Search

We report water cluster formation in the uniform postnozzle flow of a Laval nozzle at low temperatures of 87.0 and 47.5 K and high supersaturations of lnS ∼ 41 and 104, respectively. Cluster size distributions were measured after soft single-photon ionization at 13.8 eV with mass spectrometry. Critical cluster sizes were determined from cluster size distributions recorded as a function of increasing supersaturation, resulting in critical sizes of 6-15 and 1, respectively. Comparison with previous data for propane and toluene reveals a systematic trend in the nucleation behavior, i.e., a change from a steplike increase to a gradual increase of the maximum cluster size with increasing supersaturation. Experimental nucleation rates of 5 · 1015 cm−3 s−1 and 2 · 1015 cm−3 s−1 for lnS ∼ 41 and 104, respectively, were retrieved from cluster size distributions recorded as a function of nucleation time. These lie 2-3 orders of magnitude below the gas kinetic collision limit assuming unit sticking probability, but they agree very well with a recent prediction by a master equation model based on ab initio transition state theory. The experimental observations are consistent with barrierless growth at 47.5 K, but they hint at a more complex nucleation behavior for the measurement at 87.0 K. [ABSTRACT FROM AUTHOR]

We perform direct large molecular dynamics simulations of homogeneous SPC/E water nucleation, using up to ~4 · 106 molecules. Our large system sizes allow us to measure extremely low and accurate nucleation rates, down to ~1019 cm-3 s-1, helping close the gap between experimentally measured rates ~1017 cm-3 s-1. We are also able to precisely measure size distributions, sticking efficiencies, cluster temperatures, and cluster internal densities. We introduce a new functional form to implement the Yasuoka-Matsumoto nucleation rate measurement technique (threshold method). Comparison to nucleation models shows that classical nucleation theory over-estimates nucleation rates by a few orders of magnitude. The semi-phenomenological nucleation model does better, under-predicting rates by at worst a factor of 24. Unlike what has been observed in Lennard-Jones simulations, post-critical clusters have temperatures consistent with the run average temperature. Also, we observe that post-critical clusters have densities very slightly higher, ~5%, than bulk liquid. We re-calibrate a Hale-type J vs. S scaling relation using both experimental and simulation data, finding remarkable consistency in over 30 orders of magnitude in the nucleation rate range and 180 K in the temperature range. [ABSTRACT FROM AUTHOR]

Recent very large molecular dynamics simulations of homogeneous nucleation with (1 - 8) ×109 Lennard-Jones atoms [J. Diemand, R. Angélil, K. K. Tanaka, and H. Tanaka, J. Chem. Phys. 139, 074309 (2013)] allow us to accurately determine the formation free energy of clusters over a wide range of cluster sizes. This is now possible because such large simulations allow for very precise measurements of the cluster size distribution in the steady state nucleation regime. The peaks of the free energy curves give critical cluster sizes, which agree well with independent estimates based on the nucleation theorem. Using these results, we derive an analytical formula and a new scaling relation for nucleation rates: ln J'/η is scaled by ln S/η, where the supersaturation ratio is S, η is the dimensionless surface energy, and J' is a dimensionless nucleation rate. This relation can be derived using the free energy of cluster formation at equilibrium which corresponds to the surface energy required to form the vapor-liquid interface. At low temperatures (below the triple point), we find that the surface energy divided by that of the classical nucleation theory does not depend on temperature, which leads to the scaling relation and implies a constant, positive Tolman length equal to half of the mean inter-particle separation in the liquid phase. [ABSTRACT FROM AUTHOR]

We performed molecular dynamics (MD) simulations of nucleation from vapor at temperatures below the triple point for systems consisting of 104-105 Lennard-Jones (L-J) type molecules in order to test nucleation theories at relatively low temperatures. Simulations are performed for a wide range of initial supersaturation ratio (S0 ≃ 10 - 108) and temperature (kT = 0.2 - 0.6[variant_greek_epsilon]), where [variant_greek_epsilon] and k are the depth of the L-J potential and the Boltzmann constant, respectively. Clusters are nucleated as supercooled liquid droplets because of their small size. Crystallization of the supercooled liquid nuclei is observed after their growth slows. The classical nucleation theory (CNT) significantly underestimates the nucleation rates (or the number density of critical clusters) in the low-T region. The semi-phenomenological (SP) model, which corrects the CNT prediction of the formation energy of clusters using the second virial coefficient of a vapor, reproduces the nucleation rate and the cluster size distributions with good accuracy in the low-T region, as well as in the higher-T cases considered in our previous study. The sticking probability of vapor molecules onto the clusters is also obtained in the present MD simulations. Using the obtained values of sticking probability in the SP model, we can further refine the accuracy of the SP model. [ABSTRACT FROM AUTHOR]

Two kinds of the homogeneous nucleation theory exist at the present: the classical nucleation theory and the semiphenomenological model. To test them, we performed molecular-dynamics (MD) simulations of nucleation from vapor to liquid with 5000–20 000 Lennard-Jones-type molecules. Simulations were done for various values of supersaturation ratios (from 2 to 10) and temperatures (from 80 to 120 K). We compared the size distribution of clusters in MD simulations with those in the theoretical models because the number density of critical clusters governs the nucleation rate. We found that the semiphenomenological model achieves excellent agreements in size distributions of the clusters with all MD simulations we done. The classical theory underestimates the number density of the clusters in the temperature range of 80–100 K, but overestimates in 100–120 K. The semiphenomenological model also predicts well the nucleation rate in MD simulations, while the classical nucleation theory does not. Our results confirmed the validity of the semiphenomenological model for Lennard-Jones-type molecules. [ABSTRACT FROM AUTHOR]

We performed molecular dynamics simulations of the nucleation of water vapor in order to test nucleation theories. Simulations were performed for a wide range of supersaturation ratios (S = 3-25) and water temperatures (T(w) = 300-390 K). We obtained the nucleation rates and the formation free energies of a subcritical cluster from the cluster size distribution. The classical nucleation theory and the modified classical nucleation theory (MCNT) overestimate the nucleation rates in all cases. The semi-phenomenological model, which corrects the MCNT prediction using the second virial coefficient of a vapor, reproduces the formation free energy of a cluster with the size ≲20 to within 10% and the nucleation rate and cluster size distributions to within one order of magnitude. The sticking probability of the vapor molecules to the clusters was also determined from the growth rates of the clusters. The sticking probability rapidly increases with the supersaturation ratio S, which is similar to the Lennard-Jones system.

We have performed large-scale Lennard-Jones molecular dynamics simulations of homogeneous vapor-to-liquid nucleation, with 10(9) atoms. This large number allows us to resolve extremely low nucleation rates, and also provides excellent statistics for cluster properties over a wide range of cluster sizes. The nucleation rates, cluster growth rates, and size distributions are presented in Diemand et al. [J. Chem. Phys. 139, 74309 (2013)], while this paper analyses the properties of the clusters. We explore the cluster temperatures, density profiles, potential energies, and shapes. A thorough understanding of the properties of the clusters is crucial to the formulation of nucleation models. Significant latent heat is retained by stable clusters, by as much as ΔkT = 0.1ε for clusters with size i = 100. We find that the clusters deviate remarkably from spherical-with ellipsoidal axis ratios for critical cluster sizes typically within b/c = 0.7 ± 0.05 and a/c = 0.5 ± 0.05. We examine cluster spin angular momentum, and find that it plays a negligible role in the cluster dynamics. The interfaces of large, stable clusters are thinner than planar equilibrium interfaces by 10%-30%. At the critical cluster size, the cluster central densities are between 5% and 30% lower than the bulk liquid expectations. These lower densities imply larger-than-expected surface areas, which increase the energy cost to form a surface, which lowers nucleation rates.

We present results from large-scale molecular dynamics (MD) simulations of homogeneous vapor-to-liquid nucleation. The simulations contain between 1 × 10(9) and 8 × 10(9) Lennard-Jones (LJ) atoms, covering up to 1.2 μs (56 × 10(6) time-steps). They cover a wide range of supersaturation ratios, S ≃ 1.55-10(4), and temperatures from kT = 0.3 to 1.0ε (where ε is the depth of the LJ potential, and k is the Boltzmann constant). We have resolved nucleation rates as low as 10(17) cm(-3) s(-1) (in the argon system), and critical cluster sizes as large as 100 atoms. Recent argon nucleation experiments probe nucleation rates in an overlapping range, making the first direct comparison between laboratory experiments and molecular dynamics simulations possible: We find very good agreement within the uncertainties, which are mainly due to the extrapolations of argon and LJ saturation curves to very low temperatures. The self-consistent, modified classical nucleation model of Girshick and Chiu [J. Chem. Phys. 93, 1273 (1990)] underestimates the nucleation rates by up to 9 orders of magnitudes at low temperatures, and at kT = 1.0ε it overestimates them by up to 10(5). The predictions from a semi-phenomenological model by Laaksonen et al. [Phys. Rev. E 49, 5517 (1994)] are much closer to our MD results, but still differ by factors of up to 10(4) in some cases. At low temperatures, the classical theory predicts critical clusters sizes, which match the simulation results (using the first nucleation theorem) quite well, while the semi-phenomenological model slightly underestimates them. At kT = 1.0ε, the critical sizes from both models are clearly too small. In our simulations the growth rates per encounter, which are often taken to be unity in nucleation models, lie in a range from 0.05 to 0.24. We devise a new, empirical nucleation model based on free energy functions derived from subcritical cluster abundances, and find that it performs well in estimating nucleation rates.