We present the deformation pathway of critically charged glycol and water droplets from the onset of the Rayleigh instability and compare it to numerical results, obtained for perfectly conducting inviscid droplets. In this simple model presented here, the time evolution of the droplet shape is given by the velocity potential equation. The Laplace equation for the velocity potential is solved by expanding the potential onto harmonic functions. For the part of the pathway dominated by electrostatic pressure, the calculations reproduce the experimental data nicely, obtained for both, glycol and water microdroplets. We find that the droplet shape and in particular the tips, just before charge emission, are well fitted by a lemon shape. We stress that the tip is tangent to a cone of 39 degrees and thus significantly narrower than a Taylor cone.

We present a theoretical model to study the dynamics of metallic clusters embedded in a rare gas matrix. We describe the active electrons of the embedded cluster using time dependent density functional theory, while the surrounding matrix is described in terms of classical molecular dynamics of polarizable atoms. The coupling between the cluster and the rare gas atoms is deduced from the work of Gross and Spiegelmann [J. Chem. Phys. 108, 4148 (1998)] and reformulated explicitly in a simple and efficient density functional form. The electron rare gas interaction takes the form of an averaged dipole fluctuation term, which retains the van der Waals long range interaction, and a short range repulsive pseudopotential, which accounts for the Pauli repulsion of the electron by the rare gas atom. We applied our model to Na clusters embedded in Ar matrix. For the latter we developed an efficient local pseudopotential, which allows studying systems containing more than 10(3) Ar atoms. We show that large systems are indeed necessary to account properly for long range polarization of the matrix, that competes with the matrix confinement effect. We focus our study on Na(2), Na(4), and Na(8). For each system, we have determined the geometry of the most favorable trapping site by means of damped molecular dynamics. We present the effect of matrix embedding on the optical absorption spectrum. For Na(2), the trapping site can be unambiguously identified by comparison of the absorption spectrum with experiment. For Na(4) the spectrum of the embedded cluster is significantly different from the free cluster spectrum, while for Na(8) differences are less pronounced.