Zigzag and spiral configurations for fullerenes in carbon nanotubes

The success or otherwise of nanoscale devices hinges on a correct understanding of the physical effects at this scale. Research in nanotechnology is predominantly through either experimentation using electron and atomic force microscopy or through large- scale computation using molecular dynamics simulation. In this paper, we employ elementary mechanical principles and classical modelling procedures to investigate the packing of C-60 fullerene chains inside a single- walled carbon nanotube by utilizing the Lennard - Jones potential function and the continuum approximation. Such assemblies are often referred to as nanopeapods. We examine both zigzag and spiral chain configurations inside ( 10, 10), ( 16, 16) and ( 20, 20) carbon nanotubes and we obtain analytical expressions in terms of hypergeometric functions for the potential energy for such configurations. We find that for a ( 10, 10) tube, the C60 fullerene chain is formed linearly along the tube axis. In the case of both ( 16, 16) and ( 20, 20) tubes, both zigzag and spiral configurations are more clearly evident along the tube. In particular, the resulting pattern obtained for the zigzag chain is entirely consistent with a specific angular spacing for the spiral pattern.