Frictional Forces can Disappear in Symmetric Molecular Scale Systems

Viscous and frictional forces are essentially zero in a nanotechnology envisioned by Drexler [4] in which moving elements such as bearings and gears of high symmetry are fashioned from diamond-like "diamondoid" covalently bonded materials. (To be sure, these are only computer models, no such structures have been fabricated.) The envisioned nanometer scaled wheels and axles are precisely self-aligned in vacuum by balances of attractive and repulsive forces, with no space for any fluid. Such moving parts basically encounter frictional forces only at a much lower level than fluid viscous forces.

There are natural examples of high symmetry nested systems. One example is provided by nested carbon nanotubes, which are shown in Figures 2.1 and 2.2 (after Cumings and Zettl, [5]). Nanotubes are essentially rolled sheets of graphite, which

Figure 2.1 Nested carbon nanotubes [5]. This is a computer generated image. Zettl [5] has experimentally demonstrated relative rotation and translation of nested nanotubes, a situation very similar to that in this image. The carbon-carbon bonding is similar to that in graphite. The spacer between the tubes is simply vacuum

2.6 Frictional Forces can Disappear in Symmetric Molecular Scale Systems have no dangling bonds perpendicular to their surfaces. Graphite is well known for its lubricating properties, which arise from the easy translation of one sheet against the next sheet. It is clear that there are no molecules at all between the layers of graphite, and the same is true of the nanotubes. The whole structure is simply made of carbon atoms. The medium between the very closely spaced moving elements is vacuum.

A second example in nature of friction-free motion may be provided by the molecular bearings in biological rotary motors. Such motors, for example, rotate flagella (propellers) to move cells in liquid. The flagellum is attached to a shaft which rotates freely in a molecular bearing structure. The rotation transmits torque and power and the motors operate continuously over the life of the cell, which suggests a friction-free molecular bearing. This topic will be taken up again in Chapter 3.

The double nanotube structure is maintained in its concentric relation by forces between the carbon atoms in the inner and outer tubes. These forces are not easy to fully characterize, but one can say that there is negligible covalent bonding between individual atoms on the adjacent tubes. Presumably there are repulsive overlap forces between atoms on adjacent tubes, such that a minimum energy (stable configuration) occurs when the tubes are parallel and coaxial. Attractive forces are presumably of the van der Waals type, and again the symmetry would likely favor the concentric arrangement. In the elegant experiments of Zettl [5], it was found that a configuration as shown in Figure 2.2 would quickly revert to a fully nested configuration when the displaced tube was released. This indicates a net negative energy of interaction between the two tubes, which will pull the inner tube back to full nesting. This is in accordance with the fact that the attractive van der Waals force is of longer range than the repulsive overlap force, which would be expected to have a negative exponential dependence on the spacing of the two tubes.

The structures of Figures 2.1 and 2.2 make clear that there will be a corrugated potential energy function with respect to relative translation and relative rotation, with periodicity originating in the finite size of the carbon atoms. The barriers to rotation and translation must be small compared to the thermal energy kT, for free rotation and translation to occur, and also for apparently friction-free motions to occur without damage to the structures. Incommensurability of the two structures will reduce such locking tendencies. An analysis of incommensurability in the ffiBBHMHHHHHMRHH

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Figure 2.2 TEM image of partially nested nanotubes, after relative translation (Cumings and Zettl [6]). It was found that the inner tube could repeatedly be slid and rotated within the outer tube, with no evidence of wear or friction. Attractive forces very rapidly pulled a freed tube back into its original full nesting design of molecular bearings has been given by Merlcel [7]. Again, there are no known methods by which any such structures can be fabricated, nor are there immediate applications.

Rotational and translational relative motions of nested carbon nanotubes, essentially free of any friction, are perhaps prototypes for the motions envisioned in the projected diamondoid nanotechnology. The main question is whether elements of such a nanotechnology can ever be fabricated in an error-free fashion so that the unhindered free motions can occur.

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