Interaction between Thin Rods: An Analytical Potential and Its Implementation

In Hamaker theory, the interaction between two objects is computed via a double summation of all pairwise intermolecular interactions across the two bodies. The intermolecular interactions are often described with a Lennard-Jones (LJ) 12-6 potential. Analytical and approximate forms of integrated LJ potentials are available for two spheres, two walls, a sphere and a wall, and two ellipsoids. In this work, we have extended Hamaker theory to the system of two thin rods and derived an analytical expression of the integrated LJ potential between two rods with arbitrary lengths, separations, and orientations. The analytical potential is fully verified by comparisons with direct numerical integrations. Furthermore, the integrated potential between a rod and a point mass is obtained. The expressions for force and torque are derived and implemented within the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). These potentials can be easily used to model rod-based systems such as liquid crystals, colloidal rods, carbon nanotubes, nanowires, filaments, and their bundles.