Analytical interaction potential for Lennard-Jones rods

Abstract

An analytical form has been derived using Ostrogradsky's integration method for the interaction between two thin rods of finite lengths in arbitrary relative configurations in a three-dimensional space, each treated as a line of point particles 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 rodlike objects such as liquid crystals, colloids, polymers, elongated viruses and bacteria, and filamentous materials including carbon nanotubes, nanowires, biological filaments, and their bundles.