Analytical Interaction Potential for Lennard-Jones Rods

TL;DR

This paper derives an analytical interaction potential for Lennard-Jones rods, providing exact formulas for forces and torques, useful for modeling various rod-like systems in physics and biology.

Contribution

It introduces a novel analytical form for Lennard-Jones interactions between finite rods, including special cases and interactions with point particles.

Findings

Exact expressions for force and torque between rods.

Simplified forms for coplanar, parallel, and collinear rods.

Potential applications in modeling biological and nanomaterial systems.

Abstract

An analytical form has been derived using Ostrogradski's integration method for the interaction between two thin rods of finite lengths in arbitrary relative configurations in a 3-dimensional space, each treated as a line of material points interacting through the Lennard-Jones 12-6 potential. Simplified analytical forms for coplanar, parallel, and collinear rods are also derived. Exact expressions for the force and torque between the rods are obtained. Similar results for a point particle interacting with a thin rod are provided. These interaction potentials can be widely used for analytical descriptions and computational modeling of systems involving rod-like objects such as liquid crystals, colloids, polymers, elongated viruses and bacteria, and filamentous materials including carbon nanotubes, nanowires, biological filaments, and their bundles.