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.     

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.     

Nucleation of ethanol, propanol, butanol, and pentanol: A systematic experimental study along the homologous series

We present homogeneous vapor-liquid nucleation rates of the 1-alcohols (C(n)H(2n+1)OH, n = 2-4) measured in the well-established two-valve nucleation pulse chamber as well as in a novel one-piston nucleation pulse chamber at temperatures between 235 and 265 K. The nucleation rates and critical cluster sizes show a very systematic behavior with respect to the hydrocarbon chain length of the alcohol, just as their thermo-physical parameters such as surface tension, vapor pressure, and density would suggest. For all alcohols, except ethanol, predictions of classical nucleation theory lie several orders of magnitude below the experimental results and show a strong temperature-dependence typically found in nucleation experiments. The more recent Reguera-Reiss theory [J. Phys. Chem. B 108(51), 19831 (2004)] achieves reasonably good predictions for 1-propanol, 1-butanol, and 1-pentanol, and independent of the temperature. Ethanol, however, clearly shows the influence of strong association between molecules even in the vapor phase. We also scaled all experimental results with classic nucleation theory to compare our data with other data from the literature. We find the same overall temperature trend for all measurement series together but inverted and inconsistent temperature trends for individual 1-propanol and 1-butanol measurements in other devices. Overall, our data establishe a comprehensive and reliable data set that forms an ideal basis for comparison with nucleation theory.     

Nucleation rate isotherms of argon from molecular dynamics simulations

We report six nucleation rate isotherms of vapor-liquid nucleation of Lennard-Jones argon from molecular dynamics simulations. The isotherms span three orders of magnitude in nucleation rates, 10(23)相似文献   

Homogeneous nucleation of water between 200 and 240 K: new wave tube data and estimation of the Tolman length

We have measured homogeneous nucleation rates of water at 200-240 K in the carrier gas helium, in the range of 10(13) - 10(17) m(-3) s(-1) using an expansion wave tube. The rates agree well with the results of Wolk and Strey [J. Phys. Chem. B 105, 11683 (2001)] in the range of overlap (220-240 K), and are summarized by the empirical fit J = S exp[4.6 + 0.244T-(906.8 - 2.914T)(ln S)(2)], with J the nucleation rate in m(-3) s(-1), S the supersaturation, and T the temperature in K. We find that the supersaturation dependence of both our rates and those of Wolk and Strey is lower than classical theory predicts, and that the critical cluster is smaller than the classical critical size. These deviations are explained in the framework of the Tolman theory for surface tension, and the "Tolman length" is estimated from our experimental results. We find a positive Tolman length that increases with decreasing temperature, from about 0.1 Angstrom at 260 K to (0.6 +/- 0.4) Angstroms at 200 K. We present a nucleation rate expression that takes the Tolman length into account and show that both the supersaturation and temperature dependence are improved, compared to the classical theory.     

Molecular Dynamics Studies of the Kinetics of Phase Changes in Clusters IV： Crystal Nucleation from Molten （NaCl）256 and （NaCl）500 Clusters

Molecular dynamics computer simulation based on the Born-Mayer-Huggins potential function has been carried out to study the effects of duster size and temperature on the nucleation rate of sodium chloride dusters in the temperature range of 580 K to 630 K. Clusters with 256 and 500 NaCl molecules have been studied and the results have been compared with those obtained from 108 molecule dusters. The melting point (MP) of the clusters were observed to increase with the size of the clusters and can be well described by a linear equation MP =1107(37)-1229(23)N^-1/3(N is the number of molecules in the duster).The nucleation rate was found to decrease with increasing the duster size or temperature. Various nucleation theories have been used to interpret the nucleation rates obtained from this molecular dynamics simulation. It is possible to use a constant diffuse interface thickness to interpret the nucleation rate from the diffuse interface theory in the temperature range of this study. However, the interfacinl free energy estimated from classical nucleation theory and diffuse interface theory increases too fast with increasing the temperature while that from Gran-Gunton theory does not change with changing temperatures.The sizes of critical nuclei estimated from all the theories are smaller than those estimated from our simulations.     

Recent developments in the kinetic theory of nucleation

A review of recent progress in the kinetics of nucleation is presented. In the conventional approach to the kinetic theory of nucleation, it is necessary to know the free energy of formation of a new-phase particle as a function of its independent variables at least for near-critical particles. Thus the conventional kinetic theory of nucleation is based on the thermodynamics of the process. The thermodynamics of nucleation can be examined by using various approaches, such as the capillarity approximation, density functional theory, and molecular simulation, each of which has its own advantages and drawbacks. Relatively recently a new approach to the kinetics of nucleation was proposed [Ruckenstein E, Nowakowski B. J Colloid Interface Sci 1990;137:583; Nowakowski B, Ruckenstein E. J Chem Phys 1991;94:8487], which is based on molecular interactions and does not employ the traditional thermodynamics, thus avoiding such a controversial notion as the surface tension of tiny clusters involved in nucleation. In the new kinetic theory the rate of emission of molecules by a new-phase particle is determined with the help of a mean first passage time analysis. This time is calculated by solving the single-molecule master equation for the probability distribution function of a surface layer molecule moving in a potential field created by the rest of the cluster. The new theory was developed for both liquid-to-solid and vapor-to-liquid phase transitions. In the former case the single-molecule master equation is the Fokker-Planck equation in the phase space which can be reduced to the Smoluchowski equation owing to the hierarchy of characteristic time scales. In the latter case, the starting master equation is a Fokker-Planck equation for the probability distribution function of a surface layer molecule with respect to both its energy and phase coordinates. Unlike the case of liquid-to-solid nucleation, this Fokker-Planck equation cannot be reduced to the Smoluchowski equation, but the hierarchy of time scales does allow one to reduce it to the Fokker-Plank equation in the energy space. The new theory provides an equation for the critical radius of a new-phase particle which in the limit of large clusters (low supersaturations) yields the Kelvin equation and hence an expression for the macroscopic surface tension. The theory was illustrated with numerical calculations for a molecular pair interaction potential combining the dispersive attraction with the hard-sphere repulsion. The results for the liquid-to-solid nucleation clearly show that at given supersaturation the nucleation rate depends on the cluster structure (for three cluster structures considered-amorphous, fcc, and icosahedral). For both the liquid-to-solid and vapor-to-liquid nucleation, the predictions of the theory are consistent with the results of classical nucleation theory (CNT) in the limit of large critical clusters (low supersaturations). For small critical clusters the new theory provides higher nucleation rates than CNT. This can be accounted for by the fact that CNT uses the macroscopic interfacial tension which presumably overpredicts the surface tension of small clusters, and hence underpredicts nucleation rates.     

Homogeneous nucleation of n-propanol, n-butanol, and n-pentanol in a supersonic nozzle

We have measured the nucleation conditions of n-propanol, n-butanol, and n-pentanol in a supersonic Laval nozzle, and estimated that the maximum nucleation rate J is 5 x 10(16) cm(-3) s(-1) with an uncertainty factor of 2. Plotting the vapor pressures p(J(max) ) and temperatures T(J(max) ) corresponding to the maximum nucleation rate as ln(p) versus 1T, produces a series of well separated straight lines. When these values are scaled by their respective critical parameters, p(c) and T(c), the data lie close to a single straight line. Comparing the experimental data to the predictions of classical nucleation theory reveals much higher experimental rates, and the deviation increases with increasing alcohol chain length and decreasing temperature. A scaling analysis in terms of Hale's scaled nucleation model [Phys. Rev. A 33, 4156 (1986); Metall. Trans. A 23, 1863 (1992)], clearly shows that our data are consistent with experimental nucleation rates measured using other devices that have characteristic rates many orders of magnitude lower.     

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.     

Homogeneous nucleation rates of 1-pentanol

We have measured isothermal homogeneous nucleation rates J for 1-pentanol vapor in two different carrier-gases, argon, and helium, using a two-valve nucleation pulse chamber. The nucleation rates cover a range of 10(5)相似文献   

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.     

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.     

Crystallization of aqueous ammonium sulfate particles internally mixed with soot and kaolinite: crystallization relative humidities and nucleation rates

Using optical microscopy, we investigated the crystallization of aqueous ammonium sulfate droplets containing soot and kaolinite, as well as the crystallization of aqueous ammonium sulfate droplets free of solid material. Our results show that soot did not influence the crystallization RH of aqueous ammonium sulfate particles under our experimental conditions. In contrast, kaolinite increased the crystallization RH of the aqueous ammonium sulfate droplets by approximately 10%. In addition, our results show that the crystallization RH of aqueous ammonium sulfate droplets free of solid material does not depend strongly on particle size. This is consistent with conclusions made previously in the literature, based on comparisons of results from different laboratories. From the crystallization results we determined the homogeneous nucleation rates of crystalline ammonium sulfate in aqueous ammonium sulfate droplets and the heterogeneous nucleation rates of crystalline ammonium sulfate in aqueous ammonium sulfate particles containing kaolinite. Using classical nucleation theory and our experimental data, we determined that the interfacial tension between an ammonium sulfate critical nucleus and an aqueous ammonium sulfate solution is 0.064 +/- 0.003 J m(-2) (in agreement with our previous measurements), and the contact angle between an ammonium sulfate critical nucleus and a kaolinite surface is 59 +/- 2 degrees. On the basis of our results, we argue that soot will not influence the crystallization RH of aqueous ammonium sulfate droplets in the atmosphere, but kaolinite can significantly modify the crystallization RH of atmospheric ammonium sulfate droplets. As an example, the CRH50 (the relative humidity at which 50% of the droplets crystallize) ranges from about 41 to 51% RH when the diameter of the kaolinite inclusion ranges from 0.1 to 5 microm. For comparison, the CRH50 of aqueous ammonium sulfate droplets (0.5 microm diameter) free of solid material is approximately 34.3% RH under atmospheric conditions.     

Bond energies and structures of ammonia-sulfuric acid positive cluster ions

New particle formation in the atmosphere is initiated by nucleation of gas-phase species. The small molecular clusters that act as seeds for new particles are stabilized by the incorporation of an ion. Ion-induced nucleation of molecular cluster ions containing sulfuric acid generates new particles in the background troposphere. The addition of a proton-accepting species to sulfuric acid cluster ions can further stabilize them and may promote nucleation under a wider range of conditions. To understand and accurately predict atmospheric nucleation, the stabilities of each molecular cluster within a chemical family must be known. We present the first comprehensive measurements of the ammonia-sulfuric acid positive ion cluster system NH(4)(+)(NH(3))(n)(H(2)SO(4))(s). Enthalpies and entropies of individual growth steps within this system were measured using either an ion flow reactor-mass spectrometer system under equilibrium conditions or by thermal decomposition of clusters in an ion trap mass spectrometer. Low level ab initio structural calculations provided inputs to a master equation model to determine bond energies from thermal decomposition measurements. Optimized ab initio structures for clusters up through n = 3, s = 3 are reported. Upon addition of ammonia and sulfuric acid pairs, internal proton transfer generates multiple NH(4)(+) and HSO(4)(-) ions within the clusters. These multiple-ion structures are up to 50 kcal mol(-1) more stable than corresponding isomers that retain neutral NH(3) and H(2)SO(4) species. The lowest energy n = s clusters are composed entirely of ions. The addition of acid-base pairs to the core NH(4)(+) ion generates nanocrystals that begin to resemble the ammonium bisulfate bulk crystal starting with the smallest n = s cluster, NH(4)(+)(NH(3))(1)(H(2)SO(4))(1). In the absence of water, this cluster ion system nucleates spontaneously for conditions that encompass most of the free troposphere.     

Quasihomogeneous nucleation of amyloid beta yields numerical bounds for the critical radius, the surface tension, and the free energy barrier for nucleus formation

Amyloid aggregates are believed to grow through a nucleation mediated pathway, but important aggregation parameters, such as the nucleation radius, the surface tension of the aggregate, and the free energy barrier toward aggregation, have remained difficult to measure. Homogeneous nucleation theory, if applicable, can directly relate these parameters to measurable quantities. We employ fluorescence correlation spectroscopy to measure the particle size distribution in an aggregating solution of Alzheimer's amyloid beta molecule (Abeta(1-40)) and analyze the data from a homogeneous nucleation theory perspective. We observe a reproducible saturation concentration and a critical dependence of various aspects of the aggregation process on this saturation concentration, which supports the applicability of the nucleation theory to Abeta aggregation. The measured size distributions show a valley between two peaks ranging from 5 to 50 nm, which defines a boundary for the value of the nucleation radius. By carefully controlling the conditions to inhibit heterogeneous nucleation, we can hold off nucleation in a 25 times supersaturated solution for at least up to 3 h at room temperature. This quasi-homogeneous kinetics implies that at room temperature, the surface energy of the Abeta/water interface is > or =4.8 mJ/m(2), the free energy barrier to nucleation (at 25 times supersaturation) is > or =1.93x10(-19) J, and the number of monomers in the nucleus is > or =29.     

To the theory of homogeneous nucleation: Cluster energy

An attempt is made to critically analyze the modern state of the theory of homogeneous nucleation as concerns its ability to describe experiments with high accuracy. An analysis of the experimental data led us to conclude that the dependence of the nucleation rate on supersaturation and temperature T was not described by the theory, which underestimates the critical cluster size compared with the Gibbs-Thomson equation. The possibility of applying density functional theory (one of the latest achievements in the theory of homogeneous nucleation) was questioned. Within this theory, the Gibbs-Thomson equation remains valid even outside the classic capillary approximation. It is suggested that, to bring theory in consistency with experiment, certain fundamental propositions of the theory of nucleation should be revised. The inclusion of an additional contribution to the Gibbs energy of a cluster caused by the size dependence of the specific heat capacity of the cluster decreases the critical cluster size compared with the value calculated by the Gibbs-Thomson equation. The calculated dependence of nucleation rate on supersaturation was in agreement with the experimental results.     

Two-component heterogeneous nucleation kinetics and an application to Mars

We develop a two-component heterogeneous nucleation model that includes exact calculation of the Stauffer-type [D. Stauffer, J. Aerosol Sci. 7, 319 (1976)] steady-state kinetic prefactor using the correct heterogeneous Zeldovich factor for a heterogeneous two-component system. The model, and a simplified version of it, is tested by comparing its predictions to experimental data for water-n-propanol nucleating on silver particles. The model is then applied to water-carbon dioxide system in Martian conditions, which has not been modeled before. Using the ideal mixture assumption, the model shows theoretical possibilities for two-component nucleation adjacent to the initial stages of one-component water nucleation, especially with small water vapor amounts. The numbers of carbon dioxide molecules in the critical cluster are small in the case of large water amounts (up to 300 ppm) in the gas phase, but larger when there is very little water vapor (1 ppm).