Nanobalance application for carbon nanotubes: a mass attached at the end of a nanotube shifts its resonance frequency. If the nanotube is calibrated (i.e., its spring constant known), it is possible to measure the mass of the attached particle. In this example, the resonant frequency was 968 kHz, compared to 3.28 MHz when unloaded (calculated). The mass of this carbon sphere was then determined to be 22±6 femtograms (one fg is a quadrillionth of a gram). Direct estimate based on volume and the density of amorphous graphite gives a mass close to 30 fg.
Induced resonance of a nanotube. On left, the nanotube is at rest: the blurring in the picture is due to thermal vibration. The central picture shows this nanotube excited in its fundamental vibrational mode (530 KHz). It is possible to go even further and excite its second harmonic (3.01 MHz). Both the frequency ratio and the shapes correspond reasonably well to what is calculated for a clamped beam.
This research was reported by Philippe Poncharal, Z. L. Wang, Daniel Ugarte, and Walt A. de Heer in the March 5, 1998 issue of the journal Science.
Images and captions courtesy of Walt de Heer's group at Georgia Tech.
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