Nucleation Of Supersaturated Vapor Research Articles

Reweighted Jarzynski Sampling: Acceleration of Rare Events and Free Energy Calculation with a Bias Potential Learned from Nonequilibrium Work.

We introduce a simple enhanced sampling approach for the calculation of free energy differences and barriers along a one-dimensional reaction coordinate. First, a small number of short nonequilibrium simulations are carried out along the reaction coordinate, and the Jarzynski equality is used to learn an approximate free energy surface from the nonequilibrium work distribution. This free energy estimate is represented in a compact form as an artificial neural network and used as an external bias potential to accelerate rare events in a subsequent molecular dynamics simulation. The final free energy estimate is then obtained by reweighting the equilibrium probability distribution of the reaction coordinate sampled under the influence of the external bias. We apply our reweighted Jarzynski sampling recipe to four processes of varying scales and complexities─spanning chemical reaction in the gas phase, pair association in solution, and droplet nucleation in supersaturated vapor. In all cases, we find reweighted Jarzynski sampling to be a very efficient strategy, resulting in rapid convergence of the free energy to high precision.

Thermodynamic stability of finely dispersed Na+Cl−(H2O) n aerosol particles in water vapor

Four qualitatively different thermodynamic states have been identified for hydrated sodium chloride ion pairs in water vapor. Two of the states are stable, and the other two are unstable. The stable states of a contact ion pair (CIP) and a solvent-separated ion pair (SSIP) represent sites of heterogeneous nucleation in supersaturated vapors. The unstable states form free energy barriers that separate the stable states. As the temperature is elevated, the SSIP states become more stable than the CIP states already in unsaturated water vapors. Hydrated ion pairs that contain hydroxonium ions instead of alkali metal cations are absolutely stable in the SSIP state already in the range of unsaturated vapors and low temperatures. Computer-assisted calculations of the free energy and work of hydration have been carried out by the Monte Carlo bicanonical statistical ensemble method in terms of a detailed model of interactions comprising polarization, many-particle covalent interactions, and charge transfer phenomena.

Thermodynamics of supersaturated vapor nucleation on molecular condensation nuclei

A key problem in the theory of a supersaturated vapor nucleation on molecular condensation nuclei (namely, the work of formation and the equilibrium concentrations of clusters) is considered. To calculate these quantities using the structural models of clusters, which are better suited for this purpose than the classical droplet model, we derive the equation connecting the work of transfer of a molecular condensation nucleus from the gas phase to a homogeneous cluster with a change in the number of contacts between molecules, occurring in the course of this transfer, and with the work of rupture of individual contacts.

Simulation of supersaturated vapor nucleation on molecular condensation nuclei

The results of model calculations of nucleation of di(2-ethylhexyl)sebacate (DEHS) supersatu-rated vapor on FeO molecules based of the simplest structural models of clusters are considered. The earlier conclusion that the allowance for the escape of a molecular condensation nucleus (MCN) from a cluster weakly affects the results of analysis of nucleation on a MCN is confirmed. It is found that the interaction of electric charges of the FeO molecule and the ester groups of the DEHS molecule plays the important role in the DEHS nucleation. The importance of the strength of the bond between the MCN and the first condensate molecule is established. The strength of this bond considerably affects the coefficient of conversion of the MCN into aerosol particles as well as the form of the dependence of this quantity on the spontaneous condensation background.

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.

Homogeneous nucleation rate measurements in supersaturated water vapor

The rate of homogeneous nucleation in supersaturated vapors of water was studied experimentally using a thermal diffusion cloud chamber. Helium was used as a carrier gas. Our study covers a range of nucleation rates from 3x10(-1) to 3x10(2) cm(-3) s(-1) at four isotherms: 290, 300, 310, and 320 K. The molecular content of critical clusters was estimated from the slopes of experimental data. The measured isothermal dependencies of nucleation rate of water on saturation ratio were compared with the prediction of the classical theory of homogeneous nucleation, the empirical prediction of Wolk et al. [J. Chem. Phys. 117, 10 (2002)], the scaled model of Hale [Phys. Rev. A 33, 4156 (1986)], and the former nucleation onset data.

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.

Modification of the classical nucleation theory based on molecular simulation data for surface tension, critical nucleus size, and nucleation rate

Nucleation in supersaturated vapor is investigated with two series of molecular-dynamics simulations in the canonical ensemble. The applied methods are (a) analysis of critical nuclei at moderate supersaturations by simulating equilibria of single droplets with surrounding vapors in small systems; (b) simulation of homogeneous nucleation during condensation with large systems containing 10(5)-10(6) particles for calculating the nucleation rate of vapors at high supersaturations. For the Lennard-Jones fluid, truncated and shifted at 2.5 times the size parameter, it is shown that the classical nucleation theory underestimates both the nucleation rate and the size of the critical nucleus. A surface property corrected modification of this theory is proposed to consistently cover data on the surface tension of the curved interface, the critical nucleus size, and the nucleation rate.

Homogeneous nucleation in supersaturated vapors of methane, ethane, and carbon dioxide predicted by brute force molecular dynamics

Molecular dynamics (MD) simulation is applied to the condensation process of supersaturated vapors of methane, ethane, and carbon dioxide. Simulations of systems with up to a 10(6) particles were conducted with a massively parallel MD program. This leads to reliable statistics and makes nucleation rates down to the order of 10(30) m(-3) s(-1) accessible to the direct simulation approach. Simulation results are compared to the classical nucleation theory (CNT) as well as the modification of Laaksonen, Ford, and Kulmala (LFK) which introduces a size dependence of the specific surface energy. CNT describes the nucleation of ethane and carbon dioxide excellently over the entire studied temperature range, whereas LFK provides a better approach to methane at low temperatures.

Homogeneous nucleation rate measurements of 1-propanol in helium: The effect of carrier gas pressure

Kinetics of homogeneous nucleation in supersaturated vapor of 1-propanol was studied using an upward thermal diffusion cloud chamber. Helium was used as a noncondensable carrier gas and the influence of its pressure on observed nucleation rates was investigated. The isothermal nucleation rates were determined by a photographic method that is independent on any nucleation theory. In this method, the trajectories of growing droplets are recorded using a charge coupled device camera and the distribution of local nucleation rates is determined by image analysis. The nucleation rate measurements of 1-propanol were carried out at four isotherms 260, 270, 280, and 290 K. In addition, the pressure dependence was investigated on the isotherms 290 K (50, 120, and 180 kPa) and 280 K (50 and 120 kPa). The isotherm 270 K was measured at 25 kPa and the isotherm 260 K at 20 kPa. The experiments confirm the earlier observations from several thermal diffusion chamber investigations that the homogeneous nucleation rate of 1-propanol tends to increase with decreasing total pressure in the chamber. In order to reduce the possibility that the observed phenomenon is an experimental artifact, connected with the generally used one-dimensional description of transfer processes in the chamber, a recently developed two-dimensional model of coupled heat, mass, and momentum transfer inside the chamber was used and results of both models were compared. It can be concluded that the implementation of the two-dimensional model does not explain the observed effect. Furthermore the obtained results were compared both to the predictions of the classical theory and to the results of other investigators using different experimental devices. Plotting the experimental data on the so-called Hale plot shows that our data seem to be consistent both internally and also with the data of others. Using the nucleation theorem the critical cluster sizes were obtained from the slopes of the individual isotherms and compared with the Kelvin prediction. The influence of total pressure on the observed isothermal nucleation rate was studied in another experiment, where not only temperature but also supersaturation was kept constant as the total pressure was changed. It was shown that the dependence of the nucleation rate on pressure gets stronger as pressure decreases.

On the Kinetics of Nonisothermal Nucleation

The kinetics of supersaturated vapor nucleation is considered with allowance for the possible difference between the temperature of the clusters and that of the gaseous phase. The resultant equation for the steady-state nucleation rate has the same form as the equation of the classical theory but contains the work of the thermodynamically irreversible droplet formation. This equation relates the nucleation rate to the cluster temperatures. It is transformed into the equation of the classical theory if the clusters have the same temperature as the gaseous phase. On the basis of the thermal balance for the clusters, an equation relating their temperature and concentration to the nucleation rate is derived. The form of this equation is similar to the equation of heat propagation in a moving medium in the presence of heat sources and sinks.

Heterogeneous nucleation on aerosol particles

We have applied density functional theory in statistical mechanisms to study the heterogeneous nucleation of supersaturated vapors on spherical aerosol-like substrates. Our calculations reveal the inadequacy of the classical nucleation theory in describing the condensation of droplets on very small particles. The latter approach is particularly inaccurate both at high supersaturations and in the vicinity of the wetting transition. Comparisons are also made with recent experimental results for the condensation of supersaturated vapors on submicrometer particles.

Experimental Determination of the Surface Energy of Critical Nuclei During the Nucleation of Supersaturated Vapor

Theoretical substantiation of the empirical method for determining the surface (or excess) energy of critical nuclei was performed within the framework of thermodynamic approach. Characteristics of critical nuclei were determined based on the studies of the nucleation of supersaturated vapors of glycerol in the vicinity of its melting point and the critical temperature of carrier gas. The effect of the specific features of physicochemical parameters of the studied substance and carrier gas on the parameters of critical nuclei was revealed. Experimental values of the surface energy of critical nuclei were compared with those calculated by the droplet model. The necessity for the allowance for the temperature dependence of the surface energy of critical nuclei was demonstrated. It was noted that the largest deviation from the predictions of droplet model arises at small (about 10) numbers of molecules in a critical nucleus; as the size of a nucleus increases, the surface energy, in the limiting case, tends to physically correct value.

Molecular dynamics simulation of supersaturated vapor nucleation in slit pore

Molecular dynamics simulations of nucleation of Lennard-Jones vapor confined in a slit pore have been performed. The walls of the slit pore are structureless walls; each wall interacts with vapor molecules via Lennard-Jones 9–3 potential. The rate of nucleation in the steady state is determined by analyzing time evolution of the cluster size distribution. At the same vapor density and temperature, the nucleation rate in the slit pore is higher than in the homogeneous vapor [K. Yasuoka and M. Matsumoto, J. Chem. Phys. 109, 8451 (1998)], irrespective of the strength of attraction between the wall and vapor molecules. However, this attraction strongly affects the process of nucleus formation: if the attraction is weak (a drying wall), nuclei tend to form in the middle of the pore, whereas if the attraction is strong (a wetting wall), the nucleus formation originates from two sources, the surface diffusion of adsorbed molecules and deposition of clusters formed in the middle of the pore.

Experimental detection of nucleation rate surface singularity

As a rule, the modern theories of nucleation represent only modifications of classical theory, and they still remain unsuitable for quantitative prediction of experimental results. In order to create the universal description of supersaturated vapor nucleation, as well as evaluate other theories, we need to get the reliable experimental results. Now experimental skills are high enough for precision measurements of the vapor nucleation rates as well as for detecting and evaluating, for example, temperatures of phase transitions in the new phase critical embryos. That is, one can find experimentally the singularity of the nucleation rate surface at conditions for the critical embryo phase transitions. Visual analysis of the experimental results has the low potential to detect the nucleation rate surface singularity and the surface singularity can be missed sometimes. One major problem for singularity detection is the noise of experimental results. This problem still exists even if one has experimental results of high accuracy. The condition for surface continuity and monotony could be applied as a criterion for analysis of experimental data for the vapor nucleation rates. The criterion is tested for the broad spectrum of the experimental results in the vapor nucleation. As an example of the criterion being used, the experimental results for the n-pentanol–water binary system of nucleation have been analyzed. A peculiarity of this system is the existence of a miscibility gap between the components. It was found that the criterion as a function of n-pentanol mole fraction has the singularity in the vicinity of this gap. This singularity was smoothed in the experimental results presentation and omitted in the original research. The proposed criterion can be used to search the experimental data set singularity as a function of their variable(s).

Molecular dynamics study of nucleation in supersaturated vapor of carbon dioxide

Molecular dynamics study has been carried out for nucleation in supersaturated vapor of carbon dioxide. The molecular model is of Lennard–Jones (LJ)+Coulomb type proposed by Murthy et al. [C.S. Murthy, S.F. O'Shea, I.R. McDonald, Mol. Phys. 50 (1983) 531.] and molecular dynamics simulation is within an NEV ensemble. Detailed analyses have been performed for the cluster size distribution, percolation phenomena, reaction rates and equilibrium constants of nucleation, and others.

Homogeneous nucleation rate measurements in 1-pentanol vapor with helium as a buffer gas

The rate of homogeneous nucleation in supersaturated vapors of n-pentanol was studied experimentally using an upward static diffusion chamber. Helium was used as a buffer gas, holding the total pressure in the chamber at P t=25 kPa. A recently improved photographic technique was used to determine the nucleation rate as a function of supersaturation at temperature T=260 K. This dependence was compared with predictions made by the classical theory of homogeneous nucleation. Furthermore, the influence of gaseous ions on nucleation rate was studied, and a minimum voltage across the chamber, necessary to avoid nucleation on ions, was determined. The effect of the wall heating power on nucleation was found to be negligible in the range studied.

Ion nucleation as a detector: application of REMPI to generate selected ions in supersaturated vapors

Resonance enhanced multiphoton ionization (REMPI) of aromatic molecules present in a small concentration within a supersaturated host vapor is demonstrated. The method is applied to the study of ion nucleation in supersaturated vapors of methanol, acetonitrile and nonane induced by the molecular ions of benzene, toluene, and p-xylene. With this method it is now possible to selectively and unambiguously generate specific ions of interest and study their nucleating behavior. Furthermore, the selectivity of REMPI combined with the amplification and detection capabilities of nucleation and growth offer valuable analytical features for the identification of trace components in supersaturated vapors.

Homogeneous Nucleation in Supersaturated Vapors of n-Nonane

The upward thermal diffusion cloud chamber was used to measure the supersaturations of n-nonane vapors required to cause an observed rate of homogeneous nucleation of 1 droplet/cm3 s. New temperature-dependent correlations for the surface tension and the density of n-nonane have been applied in theoretical prediction of the corresponding supersaturation. The measurements are found to be in reasonable agreement with the predictions of the classical (Becker-Doering) theory whereas both the Dillmann-Meier and the Girshick-Chiu theories lead to a significant underestimation of supersaturation in the whole range of temperatures measured.

Homogeneous nucleation in supersaturated vapors of polar molecules: Acetonitrile, benzonitrile, nitromethane, and nitrobenzene

The critical supersaturations (Sc) required for the homogeneous nucleation of acetonitrile, benzonitrile, nitromethane, and nitrobenzene vapors have been measured over wide temperature ranges using a thermal diffusion cloud chamber. At Tr=0.44, the experimental results are higher than the predictions of the classical nucleation theory by 20% (CH3NO2), 50% (CH3CN), 57% (C6H5NO2), and 112% (C6H5CN). This trend correlates well with the dipole moments and to a lesser extent with the polarizabilities of these substances. Corresponding states of simple fluids and scaled nucleation law show that CH3CN and CH3NO2 have similar nucleation behavior which is different from that of C6H5CN and C6H5NO2. Correlations with other less polar substances are examined. The scaled law, with Ω (the excess surface entropy per molecule) determined from the temperature dependence of the bulk surface tension, gives a better description of the experimental results than the classical theory with the exception of nitromethane. The results suggest that the classical theory does not take proper account of the dipole–dipole interaction in calculating the free energy of the embryonic droplets.