Analytical Interaction Potential for Lennard-Jones Rods

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.