Oscillating carbon nanotori along carbon nanotubes

The discovery of carbon nanostructures, such as nanotubes and ${\mathrm{C}}_{60}$ fullerenes, has given rise to a number of potential nanoscale devices. One such device is the gigahertz oscillator, comprising an inner shell sliding inside an outer shell of a multiwalled carbon nanotube, and which, at least theoretically, generates oscillatory frequencies in the gigahertz range. Following the concept of these gigahertz oscillators and the recent discovery of “fullerene crop circles,” here we propose the notion of a nanotorus-nanotube oscillator comprising a carbon nanotorus which is sucked by the van der Waals force onto the carbon nanotube, and subsequently oscillates along the nanotube axis due to the equal and opposite pulselike forces acting at either end of the nanotube. Assuming a continuum approach, where the interatomic interactions are replaced by uniform atomic surface densities, and assuming that the geometry of the nanotube and nanotorus is such that the nanotorus always remains symmetrically situated around the nanotube, we present the basic mechanics of such a system, including the determination of the suction and acceptance energies, and the frequency of the resulting oscillatory motion. In contrast to the previously studied gigahertz nanoscale oscillators, here the oscillatory frequencies are shown to be in the megahertz range. Our study, although purely theoretical must necessarily precede any experimental implementation of such oscillatory systems.

Figure 1

Cross section of nanotorus offset a distance $ϵ$ from nanotube axis.

Figure 2

Nanotorus oscillating along the exterior of a nanotube.

Figure 3

Lennard-Jones potential energy $E$ against nanotorus position $Z$.

Figure 4

Axial force against nanotorus position $Z$.

Figure 5

(Color online) Frequency of oscillation for nanotorus($b=3.39\mathrm{\AA }$, $c=55\mathrm{\AA }$) as a function of the nanotube radius $a$.

Figure 6

(Color online) Frequency of oscillation for nanotorus $(b=3.39\mathrm{\AA })$ oscillating along a nanotube $(a=48.21\mathrm{\AA })$ as a function of the nanotorus ring radius $c$.