Singular electrostatic energy of nanoparticle clusters

TL;DR

This paper develops a theoretical framework to calculate the electrostatic energy of nanoparticle clusters considering charge quantization effects, revealing a logarithmic dependence on particle separation and validating it with numerical comparisons.

Contribution

It introduces a general law for electrostatic energy in nanoparticle clusters accounting for charge quantization and contact topology, advancing understanding of cluster electrostatics.

Findings

Electrostatic energy exhibits a strong logarithmic dependence on separation h.

The theory accurately predicts energies for tetrahedral clusters.

Validation through numerical calculations confirms the theoretical model.

Abstract

The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation $h$ has a strong logarithmic dependence on $h$. We give a general law for the strength of this logarithmic correction in terms of a) the energy at contact ignoring the charge quantization effects and b) an adjacency matrix specifying which spheres of the cluster are in contact and which is charged. We verify the theory by comparing the predicted energies for a tetrahedral cluster with an explicit numerical calculation.