Modelling the joining of nanocones and nanotubes

Carbon nanocones have been proposed as probes for scanning tunnelling microscopes, but there is currently no precise procedure to design such a nano-device. The successful design of many novel nano-electronic devices may require a thorough understanding of the geometric joining issues of certain nanostructures. In this paper, we propose a calculus of variations model of the composite nanostructure obtained by joining a carbon nanocone and a carbon nanotube. We propose a continuous approximation to the discrete composite structure and we assume rotational symmetry of the proposed nanostructure, so that the three dimensional problem can be reduced to a problem in two dimensions. In making these assumptions, we recognise that the existence of pentagons in the cone may result in some minor undulations of the proposed axially symmetric structure. However, our purpose is to formulate the basic underlying structure from which any such small perturbations may be viewed as departures from an ideal model. We examine two models depending upon the curvature of the join profile which can be either positive or both positive and negative. There is at present no experimental or simulation data for comparison with the theoretical connecting structures predicted by this study, which in itself is some justification for the proposed simple model presented here.