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Comment on ‘‘The Effect of Stress Transfer WithinDouble-Walled Carbon Nanotubes Upon Their Ability toReinforce Composites’’

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By Wei Lin and C. P. Wong*

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[*] Prof. C. P. Wong, W. LinSchool of Materials Science & Engineering andPackaging Research CenterGeorgia Institute of Technology771 Ferst Drive NW., Atlanta, GA 30332 (USA)E-mail: cp.wong@mse.gatech.edu

DOI: 10.1002/adma.200902189

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In a recent Communication published in Advanced Materials,[1]

Cui et al. discussed wall-to-wall stress transfer withindouble-walled carbon nanotubes (DWNTs) in a compositeon the basis of stress-induced Raman band shifts. The RamanG0 band of the DWNTs was split into two components; only theone corresponding to the outer wall shifted distinctly withstrain. This phenomenon was considered a reflection of theineffective stress transfer from the outer wall to the inner wallduring the DWNT deformation in the composite, which wouldgreatly reduce the effective modulus of the DWNTs asreinforcement filler. Coincidently, it was found that theRaman band shift rate of the outer wall of the DWNTs wassmaller than that of single-walled carbon nanotubes (SWNTs)when dispersed in an epoxy matrix. From the G0-band shiftrates, Cui et al.[1] calculated the effective moduli of the SWNTsand the outer wall of the DWNTs to be 762GPa and 552GPa,respectively. This was considered a proof of the reduction ineffective modulus of the DWNTs, the reason being theineffective wall-to-wall stress transfer. This work has signifi-cance in providing an experimental proof on what many in thisresearch field have long hypothesized regarding the ‘‘poor loadtransfer to the inner walls of a multi-walled carbon nanotube’’(MWNT). However, misinterpretations of some results found inliterature regarding the Raman band shift rate and effectivemodulus led Cui et al. to the controversial conclusion that thereduced Raman band shift rate indicated a reduced effectivemodulus for the DWNTs.

The theoretical foundation of the study in Ref. [1] is theconclusion in Ref. [2] (Ref. [4] of Ref. [1]), in which Cooperet al.[2] reported an empirical linear relation (a ‘‘constant ofproportionality’’) between the moduli of carbon fibers and theirRaman band shift rates under tensile strains: the higher theshift rate, the higher the effective modulus of a CNT. The‘‘constant of proportionality’’ of �0.05 cm�1(GPa%)�1 in thelinear relation was taken for granted in Ref. [2] and, therefore, inRef. [1] as well, to be valid for calculating the effective moduli ofcarbon nanotubes (CNTs) by investigating the strain-inducedRaman band shift rate of CNTs in a polymer matrix. We doacknowledge the possible ‘‘linear’’ relation between the

carbon-fiber moduli and their Raman band shift rates; however,we do not agree with this being a general relation for evaluatingthe CNT modulus. There are two fundamental and/or logicalproblems with this extension.

First, in Ref. [2], it was mentioned that the linear behavior hadbeen attributed, by Huang and Young,[3] to different micro-structures of the fibers under investigation, where ‘‘microstruc-ture’’ referred specifically to the levels of orientation of thegraphitic grains along a fiber. In the case of the CNTs used inRef. [1], the as-defined microstructure shows little differencebetween the SWNTs and the DWNTs, since the graphitic planes(walls in CNTs) are oriented along the fiber (tube) axis with theonly exception of CNTends. Thus, even though SWNTs, DWNTsand MWNTs may have different effective moduli, the modulusdifference is not due to the microstructure/orientation (theeffective modulus of CNTs will be discussed in details later).Moreover, it is commonsense that the deformation mechanismand, therefore, performance of a polycrystalline material (carbonfiber in this case), is quite different from its single-crystallineform (CNT). With these in mind, the ‘‘constant of proportion-ality’’ observed for carbon fibers will not hold for CNT-moduluscalculations, not to say the ‘‘linearity’’ is not good enough (Fig. 12in Ref. [2]). Therefore, the smaller G0 band shift rate of the outerwall of the DWNTs compared with that of the SWNTs does notindicate a lower modulus of the DWNTs. Or even if we assumethat the DWNTs and the SWNTs have the same modulus, theirRaman responses may not be identical.

Second, the essential difference—orders of magnitudedifferent in surface area—between carbon fibers and CNTssignificantly increases the complexity of interpreting Raman bandshift rates in CNT/polymer composites. The interface effect or, inother words, the influence by the interphase, plays a significantrole in CNT/polymer composites.[4,5] It might be true that forcarbon fibers and their composites, the Raman band shift rate ismore a reflection of the intrinsic modulus of the carbon fibersthan of the fiber/polymer interfacial load transfer;[2,3] however,the opposite seems to hold for CNT/polymer composites.[6] Infact, Cooper et al.[2] found a sharp difference in modulus betweenSWNT-A (SWNTs prepared by an arc-discharge process) andSWNT-P (SWNTs prepared by a pulsed-laser vaporizationprocess) derived from their G0 band shift rates. Although itwas postulated that SWNT-A may have a lower intrinsic modulusthan SWNT-P, it might not be true.[7] A poorer dispersion ofSWNT-A in the composite was proposed as a second possiblereason, however, without solid evidence. Neither TEM images norcomparisons of the mechanical properties of the composites weregiven. Basically, the poor dispersion, bundling, and consequently

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small effective aspect ratio are all related directly to the surfacestatus of the SWNT-A, which, in turn, determines interfacialstress transfer from the polymer matrix to the CNTs upondeformation. In this sense, the difference in the Ramanresponses between SWNT-A and SWNT-P in Ref. [2] wasprobably a reflection of CNT/polymer interface status ratherthan of the intrinsic modulus of the CNTs. As such, the observedrelatively small G0 band shift rate from the MWNTs may,compared with the SWNT-P, be also explained by a relatively poorCNT/polymer interface, since the MWNTs were prepared by anarc-discharge process as well.[2] The reason why the MWNTsshowed a higher G0 shift rate than the SWNT-A was probably abetter dispersion in the composite. Therefore, the conclusion inRef. [2], which is the theoretical presumption of Ref. [1], is notcorrect.

Not only is the theoretical foundation problematic in Ref. [1],the most important concept—effective modulus—seems to havebeen used confusingly. Cui et al.[1] thought that the poor loadtransfer from the outer wall of a DWNT to the inner wall resultedin a reduction in the effective modulus of the DWNT. Formodulus measurements of CNTs,[8–10] the results reported weremostly ‘‘effective moduli’’ because in those measurements, ‘‘alllayers have the same circumferential strain, since they have thesame axial strain after the uniform stresses loading’’.[11] Inaddition, in Ref. [11] (Ref. [9] of Ref. [1]), Tu et al. pointed out that‘‘the value of Ym (effective modulus) does not reflect the physicschange in the true lattice rigidity but just a choice of the crosssection’’. Moreover, conclusions in Ref. [11] are ‘‘valid only fortubes whose radii are not very small’’. Therefore, the as-defined‘‘effective modulus’’ for a CNTunit is treated as conventional fillerin contrast to that for a specific CNT wall. In comparison, inRef. [1], the inner wall of a DWNTupon extension seems to takeon little stress and little axial strain. In this sense, the as-defined‘‘effective modulus’’ no longer makes any sense. Alternatively,Cui et al.[1] turned to a different concept—the effective modulusof the outer-wall material. With this concept, they attempted toindicate that the capability of the outer wall of taking on the loadtransferred from the polymer matrix is reduced due to the poorwall-to-wall stress transfer; we do not agree with them.

First, Cui et al.[1] took for granted that upon tensiledeformation, ‘‘the stress transfer from the matrix to nanotubesin composites and then subsequently through the different layersoccurs principally through shear’’. A question arises as: whyshould the load be transferred from the outer wall to the innerwall? Actually, it is apparent that for tensile deformation thewall-to-wall stress transfer is not necessary or should rarelyhappen in ideal cases.[12,13] This can be easily understood in thefollowing way: Typically, non-functionalized CNTs are clo-se-ended, which means that a CNT has a sealed outer shell toprevent the inner walls from communicating with the polymerchains around the outer shell. Thinking about a tensiledeformation of a close-ended DWNT in a polymer composite,it is the outer shell that is taking the load from the matrix anddeforming until its final fracture or failure at the polymer/outer-shell interface.[12] The outer shell itself is eligible to take onthe stress and, ideally, there is no wall-to-wall bridging bond.There is no tendency or need for a wall-to-wall load transfer—keeping in mind that we are not using the concept of an ‘‘effectivemodulus of a CNT’’ here but, instead, the concept of an ‘‘effective

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modulus of the outer wall of a CNT’’. This is probably the rightreason why the Raman G0 band corresponding to the inner wall ofthe DWNTs showed little shift in Ref. [1]. Based on theDWNT-synthesis process and the TEM images provided in theSupporting Information of Ref. [1], we think that the DWNTsused in Ref. [1] have the same outer diameter, tube helicity, andsurface chemistry as the SWNTs used; as such, the effectivemodulus of the outer wall of the DWNTs should be the same asthat of the SWNTs.[14] Even a weak, if any, wall-to-wall stresstransfer should have enhanced rather than reduced the effectivemodulus of the outer shell. However, in Ref. [1], 762GPa and552GPa were obtained for the SWNTs and the outer wall of theDWNTs, respectively, on the basis of the aforementionedquestionable linear relation.

Cui et al.[1] cited the work on ‘‘interlayer forces and ultralowsliding friction in multiwalled carbon nanotubes’’ by Kis et al.,[15]

and claimed that ‘‘it is this relatively easy shear between the layersthat reduces the stress transfer and leads to the large reduction ineffective Young’s modulus for MWNTs for reinforcement incomposites.’’ In Ref. [15], a MWNT was glued onto a platinumwire and its outer layers were removed by electrical breakdown.The as-exposed CNTcore was welded to a force sensor during thepullout experiment. This situation is, by nomeans, comparable tothe situation of a close-ended DWNT or MWNT in a polymercomposite. In fact, a DWNT or MWNT under tensile load in acomposite is analogous to the case studied by Yu et al.,[16] where alarge modulus value was found for the outermost wall of aMWNT. Although the modulus value of the outermost wall inRef. [16] seems a little bit lower than the measurement result of aSWNT,[17] a direct comparison between the results by differentmeasurement techniques is not wise. Also, note that sampledefects, measurement errors, and possibly the Russian rollstructure[18,19] of aMWNTmay account for such a difference. Onemay claim that an open-ended CNT in a polymer matrix lookssimilar to the situation in Ref. [15]. Not actually. Note that thewall–wall distance in a DWNTorMWNT is only�0.34 nm but theradius of gyration of a polymer chain is typically at least tens oftimes larger than 0.34 nm. Therefore, for open-ended small-diameter DWNTs, the probability of a chemical attachment of theends of themultiple walls to the polymermatrix in such a way thatthey will have the chance to slide relative to each other isextremely low.

Second, Cui et al.[1] cited the modeling results by Zelameaet al.[20] to support their statement of the ‘‘significant reduction inthe effective Young’s modulus of the reinforcement by MWNTs’’.In fact, although lots of papers have been published onmechanical properties of CNT reinforced polymer composites,a direct comparison among the experimental data is verychallenging due to the different CNT sources, treatments,composite preparation processes, and so on.[21] Fortunately, wecan still use the data for discussion from the systematic work byGojny et al.[12] In Ref. [12], SWNT/polymer composites do showsomewhat higher moduli than MWNT/polymer composites withthe same filler weight fraction. However, the essential reasonmaynot be the postulated inferior effective moduli of the MWNTs.Note that the SWNTs used in Ref. [12] have an average diametersmaller than 2 nm, while the MWNTs are much larger (15 nm indiameter). This means that the SWNTs have around seven timesmore surface area than theMWNTs in the composites at the same

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volumetric filler loading. Considering such a big difference insurface area, we have to say that the better modulus enhancementof the composites by the SWNTs compared with MWNTs issignificantly below expectation, not to mention the assumptionthat MWNTs may have lower effective modulus than SWNTs.[12]

In summary, we have found that the theoretical presumptionof Ref. [1] on the ‘‘linear relation’’ between the Raman bandshift rate and the CNT modulus is not logically sound.Misinterpretations of ‘‘effective modulus’’ and ‘‘load transfer’’during CNT deformations resulted in their unreasonableconclusion that the reduced wall-to-wall stress transfer led to areduced effective modulus of the outer CNT wall. More detaileddiscussion on the influences of the CNT purity, the DWNTdiameter, the wall defect after the DWNT formation, anddispersion in a polymer matrix is desired. A proper reinterpreta-tion of their experimental results and a more systematic studycould indeed have profound effects on better understandings ofRaman responses of CNTs under strains, especially incomposites.

Received: June 30, 2009

Published online: December 4, 2009

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