Effective pair potentials for spherical nanoparticles

TL;DR

This paper derives effective spherically symmetric pair potentials for spherical nanoparticles in a fluid, accounting for overlap and internal structure, with explicit formulas for common interaction types and validation against atomic models.

Contribution

It introduces a unified framework for effective potentials of spherical nanoparticles, including hollow ones, with explicit formulas for various interaction types and validation against atomic models.

Findings

Explicit formulas for effective potentials from common pair interactions.

Effective potentials account for particle overlap and internal structure.

Validation against atomic models confirms applicability.

Abstract

An effective description for spherical nanoparticles in a fluid of point particles is presented. The points inside the nanoparticles and the point particles are assumed to interact via spherically symmetric additive pair potentials, while the distribution of points inside the nanoparticles is taken to be spherically symmetric and smooth. The resulting effective pair interactions between a nanoparticle and a point particle, as well as between two nanoparticles, are then given by spherically symmetric potentials. If overlap between particles is allowed, the effective potential generally has non-analytic points, but for each effective potential the expressions for different overlapping cases can be written in terms of one analytic auxiliary potential. Effective potentials for hollow nanoparticles (appropriate e.g. for buckyballs) are also considered, and shown to be related to those for solid nanoparticles. Finally, explicit expressions are given for the effective potentials derived from basic pair potentials of power law and exponential form, as well as from the commonly used London-Van der Waals, Morse, Buckingham, and Lennard-Jones potential. The applicability of the latter is demonstrated by comparison with an atomic description of nanoparticles with an internal face centered cubic structure.