  When a cluster or nanodroplet bears charge, its structure and thermodynamics
are altered and, if the charge exceeds a certain limit, the system becomes
unstable with respect to fragmentation. Some of the key results in this area
were derived by Rayleigh in the nineteenth century using a continuum model of
liquid droplets. Here we revisit the topic using a simple particle-based
description, presenting a systematic case study of how charge affects the
physical properties of a Lennard-Jones cluster composed of 309 particles. We
find that the ability of the cluster to sustain charge depends on the number of
particles over which the charge is distributed---a parameter not included in
Rayleigh's analysis. Furthermore, the cluster may fragment before the charge is
strong enough to drive all charged particles to the surface. The charged
particles in stable clusters are therefore likely to reside in the cluster's
interior even without considering solvation effects.
