Effective pair potentials for spherical nanoparticles

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.

A generalized method for the inversion of cohesive energy curves from isotropic and anisotropic lattice expansions

“…The coarse-graining method provides the advantage of significantly reducing the number of interactions required and has been used to study gold nanoparticles 17 , spherical silica nanoparticles 19 , and generic spherical nanoparticles 18 . They either (i) model the entire cluster as a single coarse-grained entity or (ii) model the cluster as a rigid unit composed of atoms, interacting through general exponential or power-law potentials to describe the energetics of cluster-atom and atomic cluster-cluster pairs.…”

“…Molecular dynamics studies of cluster systems 17,18 generally use one of two approaches to perform bulk simulations. They either (i) model the entire cluster as a single coarse-grained entity or (ii) model the cluster as a rigid unit composed of atoms, interacting through general exponential or powerlaw potentials to describe the energetics of cluster-atom and atomic cluster-cluster pairs.…”

“…The coarse-graining method provides the advantage of significantly reducing the number of interactions required and has been used to study gold nanoparticles, 17 spherical silica nanoparticles, 19 and generic spherical nanoparticles. 18 These methods essentially replace the cluster with a single point mass interacting through an effective pair-potential and seem to be solely applicable to spherical particles. The all-atom methods have been used to investigate aggregation of fullerenes 20 and rheology of arbitrarily shaped nanoparticles 21 with interactions described by basic Lennard-Jones potentials.…”

Acute effect of trace component on capillary phase transition of n-alkanes

“…Thanks to advances in synthetic techniques it is now possible to produce colloidal spheres of different chemical compositions that are monodisperse in size and can be modified by attaching the desired modifying groups on the surface of the colloid sphere [10,11]. It has been demonstrated that properties of these colloidal spheres can be further modified by coating them with thin shells of a different chemical composition, as well as varying thickness in a controllable way [12,13], and this modification is useful in tuning interactions between colloidal spheres [14]- [16]. In short, it is now not difficult to prepare synthetic particles with desired inter-particle interactions.…”