Article

# Performance of some nucleation theories with a nonsharp droplet-vapor interface.

Department of Physics, P.O. Box 64, University of Helsinki, Helsinki 00014, Finland.

The Journal of Chemical Physics (Impact Factor: 3.16). 10/2010; 133(15):154503. DOI: 10.1063/1.3502643 Source: PubMed

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**ABSTRACT:**Recent very large molecular dynamics simulations of homogeneous nucleation with $(1-8) \cdot 10^9$ Lennard-Jones atoms [Diemand et al. J. Chem. Phys. {\bf 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: $\ln J' / \eta$ is scaled by $\ln S / \eta$, where the supersaturation ratio is $S$, $\eta$ 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.The Journal of Chemical Physics 05/2014; 140(19):194310. · 3.16 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**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.The Journal of Chemical Physics 08/2013; 139(7):074309. · 3.16 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The nucleation of particles from trace gases in the atmosphere is an important source of cloud condensation nuclei, and these are vital for the formation of clouds in view of the high supersaturations required for homogeneous water droplet nucleation. The methods of quantum chemistry have increasingly been employed to model nucleation due to their high accuracy and efficiency in calculating configurational energies; and nucleation rates can be obtained from the associated free energies of particle formation. However, even in such advanced approaches, it is typically assumed that the nuclei have a classical nature, which is questionable for some systems. The importance of zero-point motion (also known as quantum nuclear dynamics) in modelling small clusters of sulphuric acid and water is tested here using the path integral molecular dynamics method at the density functional level of theory. The general effect of zero-point motion is to distort the mean structure slightly, and to promote the extent of proton transfer with respect to classical behaviour. In a particular configuration of one sulphuric acid molecule with three waters, the range of positions explored by a proton between a sulphuric acid and a water molecule at 300 K (a broad range in contrast to the confinement suggested by geometry optimisation at 0 K) is clearly affected by the inclusion of zero point motion, and similar effects are observed for other configurations.The Journal of Chemical Physics 01/2014; 140(2):024306. · 3.16 Impact Factor

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