Van der Waals interaction between two crossed carbon nanotubes

TL;DR

This paper derives analytical formulas for van der Waals interactions between crossed carbon nanotubes, enabling precise calculations of potential energy and forces, with implications for nanotechnology applications.

Contribution

It introduces exact analytical expressions for van der Waals potential and force between crossed nanotubes using Lennard-Jones and smeared out approximations.

Findings

Derived explicit formulas for potential and force

Calculated equilibrium distances and maximal forces

Plotted potential energy curves for nanotubes

Abstract

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.