Nucleation Of Argon Research Articles

Hypersonic nozzle for laser-spectroscopy studies at 17 K characterized by resonance-ionization-spectroscopy-based flow mapping

The in-gas-jet laser spectroscopy method relies on the production of uniform and low-temperature gas jets to fully resolve the atomic hyperfine structure and efficiently determine fundamental nuclear properties of short-lived isotopes from, e.g., the hardly accessible actinide and transactinide elements. In this article we present the studies devoted to designing, producing, and characterizing the flow properties of a convergent-divergent (de Laval) hypersonic nozzle with a superior performance for laser spectroscopy applications. A novel flow mapping technique, based on resonance ionization spectroscopy (RIS), has been employed to characterize the local flow properties of an argon gas jet formed by this nozzle, revealing a 61.5-mm long, highly collimated atomic jet at a uniform low temperature of 16.6(5) K [Mach 8.11(12)] that will enable laser spectroscopy experiments on heavy-exotic nuclei with an unprecedented spectral resolution and a high efficiency. These results have been compared with those obtained by planar laser induced fluorescence spectroscopy (PLIFS) studies and show a good agreement between the two techniques and a significant improvement in efficiency of the RIS mapping method with respect to PLIFS. The data are compared to state-of-the-art fluid-dynamics calculations that were carried out to obtain the nozzle contour and simulate its performance, as well as to explain the observation of a possible onset of argon nucleation.

Dependence of the condensate chemical potential on droplet size in thermodynamics of heterogeneous nucleation within the gradient DFT

A scheme of computation of the condensate chemical potential per molecule as a function of the droplet equimolecular radius for stable and critical droplets on uncharged or charged spherical particle of molecular size at heterogeneous nucleation has been considered. The scheme is based of the gradient density functional theory (DFT) with the van der Waals (vdW) and Carnahan–Starling (СS) models for the hard-sphere contribution to intermolecular interaction in liquid and vapor phases and interfaces. The particle serving as a condensation center in the case of heterogeneous nucleation has been characterized by an attractive short-range molecular potential and the long-range electric Coulomb potential. The dielectric permittivities of the droplet–vapor systems have been taken as known functions of the local condensate density and temperature for polar and nonpolar fluids. Detailed numerical calculations of the density profiles in critical and stable equilibrium droplets at water or argon nucleation in presence of the capillary, electrostatic and molecular forces have been performed. Dependence of the condensate chemical potential in the droplet on the droplet equimolecular radius has been analyzed in the case of homogeneous and heterogeneous nucleation and compared for water and argon within the vdW and СS models for the hard-sphere part of the equation of state.

Large scale molecular dynamics simulations of homogeneous nucleation

We present results from large-scale molecular dynamics (MD) simulations of homogeneous vapor-to-liquid nucleation. The simulations contain between 1 × 10(9) and 8 × 10(9) Lennard-Jones (LJ) atoms, covering up to 1.2 μs (56 × 10(6) time-steps). They cover a wide range of supersaturation ratios, S ≃ 1.55-10(4), and temperatures from kT = 0.3 to 1.0ε (where ε is the depth of the LJ potential, and k is the Boltzmann constant). We have resolved nucleation rates as low as 10(17) cm(-3) s(-1) (in the argon system), and critical cluster sizes as large as 100 atoms. Recent argon nucleation experiments probe nucleation rates in an overlapping range, making the first direct comparison between laboratory experiments and molecular dynamics simulations possible: We find very good agreement within the uncertainties, which are mainly due to the extrapolations of argon and LJ saturation curves to very low temperatures. The self-consistent, modified classical nucleation model of Girshick and Chiu [J. Chem. Phys. 93, 1273 (1990)] underestimates the nucleation rates by up to 9 orders of magnitudes at low temperatures, and at kT = 1.0ε it overestimates them by up to 10(5). The predictions from a semi-phenomenological model by Laaksonen et al. [Phys. Rev. E 49, 5517 (1994)] are much closer to our MD results, but still differ by factors of up to 10(4) in some cases. At low temperatures, the classical theory predicts critical clusters sizes, which match the simulation results (using the first nucleation theorem) quite well, while the semi-phenomenological model slightly underestimates them. At kT = 1.0ε, the critical sizes from both models are clearly too small. In our simulations the growth rates per encounter, which are often taken to be unity in nucleation models, lie in a range from 0.05 to 0.24. We devise a new, empirical nucleation model based on free energy functions derived from subcritical cluster abundances, and find that it performs well in estimating nucleation rates.

Vapor-liquid nucleation of argon: Exploration of various intermolecular potentials

The homogeneous vapor-liquid nucleation of argon has been explored at T=70 and 90 K using classical nucleation theory, semiempirical density functional theory, and Monte Carlo simulations using the aggregation-volume-bias algorithm with umbrella sampling and histogram-reweighting. In contrast with previous simulation studies, which employed only the Lennard-Jones intermolecular potential, the current studies were carried out using various pair potentials including the Lennard-Jones potential, a modified Buckingham exponential-six potential, the Barker-Fisher-Watts pair potential, and a recent ab initio potential developed using the method of effective diameters. It was found that the differences in the free energy of formation of the critical nuclei between the potentials cannot be explained solely in terms of the difference in macroscopic properties of the potentials, which gives a possible reason for the failure of classical nucleation theory.

Argon nucleation in a cryogenic supersonic nozzle

We have measured pressures p and temperatures T corresponding to the maximum nucleation rate of argon in a cryogenic supersonic nozzle apparatus where the estimated nucleation rates are J=10(17+/-1) cm(-3) s(-1). As T increases from 34 to 53 K, p increases from 0.47 to 8 kPa. Under these conditions, classical nucleation theory predicts nucleation rates of 11-13 orders of magnitude lower than the observed rates while mean field kinetic nucleation theory predicts the observed rates within 1 order of magnitude. The current data set appears consistent with the measurements of Iland et al. [J. Chem. Phys. 127, 154506 (2007)] in the cryogenic nucleation pulse chamber. Combining the two data sets suggests that classical nucleation theory fails because it overestimates both the critical cluster size and the excess internal energy of the critical clusters.

A cryogenic supersonic nozzle apparatus to study homogeneous nucleation of Ar and other simple molecules

We present a supersonic nozzle apparatus to study homogeneous nucleation of argon and other simple molecules. Experiments can be conducted with pure condensable vapor or with condensable vapor-carrier gas mixtures. The flow through the nozzle is continuous, and expansions typically start at temperatures T(0) in the range of 100<T(0)/K<120, and pressures p(0) in the range of 30<p(0)/kPa<36. The gas mixture is cooled using a tube and fin heat exchanger by evaporating liquid nitrogen on the tube side. The nozzle sidewalls are also cooled with liquid nitrogen to maintain them at a temperature approximately 20 K higher than the stagnation temperature. Static pressure measurements detect the onset of condensation, and the other properties of the flow are derived by integrating the diabatic flow equations. We present sample experimental results for pure argon where at the onset of condensation, temperatures T(on) range from 47.5<T(on)/K<49.5 and pressures p(on) range from 4.2<p(on)/kPa<4.9.

New concept of the nucleation process

Modern experiments on homogeneous nucleation of argon show a sharp disagreement with the theoretical values predicted by the classical theory. We suggest a new approach to this problem.

Argon nucleation: Bringing together theory, simulations, and experiment

We present an overview of the current status of experimental, theoretical, molecular dynamics (MD), and density functional theory (DFT) studies of argon vapor-to-liquid nucleation. Since the experimental temperature-supersaturation domain does not overlap with the corresponding MD and DFT domains, separate comparisons have been made: theory versus experiment and theory versus MD and DFT. Three general theoretical models are discussed: Classical nucleation theory (CNT), mean-field kinetic nucleation theory (MKNT), and extended modified liquid drop model-dynamical nucleation theory (EMLD-DNT). The comparisons are carried out for the area below the MKNT pseudospinodal line. The agreement for the nucleation rate between the nonclassical models and the MD simulations is very good--within 1-2 orders of magnitude--while the CNT deviates from simulations by about 3-5 orders of magnitude. Perfect agreement is demonstrated between DFT results and predictions of MKNT (within one order of magnitude), whereas CNT and EMLD-DNT show approximately the same deviation of about 3-5 orders of magnitude. At the same time the agreement between all theoretical models and experiment remains poor--4-8 orders of magnitude for MKNT, 12-14 orders for EMLD-DNT, and up to 26 orders for CNT. We discuss possible reasons for this discrepancy and the ways to carry out experiment and simulations within the common temperature-supersaturation domain in order to produce a unified picture of argon nucleation.

Argon nucleation in a cryogenic nucleation pulse chamber

Homogeneous nucleation of argon droplets has been measured with a newly designed cryogenic nucleation pulse chamber presented already in a previous paper [Fladerer and Strey, J. Chem. Phys. 124, 16 (2006)]. Here we present the first systematic nucleation onset data for argon measured in a temperature range from 42 to 58 K and for vapor pressures from 0.3 to 10 kPa. For these data we provide an analytical fit function. From the geometry of the optical detection system and the time of nucleation the experimental nucleation-rate range can be estimated. This allows a comparison of the data with the predictions of classical nucleation theory. We found 16-26 orders of magnitude difference between theory and experiment, and a too strong theoretical dependence of the nucleation rate on temperature. A comparison with the self-consistent theory of Girshick and Chiu [J. Chem. Phys. 93, 1273 (1990)] showed improved temperature dependence but still discrepancies of 11-17 orders of magnitude compared to experimental data. The thermodynamically consistent theory of Kashchiev [J. Chem. Phys. 118, 1837 (2003)] was found to agree rather well with experiment in respect to the temperature dependence and to predict rates about 5-7 orders of magnitude below the experimental ones. With the help of the Gibbs-Thomson equation we were able to evaluate the size of the critical nucleus to be 40-80 argon atoms.

Comparison between the classical theory predictions and molecular simulation results for heterogeneous nucleation of argon

We have performed Monte Carlo simulations of homogeneous and heterogeneous nucleations of Lennard-Jones argon clusters. The simulation results were interpreted using the major concept posing a difference between the homogeneous and heterogeneous classical nucleation theories-the contact parameter. Our results show that the multiplication concept of the classical heterogeneous nucleation theory describes the cluster-substrate interaction surprisingly well even for small molecular clusters. However, in the case of argon nucleating on a rigid monolayer of fcc(111) substrate at T=60 K, the argon-substrate atom interaction being approximately one-third as strong as the argon-argon interaction, the use of the classical theory concept results in an underestimation of the heterogeneous nucleation rate by two to three orders of magnitude even for large clusters. The main contribution to this discrepancy is induced by the failure of the classical theory of homogeneous nucleation to predict the energy involved in bringing one molecule from the vapor to the cluster for clusters containing less than approximately 15 molecules.

Molecular-dynamics simulation of argon nucleation from supersaturated vapor in the NVE ensemble

The possibility to conduct simulations of homogeneous nucleation of argon from a supersaturated vapor phase using a microcanonical or NVE ensemble is evaluated (NVE: number of particles N, volume V, and energy E are constant). In order to initiate a phase separation kinetic energy is removed from the system in one step which transfers the system into a supersaturated state. After this temperature jump the simulation is continued in a NVE ensemble. The simulations are performed for different initial-state points and different temperature jumps. The cluster formation and growth over the course of the adiabatic simulations are analyzed. The progression of the temperature being related to the cluster size in NVE systems is traced. Also the influence of the size of the simulation system is investigated. For a certain range of low supersaturation a dynamic coexistence between two states has been found. Furthermore, the obtained nucleation rates are correlated with two simple functions. By applying the nucleation theorems to these functions the size and excess energy of the critical cluster are estimated. The results are consistent with other theoretical data and experimental data available in the literature.

Crossover model for the work of critical cluster formation in nucleation theory

We propose a relation for the work of critical cluster formation in nucleation theory W for the systems with long-range interparticle interactions. The method of bridge functions is used to combine the system behavior at sufficiently small quenches, adequately predicted by the classical nucleation theory, with nonclassical effects at deep quenches in the vicinity of the thermodynamic spinodal, described within the framework of the field theoretical approach with an appropriate Ginzburg-Landau functional. The crossover between the two types of nucleation behavior takes place in the vicinity of the kinetic spinodal where the lifetime of a metastable state is of the order of the relaxation time to local equilibrium. We argue that the kinetic spinodal corresponds to the minimum of the excess number of molecules in the critical cluster. This conjecture leads to the form of W containing no adjustable parameters. The barrier scaling function Gamma = W/W(cl), where W(cl) is the classical nucleation barrier, depends parametrically on temperature through the dimensionless combination of material properties. The results for argon nucleation are presented.

Homogeneous nucleation of argon in an unsteady hypersonic flow field

The vapor nucleation of argon was investigated in shock tube expansions starting from room temperature. The cooling from the superheated initial state to nucleation onset was attained in unsteady flow fields at high Mach numbers M=5. Thermodynamic states for homogeneous nucleation were observed between 30 and 180 Torr at corresponding temperatures in the range of 50–70 K. The high starting temperatures do not affect the nucleation onset states compared to previous experiments on the subject, where the expansions started from much lower temperatures. The slight differences in the onset states to previous experiments employing cryogenic shock and Ludwieg tubes may be attributed to the higher cooling rates and to nonisentropic expansion effects.

Formation of argon clusters by homogeneous nucleation in supersonic shock tube flow

The formation of argon clusters by homogeneous nucleation of pure argon diluted in helium was investigated in the supersonic outflow of a shock tube, where the clusters were detected by laser light scattering from the particles in supersaturated states. The thermodynamic states for the onset of homogeneous nucleation varied between 48 and 85 K with corresponding argon partial pressures in the range 2–850 Torr. Values of adiabatic supercooling with respect to the argon phase equilibrium ranged between 3 and 10 K. The experiments are in agreement with previous investigations in subsonic shock tube and supersonic Ludwieg tube expansions but disagree with previous investigations in steady supersonic nozzle expansions. It is possible to explain qualitatively the observed differences in argon nucleation behavior on the basis of a thermodynamic and kinetic concept independent of the basic assumptions of existing nucleation theories.

Quantum Monte Carlo study of the thermodynamic properties of argon clusters: The homogeneous nucleation of argon in argon vapor and ‘‘magic number’’ distributions in argon vapor

The thermodynamic properties of clusters of argon atoms are studied by a combination of classical and quantum mechanical Monte Carlo methods. The argon atoms are represented by Lennard-Jones interactions and internal energies, free energies, and entropies are calculated as a function of temperature and cluster size. For the argon system quantum effects and anharmonicity corrections are found to be simultaneously important for a temperature range from 15 to 20 K. By examining local minima in the free energy of formation of argon clusters as a function of cluster size, magic numbers in the Boltzmann mass distribution are observed at n=7, 13, and 19 under some conditions of temperature and pressure. In some cases magic numbers are predicted in the quantum and not in the classical calculation. The entropy changes associated with cluster growth are found to be insensitive to cluster size. Quantum corrections are calculated to nucleation rates and found to be very important at low temperatures.

Argon clusters and homogeneous nucleation: Comparison of experiment and theory

Free energies for the formation of atomic microclusters of Lennard-Jones argon are computed. All interactions are considered in the calculation of the force-constant matrix for the vibrational analysis. Introduction of these results into the early kinetic formulation of the classical theory of nucleation yielded nucleation rates for states of realistic isentropic expansions. The calculations are compared with recent Rayleigh light scattering experiments on homogeneous nucleation of argon in helium in steady supersonic nozzle flow. A steep rise of calculated nucleation rate at certain states in the expansion coincides with the observed location of the onset of condensation and remarkable agreement of experiment and theory is found. Further comparisons of the experiments with predictions obtained with the classical theory are not successful. As expected in an extreme situation of small clusters, no agreement of the liquid drop model with experiment can be obtained in a wide range of assumed material properties.

Homogeneous nucleation of argon carried in helium in supersonic nozzle flow

Homogeneous nucleation of argon carried in helium in supersonic nozzle flow

Homogeneous nucleation of argon carried in helium II in supersonic nozzle flow : By B.J.C. Wu, P.P. Wegener and G.D. Stein; Department of Engineering and Applied Science, Yale University, New Haven, CT 06520, U.S.A.

Homogeneous nucleation of argon carried in helium II in supersonic nozzle flow : By B.J.C. Wu, P.P. Wegener and G.D. Stein; Department of Engineering and Applied Science, Yale University, New Haven, CT 06520, U.S.A.

Statistical mechanics of homogeneous nucleation in vapor

Statistical mechanics of homogeneous nucleation in vapor