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.

https://web.mst.edu/~hale/argonMC/References/JCP.2001.Chen.MC.LJ.nucleation.pdf

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

Ten independent quenches of a gas of 40 000 Lennard-Jones particles are followed until the systems exhibit droplet growth. The cluster distributions and the kinetics are determined for the quenched quasi-equilibrium state, at the onset of nucleation and at droplet growth. All the distributions are isomorphic with the particle distribution in the equilibrium gas state and asymptotically given by simple exponentials. The kinetics show detailed balance of particles and clusters which join and which leave the successful critical nuclei. The systems exhibit chaoticlike behavior with respect to the onset of nucleation, so that only marginal changes in a system will change the onset of nucleation.

Molecular-dynamics simulation of homogeneous nucleation in the vapor phase

We present results from large-scale molecular dynamics (MD) simulations of homogeneous vapor-to-liquid nucleation. The simulations contain between one and eight billion Lennard-Jones (LJ) atoms, covering up to 1.2 {\mu}s (56 million time-steps). They cover a wide range of supersaturation ratios, S=1.55 to 10^4, and temperatures from kT = 0.3 to 1.0 {\epsilon} (where {\epsilon} is the depth of the LJ potential, and k 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 = 1.0 {\epsilon} 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 104 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 = 1.0 {\epsilon} the critical sizes from both models are clearly too small. (abridged)

/pdf/large-scale-molecular-dynamics-simulations-of-homogeneous-3qa96lpra2.pdf

Large Scale Molecular Dynamics Simulations of Homogeneous Nucleation

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 1.0e (where e 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 = 1.0e 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 = 1.0e, 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.

/pdf/large-scale-molecular-dynamics-simulations-of-homogeneous-4cr631rl3f.pdf

Large scale molecular dynamics simulations of homogeneous nucleation

Neat methanol and tert-butanol are studied by molecular dynamics with the focus on the microstructure of these two alcohols. The site-site radial distribution functions, the corresponding structure factors, and an effective local one-body density function are shown to be the appropriate statistical quantities that point in a complementary manner towards the same microstructure for any given liquid. Methanol is found to be a weakly associated liquid forming various chainlike patterns (open and closed) while tert-butanol is almost entirely associated and forms micellelike primary pattern. The presence of stable local microheterogeneity within homogeneous disordered phase appears as a striking feature of these liquids. The absence of any such apparent clustering in water—a stronger hydrogen bonding liquid—through the same two statistical quantities is analyzed.

Microstructure of neat alcohols: A molecular dynamics study

The molecular theory of the homogeneous nucleation rate based on the n/v-Stillinger cluster, and developed in the preceding paper (paper I), is applied to the condensation of supersaturated argon vapor, in a preliminary calculation of the rate of nucleation for a single set of conditions (temperature=85 K, pressure=2500 Torr). Free energies are obtained by means of Monte Carlo simulation. Upper and lower bounds differing by only two orders of magnitude are obtained. Since the best current measurements of vapor phase nucleation rates are accurate to within about a single order of magnitude, this result is considered promising. The direction of future work to improve the accuracy of the predicted rate is clear, and considerable improvement should be possible. These directions are discussed in the paper. Also, the essentially non ad hoc nature of the n/v-Stillinger cluster is demonstrated by the appearance of a range of connectivity distances (in a predicted location) within which the calculated nucleation r...

http://web.mst.edu/~hale/argonMC/References/JCP.1999.Reiss.Senger.LJ.MC.nucl,.pdf

D. Pointu

Papers

A molecular theory of the homogeneous nucleation rate. II. Application to argon vapor