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.     

Homogeneous nucleation and growth in supersaturated zinc vapor investigated by molecular dynamics simulation

Homogeneous nucleation and growth of zinc from supersaturated vapor are investigated by nonequilibrium molecular dynamics simulations in the temperature range from 400 to 800 K and for a supersaturation ranging from log S=2 to 11. Argon is added to the vapor phase as carrier gas to remove the latent heat from the forming zinc clusters. A new parametrization of the embedded atom method for zinc is employed for the interaction potential model. The simulation data are analyzed with respect to the nucleation rates and the critical cluster sizes by two different methods, namely, the threshold method of Yasuoka and Matsumoto [J. Chem. Phys. 109, 8451 (1998)] and the mean first passage time method for nucleation by Wedekind et al. [J. Chem. Phys. 126, 134103 (2007)]. The nucleation rates obtained by these methods differ approximately by one order of magnitude. Classical nucleation theory fails to describe the simulation data as well as the experimental data. The size of the critical cluster obtained by the mean first passage time method is significantly larger than that obtained from the nucleation theorem.     

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.     

Homogeneous nucleation of droplets from supersaturated vapor in a closed system

Kinetic equations describing homogeneous nucleation kinetics within standard model are solved numerically under the condition of a constant number of molecules in the considered system. It has consequences to decrease the supersaturation of the supersaturated vapor during the process of the formation of small droplets of a new phase. The decrease of supersaturation occurs in a short time and reaches some value which remains unchanged for a relatively long time (quasistationary regime), especially at lower initial supersaturations. This time interval decreases with increasing value of the initial supersaturation. In the quasistationary regime the nucleation rate reaches its stationary value. At higher initial supersaturation, the rate of formation of nuclei goes to some maximum value corresponding to the stationary nucleation rate and then decreases with time due to the decrease of supersaturation.     

Postnucleation droplet growth in supersaturated gas with arbitrary vapor concentration

This work concerns the reexamination and extension of the current theory of phase transition dynamics for liquid droplets growing on soluble aerosols from a supersaturated gas mixture for the general case of arbitrary value of vapor concentration. We found that the inconsistency in the common treatment of the vapor diffusion, due to an implicit assumption of the constancy of gas density in the vicinity of a droplet by neglecting its dependency on temperature and vapor concentration, leads to the obvious discrepancy in the Maxwell expression for the growth rate regarding droplets of near critical size. Restoring the correct treatment of the vapor diffusion in terms of the mass concentration of water vapor and taking into the consideration variations of gas density in the vicinity of a droplet in compliance with the equation of state of moist air, we have obtained a new expression for the droplet growth rate valid for an arbitrary value of vapor concentration. The limitations imposed by the molecular kinetic fluxes to postnucleation diffusional growth of small droplets with a large Knudsen number are also reevaluated to include previously neglected physical effects. In particular, the essential contribution of the vapor molecular energy flux into the total kinetic molecular heat flux as well as the temperature variations of mean thermal velocities of air and vapor molecules in the vicinity of the droplet interface have been taken into consideration. Surprisingly significant differences have been found in new expressions derived for the droplet growth rate and droplet temperature, even in the limit of small vapor concentration, if comparing with commonly used results. These findings could help with better interpretation of experimental measurements to infer more reliable data for the mass and thermal accommodations coefficients.     

A study of nucleation in supersaturated ibuprofen vapor in a flow diffusion chamber

Isothermal nucleation of supersaturated ibuprofen racemate vapor has been experimentally studied in a flow diffusion chamber at 293.3 and 301.2 K. Nucleation rates have been measured in the range of 10⁴?10⁴ cm^?3 s^?1 as functions of supersaturation. According to the first nucleation theorem, the numbers of molecules in critical nuclei have been found and used to determine the nucleation rate and supersaturation values as depending on the sizes of critical nuclei. The comparison of the experimental data with theoretical predictions has shown that the nucleation rates measured as functions of the numbers of molecules in critical nuclei are higher than the rates predicted by the classical theory by six to seven decimal orders of magnitude but, within one order of magnitude, coincide with the rates predicted by a theory previously proposed in a work by one of the authors, in which nucleation clusters were considered to be microscopic objects.     

Study of nonsteady diffusional growth of a droplet in a supersaturated vapor: treatment of the moving boundary and material balance

A new mathematical treatment of the problem of droplet growth via diffusion of molecules from a supersaturated vapor is presented. The theory is based on a semiquantitative analysis with good physical arguments and is justified by its reasonable predictions. For example it recovers the time honored growth law in which, to a high degree of approximation, the droplet radius increases with the square root of time. Also, to a high degree of approximation, it preserves material balance such that, at any time, the number of molecules lost from the vapor equals the number in the droplet. Estimates of the remaining approximational error are provided. On another issue, we show that, in contrast, the conventional treatment of droplet growth does not maintain material balance. This issue could be especially important for the nucleation of another droplet in the vicinity of the growing droplet where the rate of nucleation depends exponentially on supersaturation. Suggestions for further improvement of rigor are discussed.     

Role of nearest-neighbor drops in the kinetics of homogeneous nucleation in a supersaturated vapor

A theory of simultaneous nucleation and drop growth in a supersaturated vapor is developed. The theory makes use of the concept of "nearest-neighbor" drops. The effect of vapor heterogeneity caused by vapor diffusion to a growing drop, formed previously, is accounted for by considering the nucleation of the nearest-neighbor drop. The diffusional boundary value problem is solved through the application of a recent theory that maintains material balance between the vapor and the drop, even though the drop boundary is a moving one. This is fundamental to the use of the proper time and space dependent vapor supersaturation in the application of nucleation theory. The conditions are formulated under which the mean distance to the nearest-neighbor drop and the mean time to its appearance can be determined reliably. Under these conditions, the mean time provides an estimate of the duration of the nucleation stage, while the mean distance provides an estimate of the number of drops formed per unit volume during the nucleation stage. It turns out, surprisingly, that these estimates agree fairly well with the predictions of the simpler and more standard approach based on the approximation that the density of the vapor phase remains uniform during the nucleation stage. Thus, as a practical matter, in many situations, the use of the simpler and less rigorous method is justified by the predictions of the more rigorous, but more complicated theory.     

Accounting for fluctuations in cluster parameters upon the description of nucleation in supersaturated vapor

A theory is proposed for stationary homogeneous nucleation in supersaturated vapor in which a modified expression for the rate of cluster evaporation was used to calculate the equilibrium distribution over the nucleus sizes and the rates of their formation. This rate was determined by the extrapolation to the region of small sizes of the corresponding expression for the macroscopic droplet derived according to thermodynamic notions that take fluctuations into account. Modified dependences of the size of critical nucleus and the rate of nucleation on the supersaturation and the temperature are determined and compared with the data of the classical theory of nucleation and experimental results.     

Melting dynamics of superheated argon: nucleation and growth

We investigate the microscopic melting process of a superheated argon solid using molecular dynamics simulations. We characterize the melting dynamics by following the temperature and time evolutions of liquid atoms and demonstrate the formation of a critical liquid nucleus via fluctuations and subsequent growth. The critical liquid nucleus size (about 120 atoms) obtained from our direct simulations is in accord with the prediction of the classical nucleation theory. The dynamic nucleation and growth of liquid also agree with the Johnson-Mehl-Avrami law, and the growth exponent n approximately 3 at the early stage followed by a substantial increase in n thereafter.     

Homogeneous nucleation and growth of melt in copper

Molecular dynamics simulations are conducted to investigate homogeneous nucleation and growth of melt in copper described by an embedded-atom method (EAM) potential. The accuracy of this EAM potential for melting is validated by the equilibrium melting point obtained with the solid-liquid coexistence method and the superheating-supercooling hysteresis method. We characterize the atomistic melting process by following the temperature and time evolution of liquid atoms. The nucleation behavior at the extreme superheating is analyzed with the mean-first-passage-time (MFPT) method, which yields the critical size, steady-state nucleation rate, and the Zeldovich factor. The value of the steady-state nucleation rate obtained from the MFPT method is consistent with the result from direct simulations. The size distribution of subcritical nuclei appears to follow a power law similar to three-dimensional percolation. The diffuse solid-liquid interface has a sigmoidal profile with a 10%-90% width of about 12 A near the critical nucleation. The critical size obtained from our simulations is in reasonable agreement with the prediction of classical nucleation theory if the finite interface width is considered. The growth of melt is coupled with nucleation and can be described qualitatively with the Johnson-Meh-Avrami law. System sizes of 10(3)-10(6) atoms are explored, and negligible size dependence is found for bulk properties and for the critical nucleation.     

Homogeneous nucleation of particles from the vapor phase in thermal plasma synthesis

Particle nucleation and growth are simulated for iron vapor in a thermal plasma reactor with an assumed one-dimensional flow field and decoupled chemistry and aerosol dynamics. Including both evaporation and coagulation terms in the set of cluster-balance rate equations, a sharply defined homogeneous nucleation event is calculated. Following nucleation the vapor phase is rapidly depleted by condensation, and thereafter particle growth occurs purely by Browntan coagulation. The size and number of nucleated particles are found to be affected strongly by the cooling rate and by the initial monomer concentration. An explanation is presented in terms of the response time of the aerosol to changing thermodynamic conditions.This work appears in abbreviated from in the proceedings of the International Symposium on Combustion and Plasma Synthesis of High Temperature Materials, San Francisco, Oct. 24–26, 1988, to be published asCombustion and Plasma Synthesis of Hig Temperature Materials, Z. A. Munir and J. B. Holt (eds.), VCH, New York (in press).     

Surface tension of water droplets upon homogeneous droplet nucleation in water vapor

A method has been proposed for determining interfacial free energy from the data of molecular dynamics simulation. The method is based on the thermodynamic integration procedure and is distinguished by applicability to both planar interfaces and those characterized by a high curvature. The workability of the method has been demonstrated by the example of determining the surface tension for critical nuclei of water droplets upon condensation of water vapor. The calculation has been performed at temperatures of 273–373 K and a pressure of 1 atm, thus making it possible to determine the temperature dependence of the surface tension for water droplets and compare the results obtained with experimental data and the simulation results for a “planar” vapor–liquid interface.     

Statistico-probabilistic approach to taking account of the vapor depletion in the kinetics of homogeneous nucleation: a free-molecular regime of droplet growth

We propose a statistico-probabilistic approach to investigate the process of homogeneous formation of droplets in a vapor phase in the presence of an already formed and growing droplet under free-molecular regime of droplet growth after the instantaneous creation of initial vapor supersaturation. We find the probability density for the formation of a new, nearest (neighbor) droplet in the vicinity of an initially formed droplet. The mean distance between two neighboring droplets is also determined, as well as the average time lag for the formation of the nearest (neighbor) droplet; the latter quantity serves as an estimate for the duration of the nucleation stage. An estimate for the average number of droplets forming in unit volume by the end of the nucleation stage is also given. Our results are compared with the predictions of classical nucleation theory which assumes the density uniformity of a metastable phase. Where the proposed approach is applicable, there is observed qualitative agreement between the results. The underlying cause of this agreement is analyzed and the limits of applicability of the uniformity approximation are clarified.     

Experimental study of homogeneous nucleation from the bismuth supersaturated vapor: evaluation of the surface tension of critical nucleus

The homogeneous nucleation of bismuth supersaturated vapor is studied in a laminar flow quartz tube nucleation chamber. The concentration, size, and morphology of outcoming aerosol particles are analyzed by a transmission electron microscope (TEM) and an automatic diffusion battery (ADB). The wall deposit morphology is studied by scanning electron microscopy. The rate of wall deposition is measured by the light absorption technique and direct weighting of the wall deposits. The confines of the nucleation region are determined in the "supersaturation cut-off" measurements inserting a metal grid into the nucleation zone and monitoring the outlet aerosol concentration response. Using the above experimental techniques, the nucleation rate, supersaturation, and nucleation temperature are measured. The surface tension of the critical nucleus and the radius of the surface of tension are determined from the measured nucleation parameters. To this aim an analytical formula for the nucleation rate is used, derived from author's previous papers based on the Gibbs formula for the work of formation of critical nucleus and the translation-rotation correction. A more accurate approach is also applied to determine the surface tension of critical drop from the experimentally measured bismuth mass flow, temperature profiles, ADB, and TEM data solving an inverse problem by numerical simulation. The simulation of the vapor to particles conversion is carried out in the framework of the explicit finite difference scheme accounting the nucleation, vapor to particles and vapor to wall deposition, and particle to wall deposition, coagulation. The nucleation rate is determined from simulations to be in the range of 10(9)-10(11) cm(-3) s(-1) for the supersaturation of Bi(2) dimers being 10(17)-10(7) and the nucleation temperature 330-570 K, respectively. The surface tension σ(S) of the bismuth critical nucleus is found to be in the range of 455-487 mN/m for the radius of the surface of tension from 0.36 to 0.48 nm. The function σ(S) changes weakly with the radius of critical nucleus. The value of σ(S) is from 14% to 24% higher than the surface tension of a flat surface.     

Homogeneous nucleation rates of higher n-alcohols measured in a laminar flow diffusion chamber

Nucleation rate isotherms of n-butanol, n-pentanol, n-hexanol, n-heptanol, and n-octanol were measured in a laminar flow diffusion chamber using helium as carrier gas. The measurements were made at 250-310 K, corresponding to reduced temperatures of 0.43-0.50, and at atmospheric pressure. Experimental nucleation rate range was from 10(3) to 10(7) cm(-3) s(-1). The expression and accuracy of thermodynamic parameters, in particular equilibrium vapor pressure, were found to have a significant effect on calculated nucleation rates. The results were compared to the classical nucleation theory (CNT), the self-consistency corrected classical theory (SCC) and the Hale's scaled model of the CNT. The average ratio between the experimental and theoretical nucleation rates for all alcohols used was 1.5x10(3) when the CNT was used, and 0.2x10(-1) when the SCC was used and 0.7x10(-1) when the Hale's scaled theory was used. The average values represent all the alcohols used at the same reduced temperatures. The average ratio was about the same throughout the temperature range, although J(exp)/J(the) calculated with the Hale's scaled theory increased slightly with increasing temperature. The saturation ratio dependency was predicted closest to experiment with the classical nucleation theory. The nucleation rates were compared to those found in the literature. The measurements were in reasonable agreement with each other. The molecular content of critical alcohol clusters was between 35 and 80 molecules. At a fixed reduced temperature, the number of molecules in a critical cluster decreased as a function of alcohol carbon chain length. The number of molecules in critical clusters was compared to those predicted by the Kelvin equation. The theory predicted the critical cluster sizes well.