The directional contact distance of two ellipsoids: Coarse-grained potentials for anisotropic interactions

TL;DR

This paper introduces a new method to calculate the closest approach distance between two ellipsoids in any orientation, enabling the development of anisotropic interaction potentials for complex particle systems.

Contribution

It presents a novel directional distance measure derived from the Elliptic Contact Function, along with explicit force and torque expressions for modeling anisotropic particle interactions.

Findings

Derived a general distance measure for ellipsoids at any orientation

Proposed an elliptic pair potential based on this distance

Compared the new potential with Gay-Berne potentials

Abstract

We obtain the distance of closest approach of the surfaces of two arbitrary ellipsoids valid at any orientation and separation, measured along their inter-center vector. This directional distance is derived from the Elliptic Contact Function. The geometric meaning behind this approach is clarified. An elliptic pair potential for modelling arbitrary mixtures of elliptic particles, whether hard or soft, is proposed based on this distance. Comparisons to Gay-Berne potentials are discussed. Analytic expressions for the forces and torques acting on the elliptic particles are given.