Mechanics of spheroidal fullerenes and carbon nanotubes for drug and gene delivery

There is considerable interest in the mechanics of carbon nanostructures, such as carbon nanotubes and fullerenes, and the manner of their interactions at the intermolecular level. Medical applications include the use of carbon nanotubes for targeted drug and gene delivery, for which issues relating to the acceptance and containment of drugs or genes are not properly understood. A spheroid is an ellipsoid with two equal axes and the general spheroidal shape includes a wide variety of possible molecular configurations such as spheres, capped cylindrical tubes and ellipsoids of revolution, and therefore the determination of the interaction forces for this general shape may have many applications. Phenomena such as the suction of fullerenes into carbon nanotubes due to the van der Waals interatomic interactions and ultra-low friction of a molecule moving inside a carbon nanotube give rise to the possibility of constructing nanoscaled oscillators with frequencies in the gigahertz range. This paper models the mechanics of such a system by employing a six-twelve Lennard-Jones potential taken over two surfaces assumed to be composed of mean distributions of atoms over the two idealized surfaces of an open-ended semi-infinite circular cylinder and a spheroid. Following the methodology of previous work with spherical surfaces, the acceptance energy and suction energy for spheroidal molecules are given and the special case of spherical molecules is also reproduced to validate the method. The results for elliptical molecules are novel and cannot be validated experimentally at this stage, but the results for the special case of spherical molecules are given and shown to be in good agreement with published molecular dynamical simulations. Finally, a general numerical -analytical procedure is proposed to calculate the Lennard-Jones potential for any axially symmetric surface, and the prior results obtained for the spheroid are used to validate the procedure.