We study the bouncing, rolling and sliding of carbon nanotubes on a graphite surface. The energy barriers of and frequencies associated with various types of motions of a nanotube on the graphitic surface are being reported in this paper.
We study the variation of potential energy with distance or angle (as the case may be) as a SWNT is bounced i.e. the interseparation between the tube and the surface is varied, spun i.e. the tube is rotated about its various axes, slid lengthwise and breadthwise, as well as rolled on a graphite surface. For this calculation, the interaction between a carbon nanotube and the surface is dictated by C-C interaction, assumed to be governed by a 6-exponential potential.
In our model, the tube is taken to be rigid, and so is the sheet. Moreover, it may be mentioned that this energy of interaction of a tube with a graphite surface is quite close to that between a tube and a graphite sheet since the interaction between the tube and other sheets (other than the topmost) of graphite is neglected as it will add only a small constant term to the potential energy, being far away from the tube concerned.
From the results thus obtained, the minimum energy configuration of the carbon nanotube happens to be the one that matches the hexagonal pattern of the graphite surface below it. The distance of separation (in z- direction) comes out to be 3.1 Å and energy per unit length is obtained to be ≅ .16653 eV/Å.
The various types of motion of a nanotube on a graphite surface, placed in minimum energy position, have been depicted in Fig. 1. The corresponding frequencies and the barrier heights have been calculated. We find that the rolling motion is the easiest, as there is practically no barrier to this motion. This confirms the earlier observations (references 1 and 2). The corresponding frequency is the softest. Likewise, when the tube is sitting at a position of energy minimum w.r.t. the sheet, the spin about its cylinder axis requires very little energy. The corresponding frequency (ω4) is rather soft too. Another motion requiring very little energy is the lengthwise drag when the tube and substrate are out of registry. The only one of these frequencies falling in the sonic range is that of bounce (ω1). Also associated with motion in this direction is the temperature of evaporation (K.E. at which the tube will escape) and our estimates give this temperature for a SWNT of given diameter and length as ~ 105 K, rather high compared to room temperature. The next hard frequency in our list is ω6 which involves one end of the tube tipping close to the graphene surface. However this motion needs to take flexibility of the tube into account which is not done in the present calculation. We have made similar calculations for double walled nanotube of same diameter and get the similar energy barriers as that for SWNT.
It would be interesting to find ways to verify these frequencies experimentally. They can be used in NEMS (nano-electro-mechanical systems). The estimates using the energy barriers show that at room temperatures the SWNT's are pretty free to roll, slide and spin on the graphite surface. More significantly, the energy required to separate the tube from the graphite surface is enormous and it seems extremely unlikely, for a tube of length of about 100 Å or so, during manipulation experiments, to detach it from the graphite surface. In conclusion, graphite sheets seem to be nice storage materials for long carbon nanotubes, where nanotubes can easily rotate, slide and roll but can't be easily taken away from the surface.
Fig. 1: A SWNT placed on a graphene sheet
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