Molecular Dynamics Simulation of Disks and Rods in Two Dimensions with Integrated Lennard-Jones Potentials

The Lennard-Jones (LJ) 12-6 potential has been widely used in molecular simulations. It is also integrated for objects with various geometric shapes, including spheres and rods, by treating each object as a continuous medium consisting of uniformly distributed LJ point particles. These integrated potentials have found wide applications in modeling colloids, liquid crystals, polymers, and granular materials. We have derived compact analytical expressions for the integrated LJ potentials among various objects in two dimensions: disks, rods, and LJ point particles. Their interaction potentials with a half-plane are also derived. The expressions for force and torque are obtained. These analytical potentials are implemented in the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) as a user package to enable molecular dynamics simulations of disks and rods in two dimensions, with the possibility of imposing various wall confinements and including a solvent explicitly as a LJ liquid. This new tool is applied to model the evaporation process of two-dimensional suspensions of monodisperse or bidisperse disks. Crystallization is observed in the final drying stage of monodisperse systems and stratification phenomena are found in drying bidisperse suspensions. The findings are compared with their three-dimensional counterparts to understand the role of dimensionality in evaporation.