Rayleigh limit and fragmentation of multiply charged Lennard-Jones clusters: Can charged clusters provide clues to investigate the stability of electrospray droplets?

The fragmentation of multiply charged clusters composed of $N≤1000$ Lennard-Jones particles augmented with electrostatic interactions is explored by classical Monte Carlo and molecular dynamics simulations with the stated goal of establishing possible analogies with electrospray droplets. Clusters with few charge carriers are shown to be only subject to particle ejection and their Rayleigh limit can be estimated by quantifying the loss of charged particles. On the contrary, uniformly charged clusters can both evaporate particles and undergo fission, making them better candidates to model electrospray droplets. Critical charges delimiting regions of instability of these clusters are defined from the calculation of lower order multipole moments and asymmetry parameters based on the knowledge of moments of inertia. The first discontinuity of quadrupole moments and asymmetry parameters is related to cluster elongation before twofold fission and the corresponding charge is deemed to be a good estimate of the Rayleigh limit. Octopole moments are negligible about this charge, their discontinuities arising at higher charges when threefold fissions are allowed. The size dependence of these critical charges is qualitatively predicted from Rayleigh’s formula and the expression of surface energy advocated in liquid drop models. Deviations below 15% are commonly achieved when comparing Rayleigh limits extracted from experimental data with theoretical predictions based on Monte Carlo simulations or liquid drop models for a set of eleven atomic and molecular liquid clusters. Although manifold fission of uniformly charged clusters is unlikely close to the Rayleigh limit, successive asymmetric fissions are found to occur in conjunction with other fragmentation mechanisms, including the expansion of ring-shaped structures, at charges more than twice as large as the Rayleigh limit.