Comment on ‘‘The Effect of Stress Transfer Within
Double-Walled Carbon Nanotubes Upon Their Ability to
By Wei Lin and C. P. Wong*
In a recent Communication published in Advanced Materials, carbon-ﬁber moduli and their Raman band shift rates; however,
Cui et al. discussed wall-to-wall stress transfer within we do not agree with this being a general relation for evaluating
double-walled carbon nanotubes (DWNTs) in a composite the CNT modulus. There are two fundamental and/or logical
on the basis of stress-induced Raman band shifts. The Raman problems with this extension.
G0 band of the DWNTs was split into two components; only the First, in Ref. , it was mentioned that the linear behavior had
one corresponding to the outer wall shifted distinctly with been attributed, by Huang and Young, to different micro-
strain. This phenomenon was considered a reﬂection of the structures of the ﬁbers under investigation, where ‘‘microstruc-
ineffective stress transfer from the outer wall to the inner wall ture’’ referred speciﬁcally to the levels of orientation of the
during the DWNT deformation in the composite, which would graphitic grains along a ﬁber. In the case of the CNTs used in
greatly reduce the effective modulus of the DWNTs as Ref. , the as-deﬁned microstructure shows little difference
reinforcement ﬁller. Coincidently, it was found that the between the SWNTs and the DWNTs, since the graphitic planes
Raman band shift rate of the outer wall of the DWNTs was (walls in CNTs) are oriented along the ﬁber (tube) axis with the
smaller than that of single-walled carbon nanotubes (SWNTs) only exception of CNT ends. Thus, even though SWNTs, DWNTs
when dispersed in an epoxy matrix. From the G0 -band shift and MWNTs may have different effective moduli, the modulus
rates, Cui et al. calculated the effective moduli of the SWNTs difference is not due to the microstructure/orientation (the
and the outer wall of the DWNTs to be 762 GPa and 552 GPa, effective modulus of CNTs will be discussed in details later).
respectively. This was considered a proof of the reduction in Moreover, it is commonsense that the deformation mechanism
effective modulus of the DWNTs, the reason being the and, therefore, performance of a polycrystalline material (carbon
ineffective wall-to-wall stress transfer. This work has signiﬁ- ﬁber in this case), is quite different from its single-crystalline
cance in providing an experimental proof on what many in this form (CNT). With these in mind, the ‘‘constant of proportion-
research ﬁeld have long hypothesized regarding the ‘‘poor load ality’’ observed for carbon ﬁbers will not hold for CNT-modulus
transfer to the inner walls of a multi-walled carbon nanotube’’ calculations, not to say the ‘‘linearity’’ is not good enough (Fig. 12
(MWNT). However, misinterpretations of some results found in in Ref. ). Therefore, the smaller G0 band shift rate of the outer
literature regarding the Raman band shift rate and effective wall of the DWNTs compared with that of the SWNTs does not
modulus led Cui et al. to the controversial conclusion that the indicate a lower modulus of the DWNTs. Or even if we assume
reduced Raman band shift rate indicated a reduced effective that the DWNTs and the SWNTs have the same modulus, their
modulus for the DWNTs. Raman responses may not be identical.
The theoretical foundation of the study in Ref.  is the Second, the essential difference—orders of magnitude
conclusion in Ref.  (Ref.  of Ref. ), in which Cooper different in surface area—between carbon ﬁbers and CNTs
et al. reported an empirical linear relation (a ‘‘constant of signiﬁcantly increases the complexity of interpreting Raman band
proportionality’’) between the moduli of carbon ﬁbers and their shift rates in CNT/polymer composites. The interface effect or, in
Raman band shift rates under tensile strains: the higher the other words, the inﬂuence by the interphase, plays a signiﬁcant
shift rate, the higher the effective modulus of a CNT. The role in CNT/polymer composites.[4,5] It might be true that for
‘‘constant of proportionality’’ of À0.05 cmÀ1(GPa%)À1 in the carbon ﬁbers and their composites, the Raman band shift rate is
linear relation was taken for granted in Ref.  and, therefore, in more a reﬂection of the intrinsic modulus of the carbon ﬁbers
Ref.  as well, to be valid for calculating the effective moduli of than of the ﬁber/polymer interfacial load transfer;[2,3] however,
carbon nanotubes (CNTs) by investigating the strain-induced the opposite seems to hold for CNT/polymer composites. In
Raman band shift rate of CNTs in a polymer matrix. We do fact, Cooper et al. found a sharp difference in modulus between
acknowledge the possible ‘‘linear’’ relation between the SWNT-A (SWNTs prepared by an arc-discharge process) and
SWNT-P (SWNTs prepared by a pulsed-laser vaporization
[*] Prof. C. P. Wong, W. Lin
process) derived from their G0 band shift rates. Although it
School of Materials Science & Engineering and was postulated that SWNT-A may have a lower intrinsic modulus
Packaging Research Center than SWNT-P, it might not be true. A poorer dispersion of
Georgia Institute of Technology SWNT-A in the composite was proposed as a second possible
771 Ferst Drive NW., Atlanta, GA 30332 (USA) reason, however, without solid evidence. Neither TEM images nor
comparisons of the mechanical properties of the composites were
DOI: 10.1002/adma.200902189 given. Basically, the poor dispersion, bundling, and consequently
Adv. Mater. 2009, 21, 1–3 ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1
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small effective aspect ratio are all related directly to the surface modulus of the outer wall of a CNT’’. This is probably the right
status of the SWNT-A, which, in turn, determines interfacial reason why the Raman G0 band corresponding to the inner wall of
stress transfer from the polymer matrix to the CNTs upon the DWNTs showed little shift in Ref. . Based on the
deformation. In this sense, the difference in the Raman DWNT-synthesis process and the TEM images provided in the
responses between SWNT-A and SWNT-P in Ref.  was Supporting Information of Ref. , we think that the DWNTs
probably a reﬂection of CNT/polymer interface status rather used in Ref.  have the same outer diameter, tube helicity, and
than of the intrinsic modulus of the CNTs. As such, the observed surface chemistry as the SWNTs used; as such, the effective
relatively small G0 band shift rate from the MWNTs may, modulus of the outer wall of the DWNTs should be the same as
compared with the SWNT-P, be also explained by a relatively poor that of the SWNTs. Even a weak, if any, wall-to-wall stress
CNT/polymer interface, since the MWNTs were prepared by an transfer should have enhanced rather than reduced the effective
arc-discharge process as well. The reason why the MWNTs modulus of the outer shell. However, in Ref. , 762 GPa and
showed a higher G0 shift rate than the SWNT-A was probably a 552 GPa were obtained for the SWNTs and the outer wall of the
better dispersion in the composite. Therefore, the conclusion in DWNTs, respectively, on the basis of the aforementioned
Ref. , which is the theoretical presumption of Ref. , is not questionable linear relation.
correct. Cui et al. cited the work on ‘‘interlayer forces and ultralow
Not only is the theoretical foundation problematic in Ref. , sliding friction in multiwalled carbon nanotubes’’ by Kis et al.,
the most important concept—effective modulus—seems to have and claimed that ‘‘it is this relatively easy shear between the layers
been used confusingly. Cui et al. thought that the poor load that reduces the stress transfer and leads to the large reduction in
transfer from the outer wall of a DWNT to the inner wall resulted effective Young’s modulus for MWNTs for reinforcement in
in a reduction in the effective modulus of the DWNT. For composites.’’ In Ref. , a MWNT was glued onto a platinum
modulus measurements of CNTs,[8–10] the results reported were wire and its outer layers were removed by electrical breakdown.
mostly ‘‘effective moduli’’ because in those measurements, ‘‘all The as-exposed CNT core was welded to a force sensor during the
layers have the same circumferential strain, since they have the pullout experiment. This situation is, by no means, comparable to
same axial strain after the uniform stresses loading’’. In the situation of a close-ended DWNT or MWNT in a polymer
addition, in Ref.  (Ref.  of Ref. ), Tu et al. pointed out that composite. In fact, a DWNT or MWNT under tensile load in a
‘‘the value of Ym (effective modulus) does not reﬂect the physics composite is analogous to the case studied by Yu et al., where a
change in the true lattice rigidity but just a choice of the cross large modulus value was found for the outermost wall of a
section’’. Moreover, conclusions in Ref.  are ‘‘valid only for MWNT. Although the modulus value of the outermost wall in
tubes whose radii are not very small’’. Therefore, the as-deﬁned Ref.  seems a little bit lower than the measurement result of a
‘‘effective modulus’’ for a CNTunit is treated as conventional ﬁller SWNT, a direct comparison between the results by different
in contrast to that for a speciﬁc CNT wall. In comparison, in measurement techniques is not wise. Also, note that sample
Ref. , the inner wall of a DWNT upon extension seems to take defects, measurement errors, and possibly the Russian roll
on little stress and little axial strain. In this sense, the as-deﬁned structure[18,19] of a MWNTmay account for such a difference. One
‘‘effective modulus’’ no longer makes any sense. Alternatively, may claim that an open-ended CNT in a polymer matrix looks
Cui et al. turned to a different concept—the effective modulus similar to the situation in Ref. . Not actually. Note that the
of the outer-wall material. With this concept, they attempted to wall–wall distance in a DWNT or MWNT is only $0.34 nm but the
indicate that the capability of the outer wall of taking on the load radius of gyration of a polymer chain is typically at least tens of
transferred from the polymer matrix is reduced due to the poor times larger than 0.34 nm. Therefore, for open-ended small-
wall-to-wall stress transfer; we do not agree with them. diameter DWNTs, the probability of a chemical attachment of the
First, Cui et al. took for granted that upon tensile ends of the multiple walls to the polymer matrix in such a way that
deformation, ‘‘the stress transfer from the matrix to nanotubes they will have the chance to slide relative to each other is
in composites and then subsequently through the different layers extremely low.
occurs principally through shear’’. A question arises as: why Second, Cui et al. cited the modeling results by Zelamea
should the load be transferred from the outer wall to the inner et al. to support their statement of the ‘‘signiﬁcant reduction in
wall? Actually, it is apparent that for tensile deformation the the effective Young’s modulus of the reinforcement by MWNTs’’.
wall-to-wall stress transfer is not necessary or should rarely In fact, although lots of papers have been published on
happen in ideal cases.[12,13] This can be easily understood in the mechanical properties of CNT reinforced polymer composites,
following way: Typically, non-functionalized CNTs are clo- a direct comparison among the experimental data is very
se-ended, which means that a CNT has a sealed outer shell to challenging due to the different CNT sources, treatments,
prevent the inner walls from communicating with the polymer composite preparation processes, and so on. Fortunately, we
chains around the outer shell. Thinking about a tensile can still use the data for discussion from the systematic work by
deformation of a close-ended DWNT in a polymer composite, Gojny et al. In Ref. , SWNT/polymer composites do show
it is the outer shell that is taking the load from the matrix and somewhat higher moduli than MWNT/polymer composites with
deforming until its ﬁnal fracture or failure at the polymer/ the same ﬁller weight fraction. However, the essential reason may
outer-shell interface. The outer shell itself is eligible to take on not be the postulated inferior effective moduli of the MWNTs.
the stress and, ideally, there is no wall-to-wall bridging bond. Note that the SWNTs used in Ref.  have an average diameter
There is no tendency or need for a wall-to-wall load transfer— smaller than 2 nm, while the MWNTs are much larger (15 nm in
keeping in mind that we are not using the concept of an ‘‘effective diameter). This means that the SWNTs have around seven times
modulus of a CNT’’ here but, instead, the concept of an ‘‘effective more surface area than the MWNTs in the composites at the same
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