Discrete and continuous approximations for nanobuds

Abstract

Both discrete and continuous approximations are employed to determine the join structure involved in the novel carbon nanostructure formed from a C60 fullerene and a carbon nanotube, namely a nanobud. First, following the methodology of the authors' previous work, using a least squares minimization procedure, discrete models are used to join a fullerene and a carbon nanotube by minimizing both the variation in the bond length and the variation in the bond angle. These purely geometrical approaches are closely related to the bonded potential energy method adopted by several authors. Second, by employing a calculus of variations technique, a continuous approximation to the nanobud is determined. In this case, there are also two models depending upon the sign of the curvature of the join profile. We find that the discrete and the continuous approximations are in reasonable overall agreement. However, there is no experimental or simulation data to determine which procedure gives the more realistic results.