Integrated Lennard-Jones Potential between a Sphere and a Thin Rod

TL;DR

This paper derives a compact analytical expression for the Lennard-Jones potential between a sphere and a thin rod, applicable to finite and infinite lengths, including force and torque calculations and asymptotic analysis.

Contribution

It introduces a new analytical formulation for sphere-rod Lennard-Jones interactions, covering finite and infinite rod lengths with force and torque expressions.

Findings

Derived a closed-form potential expression for sphere-rod interactions.

Provided formulas for forces and torques based on the potential.

Discussed asymptotic behaviors of the potential.

Abstract

A compact analytical form is derived via an integration approach for the interaction between a sphere and a thin rod of both finite and infinite lengths, with each object treated as a continuous medium of materials points interacting by the Lennard-Jones 12-6 potential. Expressions for the resultant forces and torques are obtained. Various asymptotic limits of the analytical sphere-rod potential are discussed.