Multiscale approach to the theory of nonisothermal homogeneous nucleation.

Molecular dynamics (MD) of the Lennard-Jones cluster in the environment of supersaturated vapor at fixed temperature and density is used for the investigation of nonisothermal nucleation. The results allow one to single out different processes occurring at different time scales, the Ornstein-Uhlenbeck fluctuations at the short time scale and a combination of slow diffusion and drift of the fluctuation packet that represents a cluster, at the long time scale. The multiscale approach is developed, in which a separate treatment of different time scales makes it possible to consider strongly correlated cluster size and temperature. This reduces the nonisothermal cluster evolution to a one-dimensional problem. The fluctuation packet drift velocity and diffusivity are calculated based on the cluster microscopic thermophysical parameters determined in this work from MD data for isothermal clusters. The proposed approach is consistent with the results of our MD simulation.

Thermodynamics and the structure of clusters in the dense Au vapor from molecular dynamics simulation.

Clusters of atoms in dense gold vapor are studied via atomistic simulation with the classical molecular dynamics method. For this purpose, we develop a new embedded atom model potential applicable to the lightest gold clusters and to the bulk gold. Simulation provides the equilibrium vapor phases at several subcritical temperatures, in which the clusters comprising up to 26 atoms are detected and analyzed. The cluster size distributions are found to match both the two-parameter model and the classical nucleation theory with the Tolman correction. For the gold liquid-vapor interface, the ratio of the Tolman length to the radius of a molecular cell in the liquid amounts to ∼0.16, almost exactly the value at which both models are identical. It is demonstrated that the lightest clusters have the chain-like structure, which is close to the freely jointed chain. Thus, the smallest clusters can be treated as the quasi-fractals with the fractal dimensionality close to two. Our analysis indicates that the cluster structural transition from the solid-like to chain-like geometry occurs in a wide temperature range around 2500 K.

Dust coupling parameter of radio-frequency-discharge complex plasma under microgravity conditions.

Oscillation of particles in a dust crystal formed in a low-pressure radio-frequency gas discharge under microgravity conditions is studied. Analysis of experimental data obtained in our previous study shows that the oscillations are highly isotropic and nearly homogeneous in the bulk of a dust crystal; oscillations of the neighboring particles are significantly correlated. We demonstrate that the standard deviation of the particle radius vector along with the local particle number density fully define the coupling parameter of the particle subsystem. The latter proves to be of the order of 100, which is two orders of magnitude lower than the coupling parameter estimated for the Brownian diffusion of particles with the gas temperature. This means significant kinetic overheating of particles under stationary conditions. A theoretical interpretation of the large amplitude of oscillation implies the increase of particle charge fluctuations in the dust crystal. The theoretical estimates are based on the ionization equation of state for the complex plasma and the equation for the plasma perturbation evolution. They are shown to match the results of experimental data processing. Estimated order of magnitude of the coupling parameter accounts for the existence of the solid-liquid phase transition observed for similar systems in experiments.

Density distribution of a dust cloud in three-dimensional complex plasmas.

We propose a method of determination of the dust particle spatial distribution in dust clouds that form in three-dimensional (3D) complex plasmas under microgravity conditions. The method utilizes the data obtained during the 3D scanning of a cloud, and it provides reasonably good accuracy. Based on this method, we investigate the particle density in a dust cloud realized in gas discharge plasma in the PK-3 Plus setup onboard the International Space Station. We find that the treated dust clouds are both anisotropic and inhomogeneous. One can isolate two regimes in which a stationary dust cloud can be observed. At low pressures, the particle density decreases monotonically with the increase of the distance from the discharge center; at higher pressures, the density distribution has a shallow minimum. Regardless of the regime, we detect a cusp of the distribution at the void boundary and a slowly varying density at larger distances (in the foot region). A theoretical interpretation of the obtained results is developed that leads to reasonable estimates of the densities for both the cusp and the foot. The modified ionization equation of state, which allows for violation of the local quasineutrality in the cusp region, predicts the spatial distributions of ion and electron densities to be measured in future experiments.

Enhancement of the droplet nucleation in a dense supersaturated Lennard-Jones vapor.

The vapor-liquid nucleation in a dense Lennard-Jones system is studied analytically and numerically. A solution of the nucleation kinetic equations, which includes the elementary processes of condensation/evaporation involving the lightest clusters, is obtained, and the nucleation rate is calculated. Based on the equation of state for the cluster vapor, the pre-exponential factor is obtained. The latter diverges as a spinodal is reached, which results in the nucleation enhancement. The work of critical cluster formation is calculated using the previously developed two-parameter model (TPM) of small clusters. A simple expression for the nucleation rate is deduced and it is shown that the work of cluster formation is reduced for a dense vapor. This results in the nucleation enhancement as well. To verify the TPM, a simulation is performed that mimics a steady-state nucleation experiments in the thermal diffusion cloud chamber. The nucleating vapor with and without a carrier gas is simulated using two different thermostats for the monomers and clusters. The TPM proves to match the simulation results of this work and of other studies.

Dust acoustic waves in three-dimensional complex plasmas with a similarity property.

Dust acoustic waves in the bulk of a dust cloud in complex plasma of low-pressure gas discharge under microgravity conditions are considered. The complex plasma is assumed to conform to the ionization equation of state (IEOS) developed in our previous study. This equation implies the ionization similarity of plasmas. We find singular points of IEOS that determine the behavior of the sound velocity in different regions of the cloud. The fluid approach is utilized to deduce the wave equation that includes the neutral drag term. It is shown that the sound velocity is fully defined by the particle compressibility, which is calculated on the basis of the used IEOS. The sound velocities and damping rates calculated for different three-dimensional complex plasmas both in ac and dc discharges demonstrate a good correlation with experimental data that are within the limits of validity of the theory. The theory provides interpretation for the observed independence of the sound velocity on the coordinate and for a weak dependence on the particle diameter and gas pressure. Predictive estimates are made for the ongoing PK-4 experiment.

The cluster model of a hot dense vapor.

We explore thermodynamic properties of a vapor in the range of state parameters where the contribution to thermodynamic functions from bound states of atoms (clusters) dominates over the interaction between the components of the vapor in free states. The clusters are assumed to be light and sufficiently "hot" for the number of bonds to be minimized. We use the technique of calculation of the cluster partition function for the cluster with a minimum number of interatomic bonds to calculate the caloric properties (heat capacity and velocity of sound) for an ideal mixture of the lightest clusters. The problem proves to be exactly solvable and resulting formulas are functions solely of the equilibrium constant of the dimer formation. These formulas ensure a satisfactory correlation with the reference data for the vapors of cesium, mercury, and argon up to moderate densities in both the sub- and supercritical regions. For cesium, we extend the model to the densities close to the critical one by inclusion of the clusters of arbitrary size. Knowledge of the cluster composition of the cesium vapor makes it possible to treat nonequilibrium phenomena such as nucleation of the supersaturated vapor, for which the effect of the cluster structural transition is likely to be significant.

Molecular dynamics study of nanobubbles in the equilibrium Lennard-Jones fluid.

We employ a model, in which the density fluctuations in a bulk liquid are represented as presence of the clusters of molecules with the lowered number of nearest neighbors (number of bonds). The nanobubble size distribution is calculated on the basis of a close analogy between the surface part of the work of formation for a cluster and for a nanobubble. The pre-exponential factor for this distribution is related to the fluid compressibility. Estimates made for different liquids show that it can be noticeably different from that adopted in the classical nucleation theory (CNT). Molecular dynamics (MD) simulation is performed for a liquid inside a macroscopic droplet of molecules interacting via the Lennard-Jones potential plus a long-range tail. The nanobubbles are identified by clusters of bond-deficient particles with the optimum number of bonds that provide the maximum nanobubble number density and maximum resolvable nanobubble equimolar size. The results of MD simulation are in qualitatively better agreement with proposed theory than with CNT.

Onset of cavity deformation upon subsonic motion of a projectile in a fluid complex plasma.

We study the deformation of a cavity around a large projectile moving with subsonic velocity in the cloud of small dust particles. To solve this problem, we employ the Navier-Stokes equation for a compressible fluid with due regard for friction between dust particles and atoms of neutral gas. The solution shows that due to friction, the pressure of a dust cloud at the surface of a cavity around the projectile can become negative, which entails the emergence of a considerable asymmetry of the cavity, i.e., the cavity deformation. Corresponding threshold velocity is calculated, which is found to decrease with increasing cavity size. Measurement of such velocity makes it possible to estimate the static pressure inside the dust cloud.

Nonviscous motion of a slow particle in a dust crystal under microgravity conditions.

Subsonic motion of a large particle moving through the bulk of a dust crystal formed by negatively charged small particles is investigated using the PK-3 Plus laboratory onboard the International Space Station. Tracing the particle trajectories shows that the large particle moves almost freely through the bulk of the plasma crystal, while dust particles move along characteristic α-shaped pathways near the large particle. In the hydrodynamic approximation, we develop a theory of nonviscous dust particle motion about a large particle and calculate particle trajectories. Good agreement with experiment validates our approach.

Thermal fluctuations of clusters with the long-range interaction.

Analysis of surface fluctuation spectra is performed for a large cluster of particles interacting via a sum of the short-range Lennard-Jones potential and long-range ±1/r potential, where the positive sign corresponds to the gravity, and negative corresponds to the electrostatic interaction. The spectral amplitudes of thermally driven capillary modes in a self-consistent field induced by cluster particles including the modes with no axial symmetry are derived in the approximation of small amplitudes. It is demonstrated that within used approximation, the surface tension is independent of the field strength. The low wave vector amplitudes are damped by attracting field that compresses the cluster and magnified by repulsing field leading to cluster fission. The fission threshold is found to be different from that found by Bohr and Wheeler and Frenkel due to the replacement of the ordinary surface tension by the bare one. Molecular dynamics study of a cluster with the long-range interaction in the vapor environment is performed using a novel integrator for a multiscale system. Simulation scheme implies rotation of the long-range components of forces acting on cluster particles thus vanishing an artificial torque. Simulation results justify theoretical conclusion of modes damping and independence of the surface tension of the field strength. Fission threshold evaluated from simulation data is in a good agreement with theory.

Equilibrium fluctuations of the Lennard-Jones cluster surface.

Spectra of the cluster surface equilibrium fluctuations are treated by decomposition into the bulk and net capillary ones. The bulk fluctuations without capillary ones are simulated by the surface of a cluster truncated by a sphere. The bulk fluctuation spectrum is shown to be generated primarily by the discontinuity in the spatial distribution of cluster internal particles. The net capillary fluctuation slice spectrum is obtained in molecular dynamics simulation by subtraction of the bulk fluctuation spectrum from the total one. This net spectrum is in the best agreement with a theoretical estimation if we assume the intrinsic surface tension to be independent of the wave number. The wave number cutoff is brought in balance with the intrinsic surface tension and excess surface area induced by the capillary fluctuations. It is shown that the ratio of the ordinary surface tension to the intrinsic one can be considered as a universal constant independent of the temperature and cluster size.

Spectra of the liquid cluster surface thermal fluctuations.

Classification of cluster particles is proposed that introduces three particle types: the internal particles, surface particles, and virtual chains of particles. Thermal fluctuations of a surface passing through the surface particles of a Lennard-Jones liquid cluster are studied using a molecular dynamics simulation. It is shown that for large clusters, the Fourier spectral amplitude of these fluctuations decays faster than 1q, where q is the wave number. The frequency Fourier spectrum shows an overdamped system behavior, which is the evidence for the absence of thermal capillary waves for clusters comprising less than 10(5) particles. The time-averaged cluster density profile is given by an error function with the width parameter diverging as the logarithm of the cluster size.