Analytical Interaction Potentials for Lennard-Jones Rings

The Lennard-Jones (LJ) potential and its integrated forms have wide applications in physics and materials science. Here we present analytical interaction potentials for thin rings in various dimensions by treating a ring as a continuous distribution of LJ material points and integrating the LJ potential for various geometries. The expressions for force and torque are also derived. The potentials are implemented in the LAMMPS molecular dynamics simulator and used to study a range of ring systems. Results on the structural features and phase behavior of ring suspensions will be presented. These potentials are expected to find applications in other physical systems such as cyclic organic molecules, ring polymers, and intercatenated chains of cyclic molecules.