Van der Waals interaction between two crossed carbon nanotubes
  The analytical expressions for the van der Waals potential energy and force between two crossed carbon nanotubes are presented. The Lennard-Jones potential for two carbon atoms and the method of the smeared out approximation suggested by L.A. Girifalco were used. The exact formula is expressed in terms of rational and elliptical functions. The potential and force for carbon nanotubes were calculated. The uniform potential curves for single- and multi- wall nanotubes were plotted. The equilibrium distance, maximal attractive force, and potential energy have been estimated. 
Alexander I. Zhbanov, Evgeny G. Pogorelov, Yia-Chung Chang