AFM detection of the mechanical resonances of coiled carbon nanotubes

We introduce a method for atomic force microscopy (AFM)-based detection of mechanical resonances in helix-shaped multi-walled carbon nanotubes. After deposition on an oxidized silicon substrate, the three-dimensional structure of suspended nanotubes, which bridges an artificially created step on the surface, can be visualized using AFM operating in the non-contact mode. The suspended coiled nanotubes are resonantly excited, in situ, at the fundamental frequency by an ultrasonic transducer connected to the substrate. When the AFM tip is positioned above the coiled nanotube, the cantilever is unable to follow the fast nanotube oscillations. Nevertheless, an oscillation amplitude-dependent signal is generated due to the non-linear force-to-distance dependence. Measurement of the mechanical resonances of the helix-shaped carbon nanotubes can be used to quantitatively determine their elastic properties. Assuming that a coiled nanotube can be modeled as a suspended helix-shaped uniformly thin elastic beam, the obtained resonance frequency is consistent with a Young's modulus of 0.17 +/- 0.05 TPa.