Tabular Potentials for Monte Carlo Simulation of Supertoroids with Short-Range Interactions

We describe a methodology for constructing tabular potentials of supertoroids with short-range interactions, which requires the calculation of the volume of overlap of these shapes for many relative positions and orientations. Recent advances in the synthesis of anisotropic colloids have made experimental realizations of such particles feasible and have increased the practical impact of fundamental simulation studies of these families of shapes. This extends our recent work on superquadric potentials to now include a family of ring-like shapes with a hole in the middle. Along with the addition of supertoroids, the ability to make tables for nonidentical particles and particle pairs with multiple, disconnected overlap volumes was added. Using newly developed extensions to a previously published algorithm, we produced tabular potentials for all of these new cases. The algorithmic developments in this work will enable Monte Carlo simulations of a wider variety of shapes to predict thermodynamic properties over a range of conditions.