Abstract
An analytical solution describing the electrostatic interaction between particles with inhomogeneous surface charge distributions has been developed. For particles, each carrying a single charge, the solution equates to the presence of a point charge residing on the surface, which makes it particularly suitable for investigating the Coulomb fission of doubly charged clusters close to the Rayleigh instability limit. For a series of six separate molecular dication clusters, center-of-mass kinetic energy releases have been extracted from experimental measurements of their kinetic energy spectra following Coulomb fission. These data have been compared with Coulomb energy barriers calculated from the electrostatic interaction energies given by this new solution. For systems with high dielectric permittivity, results from the point charge model provide a viable alternative to kinetic energy releases calculated on the assumption of a uniform distribution of surface charge. The equivalent physical picture for the clusters would be that of a trapped proton. For interacting particles with low dielectric permittivity, a uniform distribution of charge provides better agreement with the experimental results.
Highlights
Whether the assumption of a uniform positive or negative charge distribution over the surface of a particle is an appropriate description is open to speculation
Point charges on each of the particles have been described by a δ -function of angular variables, and electrostatic energy barriers have been calculated over the range of particle-particle distances, 10−2 ≤ L ≤ 103 nm, regions where the effects of induced interactions are found to be at their greatest
When compared with results for a uniform distribution of charge, the calculations reported in Table II show that the exact location of the point charge has a marked influence on the value of any Coulomb barrier in the electrostatic energy
Summary
Whether the assumption of a uniform positive or negative charge distribution over the surface of a particle is an appropriate description is open to speculation. The anomalous behaviour of (H2O)22+1 has been interpreted as H3O+ localized at the centre of a water cluster and a similar picture of a localized central charge has been proposed to explain optical spectra recorded from xenon cluster ions, Xe+n .30. For these examples, which are essentially spherical clusters with point charges at their centres, Gauss’s law states that such a configuration generates a potential equivalent to that of the charge being uniformly distributed across the surface. Values predicted for the Coulomb repulsion energy between separating fragments are compare with accurate kinetic energy release measurements extracted from experimental data
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