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.     

An algorithm for semi-empirical design of nucleation rate surface

During the last half of century, Classical Nucleation Theory (CNT) has been developed and there have been advances in the molecular theory of nucleation. Most of these efforts have been directed towards small molecule system modeling using intermolecular potentials. Summarizing the nucleation theory, it can be concluded that the current theory is far from complete. Agreement is generally not obtained between experimental and theoretical results. In practical applications, parametric theories can be used for the systems of interest. However, experimental measurements are still the best source of information on nucleation. Experiments are labor intensive and costly, and thus, it is useful to extend the value of limited experimental measurements to a broader range of nucleation conditions. The available nucleation parameters represent only small regions of possible nucleation conditions over the range from the critical temperature to absolute zero. Thus, it is useful to develop better tools to use the data to estimate semi-empirical nucleation rate surfaces. Following our published approach, the nucleation rate surface for any system can be constructed over its phase diagram. This concept involves using the phase equilibrium diagram to establish lines of zero nucleation rates. Nucleation rate surfaces arise from equilibrium lines and their extensions that are representing unstable equilibria. Only limited experimental data is available for use in normalizing the slopes of the linearized nucleation rate surfaces. The nucleation rate surface is described in terms of steady-state nucleation rates. To design the surfaces of nucleation rates, several assumptions are presented. In the present study, an algorithm for the semi-empirical design of nucleation rate surfaces is introduced. The topology of the nucleation rate surface for a unary system using the example of water vapor nucleation is created semi-empirically. The nucleation of two concurrent (stable and unstable) phase states of critical embryos is considered in the context of multi-surface nucleation rates. Only one phase transition (melting) in the condensed state of water is considered for simplicity. The nucleation rate surface is constructed numerically using the available experimental results for vapor nucleation and phase diagram for water. The nucleation rate for water vapor is developed for the full temperature interval, i.e. from critical point to absolute zero. The results help to suggest a new direction for experimental nucleation research.     

Kinetics of supersaturated vapor nucleation on molecular condensation nuclei

The kinetics of nucleation is calculated for a supersaturated vapor containing molecular condensation nuclei, that is, foreign molecules able to induce the formation of viable nuclei of a condensed phase by themselves. In contrast to the previous calculation, the possibility of the escape of molecular condensation nuclei from very small clusters containing a few condensed vapor molecules is taken into account. More exact equations are derived for the rate of steady-state nucleation and the concentration of aerosol particles in a quasisteady-state regime of nucleation. The calculation demonstrates that, at a high probability of the escape of a molecular condensation nucleus, the predominating mechanism of cluster formation is the attachment of a molecular condensation nucleus to a cluster formed from vapor molecules rather than their condensation on the nucleus. At the same time, allowances for the possible escape of molecular condensation nuclei from clusters slightly affect the rate of nucleation and the concentration of aerosol particles being formed.     

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.     

Free-energy landscape of nucleation with an intermediate metastable phase studied using capillarity approximation

Capillarity approximation is used to study the free-energy landscape of nucleation when an intermediate metastable phase exists. The critical nucleus that corresponds to the saddle point of the free-energy landscape as well as the whole free-energy landscape can be studied using this capillarity approximation, and various scenarios of nucleation and growth can be elucidated. In this study, we consider a model in which a stable solid phase nucleates within a metastable vapor phase when an intermediate metastable liquid phase exists. We predict that a composite critical nucleus that consists of a solid core and a liquid wetting layer as well as pure liquid and pure solid critical nuclei can exist depending not only on the supersaturation of the liquid phase relative to that of the vapor phase but also on the wetting behavior of the liquid surrounding the solid. The existence of liquid critical nucleus indicates that the phase transformation from metastable vapor to stable solid occurs via the intermediate metastable liquid phase, which is quite similar to the scenario of nucleation observed in proteins and colloidal systems. By studying the minimum-free-energy path on the free-energy landscape, we can study the evolution of the composition of solid and liquid within nuclei which is not limited to the critical nucleus.     

氩蒸气在球形固体颗粒上异质核化的分子动力学模拟

异质核化在大气中广泛存在, 但是其微观核化机理鲜为人知, 本文应用分子动力学方法模拟过热氩蒸气在纳米球形固体颗粒物上异质核化的动态特性, 讨论不同的冷却率对核化过程中系综温度、团簇分布、团簇大小以及核化速率的影响. 结果显示, 系综内蒸气的核化温度随着冷却率的增加而降低, 预先存在的球形固体颗粒在团簇的形成阶段起着重要的作用, 而且存在一个临界冷却率1.80×10^-9J·s^-1. 在该冷却率下, 在异质核化系综内均质核化出现, 并与异质核化共存, 但是异质核化在整个核化过程中仍然占主导地位.     

A thermodynamically consistent kinetic framework for binary nucleation

The traditional theory for binary homogeneous nucleation follows the classical derivation of the nucleation rate in the supposition of a hypothetical constrained-equilibrium distribution in the calculation of the cluster evaporation rate. This model enables calculation of the nucleation rate, but requires evaluation of the cluster distribution and cluster properties for an unstable equilibrium with supersaturated vapor. An alternate derivation of the classical homomolecular nucleation rate eliminated the need for this nonphysical approximation by calculating the evaporative flux at full thermodynamic equilibrium. The present paper develops that approach for binary nucleation; the framework is readily extended to ternary nucleation. In this analysis, the evaporative flux is evaluated by applying mass balance at full thermodynamic equilibrium of the system under study. This approach eliminates both the need for evaluating cluster properties in an unstable constrained-equilibrium state and ambiguity in the normalization constant required in the nucleation-rate expression. Moreover, it naturally spans the entire composition range between the two pure monomers. The cluster fluxes derived using this new model are similar in form to those of classical derivations, so previously developed methods for evaluation of the net nucleation rate can be applied directly to the new formulation.     

Evaluation of surface tension and Tolman length as a function of droplet radius from experimental nucleation rate and supersaturation ratio: metal vapor homogeneous nucleation

Zinc and silver vapor homogeneous nucleations are studied experimentally at the temperature from 600 to 725 and 870 K, respectively, in a laminar flow diffusion chamber with Ar as a carrier gas at atmospheric pressure. The size, shape, and concentration of aerosol particles outcoming the diffusion chamber are analyzed by a transmission electron microscope and an automatic diffusion battery. The wall deposit is studied by a scanning electron microscope (SEM). Using SEM data the nucleation rate for both Zn and Ag is estimated as 10(10) cm(-3) s(-1). The dependence of critical supersaturation on temperature for Zn and Ag measured in this paper as well as Li, Na, Cs, Ag, Mg, and Hg measured elsewhere is analyzed. To this aim the classical nucleation theory is extended by the dependence of surface tension on the nucleus radius. The preexponent in the formula for the vapor nucleation rate is derived using the formula for the work of formation of noncritical embryo [obtained by Nishioka and Kusaka [J. Chem. Phys. 96, 5370 (1992)] and later by Debenedetti and Reiss [J. Chem. Phys. 108, 5498 (1998)]] and Reiss replacement factor. Using this preexponent and the Gibbs formula for the work of formation of critical nucleus the dependence of surface tension on the radius R(S) of the surface of tension is evaluated from the nucleation data for above-mentioned metals. For the alkali metals and Ag the surface tension was determined to be a strong function of R(S). For the bivalent metals (Zn, Hg, and Mg) the surface tension was independent of radius in the experimental range. A new formula for the Tolman length delta as a function of surface tension and radius R(S) is derived by integration of Gibbs-Tolman-Koenig equation assuming that delta is a monotonic function of radius. The formula derived is more correct than the Tolman formula and convenient for the elaboration of experimental data. Using this formula the values of delta are determined as a function of R(S) from the experimental nucleation data. It is determined that all the metals considered are characterized by strong dependence of delta on radius; for the bivalent metals delta changes sign.     

Monte Carlo simulation study of droplet nucleation

A new rigorous Monte Carlo simulation approach is employed to study nucleation barriers for droplets in Lennard-Jones fluid. Using the gauge cell method we generate the excess isotherm of critical clusters in the size range from two to six molecular diameters. The ghost field method is employed to compute the cluster free energy and the nucleation barrier with desired precision of (1-2)kT. Based on quantitative results obtained by Monte Carlo simulations, we access the limits of applicability of the capillarity approximation of the classical nucleation theory and the Tolman equation. We show that the capillarity approximation corrected for vapor nonideality and liquid compressibility provides a reasonable assessment for the size of critical clusters in Lennard-Jones fluid; however, its accuracy is not sufficient to predict the nucleation barriers for making practical estimates of the rate of nucleation. The established dependence of the droplet surface tension on the droplet size cannot be approximated by the Tolman equation for small droplets of radius less than four molecular diameters. We confirm the conclusion of ten Wolde and Frenkel [J. Chem. Phys. 109, 9901 (1998)] that integration of the normal component of the Irving-Kirkwood pressure tensor severely underestimates the nucleation barriers for small clusters.     

Water vapor nucleation on an infinite substrate with complementary structure: 1. The mechanism of nucleation

The nucleation of water vapor on the infinite surface of a silver iodide crystal at 260 K is simulated. Long-range electrostatic and polarization interactions are taken into account by the Ewald method. The free energy and work of equilibrium formation of nuclei are calculated at the molecular level by the method of bicanonical statistical ensemble. It is shown that, at the initial stage, the substrate is completely covered with a water monolayer. The substrate tends to decrease by two orders of magnitude the vapor pressure required to form the critical nucleus of a monomolecular film with a size of 10² molecules, the nucleation rate being increased by tens of orders of magnitude as compared to homogeneous nucleation. The saturation pressure above the adsorbed monomolecular film is 12 times lower than that above the flat ice surface. The free energy at the edges of “spots” per unit length is 1.4 × 10^?11 J/m. The critical size of the spot increases with a decrease in vapor pressure as the inverse second power of the logarithm of pressure.     

Kinetics of beta-haematin formation from suspensions of haematin in aqueous benzoic acid

Kinetics of beta-haematin (synthetic malaria pigment) formation from haematin have been studied in the presence of aqueous benzoic acid and derivatives of benzoic acid. Formation of the beta-haematin product is demonstrated by X-ray diffraction and IR spectroscopy. Reactions were followed by determining the fraction of unreacted haematin at various time points during the process via reaction of extracted aliquots with pyridine. The kinetics can be fitted to the Avrami equation, indicating that the process involves nucleation and growth. Reaction kinetics in stirred benzoic acid are similar to those previously observed in acetic acid, except that benzoic acid is far more active in promoting the reaction than acetic acid. The reaction reaches completion within 2 h in the presence of 0.050 M benzoic acid (pH 4.5, 60 degrees C). This compares with 1 h in the presence of 4.5 M acetic acid and 4 h in the presence of 2 M acetic acid. The reaction rate in benzoic acid is not affected if the stirring rate is decreased to zero, but very vigorous stirring appears to disrupt nucleation. The rate constant for beta-haematin formation in benzoic acid has a linear dependence on benzoic acid concentration and follows Arrhenius behaviour with temperature. There is a bell-shaped dependence on pH. This suggests that the haematin species in which one propionate group is protonated and the other is deprotonated is optimal for beta-haematin formation. When the reaction is conducted in para-substituted benzoic acid derivatives, the log of the rate constant increases linearly with the Hammett constant. These findings suggest that the role of the carboxylic acid may be to disrupt hydrogen bonding and pi-stacking in haematin, facilitating conversion to beta-haematin. The large activation energy for conversion of precipitated haematin to beta-haematin suggests that the reaction in vivo most likely involves direct nucleation from solution and probably does not occur in aqueous medium.     

Kinetic theory of heterogeneous nucleation; effect of nonuniform density in the nuclei

The heterogeneous nucleation of a liquid from a vapor in contact with a planar solid surface or a solid surface with cavities is examined on the basis of the kinetic theory of nucleation developed by Nowakowski and Ruckenstein [J. Phys. Chem. 96 (1992) 2313] which is extended to nonuniform fluid density distribution (FDD) in the nucleus. The latter is determined under the assumption that at each moment the FDD in the nucleus is provided by the density functional theory (DFT) for a nanodrop. As a result of this assumption, the theory does not require to consider that the contact angle which the nucleus makes with the solid surface and the density of the nucleus are independent parameters since they are provided by the DFT. For all considered cases, the nucleation rate is higher in the cavities than on a planar surface and increases with increasing strength of the fluid-solid interactions and decreasing cavity radius. The difference is small at high supersaturations (small critical nuclei), but becomes larger at low supersaturations when the critical nucleus has a size comparable with the size of the cavity. The nonuniformity of the FDD in the nucleus decreases the nucleation rate when compared to the uniform FDD.     

Freezing of water and aqueous NaCl droplets coated by organic monolayers as a function of surfactant properties and water activity

This study presents heterogeneous ice nucleation from water and aqueous NaCl droplets coated by 1-nonadecanol and 1-nonadecanoic acid monolayers as a function of water activity (a(w)) from 0.8 to 1 accompanied by measurements of the corresponding pressure-area isotherms and equilibrium spreading pressures. For water and aqueous NaCl solutions of ~0-20 wt % in concentration, 1-nonadecanol exhibits a condensed phase, whereas the phase of 1-nonadecanoic acid changes from an expanded to a condensed state with increasing NaCl content of the aqueous subphase. 1-Nonadecanol-coated aqueous droplets exhibit the highest median freezing temperatures that can be described by a shift in a(w) of the ice melting curve by 0.098 according to the a(w)-based ice nucleation approach. This freezing curve represents a heterogeneous ice nucleation rate coefficient (J(het)) of 0.85 ± 0.30 cm(-2) s(-1). The median freezing temperatures of 1-nonadecanoic acid-coated aqueous droplets decrease less with increasing NaCl content compared to the homogeneous freezing temperatures. This trend in freezing temperature is best described by a linear function in a(w) and not by the a(w)-based ice nucleation approach most likely due to an increased ice nucleation efficiency of 1-nonadecanoic acid governed by the monolayer state. This freezing curve represents J(het) = 0.46 ± 0.16 cm(-2) s(-1). Contact angles (α) for 1-nonadecanol- and 1-nonadecanoic acid-coated aqueous droplets increase as temperature decreases for each droplet composition, but absolute values depend on employed water diffusivity and the interfacial energies of the ice embryo. A parametrization of log[J(het)(Δa(w))] is presented which allows prediction of freezing temperatures and heterogeneous ice nucleation rate coefficients for water and aqueous NaCl droplets coated by 1-nonadecanol without knowledge of the droplet's composition and α.     

Monte Carlo simulations of critical cluster sizes and nucleation rates of water

We have calculated the critical cluster sizes and homogeneous nucleation rates of water at temperatures and vapor densities corresponding to experiments by Wolk and Strey [J. Phys. Chem B 105, 11683 (2001)]. The calculations have been done with an expanded version of a Monte Carlo method originally developed by Vehkamaki and Ford [J. Chem. Phys. 112, 4193 (2000)]. Their method calculates the statistical growth and decay probabilities of molecular clusters. We have derived a connection between these probabilities and kinetic condensation and evaporation rates, and introduce a new way for the calculation of the work of formation of clusters. Three different interaction potential models of water have been used in the simulations. These include the unpolarizable SPC/E [J. Phys. Chem. 91, 6269 (1987)] and TIP4P [J. Chem. Phys. 79, 926 (1983)] models and a polarizable model by Guillot and Guissani [J. Chem. Phys. 114, 6720 (2001)]. We show that TIP4P produces critical cluster sizes and a temperature and vapor density dependence for the nucleation rate that agree well with the experimental data, although the magnitude of nucleation rate is constantly overestimated by a factor of 2 x 10(4). Guissani and Guillot's model is somewhat less successful, but both the TIP4P and Guillot and Guissani models are able to reproduce a much better experimental temperature dependency of the nucleation rate than the classical nucleation theory. Using SPC/E results in dramatically too small critical clusters and high nucleation rates. The water models give different average binding energies for clusters. We show that stronger binding between cluster molecules suppresses the decay probability of a cluster, while the growth probability is not affected. This explains the differences in results from different water models.     

A study of homogeneous nucleation of ibuprofen in a flow chamber. Determination of the surface tension of critical nuclei

Homogeneous nucleation of ibuprofen vapor is studied in a nucleation flow chamber, a horizontal quartz tube equipped with an external heater. The area of the chamber where the nucleation proceeds most efficiently is determined, and the volume of this area is estimated. The temperature and supersaturation are determined and the homogeneous nucleation rate is calculated for this area. Saturation vapor pressure over liquid ibuprofen is measured in a temperature range of 353–383 K. Using an exact formula that has recently been derived for the nucleation rate based on the works by Kusaka, Reiss, as well as the Frenkel liquid-kinetics theory, surface tension and the radius of surface of tension of a critical nucleus σ= 25.9 mN/m and R _s = 1.6 nm, respectively, are calculated at 318 K. The measurement of the surface tension of an ibuprofen planar surface shows that, at 318 K, σ_∞ = 24.38 mN/m; i.e., σ is higher than σ_∞ by 6%. A critical nucleus is established as containing nearly 36 ibuprofen molecules.     

Nonlinear vibrational spectroscopic studies of the adsorption and speciation of nitric acid at the vapor/acid solution interface

Nitric acid plays an important role in the heterogeneous chemistry of the atmosphere. Reactions involving HNO(3) at aqueous interfaces in the stratosphere and troposphere depend on the state of nitric acid at these surfaces. The vapor/liquid interface of HNO(3)-H2O binary solutions and HNO(3)-H(2)SO(4)-H2O ternary solutions are examined here using vibrational sum frequency spectroscopy (VSFS). Spectra of the NO2 group at different HNO(3) mole fractions and under different polarization combinations are used to develop a detailed picture of these atmospherically important systems. Consistent with surface tension and spectroscopic measurements from other laboratories, molecular nitric acid is identified at the surface of concentrated solutions. However, the data here reveal the adsorption of two different hydrogen-bonded species of undissociated HNO(3) in the interfacial region that differ in their degree of solvation of the nitro group. The adsorption of these undissociated nitric acid species is shown to be sensitive to the H2O:HNO(3) ratio as well as to the concentration of sulfuric acid.     

Molecular dynamics simulations of cluster nucleation during inert gas condensation

Molecular dynamics simulations of vapor-phase nucleation of germanium in an argon atmosphere were performed and a unexpected channel of nucleation was observed. This channel, vapor-induced cluster splitting, is important for more refractory materials since the critical nucleus size can fall below the size of a dimer. As opposed to conventional direct vapor nucleation of the dimer, which occurs by three-body collisions, cluster-splitting nucleation is a second-order reaction. The most important cluster-splitting reaction is the collision of a vapor atom and a trimer that leads to the formation of two dimers. The importance of the cluster-splitting nucleation channel relative to the direct vapor nucleation channel is observed to increase with decreasing vapor density and increasing ratio of vapor to carrier gas atoms.     

Nucleation and growth rates of poly(L-lactic acid) microparticles during precipitation with a compressed-fluid antisolvent

We measured nucleation and growth rates of poly(L-lactic acid) (PLLA) microparticles produced during precipitation with a compressed-fluid antisolvent (PCA). The injector/precipitator used in this study satisfied the constraints and assumptions incorporated in the development of the mixed-suspension, mixed-product-removal population balance theory. A semicontinuous operation mode with batch product filtering was developed, and results from product particle size distributions allowed nucleation and growth rates to be determined through the use of population balances. Kinetic data, obtained by operating the precipitator under various degrees of supersaturation and suspension density, were used to generate a nucleation rate model for PLLA. Model results indicate a relative kinetic order of 1 and a linear dependence of the nucleation rate on the suspension density. First-order dependence of the nucleation rate on suspension density suggests secondary nucleation mechanism(s) are operative within this PCA flow system and may explain the relative insensitivity of particle size distributions to changes in PCA operating conditions.     

Evaporation of ethanol/water droplets: examining the temporal evolution of droplet size, composition and temperature

The evolving size, composition, and temperature of evaporating ethanol/water aerosol droplets 25-57 microm in radius are probed by cavity enhanced Raman scattering (CERS) and laser induced fluorescence. This represents the first study in which the evolving composition of volatile droplets has been probed with spatial selectivity on the millisecond time scale, providing a new strategy for exploring mass and heat transfer in aerosols. The Raman scattering intensity is shown to depend exponentially on species concentration due to the stimulated nature of the CERS technique, providing a sensitive measure of the concentration of the volatile ethanol component. The accuracy with which we can determine droplet size, composition, and temperature is discussed. We demonstrate that the CERS measurements of evolving size and composition of droplets falling in a train can be used to characterize, and thus avoid, droplet coagulation. By varying the surrounding gas pressure (7-77 kPa), we investigate the dependence of the rate of evaporation on the rate of gas diffusion, and behavior consistent with gas diffusion-limited evaporation is observed. We suggest that such measurements can allow the determination of the vapor pressures of components within the droplet and can allow the determination of activity coefficients of volatile species.