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 ͑CNT͒ 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.

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.

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The formation free energy of clusters in a supersaturated vapor is obtained by a constrained Monte Carlo technique. A key feature of this approach is to set an upper limit to the size of cluster. This maximum cluster size serves essentially as an extra thermodynamic variable that constrains the system. As a result, clusters larger than the critical cluster of nucleation in the supersaturated vapor can no longer grow beyond the limiting size. Like changing the overall density of the system, changing the maximum cluster size also results in a different supersaturation and thereby a different formation free energy. However, at the same supersaturation and temperature it is found that the formation free energy has a unique value, independent of the upper limit of cluster size. The predicted size of critical cluster of nucleation is found to be consistent with the nucleation theorem as well as previous results using different simulation approaches.

"Toward a molecular theory of vapor-phase nucleation. V. Self-consistency in the decoupled dimer limit" (1997). Xiao Cheng Zeng Publications. 69. http://digitalcommons.unl.edu/chemzeng/69Toward a molecular theory of vapor-phase nucleation. V. Self-consistency in the decoupled dimer limit The i/v cluster theory of vapor phase nucleation has been presented in a series of papers of which the present paper is No. V. The theory has experienced some evolution throughout this series. In the first paper an attempt was made to use the classical cluster of Lee, Barker, and Abraham ͑LBA cluster͒ that is so attractive for computer simulation. Among other things, that theory uses a so-called ''shell molecule'' that does not interact with the remaining molecules of the cluster. We show that this ''decoupling'' of the shell molecule leads to a result that is not internally consistent in the sense that dimers ͑which are really single vapor molecules͒ do not have the right concentration. We show how to repair this inconsistency so that the decoupling approximation can be used and, with it, the useful LBA cluster.