Restricted three body problems at the nanoscale

TL;DR

This paper extends classical restricted three body problems to the nanoscale, modeling interactions between C60 fullerenes and carbon atoms using Lennard-Jones potential, revealing terahertz-range angular velocities.

Contribution

It introduces an analytical approach to nanoscale three body problems involving fullerenes, incorporating van der Waals forces and continuous potential approximation.

Findings

Maximum angular frequency reaches terahertz range

Identified stationary points and maximum velocity points

Analytical determination of molecular energy between fullerenes

Abstract

In this paper, we investigate some of the classical restricted three body problems at the nanoscale, such as the circular planar restricted problem for three C60 fullerenes, and a carbon atom and two C60 fullerenes. We model the van der Waals forces between the fullerenes by the Lennard-Jones potential. In particular, the pairwise potential energies between the carbon atoms on the fullerenes are approximated by the continuous approach, so that the total molecular energy between two fullerenes can be determined analytically. Since we assume that such interactions between the molecules occur at sufficiently large distance, the classical three body problems analysis is legitimate to determine the collective angular velocity of the two and three C60 fullerenes at the nanoscale. We find that the maximum angular frequency of the two and three fullerenes systems reach the terahertz range and we determine the stationary points and the points which have maximum velocity for the carbon atom for the carbon atom and the two fullerenes system.