Thermodynamic Consideratons for Single- and Multi-Wall TubesDavid Tomanek
The equilibrium diameter of a growing single-wall nanotube, consisting of a cylinder that is terminated on one side by a cap, can be estimated for a fixed number of atoms N in the following way. Suppose that a nanotube has infinite time to find the equilibrium structure under the constraint that it be a cylinder, closed by a hemisphere at one end. The energies of importance are the strain energy in the cylinder which is proportional to 1/R, the "dangling bond" or better "edge energy" that is proportional to R, and the strain energy of the hemispherical cap that is constant. The tube can be either "long and skinny", resulting in a large strain in the cylinder, but reducing the edge energy. It may be "short and fat" with the opposite energetic consequence. The equilibrium tube radius Req turns out to depend only weakly on the total number of atoms, namely to be proportional to N1/3.
These considerations have been published in
There is no reason why an existing nanotube should not become "fatter" by acquiring additional layers that grow on a "template". A similar phenomenon may be responsible for the formation of multi-wall "bucky onions". Multi-wall nanotubes apparently require no catalyst to keep the growing edge open. There are, it is believed, "lip-lip" interactions between two or more simultaneously growing layers that somewhat passivate the growing edge, thus preventing premature oxidation. There appears to be no upper limit for the diameter of the outermost tube wall. The system would be approaching, just like fattening "bucky onions", the graphitic structure.
For literature see e.g.
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