Nanotube Mechanical Properties

Taking advantage of low substrate/nanotube friction, Wong et al. [5] measured directly the bending and buckling forces for MWNTs on single-crystal MoS2. They devised a flexible method that uses a combination of conventional lithography to pin one end of the nanotube, and the AFM tip to locate and probe the nanotube region protruding from the static contact. As the AFM scanned normal to the nanotube, the lateral force vs. displacement (F-d) curves at varying distances from the pinning point was recorded, and information on the Young's modulus, toughness, and strength of the nanotube were obtained. The F-d curves recorded on the MWNTs showed several important points (Fig. 16). The initial location at which the lateral F increased in each scan was approximately the same, and thus it was possible to conclude that the nanotube deflection is elastic. Second, the lateral force recorded in each of the individual scans increased linearly once the tip contacted the nanotube (F = kd), and k decreased for scan lines recorded at increasingly large distances from the pinning point. From simple nanobeam mechanics formulae, the Young's modulus of MWNTs with diameters from 26 to 76 nm was determined to be 1.28 ± 0.59 TPa, and this value was found to be independent of diameter. The bending strength of nanotubes was also determined by recognizing that the material softens significantly at the buckling point; that is, the buckling point is taken as a measure of the bend strength. The average bending strength, which was determined directly from F-d curves, was found to be 14.2 ± 8.0 GPa.

The approach of Wong and co-workers [5] was extended by Walters et al. [62] to assess the tensile strength of SWNT ropes. In these latter measurements, the rope was freely suspended across a trench, and then deflected with the AFM. Lateral force vs. displacement curves recorded with the AFM tip at several different vertical heights across the center of the tube

Fig. 16. Surface plot showing the F-d response of a 32.9 nm diameter MWNT recorded with a normal load of 16.4 nN. The nanotube is pinned by a SiO pad beyond the top of the image. The data were recorded in water to minimize the nanotube-MoS2 friction force [5]

were modeled reasonably well as an elastic string. The resulting fit to the experimental data yielded a maximum elastic strain of 5.8 ± 0.9%. To compare this value with conventional, bulk materials, Walters et al. [62] calculated the yield strength for SWNT ropes, using a Young's modulus of 1.25 TPa for SWNTs [63], and found it to be 45 ± 7 GPa, over 20 times the yield strength of high-strength steels.

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