Spherical and spheroidal fullerenes entering carbon nanotubes
A continuous model of a fullerene inside a carbon nanotube and for which both the fullerene and carbon nanotube are treated as smooth surfaces with uniform atomic number densities and the van der Waals interaction is formulated using a 6-12 Lennard-Jones potential. From the model we derive acceptance conditions and suction energies for C60, C70 and C80 fullerenes. We show that for these systems where the fullerenes are not accepted by the nanotube, then the suction energy is particularly sensitive to the equatorial semi-axis length b. Alternatively, when the nanotube does accept the fullerene then an approximately equal suction energy per atom is obtained for all the fullerene types with little or no sensitivity to change in the equatorial semi-axis length. The analysis is given for the spherical fullerene C60 for which good agreement with molecular dynamics studies is obtained and it is repeated for C70 and C80 fullerenes using a self-consistent solution.