Mechanical Properties

It is becoming clear from recent experiments [154,155,156,157,158,159,160] [161] that Carbon NanoTubes (CNTs) are fulfilling their promise to be the ultimate high strength fibers for use in materials applications. There are many outstanding problems to be overcome before composite materials, which exploit the exceptional mechanical properties of the individual nanotubes, can

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Fig. 32. Emission spectra of three different MWNTs acquired under similar experimental conditions. Dotted lines highlight position of the background. Spectrum A is one of the most recently observed and shows a peak at about 800 nm (Vsample=2 V, I = 50 nA). Spectra B and C were obtained on two different nanotubes with the same Pt-Ir tip during another experiment (Vsample=2.05 V, I = 35 nA). In spectrum B, a peak at 900 nm is found, while in spectrum C, another peak centered at about 710 nm is also revealed. For the three spectra, the exposure time is 5 min [152]

be fabricated. Arc-discharge methods are unlikely to produce sufficient quantities of nanotubes for such applications. Therefore, catalytically grown tubes are preferred, but these generally contain more disorder in the graphene walls and consequently they have lower moduli than the arc-grown nanotubes. Cat-alytically grown nanotubes, however, have the advantage that the amount of disorder (and therefore their materials properties) can be controlled through the catalysis conditions, as mentioned before. As well as optimizing the materials properties of the individual tubes for any given application, the tubes must be bonded to a surrounding matrix in an efficient way to enable load transfer from the matrix to the tubes. In addition, efficient load bearing within the tubes themselves needs to be accomplished, since, for MWNTs, experiments have indicated that only the outer graphitic shell can support stress when the tubes are dispersed in an epoxy matrix [162]. In this section, a few basic measurements are presented on individual MWNTs with different levels of disorder. The very promising SWNT ropes also present several problems, which are reviewed by showing mechanical measurements on ropes of different diameter.

6.1 Young's Modulus of MWNTs

The AFM technique for mechanical properties measurements developed by Salvetat and collaborators enabled characterization of the moduli of SWNT bundles [158] and MWNTs, both arc-grown and catalytically grown [159], to be carried out [158,159]. Briefly, the method involves depositing CNTs from a suspension in a liquid onto well-polished alumina ultra-filtration membranes with a pore size of about 200 nm (Whatman anodisc). By chance, CNTs occasionally span the pores and these can be subjected to mechanical testing on a nanometer length scale. The attractive interaction between the nanotube and the substrate acts to clamp the tubes to the substrate. Contact mode AFM measurements under ambient conditions are used to collect images of the suspended CNTs at various loading forces. Figure 33 shows an AFM image of a SWNT bundle suspended across a pore and a schematic representation of the mechanical test set-up. The maximum deflection of the CNT into the pore as a function of the loading force can be used to ascertain whether the behavior is elastic. If the expected linear behavior is observed, the Young's

Fig. 33. (a) 3-D rendition of an AFM image of a SWNT bundle (or an individual MWNT) that adheres to an alumina ultra-filtration membrane, leading to a clamped beam configuration for mechanical testing. (b) Schematic representation of the measurement technique. The AFM applies a load, F, to the portion of nanotube with a suspended length of L and the maximum deflection 5 at the center of the beam is directly measured from the topographic image, along with L and the diameter of the tube (measured as the height of the tube above the membrane) [158]

Fig. 33. (a) 3-D rendition of an AFM image of a SWNT bundle (or an individual MWNT) that adheres to an alumina ultra-filtration membrane, leading to a clamped beam configuration for mechanical testing. (b) Schematic representation of the measurement technique. The AFM applies a load, F, to the portion of nanotube with a suspended length of L and the maximum deflection 5 at the center of the beam is directly measured from the topographic image, along with L and the diameter of the tube (measured as the height of the tube above the membrane) [158]

modulus (E) can be extracted using a continuum mechanics model for a clamped beam configuration. The suspended length of the CNT, its deflection as a function of load and its diameter can all be determined from the images, thereby enabling the modulus to be deduced. One great advantage of the AFM technique employed by Salvetat et al. [158] is its simplicity. There is no need, for example, to use complex lithographic techniques for suspending and the clamping tubes [156]. The surface forces between the CNTs and the alumina membrane are sufficiently high to maintain the clamped beam condition for the majority of MWNTs that were tested. In addition, the nano-tubes are never exposed to electron radiation during the measurement, which would be the case for TEM studies [155,160]. Electron radiation will induce defects, if the energy of the electrons is high enough, and thereby alter the material properties of the CNTs. The relative ease of sample preparation for this AFM method enables a high measurement throughput, thereby allowing measurement of a variety of CNTs synthesized under different conditions and to compare the results systematically. For MWNTs grown by the arc-discharge method, it was found that the average value of the elastic modulus (or Young's modulus) E is 810 ± 410 GPa, which is consistent with the inplane elastic constant of graphite, en = 1.06TPa [15]. The authors did not find a significant correlation between the elastic modulus and the diameter of the tube [159]. Furthermore, no apparent difference was found in the elastic modulus between annealed and unannealed nanotubes. This suggests that point defects, if present at all, do not alter the mechanical properties of MWNTs.

6.2 Disorder Effect

AFM measurements of the mechanical properties of arc-grown MWNTs and MWNTs catalytically grown at different temperatures have been compared, and the results show that the Young's modulus for the catalytically grown MWNTs are lower than for arc-grown MWNTs [7]. These data are summarized in Fig. 34, with a sketch correlating the elastic modulus with the amount of order/disorder within the nanotube walls. As one might expect, the Young's modulus of the MWNTs decreases as the disorder within the walls increases. Arc-grown MWNTs, which contain very few defects, have a modulus comparable with the high values that are measured for an individual SWNT [158]. The moduli of catalytic MWNTs can vary, depending on their structure. Those, which have a highly defective kind of stacked coffee cup structure (see Fig. 5, part ii), have a very low modulus. The other catalytic MWNTs, grown at a lower temperature, showed a higher degree of order within the tubes and consequently had slightly higher moduli. The uncertainty of the measured values in this case was large. This could be due to greater uncertainties in the measurement technique, since the catalytic MWNTs were usually curved, making the continuum beam approximation less valid.

Modulus (GPa)

Fig. 34. Correlation between the measured Young's modulus of MWNTs with the amount of disorder present within the graphitic walls. Ranges of measured moduli for three different types of MWNTs are plotted against an arbitrary scale of increasing disorder. The sketch represents arc-discharge grown, and catalytically grown MWNTs at 720° C and at 900° C, respectively [163]

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Disorder

6.3 Comparison with SWNTs

Although the elastic moduli for Single-Wall NanoTube (SWNT) bundles (also known as ropes) were expected to be higher than for MWNTs, it has been demonstrated that shearing effects due to the weak intertube cohesion gives rise to significantly reduced moduli compared to individual SWNTs [158]. This is due to the fact that the SWNTs are held together in the rope by the same van-der-Waals forces that are acting between the 2D graphene layers, and these weak van der Waals forces make turbostratic graphite [16] a very good lubricant. The reduced bending modulus of these SWNT bundles is a function of the rope diameter because the magnitude of the shear modulus varies as the ratio of the length to the rope diameter. An individual SWNT has an elastic modulus of about 1 TPa, but this falls to around 100 GPa for bundles 15 to 20 nm in diameter, as shown in Fig. 35.

In order to use nanotubes as a reinforcement in composites, there are two main challenges to address: (1) to establish strong bonding between the CNTs and the surrounding matrix, and (2) to create cross-links between the shells of MWNTs and also between the individual SWNTs in SWNT bundles, so that loads can be homogeneously distributed throughout the CNTs. To exploit the excellent mechanical properties of the individual SWNTs, both of these goals should be achieved without compromising the mechanical properties of the individual SWNTs too drastically. Efforts are in progress to address these problems using post production modification of CNTs via chemical means and controlled irradiation [7].

To produce cross-links between the shells in SWNTs of SWNT bundles, the sp2 carbon bonding must be disrupted to sp3 bonding, so that dangling bonds are available for cross-linking. Since the sp2 bonding is the essence of the CNT strength, this must not be disrupted to such a degree that the properties of the individual SWNTs in SWNT bundles are degraded. A "gentle" way to produce cross-linking is by controlled electron irradiation. In [7] the SWNT bundles were exposed to 2.5 MeV electrons with a total radiation

Fig. 35. Dependence of the apparent Young's modulus (Eapp) on the diameter of SWNT bundles measured using AFM. The untreated bundles are represented by open circles and the irradiated bundles by filled squares. The diameter of the individual SWNTs is in the 1.4 nm range [163]

dose of 11 Curie/cm2 after synthesis. A theoretical estimation of the number of displacements that this energetic electron dose produces suggests that the irradiation will create about 1 defect per 360 carbon atoms [164]. AFM measurements of the elastic modulus of irradiated SWNT bundles are shown in Fig. 35, along with similar measurements of non-irradiated SWNT bundles. Within the errors of the measurement technique, no increase in the elastic modulus of the bundles could be clearly identified. The Young's modulus was still found to decrease with increasing bundle diameter in a similar way as that found for the non-irradiated bundles. However, the irradiation treatment does not appear to have compromised the strength of the individual SWNTs either, since the smaller diameter bundles have quite high elastic moduli. In addition, it was noticed that the irradiated bundles were more difficult to disperse in ethanol, and the morphology of the sample under AFM examination showed that the irradiated bundles exhibited a higher degree of aggregation. Taken together, these data suggest that the radiation treatment produced more bonding between the tubes, but this additional bonding was not sufficient to produce enough cross-links within the bundles to reduce shearing effects and produce bundles with higher Young's moduli. Future efforts will concentrate on optimizing the chemistry and irradiation doses to improve the mechanical properties of SWNT bundles and MWNTs.

6.4 Deformation of MWNTs

There is some contention about whether the elastic modulus of MWNTs varies as a function of nanotube diameter. Poncharal et al. [160] have suggested the formation of a rippling mode on the surface of bent MWNTs with diameters greater than about 15 nm, leading to a reduction in the measured modulus. However, a strong dependence of the measured modulus on the diameter was not observed in previous AFM measurements [159]. It is conceivable that the measurement of the modulus is force dependent and the transition to the rippling mode is not reached with the loading forces used in the AFM experiments. The TEM data in Fig. 36 obtained at large loading force show a rippling with a period of 15 nm on the compressed side of a statically bent MWNT, but the bent MWNTs in typical TEM experiments showing such phenomena have rather high curvatures [160] (much higher than typical curvatures seen in the AFM experiments). Interestingly, the rippling effect has also been observed on the compressed sides of catalytically grown MWNTs [7]. Figure 37 shows a high resolution AFM image of a catalytic MWNT (grown at 720°C) lying across a pore, the edge of which can be seen on the left of the image. The image clearly shows rippling only on the right-hand side of the tube, the direction in which the CNT is bent, and the ripple in this case has a period of roughly 16 nm. These ripples are not perpendicular to the tube axis but are inclined at approximately 30°, making the CNT left-handed. This rippling could arise from the surface forces, which constrain the CNTs on the membrane. However, rippling can also arise when the tubes are loaded in the AFM. Rippling on the upper, compressed side of these MWNTs has also been observed as the imaging force is increased. Nonlinear behavior in the loading/unloading characteristics of the catalytic tubes was frequently noticed. This also contributes to the uncertainties in measuring moduli on these kinds of MWNTs by the AFM method. It is conceivable that the onset of rippling will occur at lower curvatures, i.e., lower forces, in tubes with a higher amount of disorder.

Because of the Russian-doll structure of the MWNTs and because of the high strength of the sp2 bonds, one would think that a nanotube shell cannot be easily pealed off from a MWNT. However, it is quite possible that a single

Fig. 36. High-resolution TEM image of a bent nanotube grown by the arc discharge method (radius of curvature 400nm), showing the characteristic wave-like ripple distortion. The amplitude of the ripples increases continuously from the center of the tube to the outer layers of the inner arc of the bend [160]

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