of CNTsalready dispersed in a polymer matrix is also beginning to showsome success.Fig. 11 Electric-field-induced alignment showing „a… a randomdistribution of CNTs prior to application of an electric field, „b…polarized CNTs rotating under the electric field, „c… an alignedarray of CNTs, and „d… the lateral agglomeration of the CNTs„from Ref. †152‡…In the electric-field technique, a well-dispersed CNT polymersuspension is deposited on a substrate having interdigitated electrodes,or equivalently, the electrodes are dipped into the suspension,which is poured into a cast. In the presence of an electricfield, each conductive nanotube experiences a polarization bothparallel to the tube axis and in its radial direction. It has beensuggested that the static polarizability in the direction of the tubeaxis is of greater magnitude than that across its diameter 150.This polarization introduces a dipole moment on the CNT, whichin turn leads to a torque N acting on the nanotube aligning themagainst the viscous drag of the surrounding polymer in the directionof the electric field. Both dc and ac electric fields can beapplied. However, in the case of a dc field, the nanotubes not onlyrotate to align themselves in the direction of the applied field butalso move according to their electrophoretic mobility toward theelectrode with the opposite sign 151. This is ultimately causedby the presence of a charged interface between the particle surfaceand the surrounding polymer. Thus, over extensive curing times,the application of a dc electrical field may induce favorable clusteringof the nanotubes near one end of the composite due tomigration effects. In the case of an ac field, the net electrophoreticmobility equals zero and the nanotubes only rotate to orientatethemselves 151. However, nanotubes aligned using either dc orac electric fields have a Coulombic attraction between them,which arises from their oppositely charged ends. This in turn cancause them to agglomerate in the lateral direction and form thickCNT columns extending through the composite, giving rise to acoarsening effect 152. Furthermore, a nonuniform electric fieldaround the nanotube ends results in the movement of induceddipoles toward the area with the highest field strength. This phenomenonis called dielectrophoresis, and it too can induce migrationof the nanotubes 153. Figure 11 summarizes the key processesassociated with the electric-field-induced alignmentApplied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-9Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 12 Transmission optical micrographs of an epoxy nanocompositecontaining 0.01 wt % MWCNTs during curing at 80 C in „a… adcfieldof100V/cm and „b… an ac field of 100 V/cm „from Ref. †151‡…technique. First, the nanotubes are randomly dispersed and orientedin the polymer matrix, as shown in Fig. 11a. Upon theapplication of an external electric field, the individual nanotubesbecome polarized, which in turn leads to an electrically driventorque, causing the nanotubes to rotate in the direction of the field,as shown in Fig. 11b. Once the CNTs are aligned and charged,neighboring tubes will interact by exerting attractive and repulsiveforces on each other. Consequently, the nanotubes will migrateand laterally agglomerate into thick bundles, as shown in Fig.11c, giving rise to the coarsening effect. Coarsening effects maybe desirable for applications that require anisotropic properties.Figure 12 shows transmission optical micrographs of an epoxynanocomposite with 0.1 wt % MWCNTs aligned using both dcand ac electric fields. In both the dc and ac electric-field samples,the coarsening effect is visible as bands of alternating colors,while in the case of the dc field the CNTs have also clearly migratedtoward one side of the composite. In chemically functionalizedCNTs, the lateral agglomeration process occurs muchslower because these nanotubes have additional repulsive electrostaticforces acting between them, which arise from the chargedfunctional groups on the walls of the CNTs. Chemical functionalizationhas been shown to counteract these coarsening effects andprovide a stable solution during the curing process 154,152. Alternatively,one could use a fast curing epoxy system or a rapidpolymerizing matrix to help prevent the nanotubes from agglomeratingin the lateral direction. Although the electric-field-inducedalignment technique appears straightforward, its success is verysensitive to a combination of parameters, including CNT concentration,electric-field strength and frequency, polymer viscosity,temperature, and time.Electrospinning is another related electric-field-induced alignmenttechnique that has been shown to be effective in producingaligned CNT polymer fibers 155–157. This method uses an electriccharge to draw very fine fibers from the liquid polymer. Specifically,when a sufficiently high voltage is applied to a liquidpolymer droplet, it becomes charged. The electrostatic repulsionscounteract the surface tension of the liquid, and the droplet isstretched and a charged liquid jet is formed. The liquid jet is thenelongated through a whipping process caused by an electrostaticallydriven instability until it is deposited on a collector surface.In essence, this technique is analogous to mechanical fiber drawingbut has the benefit of being very effective in producing verythin fibers without the need to apply a mechanical force to producethe desired elongation.3.2.3 Magnetic-Field-Induced Alignment. The alignment ofCNTs in a polymer matrix has recently been achieved using anexternal magnetic field. The magnetic susceptibility of CNTs ofdifferent diameters and chiralities has been predicted using a varietyof different theoretical techniques 158–160. Semiconductingnanotubes have been predicted to be diamagnetic negativesusceptibility both parallel and perpendicular to their longitudinalaxis. However, the susceptibility in the perpendicular direction hasbeen predicted to have a larger magnitude, thus causing nanotubeswith these chiralties to orientate themselves parallel to the magneticfield. Metallic nanotubes, on the other hand, have been predictedto be paramagnetic in the direction of their longitudinalaxis, thus causing them to align parallel to the magnetic field159. The magnetic-field-induced alignment technique consists indispersing the CNTs in the polymer solution and subsequentlycasting the solution on a substrate located inside a strong magnet161,162. While the film is being dried or cured, the nanotubesalign to the direction of the magnetic field, which can be eitherparallel to the substrate or normal to it. Steinert and Dean 161applied this technique to align SWCNTs in a polyethylene terephthalatePET matrix. Samples with nanotube loadings of 0.5wt %, 1.0 wt %, and 3.0 wt % were fabricated, and magnetic-fieldintensities of 3.0 T and 9.4 T were used to align the nanotubes. Itwas observed that the 3.0 T magnetic-field intensity was insufficientto promote a complete alignment of the nanotubes, with theprimary orientation being approximately 30 deg off-parallel. Theyalso observed that as the SWCNT concentration increased, theeffect of the magnetic field was diminished, which was likelycaused by increased restriction to CNT mobility due to the increasingsolution viscosity. However, it was shown that the higher9.4 T magnetic field was sufficient to overcome this obstacle andproduce a highly aligned CNT composite. These observationsshow that while the magnetic-field-induced alignment techniquelooks ideal, it also has its drawbacks associated with the relativelyweak magnetism of CNTs. It requires strong magnetic fields ofapproximately 7 T fields as high as 166 T have also been reported163. Therefore, the samples are usually placed in a narrow boreof a superconducting magnet, and there have even been caseswhere magnetic resonance imaging MRI machines have beenused to provide the intensive magnetization 161. Alternatively,one may use magnetic nanoparticles that interact with the nanotubesto increase their susceptibility to the magnetic fields164,165. The relative rarity of strong magnets and small samplesizes still limit the popularity of this alignment method. However,contrary to the electric-field-induced alignment technique, whichtends to cause lateral agglomeration of the nanotubes, a homogeneousmagnetic field only reorients them.3.2.4 Characterization of Nanotube Alignment. Once a preferredCNT alignment technique has been identified, the questionremains how to quantify the degree to which the nanotubes havebeen aligned throughout the polymer matrix. This becomes particularlyimportant when optimal processing parameters need tobe identified, and the effects of such aspects as functionalization,aspect ratio are to be quantified. The use of both azimuthal or phiscanning X-ray diffraction 166–169 and polarized Raman spectroscopy170–174 has been shown to be particularly effective inquantifying the degree of CNT alignment in composite materials.X-ray diffraction patterns tend to show modulations in the azimuthalintensity distributions for preferential orientations of thenanotubes. Two symmetric diffracted arcs in the patterns are char-050801-10 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 14 Raman spectra of a1wt%SWCNT melt-spun PMMAfiber „from Ref. †172‡…Fig. 13 2D X-ray diffraction pattern of „a… an as-cast compositefilm containing randomly oriented MWCNTs and „b… a mechanicallydrawn MWCNT composite film „from Ref. †167‡…acteristic features of highly aligned CNT composites, while a uniformintensity of the diffraction ring is characteristic of a randomorientation. The analysis of these Bragg intensities yields quantifiableinformation regarding the degree of CNT alignment in thecomposite. For example, a typical 2D X-ray diffraction pattern ofan as-cast composite film containing randomly oriented MWCNTsis shown in Fig. 13a, as taken from Ref. 167. The narrow ringmarked by the arrow is the Bragg peak of the nanotubes andnanoparticles. The data are plotted as intensity versus 2 anglebetween the transmitted and diffracted beams and azimuth angle in the rectangular panel. As can be seen, the intensity is relativelyconstant with respect to the azimuth angle. Figure 13bshows the 2D X-ray diffraction pattern of a mechanically drawncomposite film. The Bragg intensity is now concentrated at twospots located at 90 deg and 270 deg. The integrated intensity ofthese diffracted arcs as a function of the azimuthal angle results inpeaks. The breadth of the peak at half its maximum FWHM isinversely proportional to the degree of CNT alignment. For thisparticular example, the 330% drawn composite exhibits alignednanotubes with a mosaic angle of about 23.2 deg around thestretching axis.An alternative method of quantifying the degree of CNT alignmentin composites is through polarized micro-Raman spectroscopy.Since nanotubes can be considered a one-dimensional material,the use of light that is polarized parallel or perpendicular tothe tube axis will show the low dimensionality of the nanotubes.This technique consists of analyzing the intensity of the Ramanpeaks at 202 A1g-active mode and 1509 cm −1 graphiteorientedE2g mode as a function of the angle between the focusedbeam and the composite axis. It has been observed that forscattered light analyzed parallel to the incident laser polarization,all CNT Raman peaks exhibit a dramatic decrease in intensity asthe nanotube orientation is rotated from a parallel to perpendicularconfiguration with respect to the incident polarization. Therefore,higher intensity peaks along the composite axis correspond to ahigher degree of nanotube alignment. Figure 14 shows the polarizedRaman spectra of a1wt%SWCNTmelt-spun PMMA fiber172. The peak intensities decrease with increasing misalignment.3.3 Theoretical Investigations of the MechanicalProperties. There are a variety of modeling methods in use,which aim not only to simulate material behavior at a particularscale of interest but also to assist in developing new materialswith highly desirable properties. These scales can range from thebasic atomistic to the much coarser continuum levels. The hierarchyof modeling methods consists of quantum mechanics QM,MD, micromechanics MM, and finally continuum mechanics.Quantum mechanics is used to develop energy density functions atthe subatomic level. Quantum effects can be described using thetight-binding method. This method is capable of capturing thephysics of the problem at the angstrom level. However, it is unrealisticto extrapolate the results of this method to the continuumlevel for engineers to use in design. Similarly, MD is a computationalmethod fit for scales in the nanometer range. All of thephysics in the MD method are contained in the forces acting oneach atom in the system. These forces are determined from interatomicpotentials, which provide the constitutive relations at thisscale. On the other hand, MM techniques employ continuum conceptsto develop field variables for solids containing defects andinhomogeneities at the micrometer level. Finally, continuum mechanicsis best suited for scales above the millimeter range wherehomogenization and averaging techniques deem enough accuracyto describe the material. Individually, each of these methods isaccurate and best suited for its own length scale, and modelinginaccuracies can arise from the improper enforcement of a specifictechnique associated with a particular length scale on other lengthscales. Furthermore, it would not only be impractical but also verycostly to attempt to model an entire continuum using MD becauseeach individual atom would have to be simulated in the model.Many engineering problems are characterized in terms of multiplescales and require a novel approach to describe their behavior. Inthis case, it is carried out using multiscale computational modelingtechniques, which can describe the behavior of materials onscales ranging from atomistic to continuum.The outstanding mechanical, electrical, and thermal propertiesof CNTs make them ideal candidates for use as reinforcing agentsin polymer materials. However, excellent nanotube properties donot necessarily translate into the same properties for the bulk composite.Several issues pertaining to the alignment, dispersion, aspectratio, orientation, and load transfer need to be optimized inorder to achieve the best properties of the composite. Since experimentationat the nanoscale is still a developing field, the bestway to quantify the effects of such parameters is through computationalmodeling techniques. To date, there have been a vastnumber of numerical models developed for the characterization ofnanocomposites primarily because of the different modeling techniquesthat can be adopted. This section will review the numericalefforts of the research community in predicting the mechanicalproperties of CNT-reinforced composites. This section will be di-Applied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-11Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

vided into atomistic, continuum, and multiscale efforts due to theabundant research devoted to understanding the mechanics ofthese materials.3.3.1 Atomistic Modeling. Atomistic methods, such as moleculardynamics, have been extensively used to model this classof materials. In the MD approach, classical equations of motionfor each atom are integrated stepwise in time. These time stepscan range from 1 fs to 10 fs, and the corresponding simulationtimes can range from several picoseconds to nanoseconds, dependingon the system being investigated. Due to the number ofdegrees of freedom involved, these approaches are generally computationallyintensive and limited by the realistic system sizes thatthey can represent. Even the use of state-of-the-art parallel supercomputerscan only handle a limited number of atoms 10 9 ,corresponding to less than 1 m 3 175,176. Therefore, the atomisticlevel approaches can presently only model short-nanotubesegments and a small number of short polymer chains. Such modelsare normally applied in investigations related to the interfacialbonding mechanisms of CNTs with a variety of polymer systems.These include polyethylene PE, poly-m-phenylenevinylenePmPV, polystyrene PS, polyamide-6 PA6, PMMA, andpolyaniline PANI, to name a few. However, emphasis has beenplaced on the former due to its relatively simple atomic compositionof hydrogen and carbon atoms with well established bondinginteractions.Lordi and Yao 135 studied the interfacial adhesion mechanismsof CNTs embedded in a variety of polymer matrices. Theyused force-field-based molecular mechanics calculations to determinebinding energies and sliding frictional stresses between theCNTs and surrounding polymers. The results of the study indicatedthat the binding energies and frictional forces only play aminor role in determining the ISS. Figure 15 depicts the equilibriumhelical configuration of two molecular variants of PPAaround an armchair nanotube, namely, cisoidal PPA shown in Fig.15a and transoidal PPA shown in Fig. 15b. In both variants, thephenyl functional groups are clearly seen attached to the backboneof the PPA chain and extending outward in the direction of thesurrounding polymer. Lordi and Yao determined that this form ofhelical wrapping of the polymer chains in noncovalently functionalizedCNTs does in fact contribute significantly to the increase inthe ISS. Frankland et al. 177 investigated the effect of chemicalcross-linking or functionalization via molecular dynamics simulationsemploying a many-body bond-order potential that allowedfor the formation of chemical bonds and rehybridization. Theyconsidered both amorphous and crystalline polyethylene matrices.Their simulations predicted that the ISS can be increased by overan order of magnitude from the introduction of cross-links involvingless than 1% of the carbon atoms in the nanotube structure.Higher interfacial shear stresses were observed for the crystallinecomposites in both nonbonded and cross-linked configurations.Furthermore, their investigation also predicted a negligible changein the tensile modulus of the CNT considered. Gou et al. 178used both molecular mechanics and molecular dynamics simulationsto study the load transfer and interfacial properties of individualSWCNTs and CNT ropes. The ISS was calculated to be upto 75 MPa for a SWCNT embedded in a polymer matrix. Thesimulations also showed that individual CNTs have stronger interactionswith the surrounding polymer and hence provide betterload transfer when compared with the CNT rope. In a separateanalysis, Guo et al. 179 used molecular mechanics to investigatethe corresponding ISS for a three CNT rope system embedded inan epoxy resin. They performed pull-out simulations of one CNTfrom the three CNT rope system and the pull-out of the three CNTrope system from the epoxy. They reported a shear stress of 61MPa and 36 MPa for the pull-out of one CNT and the three CNTrope, respectively. More recently, Zheng et al. 180 used bothmolecular mechanics and molecular dynamics to study the effectof chemical functionalization on the interfacial bonding characteristicsof a SWCNT embedded in a polyethylene matrix. TheyFig. 15 Helical configurations of two molecular variants ofPPA: „a… cisoidal PPA and „b… transoidal PPA „from Ref. †135‡…investigated the effect of several different functional groups andfound that the ISS can improve by as much as 1700% for casesinvolving 5% of the carbon atoms in the CNT functionalized withphenyl groups. Figure 16 depicts the structure of the differentfunctional groups considered in their analysis and how they arechemisorbed on the surface of the CNT. The figure also aids inillustrating the key difference between noncovalent and covalentfunctionalizations; namely, covalently functionalized CNTs havefunctional groups grafted on their surface, whereas noncovalentfunctionalized CNTs are wrapped by a polymer chain with thefunctional groups mounted on the backbone of the chain and exposedto the surrounding matrix. Wei 181 studied the temperaturedependent adhesion behavior and the reinforcement effect ofCNTs in a polyethylene matrix through molecular dynamics simulations.Wei only considered van der Waals interactions in hismodel and established a lower bound ISS of approximately 47MPa, which was found to be in excellent agreement with theexperimental measurements of Barber et al. 182. Liu et al. 12used molecular dynamics to investigate a hybrid system of noncovalentand covalent functionalizations. They found that the interfacialshear strength for a pristine SCNT/epoxy system wasapproximately 170 MPa. When noncovalently functionalized, theISS increased to 290 MPa and to 690 MPa when covalently functionalized.Furthermore, the hybrid system resulted in an ISS of050801-12 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 16 Morphology of different functional groups grafted on the wall of aCNT „from Ref. †180‡…940 MPa. Xiao and Liao 183 developed a nonlinear micromechanicalmodel to simulate nanotube pull-out in which thermalresidual stresses, Poisson’s contraction, and the nonlinear elasticbehavior of the CNTs were considered. Their results suggestedthat the distribution of interfacial shear stress along the CNTlength is sensitive to the CNT’s elastic nonlinearity.The stress-strain response of CNT-reinforced polymers was investigatedusing molecular dynamics by Frankland et al. 184.They considered both continuous and discontinuous SWCNTsembedded in polyethylene matrices. Frankland et al. obtained thestress-strain curves for both systems under tensile and transverseloading conditions. The long-nanotube composite showed an increasein the stiffness relative to the polymer and behaved anisotropicallyunder the different loading conditions considered. Theshort-nanotube composite showed no enhancement relative to thepolymer, which they attributed to the low aspect ratio of the nanotubes.The stress-strain curves obtained from the molecular dynamicssimulations were also compared with corresponding ruleof-mixturepredictions. Similar simulations were performed byGriebel and Hamaekers 185, where they used the Parrinello–Rahman approach to apply an external stress to the system toderive the stress-strain relations of a SWCNT polyethylene composite.Again, both short and infinite nanotube configurations wereconsidered. Han and Elliot 186 used molecular dynamics tostudy the elastic moduli of a SWCNT-reinforced polymer composite.Two amorphous polymer matrices were considered,PMMA and PmPV. A constant-strain energy minimization methodwas then applied to calculate the axial and transverse elasticmoduli of the composite system. A comparison with the traditionalrule-of-mixture systems showed that for strong interfacial interactions,there can be large deviations of the results from the rule ofmixtures.Zheng et al. 187 studied the influence of nanotube chirality onthe interfacial bonding characteristics in a PMMA polymer usingMD. They considered five different SWCNTs with similar lengths,diameters, and atomic compositions but with varying chiral indices.They conducted pull-out simulations to investigate the interactionenergy, interfacial bonding energy, and shear stress of thecomposite. It was shown that all the above attain highest valuesfor the armchair system, while the zigzag nanotube compositesystem produced the lowest values. Therefore, for SWCNTs withsimilar molecular weights, diameters, and lengths, the armchairwill act as the best reinforcing agent. Chowdhury and Okabe188 studied the influence of polymer matrix density, chemicalcross-link formation, and CNT geometrical defects on the interfacialshear strength via molecular dynamics simulations. They concludedthat all parameters significantly affect the resulting ISSwith an increase observed for cases involving increased polymerdensity and cross-link density and a decrease with the considerationof structural defects in the CNT.Chen et al. 189 performed MD simulations to study the interactionenergy SWCNTs and polyphenylacetylene PPA. The influenceof nanotube chirality, temperature, and chemical modificationon the interfacial adhesion of nanotube-PPA wasApplied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-13Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 17 The use of micromechanical modeling techniques as a means of providing a bridge fromatomistic to macroscopic systemsinvestigated. The results showed that the interaction energy betweenthe SWNTs and PPA is strongly influenced by chirality, butthe influence by temperature could be negligible. They also concludedthat the armchair SWCNT would perform best as a reinforcingagent when compared with other SWCNTs with similarmolecular weights, diameters, and lengths. They also investigatedthe effect of chemical functionalization on the wrapping ability ofthe polymer chains. They concluded that the SWNTs modified bymethyl or phenyl groups can be well-wrapped by PPA, while theSWNTs modified by other types of groups cannot. The results alsoindicated that the interaction energy between the SWNTs and PPAincreases with the increase in the concentration of functionalizedgroups.Liu et al. 190 investigated the absorption of polyethylenechains on CNT walls under a wide range of temperatures. Theyobserved that the van der Waals interactions between the polymerand the nanotube provide a very large interaction energy such thatthe PE chains are absorbed as soon as they are put around theCNT. They also found that at higher temperatures the PE chainswrapped more compactly around the CNT, while at room temperaturethe polymer chains were almost linear and aligned withthe CNT axis.The influence of nanotube chirality and aspect ratio on the adhesionenergy of a SWCNT and polyethylene matrix was investigatedby Al-Haik and Hussaini 191 using a molecular mechanicsforce field. They reported that nanotubes with lower chiral angles,which have higher aspect ratios in these simulations, have higheradhesion energy. Furthermore, they also observed that the zigzagconfiguration undergoes considerable deformation to achieve anequilibrium configuration with the PE polymer, whereas the armchairnanotube with relatively low adhesion energy undergoesminimal deformation.3.3.2 Continuum Modeling. The traditional framework in mechanicshas always been the continuum. Under this framework,materials are assumed to be composed of an infinitely divisiblecontinuous medium, with a constitutive relation that remains thesame for a wide range of system sizes. The underlying atomicstructure of matter is neglected altogether and is replaced with acontinuous and homogeneous material representation. Continuumapproaches have been applied to study nanoscale materials. However,traditional continuum-based models cannot accurately describethe influence of the nanofillers upon the mechanical properties,bond formation/breakage, and their interactions in thecomposite systems because they lack the appropriate constitutiverelations that govern material behavior at this scale. At the nanoscale,traditional continuum mechanical concepts do not maintaintheir validity and gross oversimplifications can arise from the useof a purely continuum model. For example, Chang et al. 192used molecular mechanics to show that the classic relationshipbetween Young’s modulus and the shear modulus in the elastictheory of continuum mechanics is not retained for a SWCNT.Specifically, if the classic formula is used, they showed that theshear modulus would be well overestimated for SWCNTs withlarge chiral angles and underestimated for those with small chiralangles. However, the continuum approach can still provide valuableinsights into the effects of such parameters as CNT curvature,aspect ratio, and volume fraction on the effective mechanicalproperties of CNT polymer composites. Futhermore, for computationalsimplicity and to adequately address scale-up issues, it isalso desirable to couple atomistic models with established micromechanicaltechniques to describe the mechanical behavior ofpolymer nanocomposites on a macroscopic scale. In this case, theproblem is often formulated at the atomistic level using the conceptof a representative volume element RVE, which is subsequentlyhomogenized into a representative fiber having uniformproperties. The representative fiber is then used to describe thenanophase and its immediate surrounding in the micromechanicaldescription. A schematic of this process is illustrated in Fig. 17.Fisher et al. 193,194 developed a finite element FE model toinvestigate the effect of CNT waviness on the Young’s modulus ofSWNCT-reinforced polymers. A schematic of their model is depictedin Fig. 18a. The figure clearly shows the wavy nature ofthe CNT and also illustrates the continuum simplification in modelinga nanotube as a thin walled cylinder where the atomic descriptionhas been ignored. The model assumed a fully bondedconfiguration and used a sinusoidal curvature distribution functionto model different nanotube shapes in the matrix. The effectivestiffness of the curved nanotube unit cell was determined and usedin a micromechanical prediction of the effective nanocompositeproperties. They concluded that nanotube waviness can significantlyreduce the effective reinforcing modulus of the nanotubesand thus limit the overall effective modulus of the reinforcedpolymer, as shown in Fig. 18b, for a range of CNT volumefractions. The same model was employed by Bradshaw et al.195, where it was used to compute the dilute strain concentrationtensor. This tensor was in turn used in a micromechanicalanalysis to study the curvature effect on the effective elastic propertiesof aligned and randomly oriented nanocomposites. The resultsalso showed that nanotube waviness results in a reduction inthe effective modulus of the composite. Furthermore, the degreeof reduction is dependent on the ratio of the sinusoidal wavelengthto the nanotube diameter. As this wavelength ratio increased, theeffective stiffness of a composite with randomly oriented wavynanotubes converged to the result obtained with straight nanotubeinclusions.Chen et al. 196,197 developed an analytical model based onthe shear-lag theory to study the effect of CNT curvature on themechanical properties and pull-out response. The model accountedfor the entire pull-out process, namely, the bonded, debonding,and sliding stages. Two interface friction models wereapplied. They showed that a Coulomb friction model can betteraccount for the fiber curvature effect than a constant frictionmodel. A parametric study showed that fibers with more curvature,longer embedded lengths, and higher friction interfaces withthe surrounding matrix required additional pull-out force and energyfor complete pull-out. Pantano et al. 198 also studied theeffects of CNT waviness and interfacial bonding on the compositestiffness using micromechanics. They recognized that in the caseof weak interfacial bonding, CNT waviness can actually increasethe stiffness of the composite. The transverse shear loads are050801-14 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 18 „a… A representative unit cell for the analysis of wavy nanotubes and „b… the detrimentaleffect of nanotube waviness of the effective Young’s modulus of a nanocomposite as determinedfrom micromechanical methods „from Ref. †194‡…transmitted to wavy CNTs through lateral normal interactions withthe matrix. These transverse forces within the CNT generate locallyvarying bending moments along the CNTs. The strain energyassociated with local bending of wavy MWCNTs can thus providea novel mechanism for enhancing polymer composite stiffness,even in the presence of weak interfacial bonding. Thostenson andChou 199 used micromechanical techniques to investigate theelastic properties of short and aligned CNT polymer composites.They concluded that the nanocomposite elastic properties are particularlysensitive to the nanotube diameter since larger diameternanotubes show a lower effective modulus and occupy a greatervolume fraction in the composite relative to smaller diameternanotubes.Recently, an interfacial cohesive law has been developed byJiang et al. and applied to study the interaction between CNTwalls 200 and CNT polymer composites 201. The cohesivelaw and its properties are obtained directly from the Lennard–Jones potential from the van der Waals interactions. The cohesivelaw was used in a micromechanical analysis to predict the stressstrainbehavior of CNT polyethylene composites 202. The predictedstress-strain curves displayed an intermittent decrease inboth stress and strain due to the interface softening behavior displayedin the cohesive law. The studies showed that CNTs indeedimprove the mechanical behavior of composites at small strain.However, the improvement disappears at relatively large strainbecause the debonded nanotubes behave like voids in the matrixand may even weaken the composite.Chen and Liu 203,204 evaluated the effective mechanicalproperties of CNT polymer composites using a square RVE basedon continuum mechanics. They were able to extract the effectiveelastic mechanical properties of both discontinuous and continuousCNT polymer composites by analyzing the RVE under a varietyof loading conditions. They found that with the addition ofonly about 3.6% volume fraction of the CNTs, the stiffness of thecomposite in the CNT axial direction can increase as much as33% for the case of long CNTs.Lusti and Gusev 205 used FE to investigate the effect of CNTorientation, aspect ratio, and volume fraction on the elastic propertiesof CNT polymer composites. They considered fully alignedtwo-dimensional random in-plane and three-dimensional randomorientation states at various CNT concentrations. In their study,the CNTs were modeled as massive cylinders, which were randomlydistributed in a computational cell using a Monte Carloalgorithm. Their results show that fully aligned nanotubes lead toa significant enhancement in the longitudinal properties, whereastwo-dimensional random in-plane and three-dimensional randomlyoriented nanotubes increase the effective properties considerablyless, but equally, in more than one direction.Several micromechanical schemes including sequential homogenizationand various extensions of the Mori–Tanaka method werecompared in a recent study of the elastic properties of SWCNTbasedpolymers by Selmi et al. 206. The comparative studyshowed that for all composite morphologies considered fullyaligned, two-dimensional in-plane random orientation, and threedimensionalrandom orientation, the two-level Mori–Tanaka/Mori–Tanaka approach delivered the best predictions when validatedusing both experimental and FE results.3.3.3 Multiscale Modeling. The mechanical deformation andfailure of many engineering materials are in fact multiscale phenomena,and the observed macroscale behavior is governed byprocesses that occur on many different length and time scales.These processes are often dependent on each other and affect theoverall deformation. It is therefore necessary to model these systemsusing a variety of length scales, which accurately representthe governing physics. Since various scales in the system dependon each other, it is essential to formulate it in terms of multiscalemodeling, whereby the scales of interest are coupled or integratedinto a unified approach. Clearly, the degree to which these scalesare coupled would depend upon the system being investigated.Hence, varied multiscale approaches currently exist in the literature207–211.Most multiscale modeling techniques adopt either coupled oratomistic-based continuum approaches to treat this class of problems.In the coupled approach, it is common to employ MD ortight binding TB for atomistics and FE methods for continuumscales. The coupled MD-FE methods can be further subdividedinto sequential and concurrent coupling methods. The sequentialapproach assumes that the problem considered can be easily separatedinto processes that are governed by different length and timescales. In doing so, the simulations run independently of eachother, and a complete separation of both length and time scales isachieved. The outputs displacement or force fields of the finerscale simulation are used as boundary conditions for the coarserscale. Since the simulations are not integrated, it is important tofeedback the force fields for comparison to ensure that the simulationsare converging. However, it should be noted that theuniqueness of the solution is still not guaranteed. A schematic ofthe sequential approach is given in Fig. 19.Concurrent methods perform the entire multiscale simulationsimultaneously and continually feed information from one lengthscale to the other in a dynamic fashion. Concurrent methods arebetter suited in representing scales with a strong dependence becauseof the continuous transfer of information between the dif-Applied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-15Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 19 Schematic of the sequential multiscale modelingapproachferent scales. The passing of information ensures consistencyamong the field variables between the two simulation methods.This two-way transfer of boundary conditions is achieved throughthe use of a transition region depicted in Fig. 20. Unfortunately,most concurrent multiscale modeling techniques suffer from oneor more of the following difficulties: i the necessity of meshingtraditional FE regions down to the atomic scale, thus leading tophysical inconsistencies and numerical difficulties, ii contaminationof the solution due to wave reflection resulting from the improperdescription of the transition zone, and iii the FE/MDenergy mismatch leading to erroneous nonphysical effects in thetransition region. A number of reviews detailing the differentmodeling techniques, their merits, and limitations are provided inRefs. 212–214.The other multiscale modeling approach is the atomistic-basedcontinuum technique. It has the unique advantage of describingFig. 20 Transition region used to couple MD and FE methodsin concurrent multiscale techniquesatomic positions, their interactions, and their governing interatomicpotentials in a continuum framework. The interatomic potentialsdeformation measures introduced in the model capturethe underlying atomistic structure of the different phases considered.Thus, the influence of the nanophase is taken into accountvia appropriate atomistic constitutive formulations. Consequently,these measures are fundamentally different from those in the classicalcontinuum theory. The strength of atomistic-based continuumtechniques lies in their ability to avoid the large number ofdegrees of freedom encountered in the discrete modeling techniqueswhile at the same time allowing for the description of thenonlinear constitutive behavior of the constituents. A schematic ofthis approach as it relates to the modeling of CNT structures isdepicted in Fig. 21.Namilae and Chandra 215 developed a sequential multiscalemodel linking molecular dynamics and the finite element methodto study the effect of chemical functionalization of the interfacialproperties. They used molecular dynamics to simulate nanotubepull-out tests from which they obtained the corresponding tractionseparation curves. They then used these results to evaluate cohesivezone model parameters in a FE framework. They predictedthat an ISS as high as 5 GPa can be achieved through the chemicalbonding of the CNT and the matrix.A sequential multiscale model was proposed by Odegard et al.in which the nanotube, polymer matrix, and interface were allcombined and modeled by an effective continuum fiber 216,217.The fiber was developed through the use of an equivalentcontinuummodeling method. In this approach, MD was used tomodel the molecular interactions between the nanotube and thepolymer. Then, micromechanical methods were employed to determinethe bulk properties of the effective fiber embedded in acontinuous polymer. The equivalent-continuum modeling methodconsists of four steps. First, MD simulations are used to determinethe equilibrium structure of the composite, and a RVE of the molecularand equivalent-continuum models is created. The RVE canbe considered as a building block for the nanocomposite, whichencompasses the nanotube, the interface between the nanotubeand polymer matrix, and an outer polymer matrix body. Each ofthe three components of the RVE is modeled independently usingdifferent techniques. Second, the potential energies for the molecularmodel and effective fiber are derived and equated underidentical loading conditions. A truss model is used as an intermediatestep to link the molecular and equivalent-continuum modelswhereby each truss represents an atomic bond or a nonbondedinteraction. The third step consists in obtaining the constitutiverelationship for the effective fiber. Lastly, the overall constitutiveproperties of the composite are obtained by use of the Mori–Tanaka model. Figure 22 illustrates how the molecular level descriptionof the system is related to the continuum level with anintermediate truss model. The authors used this method to examinethe elastic properties of the nanocomposite. Perfect bondingbetween the effective fiber and surrounding polymer was assumed.The elastic stiffness constants were determined for bothaligned and three-dimensional randomly oriented nanotubes as afunction of nanotube length and volume fraction. The Young’smodulus was also determined for the three-dimensional randomlyoriented case as a function of volume fraction.A hierarchical multiscale Monte Carlo finite element methodMCFEM was developed by Spanos and Kontsos 218 to determinethe mechanical properties of polymer nanocomposites. Intheir approach, special consideration was taken to account for thenonuniform spatial distribution of the CNTs in the polymer in aneffort to closely replicate experimental results that are hindered bythe inhomogeneous dispersion of the nanofillers. This method effectivelydivides the composite into a grid of material regions,similar to the RVE used in other techniques, each containing amaterial point. The material points are introduced to model variationsin the volume fractions of the CNTs. The finite elementmethod is used to discretize the structure into a set of unit cells050801-16 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 21 Atomistic-based continuum technique as it relates to CNTstructureseach with different homogenized properties. Here, the model usesthe equivalent-continuum technique developed by Odegard et al.to determine the material properties of the SWCNT as an input toa Mori–Tananka micromechanical analysis, which subsequentlydetermines the averaged properties of each unit cell. The finiteelement method computes estimates for the overall mechanicalbehavior of the nanocomposite. Finally, a statistical analysis of theensemble of the numerically generated results yields values forthe Young’s modulus and Poisson ratio of the composite.The fracture behavior of CNT polymer composites and thenucleation of Stone-Wales defects have also been studied with theuse of multiscale modeling. For example, Shi et al. 219 developeda three-scale model where the atomistic region was definedas the region where Stone-Wales transformation and fracture wereexpected to initiate. A Stone-Wales defect, also termed the 5-7-7-5defect, is when four hexagons in a nanotube undergo a transformationinto two pentagons and two heptagons after reaching somecritical strain. This is achieved through the 90 deg rotation of aC–C bond resulting in the elongation of the nanotube and releaseof strain energy. This defect is thought to be one of the mainmechanisms behind plastic deformation in CNTs and is depictedin Fig. 23. In this region, the process of defect nucleation is dependenton the directions and lengths of individual C–C bonds.The bond interaction of the carbon atoms was modeled using theTersoff–Brenner potential, and a bond was assumed to be brokenonce its length exceeded 0.2 nm. The immediate region outsidethis atomistic zone is insensitive to the presence of the defects andremains approximately in the hexagonal structure. Therefore, thepositions of the atoms in this region were determined using thecontinuum medium method based on the Cauchy-born rule. Thepolymer matrix surrounding the nanotube was modeled using continuumconcepts. This model also employed the Mori–Tanakamethod to capture the interaction of individual CNTs, which mayinfluence their deformation and fracture behaviors. Throughoutthe model, perfect bonding was assumed between the nanotubeand the polymer matrix. The authors studied the dependence ofStone-Wales transformation on the chiral angle and diameter anddetermined that the critical strain needed to nucleate the defectwas indeed dependent on the chiral angle but insensitive of thediameter. The authors also concluded that Stone-Wales defectsbecome more difficult to nucleate in CNTs when they are embeddedin the polymer matrix.Li and Chou 32 are responsible for the development of amolecular structural mechanics approach that has been used extensivelyto model CNT-based structures. This approach fallswithin the class of atomistic-based continuum methods. In thisapproach, the CNT is modeled as a space-frame structure, wherethe covalent C–C bonds are represented as beams joined togetherby nodes that represent the atom positions, as depicted in Fig. 24.The tensile resistance, flexural rigidity, and torsional stiffness ofFig. 22 Equivalent-continuum modeling technique „from Refs.†216,217‡… Fig. 23 Comparison of pristine and defected CNT structuresApplied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-17Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 24Atomistic-based continuum CNT space-frame structurethe beams are determined by imposing energy equivalence on thestructural mechanic and molecular mechanic energy descriptionsof the beam and bond deformation mechanisms. This provides arelationship between the structural mechanics parameters and molecularmechanics force fields from which it is possible to obtainlinear relationships between the tensile and shear moduli of eachbeam and the harmonic force constants. Li and Chou further appliedthis technique to the development of an atomistic-based continuummodel to study the compressive behavior of the bulk composite220. In this approach, the nanotube was modeled by themolecular structural mechanics approach, the polymer matrix wasmodeled at the continuum scale by the finite element method, andthe interface between the nanotube and polymer was representedby a truss rod model whereby the atomic interactions are based onthe Lennard–Jones potential. By use of this model, the authorsconsidered two cases of loading, isostress and isostrain conditions.For both loading conditions, the model showed that the maximumshear stresses occurred at the nanotube ends and the shear stressesvanish at the middle section of the nanotube. They also concludedthat the buckling force is dependent on the volume fraction of thenanotube and increases with increasing nanotube length.The molecular structural mechanics approach was also used byGao and Li in their multiscale shear-lag model 221. It was usedto define the elastic properties of the CNT, which was then homogenizedinto an effective fiber of the same geometrical dimensions.The homogenized CNT was then used as one of the constituentsin a RVE. A continuum-based shear-lag analysis of theRVE was then carried out using the elasticity theory for axisymmetricproblems. From their analysis, predictions of the interfacialshear stress and other axial stress components in both the nanotubeand the matrix were obtained.The elastic properties of CNT polymer composites under variousloading conditions were also studied through the developmentof a multiscale model by Hu et al. 222. In this model, a RVE wascreated, which encompassed the nanotube, the transition layer betweenthe nanotube and the polymer matrix, and the outer polymermatrix body. An equivalent beam model of the nanotube wasdeveloped using a combination of molecular mechanics and structuralmechanics approaches. This way, a relationship between thematerial properties of the beam element and molecular mechanicforce fields is obtained in a similar fashion to the study by Li andChou 32. In order to describe the interaction between the nanotubeand polymer matrix, the authors used molecular mechanicand dynamic approaches to obtain the thickness of the transitionlayer or the equilibrium distance between the nanotube and thepolymer. The transition layer and outer polymer matrix were modeledusing the finite element method. In this study, no chemicalbonding was assumed between the nanotube and polymer. In thiscase, the Lennard–Jones potential was used to characterize theinteraction between the nanotubes and polymer matrix. The authorsused the model to study the effects of such parameters asvolume fraction of nanotubes, stiffness of the transition layer, andlength of the polymer chain on the elastic properties of the bulkcomposite composed of short unidirectional nanotubes.Tserpes et al. 223 developed an atomistic-based continuumRVE for modeling the tensile behavior of the bulk composite. Aprogressive fracture model based on the modified Morse potentialwas used to simulate the behavior of the individual nanotubes,which were then inserted into the matrix to form the RVE. Thechoice to use the modified Morse potential was enforced by itssimplicity over many-body potentials as well as its compatibilitywith the finite element method. From the progressive fracturemodel, the authors were able to obtain the stress-strain curves forthe nanotubes, which were then used to obtain expressions for theYoung’s modulus. These expressions were assigned to the beamelements used to represent the nanotubes in the construction of theRVE. To accurately capture the debonding between the nanotubeand polymer, the authors used a shear-lag approach to obtain theshear stresses along the nanotube element. If the shear stress exceededthe interfacial shear stress, the interface was assumed tohave failed and the load carrying ability was removed from thenanotube element by reducing the stiffness of the element to avery small number. The authors noticed a significant enhancementin the stiffness of the polymer by the addition of nanotubes. Theyalso studied the effect of the interfacial shear strength on the tensilebehavior of the composite and concluded that the stiffnesswas unaffected while the tensile strength decreased significantlywith decreasing interfacial shear strength.3.4 Experimental Investigations of the MechanicalProperties. When the structural perfections of the CNT were firstreported by Iijima in 1991 27, there was much speculation thatthese carbonaceous fibers could be the strongest known materials.Since that time, the outstanding mechanical properties of CNTshave indeed been verified, and they are now being viewed as themost promising reinforcing agents in high-performance compositematerials for a variety of structural applications. Consequently,there have been numerous efforts by researchers from laboratoriesall over the world to realize these outstanding improvements inthe mechanical properties of a variety of different host polymericmatrices. The experimental measurements of the mechanical propertiesof CNT composites are so abundant that they can very wellbe the focus of a single comprehensive review. Therefore, thissection will primarily address the most recent and significant improvementsin strength, stiffness, and fracture toughness availablein literature and will identify the dispersion technique, the optimalCNT concentration, and, if used, the details of the functionalizationor surface pretreatment process.3.4.1 Strength and Stiffness. The enhancement of the modulusof a polymer reflects the ability to transfer stress from the polymermatrix to the high modulus CNTs. Therefore, strong interfacialadhesion between the polymer and CNT is preferred for the stiffeningof the composite. An enhancement in the strength of a polymeralso reflects a strong interaction between the polymer andCNTs; however, strength is also affected by the presence of defects,voids, agglomerates, and other inclusions, which serve toinitiate fracture. The published experimental data show that thetensile stiffness of CNT composites is generally improved; however,a comparison of the data is difficult given the significant050801-18 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

variability in processing techniques, types of CNTs, surface treatments,polymer matrices, and test methods that have been used.The enhancement in stiffness is usually most prominent in the lowCNT weight fractions. With regard to reinforcing polymeric matriceswith CNTs to improve their strength and stiffness, bothMWCNTs and SWCNTs have been used with varied levels ofsuccess. MWCNTs are generally preferred due to their relativelylower production cost; however, the internal layers of MWCNTstend to slide within one another and undermine the load bearingcapability of the nanotubes; only the outer shells of MWCNTstend to carry the load. This is because only weak van der Waalsinteractions transfer loads between the neighboring shells. As aresult, the inner layers can rotate and slide freely.Perhaps the most remarkable improvement in both the tensilemodulus and yield strength of a polymer through the dispersion ofCNTs was observed by Liu et al. 224. By dispersing only 2 wt %MWCNTs in a nylon-6 PA6 matrix, Liu et al. observed an increaseof approximately 214% in the tensile modulus and of 162%in the yield strength. The MWCNTs were first purified by dissolvinga catalyst in hydrochloric acid followed by refluxing in 2.6Mnitric acid as a means of increasing more carboxylic and hydroxylgroups. Composite samples then were prepared via a melt compoundingmethod. They attributed these impressive improvementsin the stiffness and strength to a uniform and fine dispersion of theCNTs and good interfacial adhesion between the nanotubes andmatrix, which were assessed using SEM. In contrast, Liu et al.225 also used the melt compounding method to fabricateMWCNT/PA6 composite specimens. The MWCNTs used in theirstudy were synthesized in ethanol flame, which was shown,through the use of a variety of microscopy techniques, to produceactive functional groups on the surface of the MWCNTs. TheseMWCNTs were further functionalized with n-hexadecylaminemolecules. Through the use of SEM, they concluded a uniformdispersion and good wetting with the PA6 matrix. However, theobserved improvements in the tensile modulus and tensile strengthwere only approximately 29% and 6% for cases involving 1 wt %CNTs, respectively. In another recent study, Sahoo et al. 141dispersed carboxyl-functionalized MWCNTs in a PA6 matrix.They used both an internal mixer and an extrusion process todisperse the CNTs in the PA6 matrix. They observed a maximumincrease of approximately 126% in the tensile strength when 10wt % of the functionalized MWCNTs were incorporated in thePA6 matrix. This clearly demonstrates a significant variability inthe results of three separate experimental studies that used thesame fabrication method and constituent materials and both claiminguniform dispersions and good wetting with differences only inthe pretreatment processes of the MWCNTs. It is anticipated thatwhile the ethanol flame CNT synthesis method can produce CNTswith inherent functional groups it may also introduce considerabledefects in the walls of the CNTs, which may help explain thesignificantly lower improvements observed by Liu et al. 225.Gojny et al. 226 investigated the mechanical properties of anepoxy reinforced with both nonfunctionalized and aminofunctionalizedCNTs. One of the objectives of the study was toidentify the best nanofiller when SWCNTs, double-walled carbonnanotubes DWCNTs, and MWCNTs were considered. The nanocompositeswere produced using the same processing conditionsand systematically varying CNT type, content, and surface functionality.The CNTs were dispersed in the two component epoxysystem using the calendering approach followed by intense mixingwith the hardening agent. TEM micrographs seemed to confirma uniform dispersion of the CNTs with fewer agglomeratesobserved in the case of DWCNTs and MWCNTs as these nanofillerstend to exhibit lower specific surface areas when comparedwith SWCNTs. In all cases, amino-functionalized CNTs producedbetter results when compared with nonfunctionalized CNTs,which can be attributed to the better interfacial adhesion of theCNTs and epoxy and to the improved dispersion. The resultsshowed that the greatest improvements in both tensile modulusand strength were observed for the amino-functionalizedDWCNTs at concentrations of about 0.5 wt % with improvementsof approximately 14.5% and 8.4%, respectively. It was expectedthat SWCNTs would provide the highest improvement in theseproperties given that these fillers have the largest specific surfacearea and aspect ratio; however, the DWCNTs did not agglomerateas pronounced as SWCNTs. In general, MWCNTs, whether functionalizedor not, actually degraded the tensile modulus and tensilestrength over that of the pure epoxy. This was attributed to theabsence of stress transfer between the internal layers of theMWCNTs and to the relatively low specific surface area and aspectratio present. Figures 25a–25d summarize these results.Similar observations were made by Ji et al. 227 in their experimentalmeasurements of MWCNT-reinforced polystyrene composites.In a more recent study by Guo et al. 228, MWCNTswere functionalized through a nitro sulfuric acid treatment anddispersed in an epoxy using a sonication technique. They observeda 35.5% increase in the tensile modulus and a 10% increasein the tensile strength when the epoxy was reinforced with3 wt % functionalized MWCNTs. Prashantha et al. 229 fabricatedMWCNT/polypropylene composites using a melt compoundingmethod. They observed a 68% increase in the tensilemodulus and a 30% increase in the tensile yield strength at CNTconcentrations of 5 wt % and 3 wt %, respectively.PET nanocomposite films were prepared by melt-extrudingmixtures of PET and functionalized MWCNTs in a recent studyby Yoo et al. 230. Carboxyl, benzyl, and phenyl functionalizedMWCNTs were used with the view of identifying the best functionalizationprocess for improving both the thermal and mechanicalproperties. In all cases corresponding to a CNT concentrationof 3 wt %, the tensile modulus was improved over that of the purePET; however, only phenyl and benzyl functionalized MWCNTsproduced an improvement in the tensile strength. The phenylfunctionalized MWCNT samples produced the largest enhancementin both properties. This was attributed to a more uniformdispersion and better interfacial bonding arising from the phenylfunctionalization process when compared with the others.In contrast to the experiments cited above, where the nanocompositeswere fabricated as a film or cast into a desired shape, therehas also been some recent interest in fabricating polymeric compositefibers reinforced with CNTs. In this case, the improvementsin the mechanical properties have been much more significant. Forexample, Chang et al. 231 fabricated polypropylene fibers reinforcedwith SWCNTs using a fiber spinning process. The CNTswere dispersed in the polypropylene via mechanical stirring. Thetensile modulus of the composite fibers increased a remarkable300% as a result of 1 wt % SWCNT loading. Significant increaseswere also observed in the tensile strength; however, these valueswere not presented. Likewise, Rangari et al. 146 fabricated PA6composite fibers reinforced with a combination of both nonfunctionalizedand functionalized SWCNTs and MWCNTs. The compositeswere fabricated using a melt extrusion technique. As aresult of the CNT reinforcement, they observed an increase of231% in the tensile strength for cases involving 0.5 wt % functionalizedCNTs and an increase of 787% in the tensile modulusfor the same system. A possible explanation for these remarkableimprovements is that both the fiber spinning and melt extrusionfabrication techniques are known to inherently align the nanotubesin the direction of the longitudinal fiber axis, thus maximizing thereinforcing potential of the CNTs. In contrast, much of the experimentalresults discussed above employ random distributions of theCNTs in the polymeric matrix.The impact strength of polymer materials can also be significantlyimproved through the homogeneous dispersion of CNTs.Yuan et al. 232 dispersed both modified and pristine MWCNTsin a polystyrene matrix using a twin extruder system. The modifiedspecimens were noncovalently functionalized to induce PSwrapping around the MWCNT. At a nanotube content of 0.32wt %, the modified MWCNT composite displayed a 250% in-Applied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-19Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 25 A comparison of the „a… ultimate tensile strength of epoxy-based composites containing nonfunctionalized nanotubesand „b… functionalized nanotubes and „c… the Young’s modulus of epoxy-based composites containing nonfunctionalizednanotubes and „d… functionalized nanotubes „from Ref. †226‡…crease in impact strength as compared with the pure PS and thepristine MWCNT composite had a 150% increase. Furthermore,the tensile strength of the pristine MWCNT composite descendedslightly with the addition of nanotube content, whereas that of themodified MWCNT composite ascended slightly. In comparison,Prashantha et al. 229 investigated the impact strength ofMWCNT/polypropylene composites fabricated using a melt compoundingmethod. They conducted charpy impact tests on bothnotched and un-notched test specimens. With increasing nanotubecontent, the impact resistance for the un-notched samples decreasedsignificantly. On the other hand, the charpy impactstrength for the notched specimens of MWCNT/PP nanocompositesslightly increased as the MWCNT content increased. Thenotched specimens bearing 2 wt % MWNT showed a 40% increasein impact energy compared with that of the neat PP. Yang etal. 14 observed substantial improvements in the impact strengthof an epoxy system dispersed with as-received MWCNTs andtriethylenetetramine TETA functionalized MWCNTs using asonicating treatment. At 0.6 wt %, the as-received MWCNTs producedan increase of 35% in the impact strength when comparedwith that of the pure epoxy matrix. In comparison, the impactstrength of the epoxy at 0.6 wt % TETA functionalized MWCNTloading was improved by 84%, which was attributed to the improveddispersability of the nanotubes. Improvements in the bendingstrength and stiffness were also observed. For the case of 0.6wt % as-received MWCNTs, the bending strength and stiffnessincreased by 12% and 9%, respectively. In comparison, the TETAfunctionalized MWCNTs provided an enhancement of 29% and22% in the bending strength and stiffness, respectively.3.4.2 Fracture Toughness. Polymeric resins such as epoxies,which are extensively used as the matrix phase in advanced compositestructures, provide excellent strength, stiffness, thermal stability,and chemical and environmental resistivities but possessrelatively low toughness. Improving the fracture toughness ofbrittle polymers such as epoxies has the potential to significantlyimprove the service life of products made from composite materials.The stringent requirements of a number of industries, suchas aerospace and automotive, necessitate the reinforcement ofthese materials. A number of techniques have been considered toimprove the fracture toughness of epoxies. They include the formulationand modification with other materials such as the additionof carbon, nylon or glass microfibers, rubber, liquid rubberand rubber precipitates, reactive ductile diluents, and inorganichybrid particles, among others. While some improvements inbond properties have been observed 233,234, these additives canalso lead to reductions in high temperature service capabilities,low impact strength, sensitivity to moisture, and poor shrinkagecharacteristics 235. For example, a common method of tougheningepoxy adhesives is blending the primary resin with other050801-20 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 26 Experimentally determined fracture toughness valuesof DWCNT epoxy composites „from Ref. †8‡…polymers, such as thermoplastics and elastomers. However, thistechnique usually combines both the good and bad characteristicsof each resin system. Epoxy-nylon adhesives provide a major improvementin toughness over a pure epoxy formulation, but theyhave sensitivity to moisture because of the nylon constituent.Elastomeric particles such as rubber have also been used totoughen adhesives. The rubber inclusions absorb energy and stopcracks from propagating throughout the bondline. However,rubber-based adhesives have low glass transition temperatures.The addition of heat will soften the adhesive and directly affect itsfunction. In all the above hybrid systems, the added tougheningresin reduces the overall glass transition temperature of the system,thereby reducing elevated temperature performance and environmentalresistance 235. In an effort to improve the fracturetoughness of polymers, at little or no cost to other properties, anumber of researchers have attempted to use nanofillers such asCNTs, which have actually been shown to improve secondaryaspects as well, such as the glass transition temperature and thermalstability 141,230,236. Based on the experimental results, thereinforcement of brittle polymers such as epoxies through the homogeneousdispersion of CNTs has resulted in significant improvementsin fracture toughness when compared with the neatpolymer system. As a result of these experimental data, investigationsinto the dominant toughening mechanisms associated withthese improvements have begun.Several experimental efforts have been made to improve thefracture toughness of polymer systems through the homogeneousdispersion of CNTs. Gojny et al. 8 examined the fracture toughnessof CNT/epoxy composites containing functionalized andnonfunctionalized DWCNTs dispersed through shear mixing in anepoxy matrix. The fracture toughness for functionalized DWCNTswas found to increase by as much as 26% compared with the pureepoxy matrix, when a filler content of 1 wt % was used. A summaryof their results can be seen in Fig. 26. Lachman and Wagner237 investigated a multitude of different CNTs and other nanoparticlesas a means of improving the fracture toughness of acommon epoxy. These included carbon black, carbon nanofibers,pristine MWCNTs, and two different forms on functionalizedMWCNTs, namely, carboxylated and aminated. The nanofillerswere dispersed in the epoxy by means of mechanical stirring andsonication. Figure 27 presents the results of their test. As can beseen, the CB- and CNF-based composites showed no significantimprovement in fracture toughness, whereas all CNT polymercomposites displayed significantly higher fracture toughness valueswhen compared with the pure epoxy. The toughening effect isthe highest in the NH 2 −CNT nanocomposites for which it is approximatelytwice the pure epoxy value when the CNTs weredispersed in ethanol prior to mixing with the epoxy.Ganguli et al. 238 performed single edge notch three-pointFig. 27 Measured fracture toughness values for a variety ofcommonly used nanofillers „from Ref. †237‡…bending tests on MWCNT/epoxy specimens prepared using anasymmetric high speed mixer to disperse the nanotubes. Samplesof the neat polymer as well as the composite containing 1 wt %MWCNT were prepared. The results showed that the addition ofthe nanotubes resulted in a 300% increase in the stress intensityfactor over the pristine sample. Seyhan et al. 239 dispersed bothfunctionalized and nonfunctionalized DWCNTs and MWCNTs ina modified vinyl-ester/polyester hybrid matrix using a calenderapproach. The functionalized CNTs were found to provide themost significant increase in fracture toughness. Specifically, thefunctionalized MWCNTs exhibited a 40% increase in fracturetoughness at 0.3 wt % nanotube content when compared with theneat polymer. Functionalized DWCNTs exhibited a fracturetoughness increase of more than 20% at 0.3 wt % nanotube content.In addition, they found that the calendering dispersion processwas more effective at homogeneously dispersing MWCNTsthan DWCNTs. Yu et al. 240 studied the fracture toughness ofMWCNTs/epoxy composites with nanotube contents between 0wt % and 3 wt % using a sonication dispersion method and adegassing agent to prevent the formation of voids. A maximumincrease in fracture toughness of 62–66% at 3 wt % filler contentwas found over the neat polymer. In comparison, the sampleswithout the degassing agent only exhibited an increase of 29–40at 3 wt % nanotube content. The variation in fracture toughnessfor samples with the same nanotube content was attributed to theduration of the sonication and stirring treatments, with higher dispersiontimes giving higher toughness values. The experimentalresults have indicated that significant increases in the fracturetoughness of CNT-based composites can be achieved at very lowCNT contents. However, as with most of the other mechanicalproperties, there exists a critical CNT concentration above whichthe fracture toughness begins to degrade, which can be attributedto the inability of present dispersion techniques to ensure deagglomerationof CNTs at large concentrations.The incorporation of CNTs into polymeric matrices as a meansof improving the fracture toughness requires a comprehensive understandingof the toughening mechanisms associated with thisclass of materials. The microtoughening mechanisms in ductileand brittle solids have been extensively explored 241–243; however,the dominant mechanisms in nanocomposites require furtherApplied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-21Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 28Commonly observed CNT polymer composite toughening mechanismsinvestigation. Several toughening mechanisms identified in microfibercomposites, such as crack bridging and fiber pull-out,fiber deformation and fracture, and crack pinning, have also beenidentified on the nanoscale. Also, new nanoscale specific mechanismshave been identified, such as fracture ridge creation 238.Crack bridging is a toughening mechanism whereby a CNTcaught in the path of a propagating crack assists in keeping thecrack closed due to the interfacial bonding between the CNT andthe polymer matrix. The crack can only overcome this bridge bydeforming the CNT or by shearing the interface to continue propagating,leading to a dissipation of energy. If the length of the CNTis below its critical length, the crack will continue to propagate byshearing the CNT/polymer interface and the subsequent pull-outof the nanotubes from within the matrix. A related form of nanotubepull-out is sword-in-sheath pull-out, which occurs withMWCNTs when the outer layer of the CNT fractures, and theinner layers pull out from within the outer sheath. When a CNThas a length that exceeds its critical length, the bonding at theCNT/polymer interface is sufficient to withstand the shear forcesand the crack continues to propagate by means of deformation andfracture of the nanotubes. Crack pinning is a process where thepropagating tip of a crack meets a fiber, and is forced to movearound the fiber in order to continue propagating. This causes thecrack length to increase significantly as it weaves around fibers.The above toughening mechanisms are schematically depicted inFig. 28.CNT pull-out has been identified as one of the main tougheningmechanisms associated with this class of materials. Furthermore,fiber-pull-out tests have been well recognized as the standardmethod for evaluating the interfacial bonding properties of compositematerials. The output of these tests is the force required tode-bond the fibers from the surrounding polymer matrix and theshear stresses involved. In the case of CNT-reinforced polymers,experimental tests have been conducted but are limited due to thenanoscale involved. Figure 29 depicts the typical pull-out profilefor a nanotube embedded in a polymer. Previous authors havereported experimental results in which the interfacial shearstrength was found to be within the range of 35–376 MPa244–246 based on CNT pull-out using a scanning probe microscope.However, shear strengths as high as 500 MPa have alsobeen reported by Wagner et al. 247 based on fragmentation testsin urethane-CNT composites. Barber et al. 182 also conductedpull-out measurements on an individual SWCNT embedded in apolymer matrix using AFM. They found that the stress required toseparate the nanotube from the surrounding matrix was remarkablyhigh, indicting that the polymer matrix immediately surroundingthe nanotube is capable of withstanding stresses thatwould otherwise cause considerable yielding in a bulk polymerspecimen.Some work has been done to experimentally identify nanoscaletoughening mechanisms. Watts and Hsu 248 identified bothCNT bridging and CNT fiber pull-out in experiments involvingarc-generated MWCNTs in a 2-Methacryloyloxyethylphosphorylcholine-2-diethylaminoethyl methacrylate MPC-DEA diblock polymer. Fiedler et al. 126 obtained evidence ofDWCNT and MWCNT bridging cracks in a low viscosity resinsystem using TEM and SEM micrographs. Figures 30 and 31 arereproductions of those micrographs. One can see a hollow channelin the matrix of Fig. 30, providing evidence of the nanotube pulloutmechanism. Other evidence of these toughening mechanismscan be found in Prashantha et al. 229, Zhang et al. 249, andThostenson and Chou 250.Several models have been developed to assist in the understandingof the mechanisms that lead to improved fracture toughnessin CNT-reinforced polymers. Most models attempt to quantifythe effects of one particular toughening mechanism usingeither analytical or numerical methods. The authors of this revieware not aware of other works that attempt to model the combinedeffects of more than one toughening mechanism on the resultingfracture toughness of nanoreinforced composites. In fact, muchstill needs to be learned about the prevalent mechanisms in thisclass of materials. However, the models that have been developedthus far have contributed to a better understanding of the corre-Fig. 29 Typical plot of a pull-out test on a nanotube embeddedin a polymer „from Ref. †12‡…050801-22 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 30 TEM micrograph of a MWCNT bridging a matrix crack„from Ref. †126‡…Fig. 31 SEM micrograph of a crack bridged by DWCNTs „fromRef. †126‡…sponding mechanisms.Wichmann et al. 251 developed a simple analytic model of theCNT pull-out toughening mechanism. The problem was approachedby scaling the energy dissipation of a microfiber to thatof several CNTs, relying on volume equivalence to ensure compatibilityof the parameters. The model assumed the tensilestrength of carbon fibers and CNTs to be on the order of 1–7 GPaand 30–50 GPa, respectively. The results show that the energydissipated in nanotube pull-out is anywhere between 4 and 100times higher than the conventional microfiber pull-out mechanism.This shows that nanotube pull-out can contribute significantlyto the toughening of composite materials. Blanco et al.252 developed an analytic model to examine the effect of nanotubepull-out on the interlaminar fracture toughness of a doublecantilever beam specimen. Two types of nanotube pull-out mechanismswere considered: traditional pull-out and sword-in-sheathpull-out. The results showed that both the aspect ratio and thestrength of the CNTs are key parameters to fracture toughnessimprovement. Their predictions were compared with experimentalresults, and it was found that the experimental values fell betweenthe isolated traditional pull-out and sword-in-sheath predictions.This was attributed to the experimental results being a combinationof both mechanisms as well the presence of other tougheningmechanisms that were not considered in the model and the potentialagglomeration of CNTs. Seshadri and Saigal 253 developedan analytical model for CNT crack bridging of viscoelastic polymersin an attempt to identify the parameters associated with theimprovements in fracture toughness. They derived expressions forelastic and viscoelastic polymer pull-out stiffness as well as fractureenergy augmented by a single nanotube bridge. They concludedthat augmented fracture energy is dependent on severalparameters, including crack opening rate, interface stiffness, nanotubedensity, and viscoelastic relaxation of the polymer. Lachmanand Wagner 237 used a classical pull-out energy dissipation expressionto explain the toughness improvements that are seen inCNT/epoxy composites. They argued that as a result of the highstrength of CNTs, the critical length necessary to induce fractureof the nanotubes is often much larger than their typical lengths.This results in pull-out being the dominant toughening mechanism,which differs from traditional microfibers, where fiber fractureis the primary form of energy dissipation. Zhang et al. 249used an analytic model to predict the crack propagation rate ofSWCNTs and MWCNTs in an epoxy resin as a function of stressintensity factor. They considered fiber pull-out as the primarytoughening mechanism and assumed that a constant force is requiredthroughout the pull-out process. They also developed anexpression for the crack bridging length. From this, the work requiredto pull out a nanotube was calculated and incorporated intoa new stress intensity factor, which also incorporates the number,density, and orientation of the nanotubes. They used experimentaldata to calibrate and validate their model, where good correlationwas found. The model predicted that the crack propagation ratedecreases as the weight percentage of CNTs is increased. Themodel also shows that as stress intensity increases, the suppressionof the crack growth rate for the nanotube composites degradeswhen compared with the neat epoxies.3.5 Tailoring of Electrical Properties. Polymeric materialsare typically considered to be electrical insulators due to theirextremely low electrical conductivities 10 −10 –10 −15 S/m. However,dispersing nanotubes into these matrices can result in drasticallyimproved conductivities. The higher conductivities that areavailable in these nanocomposites are being explored for a varietyof applications, including housings for cell phones and computers,lightening strike protection for aircraft, chemical sensors, andtransparent conductive coatings. For example, electromagnetic interferenceshielding is essential in many portable electronic devicese.g., laptop computers, cell phones, and pagers to preventinterference with and from other electronic devices. Since there ispresently no suitable polymeric material, which can meet theserequirements, electrically conductive additives are generally usedin the electronic equipment cases made of a polymer-based material.However, such materials are frequently associated with significantincreases in the weight and cost as well as with reducedsurface quality and mechanical integrity. Therefore, electricallyconductive composites dispersed with CNTs are now being exploredas alternatives to the existing choices 254,255. Indeed,the first major commercial application of CNTs is related to theirelectrical conductivity in polymer composites 256. A basic understandingof the fundamental mechanisms associated with improvedelectrical conductivities in nanocomposites is crucial to therealization of devices for these applications.3.5.1 Electrical Percolation. In a composite consisting of conductivefillers dispersed in an insulating matrix, there exists a welldefined insulator-conductor transition when a continuous conductivenetwork or path throughout the matrix is formed. At low fillerconcentrations, the conductive particles are separated from eachother and the electrical properties of the composite are dominatedby the insulating matrix. As the concentration of conductive fillersis increased, they come into contact with each other to form aconductive three-dimensional network. This process can be welldescribed by the percolation theory. The term percolation refers tothis onset of a continuous network or cluster at which long-rangeconnectivity and conductivity are suddenly developed 257, andthe concentration of fillers at which this transition occurs is re-Applied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-23Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 32 Electrical conductivity of CNT-reinforced compositesas a function of concentration and a schematic of the percolatingnetworkferred to as the percolation threshold. Figure 32 illustrates theformation of a percolating network and the sudden rise in electricalconductivity. Some efforts have been devoted to modelingpercolation phenomena in a wide class of materials. Different expressionshave been adopted with the power law being representativeof the threshold for conductivity in polymer composites.The power law is given as − c t3where is the electrical conductivity of the composite, is theconcentration of conductive fillers in vol % or wt %, c is thepercolation threshold, and t is the conductivity exponent. The conductivityexponent was found to be uniform for systems with thesame dimensionality. For three-dimensional systems, t varies between1.6 and 2 258. The percolation threshold and conductivityexponent are both functions of the aspect ratios of the fillers, .Current experiments and theoretical studies show that CNTreinforcedcomposites exhibit a percolation threshold in the vicinityof 0.1 wt % at which the electrical conductivity rises sharplyby several orders of magnitude 259–261. However, there existsconsiderable variability in the percolation threshold among differentnanotube/polymer composite systems, and electrical percolationthresholds as low as 0.0021 wt % 262,263 and as high as 15wt % 264 have been reported. This observed variation stemsfrom the fact that the percolation threshold in nanocomposites isheavily dependent on several important chemical, physical, andgeometrical parameters such as the type of CNT, synthesismethod, surface treatment, dimensionality, polymer type, and dispersionmethod. Recently, a review of experimental investigationsinto the percolation threshold of nanocomposites was publishedby Bauhofer and Kovacs 265. In their review, nearly 200 nanotubepolymer experimental systems are summarized, and some ofthe above general dependencies of the percolation threshold areextracted. It should be noted that the above factors are not alwaysindependent, and it is often difficult to separate their effects on thepercolation threshold and the corresponding conductivities.Perhaps one of the most significant factors that influence theresulting percolation threshold in nanocomposites is the spatialdistribution or dispersion of the nanofillers. A conductive networkor path is more easily achieved when there are a number of conductiveparticles available throughout the matrix. The strong vander Waals interactions between nanotubes coupled with their largeaspect ratio causes them to bundle together and form agglomerates.As the CNTs bundle together into larger and larger agglomerates,the number of discrete conductive points in the compositeis reduced. This limits the potential for the CNTs to create a conductivenetwork or path through the insulating matrix, therebyincreasing the percolation threshold. Conversely, a very uniformdispersion can result in the sheathing of the nanotubes by thepolymer causing an increased resistance to electron tunneling, resultingagain in increased percolation thresholds. Therefore, a uniformspatial distribution of the nanotubes might not provide theoptimal conditions from an electrical performance standpoint.High aspect ratio nanotubes are generally more difficult to dispersedue to their stronger tendency to entangle and form agglomerates.Therefore, it is difficult to separate the effects of spatialdistribution and aspect ratio in experimental investigations. However,it has been experimentally determined that the percolationthreshold decreases with increasing nanotube aspect ratio 266,and these findings have been confirmed by theoretical investigations267,268. For a uniform spatial distribution of filler particles,the excluded volume concept can be used to show that thepercolation threshold is inversely proportional to the filler’s aspectratio 269. Likewise, Lu and Mai 257 used percolation theory toinvestigate the effect of nanotube aspect ratio on the percolationthreshold. Their results showed that the percolation threshold wasindeed inversely proportional to the aspect ratio of the nanotubes.Li et al. 261 developed an analytical model based on the averageimproved interparticle distance approach to investigate the effectsof nanotube dispersion state and aspect ratio on the resulting percolationthreshold. In their model, they incorporated two descriptivedispersion parameters to quantify the effects of CNT agglomeration:, a measure of the localized volume content of the CNTsin an agglomerate, and , a measure of the volume fraction ofagglomerated CNTs. A higher value of corresponded to a case ofmore tightly entangled CNTs in an agglomerate, whereas a highervalue of implied that the percentage of CNTs in the form ofagglomerates was higher. Their results show that both dispersionparameters have a significant effect on the percolation threshold.Specifically, the percolation threshold was found to vary betweenthree and four orders of magnitude over the chosen range of bothparameters. The authors concluded that in order to obtain an ultralowpercolation threshold on the order of 10 −3 vol %, both avery high aspect ratio and sufficient disentanglement of CNTs asmeasured by and are required. In addition, the authors alsoobserved that when the aspect ratio was reduced to 20, the percolationthreshold jumped to 1–10 vol % regardless of the dispersionstates of the CNTs. Hu et al. 270 also investigated the effect ofCNT aggregation on the percolation threshold using Monte Carlosimulations coupled with the three-dimensional statistical percolationtheory and resistor network modeling. They introduced asingle measure of the nonuniform spatial distribution of CNTs intheir model, which was defined as the ratio of the agglomeratevolume to that of the computational cell considered. They foundthat for cases involving very high concentrations of aggregates,the percolation threshold increased dramatically. However, the aggregatesdid not have a significant effect at low CNTconcentrations.The homogeneity of a CNT dispersion is difficult to quantify.Presently, the only techniques available to assess the uniformity ofdispersion is through electron microscopy techniques, such asTEM. For this reason, coupled with the fact that there exists significantvariability among reported test systems polymer type,CNT type, treatment, etc., it is difficult to assess the relativemerits of individual mechanical dispersion techniques on the experimentallymeasured electrical percolation thresholds. However,sonicated, mechanically stirred, and calendered approaches haveall been used in these measurements and tend to show comparablethresholds when the results are restricted to only those of epoxymatrices dispersed with MWCNTs. For example, Kovacs et al.259 dispersed MWCNTs, grown by catalytic chemical vapordeposition, into an epoxy matrix. The dispersion process consistedof mechanically stirring the MWCNTs in the epoxy using a dissolverdisk apparatus. They observed a percolation threshold of0.08 wt % for the case where the samples were stirred for 15 min050801-24 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 33 Effect of processing method on the percolationthreshold of MWCNT/epoxy composites „from Ref. †271‡…at 2000 rpm. In comparison, Li et al. 261 dispersed MWCNTs inan epoxy matrix via ultrasonication for 1hinanacetone mixture.They observed a comparable percolation threshold of 0.1 wt %.Finally, Gojny et al. 9 used a calender to disperse a variety ofdifferent CVD grown CNTs in an epoxy matrix. For all cases, theobserved percolation threshold for unfunctionalized CNTs was below0.1 wt %. In a recent experimental study by Kovacs et al.271, different processing conditions were examined to studytheir effects on the percolation threshold, and their results arepresented in Fig. 33. Again, CVD grown MWCNTs were dispersedin an epoxy matrix. Four different processing conditionswere examined. All samples were initially mechanically stirredusing a dissolver disk for 2 h at 2000 rpm. Two samples were thenprocessed using a calender. One sample of the mechanicallystirred and calendered batches was then manually stirred again for5 min at 60 rpm identified as slow stirred in Fig. 33. In all cases,the noncalendered samples had lower percolation thresholds andthose which were additionally stirred for 5 min at 60 rpm producedthe lowest percolation thresholds at 0.01 wt %. The calenderedsamples were believed to separate the nanotubes and sheaththem with an insulating polymer layer more effectively than thedissolver disk. It was believed that this polymer layer would betoo thick to allow the tunneling of electrons from neighboringnanotubes. Therefore, the calendering dispersion technique seemsto be a suitable method for improving the mechanical propertiesof polymeric composites. However, this process seems to be detrimentalto achieving low percolation thresholds. In conclusion,the best dispersion quality is not favorable for electrical conductivityapplications.In a similar context, chemical functionalization can also significantlyaffect the dispersability of the nanotubes, and in this way itis often difficult to determine its effect on the resulting electricalproperties of the nanocomposite. It should be noted that while thefunctionalizing of CNTs can increase the mechanical properties ofthe nanocomposite by forming stronger bonds between the matrixand the nanotube, it can actually have reverse effects on the electricalproperties of the composite. It has been shown that chemicalfunctionalization introduces defects into the CNT structure, whichtend to scatter electrons and generally cause a reduction in theirintrinsic electrical conductivity 99–101. This reverse effect canalso be attributed to the dependence of the percolation thresholdon the aspect ratio of the nanofillers. Chemical functionalizationtends to reduce the overall aspect ratio of the nanotubes, which isnot desirable when aiming to reduce the percolation threshold.Furthermore, the reaction of the epoxy resin with the nanotubes’surface groups forms an electrically insulating epoxy layer, whichincreases the distance between individual tubes, thus making thetunneling of electrons from tube to tube harder. Gojny et al. 9examined the effect of chemical functionalization on the percolationthreshold of a variety of different CNTs dispersed in an epoxymatrix. The lowest percolation thresholds were observed for nonfunctionalizedCNTs, being in all cases below 0.1 wt %, whereasthe amino-functionalized CNTs showed a percolation threshold inthe range of 0.1–0.5 wt %. A similar degradation of the percolationthreshold was observed by Bose et al. 272 in their experimentalinvestigations, which employed amino-functionalizedMWCNTs dispersed in a PA6/acrylonitrile-butadiene-styreneblend. However, a number of researchers have also observed increasesin the electrical conductivity in nanocomposites dispersedwith chemically functionalized CNTs and a corresponding decreasein the percolation threshold. For example, Valentini et al.273 explained that the overall conductivity is governed by theinterplay of contributions from extrinsic migrating charges ionicimpurities and intrinsic migrating charges donor-acceptor interactions.For the case of amine-functionalized SWCNTs dispersedin an epoxy matrix, they concluded that the SWCNTs act as electronacceptors and the amine groups as electron donors, thus contributingto the intrinsic charge of the system and thus increase theoverall conductivity. Tamburri et al. 274 prepared a series ofcomposite films using untreated nanotubes as well as nanotubestreated with KOH, HNO 3 , and HNO 3 /H 2 SO 4 solutions. With theuse of these reactants, the current at a given voltage was increasedby factors of 5 and 7.5. An improved dispersability of the treatedSWCNTs was cited as the main contributing factor to the enhancedcurrent in the conducting composite. Conversely, when thechemical processing was less efficient in producing –OH and–COOH groups, it is verified that the current increased only by afactor of about 2.5 relative to that of untreated nanotubes. Therefore,it seems as though the disadvantage associates with chemicalfunctionalization can be outweighed by the improved dispersabilityresulting from the process. Similarly, noncovalent functionalizationhas also been shown to increase the electrical conductivityand to decrease the percolation threshold 275,276.Nanotube alignment is also an interesting parameter that caninfluence the resulting percolation threshold in nanocomposites. Itis known that for a conductive network to be formed in the matrix,the nanotubes must come into very close proximity of each other.If the nanotubes dispersed in the matrix were all aligned in aparallel direction, it would be very difficult to meet the aboverequirement unless the nanotubes were joined end-to-end, whichis simply impossible to ensure. On the other hand, a completelyrandom orientation of the nanotubes would reduce the percolationthreshold but not entirely as a number of the nanotubes wouldlead to dead-end effects rather than contributing to the network.Therefore, it is normally preferred to have a small degree of misalignmentamong nanotubes in the matrix to ensure that they do infact cross paths and ensure contact. The effect of nanotube orientationhas been investigated experimentally by Du et al. 277.SWCNTs were aligned by melt fiber spinning. Various levels ofalignment were achieved by controlling the extensional flow inthe spinning process extrusional flow and wind-up speed. Theresults of the experiment confirm that a small degree of misalignmentis in fact desirable when attempting to reduce the percolationthreshold. The same conclusion was reached by Behnam et al.278 in their theoretical investigation of the effects of CNT alignmenton percolation resistivity using two-dimensional MonteCarlo simulations. In contrast, White et al. 279 observed that aminimum percolation threshold occurred for an isotropic casewhen the nanotubes were randomly orientated as apposed toslightly misaligned in their three-dimensional Monte Carlo simulation.They did, however, observe that there was a critical nanotubeorientation above which the percolation threshold drasticallyincreased with increasing nanotube alignment, and this effectseemed to be more pronounced for cases involving low aspectApplied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-25Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

atio nanotubes.Carbon nanotubes embedded in composites are not straight butrather have a certain degree of curvature or waviness that arisesfrom their high aspect ratio, low bending stiffness, and processinginduced effects. The effect of nanotube waviness of the percolationthreshold of nanocomposites has been investigated by a numberof researchers 260,280–284. They all found that the percolationthreshold increases with increasing degree of CNTwaviness. However, the increase in the percolation threshold doesnot seem to be significant among these results, which leads us tobelieve that the effect of waviness is not extensive. For example,Dalmas et al. 280 studied the effect of nanotube waviness andaspect ratio on the percolation threshold by modeling a threedimensionalstructure, made up of high aspect ratio nonstraightconductive fibers. The nanotubes were generated using a discretizationprocedure, which defined each nanotube by a set of nodes.A classic cubic Hermite spline was then used to define the curvebetween two consecutive nodes. They used the tortuosity of thenanotube as a measure of its waviness or curvature. They observeda 44–192% increase in the percolation threshold when thenanotube tortuosity was varied between 0 deg and 180 deg forcases involving aspect ratios of 90 and 240, respectively. Theyalso concluded that with increasing nanotube aspect ratio, the tortuosityhas a more significant effect on the percolation threshold.In comparison, Li and Chou 282 used Monte Carlo simulationsto study the combined effects of nanotube waviness and aspectratio. In their study, the nanotubes were modeled as segmentedpolygons with arbitrary orientation angles separating the neighboringsegments. They concluded that the percolation thresholddecreases with increasing nanotube waviness; however, theyfound that the effect of waviness tends to decrease with increasingaspect ratio, which is contradictory to the results of Dalmas et al.280. Their model was further extended by Li et al. 285 toinvestigate the effect of nanotube waviness on the resulting electricalconductivity of CNT polymer composites where it was observedthat the conductivity decreased with increasing waviness.Yi et al. 283 employed a very similar technique to that of Li andChou to model CNTs of varied curvature in their Monte Carlosimulations and also observed an increase in the percolationthreshold with increasing curvature; however, no observation wasmade regarding the combined effects of curvature and aspect ratio.3.5.2 Electrical Conductivity. Much like the percolationthreshold of nanocomposites, the associated electrical conductivityis highly dependent on a number of chemical, physical, andgeometrical parameters. For example, the intrinisic conductivityof the nanofiller plays an important role. Obviously, nanofillerswith higher conductivities give rise to composites with higherconductivities. The size, shape, and dispersion of the nanofillersalso have profound effects on the composite electrical conductivity.Furthermore, the parameters that tend to improve the percolationthreshold of the nanocomposite may have adverse effects onthe electrical conductivity, thus forcing a delicate balance betweenthe resulting properties. Most of the measured electrical conductivitiesof nanocomposites range from 10 −5 S/m to10 −2 S/m fornanotube concentrations exceeding the percolation threshold.However, electrical conductivities as high as 10 3 S/m have beenreported for PMMA containing 10 wt % SOCL 2 treated SWCNT286. This considerable variability clearly demonstrates thestrong dependency and interplay of a number of factors.Nanotube waviness, alignment, and aspect ratio seem to havethe same effect on the electrical conductivity as on the percolationthreshold. For example, nanotube waviness has been shown todecrease the electrical conductivity and to increase the percolationthreshold, resulting in a negative effect of both properties282,285. In addition, slightly aligned nanotubes seem to result inthe highest conductivities and lowest percolation thresholds whencompared with fully aligned and random orientations 277,278.This can be attributed to the reason that fully aligned orientationsresult in minimal contact points between CNTs, and completelyrandom orientations lead to significant dead-end effects. In addition,an increase in nanotube aspect ratio has been shown to increasethe conductivity and to decrease the percolation threshold266–268.There are three sources of electrical resistance in a percolatingCNT network. These are the intrinsic resistance of the nanotubes,the contact resistance between nanotubes, and the tunneling resistancebetween interacting nanotubes. The tunneling resistancearises from electrons having to travel through a polymer layerseparating neighboring CNTs, and the contact resistance refers tothe transfer of electrons from nanotubes, which are in direct contactwith each other. Whereas the intrinsic resistance is generallyonly affected by the CNT type, the tunneling resistance is affectedby the gap size, polymer type, and nanotube diameter, to name afew. Existing studies show that the electrical resistance innanotube-based composites is dominated by the tunneling resistanceand contact resistance 284,287–290 at nanotube junctions,and it is therefore expected that the number of contact and tunnelingpoints plays a considerable role in the resulting electrical conductivityof CNT polymer composites. As more contact and tunnelingpoints are introduced, the electrical conductivity isexpected to decrease due to the increased electrical resistance arisingfrom these points. Therefore, it becomes apparent why wavynanotubes result in a decrease in electrical conductivity and anincrease in the percolation threshold. Neighboring wavy nanotubestend to have a higher chance of contacting one another withmore than one contact point, whereas straight nanotubes can onlyhave one contact point.As homogeneous dispersions usually imply a uniform wettingof the CNTs by the polymer, i.e., the formation of a polymer layeraround each CNT, it is anticipated that the best dispersions do notnecessarily lead to the highest electrical conductivities. When examiningnanocomposite systems containing different polymericmatrices, the variation in the electrical conductivities seems to besignificant. This can be attributed to the extreme distance dependenceassociated with the electron tunneling resistance throughpolymer barriers between neighboring CNTs. Some polymer typesand dispersion methods seem to favor the formation of polymerlayers of different thicknesses on the CNTs. The electrical resistivityassociated with polymer barriers has been investigated theoreticallyby Li et al. 290. They found that the upper limit for thedistance between nanotubes separated by a polymer layer is approximately1.8 nm for electrical tunneling to occur. Within thisrange, the tunneling resistance can vary as much as 10 2 k and10 16 k. In comparison, Sun and Song 284 used a continuummodel to investigate the effect of CNT contact resistance, polymerbarrier tunneling resistance, and CNT tortousity on the effectiveelectrical conductivity of CNT polymer composites with a varietyof host polymer matrices. The model employed a generalized expressionof tunneling conduction for a nonconjugated polymer291. Using this expression, they were able to derive the effectivetunneling distance for three different polymer systems. For polyethylene,polyimide, and polyvinyl alcohol matrices, the effectivetunneling distance was calculated to be 2.00 nm, 2.50 nm, and2.27 nm, respectively. These values are comparable to the result ofLi et al. 290. The contact resistance between CNTs has also beeninvestigated. The experimental measurements of Fuhrer et al.292 indicated that the contact resistance is in the range of100–400 k for metal/metal and semiconducting/semiconducting nanotube junctions. However, the contact resistancefor metal/semiconducting junctions was approximately twoorders of magnitude higher. Buldum and Lu 293 used theoreticalcalculations to investigate the contact resistance betweenSWCNTs. They found that the contact resistance can range from100 k to 3.4 M depending on the atomic structure of thenanotubes, their diameter, the contact length, and the structuralrelaxation of the nanotubes.3.6 Tailoring of Thermal Properties. Due to the extraordi-050801-26 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 34 Variation in „a… thermal conductivity and „b… electrical conductivity of a MWCNT/PS composite as afunction of nanotube loading „from Ref. †297‡…nary intrinsic thermal conductivity of CNTs 6600 W/m K,there has been much early speculation that they can significantlyimprove the thermal conductivity of polymers, as they do with theelectrical conductivity. Such nanocomposites with good thermalconductivity would have potential applications in printed circuitboards, thermal interface materials, heat sinks 294,295, high efficiencythermoelectric devices 296, and other high-performancethermal management systems. Although electrical and thermaltransport processes are described by the same continuity equation,there have been reports of nanocomposites showing a critical percolationbehavior for electrical conductivity while sometimesshowing no signature of percolation for their thermal characteristics10. In most cases, the thermal conductivity does not showthe characteristic jump at a critical CNT concentration; rather, itincreases nearly linearly with increasing CNT loading 9,297.Figure 34 depicts the variation in thermal and electrical conductivitiesas a function of nanotube loading for a MWCNT/PS composite.As can been seen, the thermal conductivity increases linearly,whereas the electrical conductivity shows the characteristicjump of a percolating network. In other instances, the thermalpercolation threshold was found to be as high as 7 wt % forSWCNT/PMMA composites 298. Furthermore, current experimentalmeasurements have only observed modest increases in thethermal conductivity on the order of a factor of 3 or less at 1 wt %CNT loading 298–301. It has also been observed that theoreticalpredictions based on the percolation theory and the effective mediumtheory that assume a negligible interfacial thermal resistancecan yield results that are upward of 30 times larger than experimentallyobserved 302, and those based on micromechanicsmodels yield results more than a factor of 10 larger 303,304.There is a strikingly different behavior of electrical and thermaltransport processes with respect to the development of the percolatingnetwork in CNT polymer composites. However, electricalmeasurements show that the CNTs do in fact form topologicallypercolating networks, and the macroscopic descriptions of theelectric and thermal current flows are described by the same continuityequation. Specifically, for steady state heat flow, the temperature,T, satisfies Laplace’s equation,T =0with the requirement that at the filler-matrix interface the heatflux, J Q , normal to the interface is continuous,4T m− J Q = k mn = k T ffnwhere n represents a coordinate normal to the interface, and k mand k f are thermal conductivities of the matrix and the filler, respectively.Equations describing the steady state flow of the electriccurrent can be obtained by replacing the temperature by thevoltage and the thermal conductivities by the electrical conductivitiesin Eqs. 4 and 5.To explain the discrepancies, one must examine two fundamentalcharacteristics. These are the interfacial thermal resistancealso known as Kapitza resistance and the differences in the intrinsicconductivities of the nanotubes and polymers 305,306.For most semiconductor and dielectric materials, phonons quantizedlattice vibrations are the main energy carriers for heat conduction307,308. The phonon conduction of thermal energy inthese materials is dominated by scattering effects such as interfacialboundary and defect effects. Whereas electrons travel alongthe nanotubes and can tunnel through polymer barriers, thermallyactivated phonons must be coupled to the polymer by a stronginterface of intermediate thermal impedance. Due to the nanoscaleinvolved and the relatively large interfacial area associated withCNTs, the interface plays a decisive role in the resulting thermalconductivity of the nanocomposite. This large interface area leadsto strong phonon scattering effects and thus reduces the conductionof phonons in nanocomposites. This is supported by a recentmolecular dynamics study by Shenogin et al. 309 in which theyshowed that there is a weak coupling between the phonon spectraof the CNTs and the polymer matrix. Since phonons dominateheat transport in CNTs, this weak coupling leads to a backscatteringof phonons at the interface, causing a temperature drop and anassociated boundary resistance 310. Therefore, it is critical thatthe interfacial thermal resistance be accounted for in any modelused to evaluate the effective thermal conductivity of the nanocomposite.For example, Fig. 35 shows the variation in the effectivethermal conductivity of a CNT polymer composite as a functionof the interfacial thermal resistance, as predicted from thestudy by Xue in Ref. 311. As can be seen, the interfacial resistancehas a significant effect on the resulting conductivity of thecomposite. Furthermore, some researchers are able to explain thedifferences in electrical and thermal percolation phenomenon byreference to the differential contrast ratio in conductivities betweenthe nanophase and the associated matrix 305,306. Thedifferential contrast ratio CNT / m in thermal conductivities be-5Applied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-27Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 35 Effect of the interfacial thermal resistance on the effectivethermal conductivity of a CNT composite where K e isthe effective thermal conductivity and K m is the thermal conductivityof the matrix phase „from Ref. †311‡…tween typical polymers and nanotubes are approximately 10 4 forthe case of the highest reported nanotube thermal conductivity.This contrast ratio is much lower than that of the electrical conductivity,which is on the order of 10 14 –10 19 . Clearly, a largernumber of phonons would prefer to travel through the matrixwhen compared with electrons due to this relatively low contrastratio, which helps explain the formation of electrically percolatingCNT networks but the apparent lack thereof for thermal networks.Obviously, parameters that significantly affect the electrical conductivitysuch as CNT alignment, aspect ratio, spatial distribution,and waviness also tend to play a role in the resulting thermalconductivity; however, the effects are found to be less pronounced.In general, an increase in the CNT aspect ratio 312, amore uniform spatial distribution, a higher degree of CNTstraightness 313, and a higher degree of alignment 314 willresult in enhanced thermal conductivity of the nanocomposite.Huxtable et al. 302 investigated the interfacial thermal conductanceof CNTs suspended in surfactant micelles in water experimentallyusing picosecond transient absorption. They concludedthat the heat transport in nanotube composite materials willindeed be limited due to the extremely small measured interfacialthermal conductance of 12 MW m −2 K −1 . They also used moleculardynamics simulations to model heat flow from a SWCNT to asurrounding octane liquid. They estimated the interfacial thermalconductance to be approximately double that of the experimentalmeasurement, namely, 25 MW m −2 K −1 . They associate the discrepancyto the lack of quantization of high frequency modes intheir simulations, thus leading to the heat capacity of the simulatednanotubes being roughly 3.5 times as large as the experimentallyobserved heat capacity of nanotubes. In comparison, Bryninget al. 300 reported thermal conductivity measurements of purifiedSWCNT-epoxy composites. At a 0.5% volume fraction ofSWCNTs, the thermal conductivity was enhanced by 27% overthe pure epoxy. The average interfacial thermal resistance as estimatedby the effective medium theory was determined to be 2.610 −8 m 2 KW −1 . Additionally, Clancy and Gates 315 usedmolecular dynamics to predict the interfacial resistance ofSWCNTs in a bulk polyethylene vinyl acetate matrix, whichthey found to be 9.810 −8 m 2 KW −1 . Some preliminary moleculardynamics simulations have also been used to evaluate theinterfacial thermal resistance associated with nanotube-nanotubejunctions. The difference here is that the phonons are transferredfrom one nanotube to the next without the intermediate step ofphonon transfer to the polymer. Maruyama et al. 316 showedthat the thermal boundary conductance between the SWCNTs in abundle is approximately 4 MW m −2 K −1 . Zhong and Lukes 317used both molecular dynamics finite difference methods to investigatethe thermal contact resistance between two parallelSWCNTs as a function of nanotube spacing, overlap distance, andlength. A four order of magnitude reduction in interfacial thermalresistance was found as the nanotubes were brought into intimatecontact. Figure 36 shows a schematic of the overlap problem inboth molecular dynamics and finite difference domains togetherwith the dependence of the junction resistance on the nanotubeseparation distance. The thermal contact resistance rose sharplywith spacings above 0.8 nm. A reduction was also observed forlonger nanotubes and for nanotubes with increased overlap areas.For the case of a 2.5 nm overlap distance, the thermal boundaryresistance was determined to be on the same order of magnitudeas that of Maruyama et al. 316. Just recently, the first experimentalmeasurements of the thermal contact resistance betweenindividual MWCNTs were performed by Yang et al. 318. Themeasurements were performed with a suspended microdevice,which consisted of two adjacent suspended SiN x membranes withintegrated platinum heaters/thermometers, which serve as a heatsource and sink for thermophysical property measurements. Twonanotube contacts were investigated: cross contact and alignedcontact. The results showed that the contact thermal conductanceincreased by nearly two orders of magnitude from 10 −8 W/K to10 −6 W/K as the contact area increased from a cross contact toan aligned contact. The larger value for the aligned contact wasattributed to a nonuniform contact. From these predictions, it canbe expected that the interfacial thermal resistance between nanotubesand the surrounding polymer will play a dominant role inlow wt % composites, whereas the nanotube-nanotube resistancewill play a considerable role in high wt % composites.A number of researchers have also examined the effect of theinterfacial thermal resistance on the resulting effective thermalconductivity of nanocomposites using a number of theoreticaltechniques. A number of these investigations were based on effec-Fig. 36 The nanotube junction thermal resistance problem. „a… Schematic of MD and finite difference approaches and „b…the variation in the junction resistance as a function of separation distance „from Ref. †317‡….050801-28 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

tive medium approaches EMAs 300,319,303,320. These modelsconsider the nanotubes to be straight isotropic solid circularcylinders. An interfacial radius is then defined based on initialestimates of the interfacial thermal resistance, which are used toscale the conductivity of the nanotubes resulting in representativecircular cylinders with anisotropic properties to be further employedin the micromechanics modeling. These representative fibersare then considered homogeneously dispersed in the polymericmatrix with random orientations. Then, by varying theaspect ratio, interfacial thermal resistance, and nanotube conductivity,these models are capable of obtaining relatively good predictionsof the thermal conductivity of the composite comparedwith experimental data. As an example, Nan et al. 319 first proposeda model based on a Maxwell–Garnett effective mediumapproximation. However, this model did not take into account theinterfacial thermal resistance, and thus the predictions were muchlarger than the experimental results. Afterward, Nan et al. 303modified the approach to account for the resistance. They usedthis model to study multiple nanotubes with varied diameters butwith fixed aspect ratios of 2000 and obtained good agreement withthe experimental data of Choi et al. 321 for the 15 nm diameternanotube system. Bagchi and Nomura 310 also proposed amodel based on the EMA to predict the effective thermal conductivityof composites containing aligned MWCNTs. In their approach,the interfacial thermal resistance was accounted forthrough the consideration of an imperfect contact region betweenthe constituents. However, their results showed that the interfacialthermal resistance did not significantly affect the thermal conductivityof the MWCNT system. Instead, they explain that the effectiveconductivity is lower than expected due to the fact that theouter layer of the MWCNT carries the bulk of the heat flowingthrough the nanotube, while the contributions of the internal layersare negligible. In electrical conduction, it has been provenexperimentally that the individual layers of a MWCNT have differentcurrent carrying capacities 322. Similarly, with regard tothe mechanical properties, the outer layer also tends to carry mostof the mechanical load due to the weak interfacial van der Waalsinteractions. However, the role of the individual layers ofMWCNTs in thermal transport is still not clearly understood, andthe results of a model based on the assumption that the outer layeris largely responsible for the heat transport should be taken withcaution. However, it is known that MWCNTs have a lower thermalconductivity than SWCNTs and several researchers 323,324speculate that this is also due to limited phonon flow in the internallayers. Further research 322 is needed to analyze the contributionof individual layers to heat transport in MWCNT. However,it is interesting to note that MWCNTs have been found tohave the highest potential to improve the thermal conductivity ofpolymer composites even though their intrinsic conductivities areapproximately half that of SWCNTs. Gojny et al. 9 suggestedthat this is caused by the relatively low specific surface area andthe existence of shielded internal layers that promote the conductionof phonons and minimize the matrix coupling losses.Bagchi and Nomura 310 also investigated the effect of CNTlength and diameter on the resulting effective thermal conductivityof aligned polymer nanocomposites using their EMA model.They found that while the length produces insignificant effects,the thermal conductivity can increase drastically with a decreasein nanotube diameter. In contrast, Xue 311 predicted the oppositeeffect for the case of randomly orientated CNTs. His numericalmodel based on the average polarization theory showed thatthe effective thermal conductivity increases rapidly with increasingnanotube length, whereas the thermal conductivity changesvery little with changes in nanotube diameter. This contradictioncan be attributed to the different orientations considered in bothmodels.In an alternative approach, Duong et al. 325 used Monte Carlorandom walk simulations to study the effect of interfacial thermalresistance on the heat flow in different orientations of SWCNTsdispersed in PMMA. Four values of the interfacial thermal resistancewere investigated in the range of 5.510 −8 –0.1110 −8 m 2 KW −1 for a wide range of CNT wt %. The effectivethermal conductivity was shown to be in good agreement with theexperimental data of Du et al. 298 for the randomly orientatedsystem. However, large deviations were observed for CNT concentrationsabove 7 wt % where the simulations underestimatedthe conductivity. This was attributed to the formation of nanotubenanotubejunctions in the experimental system, whereas the computationalmodel failed to account for this effect. Furthermore, themodel showed that with increasing interfacial thermal resistance,the resulting effective thermal conductivity decreased dramaticallyand then seemed to level off after some critical value.Seidel and Lagoudas 326 used a micromechanics approachbased on the composite cylinder model to assess the impact of theinterfacial thermal resistance on the effective thermal conductivity.Their model included the presence of the hollow region of theCNT through the development of a nanoscale RVE and the interactionsamong the various orientations of CNTs in a random distributionthrough the use of the Mori–Tanaka method. The effectsof the interfacial thermal resistance were accounted for throughthe incorporation of an interphase layer with a thermal conductivitybased on the values observed in Ref. 302. The effect of thehollow region in the CNT on the effective thermal conductivityseemed to be significant when the interfacial thermal resistancewas ignored. When the hollow region was included, the thermalconductivity decreased by 14%, 37%, and 45% for cases involvingCNT volume fractions of 0.0001, 0.001, and 0.1, respectively.Furthermore, when the interfacial thermal resistance was included,additional decreases of 20%, 71%, and 99% in the effectivethermal conductivity for respective CNT volume fractions of0.0001, 0.001, and 0.1 were observed. The authors also observeda relatively good agreement between their results and those ofBryning et al. 300 when the interphase layer was assigned aninterfacial conductance of 12.5 MW/m 2 K and with those ofGuthy et al. 312 with values of 40 MW/m 2 K and90 MW/m 2 K.Given that the effective thermal conductivities of CNT polymercomposites are largely influenced by the interfacial thermal resistancebetween the CNTs and the surrounding polymer matrix, researchersare now examining different ways of reducing this interfacialresistance. For example, covalent functionalization hasbeen shown both experimentally 14,327 and theoretically 328to decrease the interfacial thermal resistance and to result in anincrease in the effective thermal conductivity. As with its effect onthe electrical and mechanical properties of nanocomposites, thereare a number of competing factors associated with this process. Infact, some theoretical and experimental studies have actually predicteda negative impact when compared with the unfunctionalizedcase 9,33. Chemical functionalization is known to introducedefects in the CNT structure, which act as phonon scattering sites,thus limiting the intrinsic conductivity of the nanotube. In addition,chemical functionalization can also reduce the overall aspectratio of the CNTs. These factors have adverse effects on the thermalconductivity. However, the process also results in improveddispersion and can possibly limit the mobility of the polymer matrixbackbone as a result of the denser cross-linked structure,which in turn will result in improved thermal conductivity. Clancyand Gates 315 conducted a number of molecular dynamicssimulations to investigate the effect of chemical functionalizationon the thermal interfacial resistance of a SWCNT embedded in apolyethylene vinyl acetate matrix. They also used the effectivemedium theory to extend their study to examine the effects on thethermal conductivity of the bulk nanocomposite. They studied theeffects of both the grafting density and the length of linear hydrocarbonchains covalently bonded to the CNT surface. The resultsof their simulations show that large decreases 80% in the interfacialthermal resistance can be obtained by increasing thegrafting density of hydrocarbon chains Fig. 37a. An increase inApplied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-29Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 37 Influence of grafting density on the „a… interfacial thermal resistance and „b… effective thermal conductivity „fromRef. †315‡…the chain length will also result in lowered interfacial thermalresistance. Furthermore, when defects in the form of missing C–Cbonds in the CNT structure were introduced at the grafting site,very little change was observed in the interfacial thermal resistancevalues. Clancy and Gates extended their model to investigatethe effects of the same parameters on the effective conductivity.In short, the thermal conductivity increased with increasinggrafting density Fig. 37b, chain length, CNT length, and CNTvolume fraction but did not exhibit a linear relationship in eithercase. In addition, the dependence of the thermal conductivity onthe interfacial thermal resistance seemed to be more pronouncedat shorter CNT lengths.The results of Clancy and Gates are complemented by an earliermolecular dynamics study conducted by Shenogin et al. 328 inwhich SWCNTs chemically functionalized with octane moleculeswere investigated. To illustrate the effect of chemical functionalization,the interfacial thermal resistance was represented inequivalent matrix thickness units, which correspond to the thicknessof the matrix material over which the temperature drop is thesame as that across the interface in the planar geometry. For thepristine nanotube, the interfacial resistance was equivalent toabout 7 nm of the matrix material. In the functionalized case, theinterfacial resistance decreased and was reduced by more thanthree times when an octane molecule was attached to 1 out of 15tube carbon atoms. The effective thermal conductivity of the compositewas evaluated using the effective medium theory. Theyobserved a twofold increase in the thermal conductivity for thecase of functionalized nanotubes with aspect ratios ranging from100 to 1000. For aspect ratios above 1000, unfunctionalized nanotubesseemed to provide the largest enhancement in compositethermal conductivity. This can be attributed to the competing factorsassociated with chemical functionalization. The process hasbeen shown to decrease the interfacial resistance but also lowerthe intrinsic conductivity of the CNT through the introduction ofdefects. At large aspect ratios, the interfacial resistance plays aless significant role since their large surface area allows for aneffective exchange in the thermal energy with the matrix. In thiscase, it is advantageous to preserve high intrinsic fiber conductivityrather than reduce interfacial resistance. Carbon atoms in aCNT that are covalently attached to matrix molecules have bondingstrengths and associated bonding geometries different fromthose of the remaining nanotube carbon atoms. These geometricaleffects are considered defects in the CNT structure. To illustratethe detrimental effect of chemical functionalization on the intrinsicconductivity of the nanotube, Shenogin et al. accounted forthese sp 3 hybridization effects in their model. Therefore, their defectrepresentation is more realistic than that of Clancy and Gates315. The calculated thermal conductivity for the pristine nanotubewas approximately 6000 W m −1 K −1 . With increasing degreeof functionalization and hence number of defect sites, theintrinsic conductivity dropped significantly. However, once about1% of carbon atoms were functionalized, further increase in defectdensity did not affect the intrinsic thermal conductivity, whichremained constant at 1700 W m −1 K −1 . A similar degradation ofthe intrinsic nanotube conductivity was observed by Padgett andBrenner in their molecular dynamics simulations of phenyl functionalizedSWCNTs 329.4 Structural Health Monitoring and Damage SensingCNT polymer composites are beginning to show promise for avariety of applications in the aerospace industry where improvementsin thermal, electrical, and mechanical properties of structuralmaterials are a key goal. In parallel, there is a growing demandfor multifunctional materials that provide continuous andintegrated monitoring of damage phenomena in an efficient andcost affordable way. Multifunctional polymeric materials are designedusing a bottom-up approach of deliberate molecular assemblyin order to implant multiple engineering functionalities withinone material system. Unlike traditional structural systems, whereonly one material property is enhanced e.g., strength/toughness,multifunctional systems are capable of fulfilling several designrequirements e.g., strength/toughness, condition monitoring, actuation,and power generation. The concept of multifunctionalmaterials with sensing capabilities combined with enhancedmechanical-electrical and/or thermal properties could prove usefulfor the high requirements of the aerospace sector. Continuoushealth monitoring of composite materials and structures can contributeto enhance safety and minimize cost by optimizing maintenanceprotocols. Acceptable health monitoring sensors shouldmeet specific requirements such as small weight and size, highsensitivity, structural compatibility, life long operation, ability forhealth monitoring of large critical areas, and the possibility totransmit information to a central processor in real time.The engineering community is aggressively pursuing novelsensing technologies to enable automated damage detection ofcritical load bearing components/systems, known hereafter asSHM 330–333. They rely on using sensing technologies andphysics-based models to detect damage in engineering components.The most common SHM systems that currently exist are thediscrete tethered arrangements, which typically employ a varietyof distributed nodal sensors such as thermocouples, strain gauges,linear variable differential transformers, accelerometers, and opticalfibers, among others. These discrete tethered sensors are poweredby and connected to a centralized data repository by coaxialcables. In this case, the sensors are positioned strategically instructural locations where large deformation or vibration is likelyto occur. These systems can only allow global-based structural050801-30 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

monitoring. Furthermore, they only sense significant global structuraldamage rather than the more realistic localized damage. Inaddition, these distributed sensors are unlikely to identify thenodal locations where damage is prevalent, and they are expensiveto install and maintain for large systems. Thus, for large scale andcomplex applications such as wind turbine blades, bridges, helicopters,and armour, which need to be monitored over large areasand for long periods of time, it becomes difficult to install theseSHM systems due to the large amount of wiring, weight, andoverall system complexity 331,334. Limitations such as thesehold back the feasibility of current SHM approaches. These environmentsrequire novel self-sensing and intelligent damage detectioncapabilities in order to perform at their best and to continuouslyprovide safe usability. Techniques used in the past have notbeen cost effective in structural applications that are large or complexin design 335. The best way to proceed for the SHM inthese applications is to either explore the use of multifunctionalsensing devices, which are capable of monitoring a wide range ofdamage phenomena, or better yet, use the material itself as a sensorof its own damage.By exploring the architecture and the interplay of the electricaland mechanical properties of a CNT network in a composite’smatrix, new nanoscale methodologies of SHM and internal damagesensing can be realized. As discussed in Sec. 3.5, the additionof CNTs in a polymer matrix significantly increases the electricalconductivity of the resulting composite through the formation ofan electrically percolating network. By passing an electric currentthrough the composite and measuring its electrical resistance, it ispossible to monitor the architecture of the CNT network and thestrain fields in the material. It is for this reason that CNT polymercomposites are being exploited in the field of SHM. By studyingthe electrical footprint of damage phenomena in composite materialsusing percolating CNT networks, an enhancement in thesafety of composite usage and reduced maintenance of the compositescan potentially be seen. These potential benefits have ledto an increased interest in researching CNT polymer compositeSHM systems 336–339. However, as of late, research in thisfield has been done to a small degree, and only minor correlationsbetween electrical resistance measurements and internal damagemechanisms have been made 336,337.The SHM capabilities of a CNT percolating network can beexploited in structural composite materials by directly dispersingthem in the composite’s matrix, thus using the material itself as asensor. Alternatively, a freestanding CNT polymer composite filmcan be fabricated and later bonded to the composite or metallicstructure. In this way, the nanocomposite film acts as a standalonedamage sensor. CNT-based sensors have been shown tohave multifunctional sensing properties and can potentially reducethe number of sensors required to monitor a structure. This impliesan ease in the applicability and a significant reduction incosts. However, one disadvantage of this approach is that damagewill only be detected in the areas of the structure that are beingmonitored by the sensor. One such stand-alone method of usingCNTs to recover information about the condition of a structuralcomponent was proposed by Kang et al. 334 using the conceptof a MWCNT neuron. MWCNTs were dispersed in a polymerusing a combination of intense mixing and ultrasonication. Thesolution was then sprayed within a patterned template onto astructure simulating a helicopter rotor blade. In theory, the neuronwill act as a thin conducting film that will change its resistancewhen subjected to a load or when an internal crack begins topropagate through it. In such a case, the resistance will increaseand the capacitance will decrease and the internal damage canserve as a forewarning for failure. Yeo-Heung et al. 340 demonstratedthat the MWCNT neuron did indeed show an increase inits electrical resistance and a decrease in capacitance when a crackwas propagated through the neuron Fig. 38. They also demonstratedhow the neuron can also be used to detect corrosion on ametallic substrate. Corrosion occurring on a metallic structureFig. 38 Change in electrical resistance and capacitance due tocrack propagation in MWCNT neuron „from Ref. †340‡…produces a diffusion layer at the interface between the structureand neuron 334. The corrosion ions penetrate into the neuronsensor and form a double layer charge. These ions also change theelectrical characteristics of the sensor analogous to a doping effect.By measuring the electrical resistance and capacitance, theonset of corrosion damage can be monitored. The major advantageof this spray-on neuron is its capability of conforming to avariety of materials, surfaces, and complex shapes where stressconcentrations can occur and are difficult to measure using conventionalstrain sensors. However, as mentioned before, a disadvantageof this approach is that damage will only be detected inthe areas of the structure that are being monitored by the sensor.Yeo-Heung et al. 340 presented a possible solution to this limitationby introducing the concept of a neuron mesh whereby anarray of MWCNT neurons are used to monitor a larger area of astructure. Additionally, by reducing the size of the neuron mesh tothe nano-or microscale, the neuron array can in theory detect verysmall increments in the propagation of the crack. However, becausethe neuron is mounted on the surface of the structure, it willnot detect the more prevalent, detrimental, and premature damagemechanisms that initiate directly within the host material.Apposed to using CNT polymer composites as stand-alone topicalsensors for SHM applications, it can also be desirable to tailorexisting composite materials to implant the sensing capability directlyinto the material itself. Previous studies show that the mechanicaldeformation and electrical resistance of carbon fiberreinforcedplastics CFRPs are closely connected, so that thematerial can act as an inherent sensor of its own damage. In suchcomposites with continuous carbon fibers, fiber breakage resultsin sudden increases in the axial resistance. However, fiber breakageis a damage phenomenon that often supersedes the earliersigns of failure such as matrix cracking and interfacial failure.Since the matrix phase of CFRPs composites are insulating, theseearly and premature forms of damage cannot be monitored oridentified using traditional CFRP SHM techniques. Furthermore,fiber breakage is a damage phenomenon that is often accompaniedwith the complete failure of the composite structure. Therefore, itis desirable to develop a means of measuring and monitoring thepremature matrix cracking and interfacial failure modes prior tothe often catastrophic fiber breakage event. As mentioned before,CNTs can be directly dispersed into the matrix of a traditionalcomposite material improving the composite’s SHM capabilities.In the case of CFRPs, the resulting composite consists in electricallyconducting carbon fibers with a percolating CNT network inthe matrix phase. The addition of the CNTs increases the electricalconductivity of the matrix phase, allowing for the identification ofearly matrix damage. For example, Lee and Yoon 341 doped astandard CFRP composite with CNTs and measured the electricalresistance under direct tensile loading. The electrical resistance ofApplied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-31Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 39Comparison of fiber damage detection in composites „a… with CNTs and „b… without CNTs „from Ref. †341‡…the CFRP composite with and without CNTs was measured duringloading coupled with acoustic emission measurements to help correlatethe measured signals to different damage phenomena,namely, fiber breakage and matrix cracking. The electrical resistivityof the standard CFRP composite increased suddenly whenthe first carbon fiber fractured, which resulted in an open circuitthroughout the composite Fig. 39a. Electrical resistivity in theCFRP composite with CNTs increased in a stepwise fashion withincreasing fiber breakge events Fig. 39b. This indicates that theCNTs helped bridge the fractured carbon fibers and maintain apartial electrical circuit. In a similar study, Kostopoulos et al.342 examined the electrical resistance of CFRP compositesdoped with CNTs subjected to fatigue loading. Test specimenswere subjected to cyclic loading tests, and the resistance was measuredat the maximum loading and at the unloading position ofeach cycle. The tests indicated that the doped samples were moresensitive to resistance changes. Moreover, in the first stage ofloading, the changes in resistance were only detected by the CNTdoped composite. Matrix cracking is the dominant damagemechanisms in this early stage of loading, and it was speculatedthat the matrix cracks interrupt the CNT percolation network, resultingin this early increase in resistance.Clearly, experimental validations of the SHM capabilities ofCNT doped CFRP composites and stand-alone CNT damage sensorsare well on their way. However, little theoretical work hasbeen done to predict the electrical footprint of composite damagephenomena using percolating CNT networks and even traditionalCFRP systems. This can be mainly attributed to the relative complexityassociated with modeling a system, which accounts for thevaried length scales, three-dimensional nature, and wide range ofdamage phenomena. At present, the authors are only aware of therelatively simplified works by Li and Chou 343. They modeled atwo-dimensional cross-ply glass fiber composite with an embeddedCNT network using FE methods coupled with resistor networkmodeling. Three components contribute to the electrical resistanceof a percolating CNT network, namely, the intrinsicresistance of the CNTs, the contact resistance at CNT junctions,and the tunneling resistance of electrons flowing through a polymermedium between neighboring CNTs 290. Li and Chou investigatedthese effects in separate studies and incorporated theseresistances in their SHM model. Their results indicate that matrixcracking directly cuts off adjacent conducting branches in the percolationnetwork and that any change in the electrical resistance isrepresentative of the degree of cracking. It is often the case thatwhen the matrix undergoes cracking, the networks are undamaged.Nevertheless, a change in resistance was measured as theimpact of the damage was sensed by the network nearby. Thepredicted change in composite resistance was also partly attributedto increased tunneling resistance between neighboring nanotubes.As the composite is strained, neighboring nanotubes becomeseparated by a larger amount of insulating polymer matrix.The tunneling resistance increases significantly with increasingdistance, thus contributing to a larger composite resistance withincreasing strain. Figures 40a–40c illustrate this effect underthe evolution of damage, while Fig. 40d presents the predictedchange in composite electrical resistance due to the applied load.5 Current Challenges and Future OutlookCarbon nanotubes have certainly stimulated enormous researchin the field of nanoengineering and nanomaterials since their discoveryin 1991. CNTs are extremely versatile materials: They areone of the strongest known materials, highly conductive in theelectrical and thermal sense, light weight, low in density, andsmall in size but stable. All these properties show enormous promisefor their exploitation in a wide range of applications and unquestionablya promising future. Furthermore, the incorporationof these nanofillers in host polymeric matrices offers new andexciting possibilities in the already exhausted field of compositescience. They offer the ability to tailor the mechanical, electrical,and thermal properties of the host material to yield next generationmultifunctional nanocomposites. These nanocomposites havein some cases already reached the market and become an integralpart of modern technologies. Examples include products for theelectronics and packing industries, which utilize the electromagneticshielding and electrostatic discharge capabilities of composites,structural components in aerospace and automotive industries,explosive decompression resistance pipe seals for the oil andgas industry, and light weight sports equipment. Other future applicationscould be as diverse as biological implant materials,prosthetics, photo-active polymers, and osteointegration applicationsgrowth of bone cells. However, the existing technologiesdid not evolve without considerable efforts from the researchcommunity and designers alike in understanding the fundamentalprinciples on which they rely, overcoming significant processingobstacles and ensuring their continuous and optimal performance.In fact, the time lag between concept generation and actual productdevelopment is several years to decades for these particulartechnologies. Great challenges face the development of CNTpolymer composites into future functional devices and structures,and it is not surprising that some of these technologies haveevolved at a quicker pace than others. This is entirely dependenton the function of the product and the properties of the nanocompositethat are being exploited. The items to follow are just someof the integral areas of the field that need to be given due attentionby researchers, engineers, and scientists in order to facilitate thespeedier development of future technologies that exploit the useof CNT polymer composites.050801-32 / Vol. 63, SEPTEMBER 2010 Transactions of the ASMEDownloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Fig. 40 Structural health monitoring using CNTs. „a… Electron tunneling betweenneighboring nanotubes, „b… reduced tunneling due to the increased separation distance,„c… no flow of electrons due to excessive separation, and „d… variation in electricalresistance due to the applied load „from Ref. †343‡….5.1 Carbon Nanotube Availability, Cost, and Quality. Awide variety of synthesis techniques exist to produce CNTs withvaried properties. However, the growth mechanisms of CNTs arestill not very well understood. As a result, it is not yet possible togrow nanotubes in a controlled way such that the CNTs do notshow significant variability in their properties. To some extentthere has been some success in growing CNTs of a certain diameter,and to a lesser extent chirality, by tuning the environmentalprocessing parameters through trial and error. The chirality becomesimportant for electronic applications, which rely on specificatomic arrangements of the atoms to selectively tune theintrinsic electrical conductivity. In contrast, the length and aspectratio are critical parameters that govern their reinforcing potentialin composite materials. Before the full potential of CNTs can beexploited in composite materials, it is imperative that consistentand reliable methods be developed that can control the orientation,chirality, size, and structure of the CNTs.The synthesis techniques for growing CNTs are also expensive,and as a result the achievable yield of CNTs is still very low.Aside from the equipment, even the materials used to produceCNTs represent a large percentage of the cost. For example, thecatalyst used in the chemical vapor deposition process can constituteas much as 20–50% of the cost of the final product 344.Asa result, high purity nanotubes cost approximately $800/g, andeven ones with a large percentage of defects and impurities costapproximately $35/g 345. For bulk applications such as tailoringagents in composite materials, the quality and quantity of nanotubesthat can be manufactured still fall short of what they shouldbe. These applications would require high quality nanotubes inquantities of tonnes to support not only the manufacturability ofthe nanocomposites but also the product design and conceptualresearch stages. Efficient processing routes, which can be scaledup to commercial production levels, are needed if CNTs are tohave a wider range of applications. For these reasons, arc dischargeand laser ablation techniques do not seem promising asthey are limited in terms of the quality of the nanotubes theyproduce and the difficulties in scaling these production methods.On the other hand, chemical vapor deposition methods do showpotential as they utilize a flowing gas methane, carbon monoxide,or acetylene as the source of carbon and also require less purification;however, this method still requires some sorting of thenanotubes.It should be noted, however, that the industry is moving forwardwith regard to these dilemmas. For example, Bayer MaterialScience currently operates 30 high quality CNT production facilitiesand has reportedly opened a new pilot facility that can produce200 metric tonnes of high quality CNTs annually 346.Zyvex Instruments has created a CNT certification program,which is used to verify the quality and batch-to-batch consistencyof CNTs using market-accepted analytical tests. This certificationprogram is a very important tool because there are currently nostandards for evaluating the quality of nanotubes, and buyers arenormally unaware of what they are purchasing.5.2 Nanocomposite Processing and Characterization. Perhapsthe most significant obstacle to the development of CNTcomposites and their applications is the difficulty associated withhomogeneously dispersing CNTs in the matrix, their insufficientbonding to the matrix phase, and the difficulties associated withaligning the CNTs in the matrix. It is exactly for these reasons thatthe exceptionally high Young’s modulus and strength of CNTshave of yet not been fully exploited in CNT-reinforced composites,and their properties have fallen short of theoretical predictions.There are, of course, numerous efforts being devoted tothese areas, as outlined in the review. Various methods have beendeveloped to disperse CNTs with varying levels of success. It hasbeen demonstrated that surface modification techniques can improvethe CNT/matrix interfacial bonding and also assist inachieving a more uniform dispersion. These methods do, however,compromise the intrinsic properties of the nanotubes. In addition,various alignment techniques have also proven effective to controlthe preferential orientation of the nanotubes in the matrix. However,they do have their limitations and drawbacks, which rangefrom the coarsening effect in the electric-field methods to theinability to process large samples with the magnetic-field methods.Furthermore, it is presently very difficult to characterize ormeasure the degree of dispersion, alignment, and bonding in thesematerials. Customarily, electron imaging techniques are used todeduce the uniformity of the dispersion. However, these techniquesare hindered by the extremely small field of view or volumeof the sample that can be investigated. Analytical electronmicroscopy techniques such as X-ray diffraction and polarizedRaman spectroscopy are the only available means of characterizingthe degree of CNT alignment. Although effective, these methodsare limited by the resolution of the detectors and are verysensitive to any sample inconsistencies. Finally, CNT pull-outtests can be used to measure the interfacial shear strength betweenthe CNT and matrix. Again, due to the nanoscale involved, it ispresently very difficult to conduct these tests.Applied Mechanics Reviews SEPTEMBER 2010, Vol. 63 / 050801-33Downloaded 02 Mar 2011 to 128.100.48.220. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

5.3 Standardization and Regulation. Currently, there arevery few standards or regulations for the CNT composite industryand even the general field of nanotechnology. Apart from standardsand regulations for health, safety, and toxicology, the CNTcomposite industry requires some form of standardized procedurefor evaluating the quality of the CNTs such that companies andbuyers are able to compare different nanotube sources. The lack ofstandards is considered a barrier to the CNT composite marketbecause companies and researchers are finding it difficult to ensurethat their products and processes are safe and consistentlyreliable. As a result, they are often forced to take conservativeapproaches to the handling of these materials, which can increasecosts considerably. Furthermore, without standardized proceduresand regulations and a better understanding of the safety of CNTsand their products, companies are forced to deal with mediaspeculations that can negatively influence the public’s opinionabout the safety of these materials, misleading the public to believethat these nanoparticles are hazardous.AcknowledgmentThe authors wish to acknowledge the financial support providedby the Natural Sciences and Engineering Research CouncilNSERC of Canada.NomenclatureAFM atomic force microscopyCFRP carbon fiber reinforced plasticCNF carbon nanofiberCNT carbon nanotubeDWCNT double-walled carbon nanotubeEMA effective medium approachFE finite elementFWHM full width half maximumISS interfacial shear strengthMD molecular dynamicsMM micromechanicsMWCNT multiwalled carbon nanotubeQM quantum mechanicsPA6 polyamide 6 nylon 6PA12 polyamide 12 nylon 12PANI polyanilinePE polyethylenePET polyethylene terephthalatePMMA polymethylmethacrylate acrylicPmPV poly-m-phenylenevinylenePPA polyphthalamidePS polystyreneRVE representative volume elementSEM scanning electron microscopySHM structural health monitoringSTM scanning transmission microscopySWCNT single-walled carbon nanotubeTB tight bindingTEM transmission electron microscopyTETA triethylenetetramineReferences1 Kim, B. 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