We propose a method for quantifying charge-driven instabilities in clusters, based on equilibrium simulations under confinement at constant external pressure. This approach makes no assumptions about the mode of decay and allows different clusters to
be compared on an equal footing. A comprehensive survey of stability in model clusters of 309 Lennard-Jones particles augmented with Coulomb interactions is presented. We proceed to examine dynamic signatures of instability, finding that rate constants for ejection of charged particles increase smoothly as a function of total charge with no sudden changes. For clusters where many particles carry charge, ejection of individual charges competes with a fission process that leads to more symmetric division of the cluster into large fragments. The rate constants for fission depend much more sensitively on total charge than those for ejection of individual particles.
The surface composition of charged Lennard-Jones clusters A$_N^{n+}$, composed of N particles (55 leq N leq 1169) among which n are positively charged with charge q, thus having a net total charge Q = nq, is investigated by Monte Carlo with Parallel
Tempering simulations. At finite temperature, the surface sites of these charged clusters are found to be preferentially occupied by charged particles carrying large charges, due to Coulombic repulsions, but the full occupancy of surface sites is rarely achieved for clusters below the stability limit defined in this work. Large clusters (N = 1169) follow the same trends, with a smaller propensity for positive particles to occupy the cluster surface at non-zero temperature. We show that these charged clusters rather behave as electrical spherical conductors for the smaller sizes (N leq 147) but as spheres uniformly charged in their volume for the larger sizes (N = 1169).
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 Rayle
igh 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 Rayleighs 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 clusters interior even without considering solvation effects.
