An Analytic Form of the Integrated Lennard-Jones Potential for Thin Rods

An analytic form has been derived using Ostrogradsky's integration method for the integrated interaction between two rigid and thin rods of finite lengths and in arbitrary relative configurations in three-dimensional space, each treated as a line of material points interacting through the Lennard-Jones 12-6 potential. Simplified analytic forms for coplanar or parallel rods are also derived. Exact expressions for the force and torque between the rods are obtained. The analytic forms have been fully verified via comparison to the results of direct numerical integration. These forms can be widely used for analytical descriptions of systems such as liquid crystals and colloids consisting of rod-like molecules and particles, as well as filamentous materials including carbon nanotubes, biological filaments, and their bundles.