Rayleigh instabilities in multiply charged sodium clusters

The stability of multiply charged sodium clusters Na(q+)(n) (q< or =10) produced in collisions between neutral clusters and multiply charged ions A(z+) ( z = 1 to 28) is experimentally investigated. Multiply charged clusters are formed within a large range of temperatures and fissilities. They are identified by means of a high-resolution reflectron-type time-of-flight mass spectrometer (m/deltam approximately 14 000). The maximum fissility of stable clusters is obtained for z = 28 and is X approximately 0.85+/-0.07, slightly below the Rayleigh limit (X = 1). It is mainly limited by the initial cluster temperature (T approximately 100 K).     

Landau–Ginzburg theory for ‘star’-shaped droplets

ABSTRACT

Molecular simulations have shown that when a nano-drop comprising a single spherical central ion and a dielectric solvent is charged above a well-defined threshold, it acquires a stable star morphology. A linear continuum model of the ‘star’-shapes comprised electrostatic and surface energy is not sufficient to describe these shapes. We employ combined molecular dynamics, continuum electrostatics and macroscopic modelling in order to construct a unified free energy functional that describes the observed star-shaped droplets. We demonstrate that the Landau free energy coupled to the third-order Steinhardt invariant mimics the shapes of droplets detected in molecular simulations. Using the maximum likelihood technique we build a universal free energy functional that describes droplets for a range of Rayleigh fissility parameter. The analysis of the macroscopic free energy demonstrates the origin of the finite amplitude perturbations just above the Rayleigh limit. We argue that the presence of the finite amplitude perturbations precludes the use of the small parameter perturbation method for the analysis of the shapes above the Rayleigh limit of the corresponding spherical shape.     

Computer simulations of the fission process of charged nanometre droplets

The process of fission of charged liquid droplets is an important stage of multiply charged ion formation in the electrospray ionization (ESI) process. ESI is currently the most powerful ionization method in the mass spectrometry of large molecules such as biopolymers. Fission plays a crucial role in the ion formation essentially in the range of nanosized droplets, since it determines the charge states of product ions. Usually the Rayleigh equation is used to determine critical conditions, at which the fission process takes place. This equation gives the value of the critical radius of the charged droplet as a function of its charge and specific surface energy. The Rayleigh equation does not give us the opportunity to determine charges and sizes of the fission fragments. In the present work we propose a mathematical model that describes the fission process of the charged liquid droplet in an external electrostatic field. The model is based on the quasi-equilibrium assumption that the most probable shape of the droplet corresponds to the minimum of the free energy of the system. The change in the internal kinetic energy and dissipative losses for the viscous liquid are also taken into account in the model.     

Stability of charged metal clusters in the vicinity of an ionic charge

Stability of highly charged metal clusters in the electric field of an external ion is investigated with the classical liquid drop model. We study the optimum shape of the cluster which has a local minimum of the total energy, taking account of the effects of the surface charge polarization on the Coulomb energy and the cluster deformation on the surface energy. We find that the cluster deformation greatly affects the total energy of the system and that a cluster with a fissility larger than some critical value 0.7-0.8 can become unstable against deformation. We investigate the local competition between the Coulomb force and the surface tension at the cluster surface and show that the surface charge polarization which is induced by the external electric field significantly affects the shape of the cluster and its stability. Received 5 November 2002 / Received in final form 27 January 2003 Published online 11 March 2003 RID="a" ID="a"e-mail: hamada@konan-u.ac.jp     

The Deformations Energy and Barrier Height of Super Heavy Nuclei

The liquid drop energy and barrier height are calculated for the super heavy nuclei ²⁵⁰X and ²⁵¹X, resulting from heavy ion reactions, at finite temperatures. Our calculations are compared with both the idealized nuclei ²⁵⁰Es and ²⁵¹ Es (being isobars of ²⁵⁰X and ²⁵¹X) and that obtained by previous work. The main reason of the descrepancies between the present calculated values of the barrier height and the fissility parameters and those obtained by others are found to be mainly due to the important role of Coulomb energy over the surface energy for heavy nuclei. It has been found that the temperature has the effect lowering the fission barrier and shifting the saddle point to lower values.     

Persistent droplet motion in liquid-liquid dewetting

When a nonvolatile liquid film dewets from a partly compatible liquid substrate, the advancing dewetting front leaves behind droplets formed through a Rayleigh instability mechanism at its rim. We have found that these droplets continue to move in the direction of the dewetting front for extended periods (of order one day) with an initial droplet velocity varying linearly with the droplet size, and a displacement varying logarithmically with time. We attribute this persistent motion to a transient surface tension gradient on the substrate liquid surface trailing the dewetting front.     

Stability and fragmentation processes of highly charged sodium clusters

Highly charged sodium clusters produced in collisions between neutral clusters and multiply charged ions are formed within a large range of temperatures and fissilities, and identified by means of a high-resolution reflectron-type time-of-flight mass spectrometer ( m/m 14000). The limit of stability of these charged clusters is experimentally investigated, and the time-of-flight spectra are compared with theoretical spectra based on Monte-Carlo simulations. The results indicate that the maximum fissility (X) of stable clusters is approaching the Rayleigh limit (X = 1) for larger clusters sizes. It is mainly limited by the initial neutral cluster temperature ( T 100 K) and the energy transfer in the ionizing collision. In addition, the comparison between the measured and simulated spectra suggests for high cluster charges a multi-fragmentation process, in which most of charge is emitted, creating low charged residual cluster ions.     

General solvation motifs of a charged linear macroion in an aqueous droplet

ABSTRACT

We explore the solvation patterns of a charged rigid and semi-rigid linear macroion in an aqueous droplet. The solvation patterns are summarised in an empirical ‘phase diagram’ on the parameter space defined by the length of the macroion and its charge density. In the study, we employ molecular dynamics and atomistic modelling. The macroion is represented by a positively charged carbon nanotube. Linear macroion-solvent interactions in droplets are distinct from those of spherical ions because of the interplay among several factors such as the tendency of the solvent to form spherical droplets in order to minimise the surface energy, the constraint on the charge of a spherical droplet imposed by the Rayleigh limit, the solvation energy of the macroion and its length. The combination of all these factors may lead to a variety of solvent distributions along the rigid rod such as asymmetric solvation of the linear macroion, formation of spiky ‘star’-like distribution of solvent, partial wetting of the rod by a droplet. The study provides insight into the solvation of macroions in droplets with applications in electrosprayed macroions and atmospheric aerosols. We also propose a possible path of generating a sequence of nanoparticles of different shapes (spheres, multi-point stars) along a linear macromolecule by exploiting the various solvation patterns.     

On the possibility of corona-discharge ignition in the vicinity of a weakly charged drop executing nonlinear vibrations

An analytic expression for the electric-field strength in the vicinity of a charged drop of an electrically conducting liquid is obtained for the case where the initial shape of the drop executing nonlinear vibrations is specified by a virtual excitation of an arbitrary single mode of capillary vibrations. It turns out that, even at small charges (such that the Rayleigh parameter for the drop is equal to one-tenth of the critical value associated with stability against the intrinsic charge), the electric-field strength at the drop surface in the case of an initial excitation of one of high modes is sufficient for the ignition of a corona discharge.     

Nonlinear electrohydrodynamic phenomena and droplet generation in charged jets of conducting liquid

Phenomena occurring at the tip of a charged conducting jet are analyzed in detail using numerical methods developed for axially symmetric flows. Universal mechanisms (independent of the method for producing the jet) for droplet formation with different ratios of the Laplace and electrical pressures on the lateral surface are identified. An explanatory analysis is given for all of the nonlinear stages of the classical Rayleigh instability of a charged conducting drop, beginning with the formation of a jet at the surface of the drop and culminating in the generation of a developed jet of secondary droplets. Zh. Tekh. Fiz. 69, 1–9 (November 1999)     

On the initiation of a corona discharge near the surface of a nonlinearly oscillating liquid layer on the surface of a charged hailstone

An expression is derived for the electric field strength near a wet hailstone in an approximation quadratic in the oscillation amplitude of a charged liquid layer on its surface. It is found that the electric field strength in a small neighborhood of the capillary wave crests grows with the number of a mode governing the initial deformation of the equilibrium (spherical) shape of the liquid layer. Even if the charge is small (when the Rayleigh parameter of the hailstone equals one-hundredth of the value critical for stability against the self-charge), the electric field near the hailstone is high enough for initiating a corona discharge in its vicinity.     

The shrinking instability of toroidal liquid droplets in the Stokes flow regime

We analyze the stability and dynamics of toroidal liquid droplets. In addition to the Rayleigh instabilities akin to those of a cylindrical droplet there is a shrinking instability that is unique to the topology of the torus and dominates in the limit that the aspect ratio is near one (fat tori). We first find an analytic expression for the pressure distribution inside the droplet. We then determine the velocity field in the bulk fluid, in the Stokes flow regime, by solving the biharmonic equation for the stream function. The flow pattern in the external fluid is analyzed qualitatively by exploiting symmetries. This elucidates the detailed nature of the shrinking mode and the swelling of the cross-section following from incompressibility. Finally the shrinking rate of fat toroidal droplets is derived by energy conservation.     

Nonlinear capillary vibration of a charged bubble in an ideal dielectric liquid

The problem of nonlinear radial pulsations and surface vibrations of a charged bubble placed in an ideal incompressible dielectric liquid is asymptotically solved up to the second order of smallness by the method of many scales. It is shown that, in the case of nonlinear vibrations, resonance energy exchange may take place not only between surface modes but also between the radial mode and a surface mode. A new type of instability (other than Rayleigh instability against the self-charge), instability against the excess vapor pressure in the bubble, is discovered. The new type of instability shows up as energy transfer from the centrosymmetric pulsation mode to all initially excited surface vibration modes simultaneously.     

Nonlinear vibrations of a charged drop in a third-order approximation in the amplitude of multimode initial deformation

A solution to the problem of nonlinear surface vibration of a charged ideal liquid drop is found in a third-order approximation in initial multimode deformation of the equilibrium spherical shape by the method of many scales. It is shown that the spectrum of modes that are responsible for the shape of the drop at an arbitrary time instant depends considerably on the spectrum of modes governing the initial deformation of the drop. The latter spectrum also has an effect on nonlinear corrections to the vibration frequencies and, consequently, on a nonlinear correction to the critical Rayleigh parameter, which specifies the stability of the drop against self-charge.     

Bifurcation of the equilibrium droplet geometry in electric field

It is shown that neutral and charged liquid droplets placed in an external electric field admit two branches of stable ellipsoidal shapes (corresponding to energy minima) with hysteretic hard transitions between them.     

Multiply charged clusters

We review progress made in understanding Coulomb explosion of multiply charged atomic clusters. Their collision with highly charged atomic ions leads to clusters in charge states as high as z=10 with little vibrational excess energy; these systems approach the Rayleigh limit. Phase transitions become evident at higher excess energies. Numerous studies have been devoted to C^z+₆₀, like collisions with surfaces, multi-coincidence fragmentation analysis and gas-phase reactions. Stability and decay of highly charged micrometer-sized droplets and of metal di- and trianions have been monitored in ion traps. Excitation by femtosecond laser pulses allows to unravel properties of highly charged transient cluster ions. To cite this article: O. Echt et al., C. R. Physique 3 (2002) 353–364.     

Electrostatic instability of a heavily charged conducting liquid jet

The effect of electric charge on the jet surface on the capillary instability of the jet and its disintegration into drops is analyzed. A theoretical explanation is given for the electrostatic mechanism of instability development and jet disintegration that is akin to the mechanisms behind the instability of a heavily charged drop (Rayleigh instability) and flat uniformly charged liquid surface (Tonks-Frenkel instability) but differs qualitatively from the conventional capillary mechanism of instability and disintegration.     

The Coulomb instability of charged microdroplets: dynamics and scaling

The stability and disintegration dynamics of evaporating highly charged liquid droplets from ethylene glycol and glycerol is investigated by ultrafast microscopy and analyzed as a function of temperature and droplet size. In the moment of instability the droplets have deformed to elongated spindle like shapes from which pairs of opposite jets of highly charged liquid are emitted. The thickness of the jets and the shape of the deformed droplet are remarkably insensitive to the size and viscosity of the unstable droplet, while the speed of disintegration is found to scale with a power law for both variables, the exponent being close to 3/2.     

Millimeter-wave scattering from neutral and charged water droplets

We investigated 94 GHz millimeter-wave (MMW) scattering from neutral and charged water mist produced in the laboratory with an ultrasonic atomizer. Diffusion charging of the mist was accomplished with a negative ion generator (NIG). We observed increased forward- and backscattering of MMW from charged mist, as compared to MMW scattering from an uncharged mist. In order to interpret the experimental results, we developed a model based on classical electrodynamics theory of scattering from a dielectric sphere with diffusion-deposited mobile surface charge. In this approach, scattering and extinction cross-sections are calculated for a charged Rayleigh particle with effective dielectric constant consisting of the volume dielectric function of the neutral sphere and surface dielectric function due to the oscillation of the surface charge in the presence of applied electric field. For small droplets with radius smaller than 100 nm, this model predicts increased MMW scattering from charged mist, which is qualitatively consistent with the experimental observations. The objective of this work is to develop indirect remote sensing of radioactive gases via their charging action on atmospheric humid air.