Homogeneous Vapor-liquid Nucleation Research Articles

Studying vapor-liquid transition using a generalized ensemble.

Homogeneous vapor-liquid nucleation is studied using the generalized Replica Exchange Method (gREM). The generalized ensemble allows the study of unstable states that cannot directly be studied in the canonical ensemble. Along with replica exchange, this allows for efficient sampling of the multiple states in a single simulation. Statistical Temperature Weighted Histogram Analysis Method is used for postprocessing to get a continuous free energy curve from bulk vapor to bulk liquid. gREM allows the study of planar, cylindrical, and spherical interfaces in a single simulation. The excess Gibbs free energy for the formation of a spherical liquid droplet in vapor for a Lennard-Jones system is calculated from the free energy curve and compared against the umbrella sampling results. The nucleation free energy barrier obtained from gREM is then used to calculate the nucleation rate without relying on any classification scheme for separating the vapor and liquid.

Free energy calculations along entropic pathways. I. Homogeneous vapor-liquid nucleation for atomic and molecular systems.

Using the entropy S as a reaction coordinate, we determine the free energy barrier associated with the formation of a liquid droplet from a supersaturated vapor for atomic and molecular fluids. For this purpose, we develop the μVT-S simulation method that combines the advantages of the grand-canonical ensemble, that allows for a direct evaluation of the entropy, and of the umbrella sampling method, that is well suited to the study of an activated process like nucleation. Applying this approach to an atomic system such as Ar allows us to test the method. The results show that the μVT-S method gives the correct dependence on supersaturation of the height of the free energy barrier and of the size of the critical droplet, when compared to predictions from the classical nucleation theory and to previous simulation results. In addition, it provides insight into the relation between the entropy and droplet formation throughout this process. An additional advantage of the μVT-S approach is its direct transferability to molecular systems, since it uses the entropy of the system as the reaction coordinate. Applications of the μVT-S simulation method to N2 and CO2 are presented and discussed in this work, showing the versatility of the μVT-S approach.

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.

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

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

Molecular Simulations of Homogeneous Vapor-Liquid Nucleation as Initial Process of Aerosol Formation

Molecular Simulations of Homogeneous Vapor-Liquid Nucleation as Initial Process of Aerosol Formation

Extended study of molecular dynamics simulation of homogeneous vapor-liquid nucleation of water

Using the simple point charge/extended water model, we performed molecular dynamics simulations of homogeneous vapor-liquid nucleation at various values of temperature T and supersaturation S, from which the nucleation rate J, critical nucleus size n(*), and the cluster formation free energy DeltaG were derived. As well as providing lots of simulation data, the results were compared with theories on homogeneous nucleation, including the classical, semi-phenomenological, and scaled models, but none of these gave a satisfactory explanation for our results. It was found that two main factors made the theories fail: (1) The average cluster structure including the nonspherical shape and the core structure that is not like the bulk liquid and (2) the forward rate which is larger than assumed by the theories by about one order of magnitude. The quantitative evaluation of these factors is left for future investigations.

Mean-field kinetic nucleation theory

A new semiphenomenological model of homogeneous vapor-liquid nucleation is proposed in which the cluster kinetics follows the "kinetic approach to nucleation" and the thermodynamic part is based on the revised Fisher droplet model with the mean-field argument for the cluster configuration integral. The theory is nonperturbative in a cluster size and as such is valid for all clusters down to monomers. It contains two surface tensions: macroscopic (planar) and microscopic. The latter is a temperature dependent quantity related to the vapor compressibility factor at saturation. For Lennard-Jones fluids the microscopic surface tension possesses a universal behavior with the parameters found from the mean-field density functional calculations. The theory is verified against nucleation experiments for argon, nitrogen, water, and mercury, demonstrating very good agreement with experimental data. Classical nucleation theory fails to predict experimental results when a critical cluster becomes small.

A random walk through the dynamics of homogeneous vapor-liquid nucleation

A method of calculating rates of homogeneous vapor-liquid nucleation based on Langevin dynamics of a few relevant degrees of freedom on a free-energy surface is proposed. The surface is obtained here from simulation and from a semi empirical expression. The mass and friction coefficients are derived from atomistic umbrella-sampling molecular-dynamics simulations. The calculated nucleation rate agrees with atomistic simulations for one particular state point of the Lennard-Jones fluid. The present method is about four orders of magnitude more computationally efficient than the direct atomistic simulation of the transmission coefficient.

Simulating vapor–liquid nucleation of n-alkanes

A combination of the aggregation-volume-bias Monte Carlo algorithm, the configurational-bias Monte Carlo algorithm, and the umbrella sampling technique was applied to investigate homogeneous vapor–liquid nucleation in ethane, n-butane, and n-heptane. The simple transferable potentials for phase equilibria-united atom (TraPPE-UA) force field was used in this investigation. It was found that for the n-heptane case, the TraPPE-UA force field predicted a nucleation rate that is about three to four orders of magnitude higher than that measured by an upward thermal diffusion cloud chamber experiment. Comparison of the simulation results to the classical nucleation theory (CNT) shows that CNT consistently overestimates the barrier heights for all chain lengths investigated. The offset on the barrier heights was found nearly independent of the supersaturation for both ethane and n-butane, similar to a Lennard-Jones system previously studied. This also directly leads to a good agreement on the cluster sizes between the simulation and the CNT calculated from the nucleation theorem. For n-heptane, however, the offset was found to depend on the supersaturation. It appears that CNT predicts a slightly weaker dependence of the nucleation rate on supersaturation, which agrees with both density functional calculations and the experiments. Structural analysis demonstrates that the orientational order near the surface differs significantly between the critical nucleus and the bulk planar liquid–vapor interface for n-heptane systems, whereas the density in the interior of the critical nucleus is in good agreement with the bulk liquid density. The different surface ordering offers a microscopic explanation for the differences observed for n-heptane between the CNT on one side and experimental observations and simulations on the other side.

Aggregation-volume-bias Monte Carlo simulations of vapor-liquid nucleation barriers for Lennard-Jonesium

A combination of the aggregation-volume-bias Monte Carlo algorithm and the umbrella sampling technique is applied to investigate homogeneous vapor–liquid nucleation. This combined approach is simple, general, and robust. Its efficiency is demonstrated for nucleation of Lennard-Jonesium, for which the precise calculation of the nucleation barriers takes only a few minutes at higher supersaturations to a few hours at lower supersaturations. Comparison of the simulation results to the classical nucleation theory (CNT) shows that CNT overestimates the barrier heights by a value nearly independent of the supersaturation, but provides a reasonable description of the critical cluster sizes.

Effect of uniform electric field on homogeneous vapor–liquid nucleation and phase equilibria. II. Extended simple point charge model water

The effects of a uniform electric field on homogeneous vapor–liquid nucleation of the extended simple point charge (SPC/E) model water have been simulated. A grand canonical Monte Carlo simulation approach [I. Kusaka et al., J. Chem. Phys. 108, 3416 (1998)], which directly gives the equilibrium distribution of physical clusters, is employed to calculate the formation free energy of the SPC/E water cluster. The results show that the formation free energy is lowered in a uniform field if the chemical potential of the supersaturated vapor is fixed; in this case, the field enhances the rate of nucleation. However, if the vapor supersaturation or pressure is fixed, the formation free energy increases with the field, that is, the field reduces the rate of nucleation. This conclusion is consistent with an earlier study using the i/v cluster theory for weakly dipolar Stockmayer fluid in a uniform field (Part I). A byproduct of this work is the vapor–liquid coexistence (binodal) of the SPC/E water in the presence of the electric field.

The effect of a uniform electric field on homogeneous vapor–liquid nucleation in a dipolar fluid. I. Stockmayer fluid

The rate of homogeneous vapor–liquid nucleation is controlled mainly by the Gibbs formation free energy of critical clusters. Within the framework of the i/v cluster theory of Reiss and co-workers, the formation free energies of Stockmayer clusters in the presence of a uniform electric field are determined. The Helmholtz free energy of the clusters, an input required in the i/v cluster theory, is calculated via Monte Carlo simulations. The most significant result is that as a uniform electric field is applied the formation free energy at fixed supersaturation of the vapor becomes larger than that in the absence of a field, whereas at fixed chemical potential the formation free energy becomes smaller.

Semiphenomenological effective-medium theory of multicomponent nucleation

We propose an effective-medium approach for homogeneous vapor-liquid nucleation of multicomponent mixtures in the regime of retrograde condensation. Transformation to an effective unary system is accompanied by renormalization of the surface tension. We formulate a generalized Fisher droplet model [M. E. Fisher, Physics 3, 255 (1967)] for the cluster distribution in the effective system. A closed-form expression for the nucleation rate is obtained within the framework of the kinetic approach to nucleation. The theory contains no adjustable parameters. Two- and four-component mixtures of hydrocarbons are studied and theoretical predictions are compared with available experimental data.

Semiphenomenological theory of homogeneous vapor–liquid nucleation

A new semiphenomenological theory of homogeneous vapor–liquid nucleation is proposed. It is based on the Fisher droplet model applied at the saturation point within the framework of the kinetic approach. The microscopic surface tension of a droplet is supposed to have the Tolman form. The unknown Tolman length is naturally identified by equating a known empirical value of saturation pressure psat to the sum of the series over all droplet sizes for psat emerging from the Fisher model. The theory contains no adjustable parameters. Predictions of the new theory for various substances are compared with available experimental data and with the three other widely used theoretical models: classical nucleation theory, corrected Dillmann–Meier and Delale–Meier theory.