On the similarity of equilibrium and critical clusters in atomic vapors

In a previous paper [I. Napari, J. Julin, and H. Vehkamäki, J. Chem. Phys. 131, 244511 (2009)] we compared sizes of critical and equilibrium clusters in Lennard-Jones vapors using various geometrical clusters definitions. In particular, we found that the critical and equilibrium clusters were of the same size if each constituent atom in the cluster was required to have at least five neighboring atoms (ten Wolde-Frenkel cluster) but the critical clusters were much larger if only one neighboring atom was sufficient to fulfill the cluster definition (Stillinger cluster). The conclusion was that the critical clusters at high vapor densities have more ramified structure than the corresponding equilibrium clusters. In this study we have performed new molecular dynamics simulations to enlighten this matter. It is found that the surprising conclusion of the earlier work can be traced to the mean first passage time method which was used to obtain critical cluster sizes from simulations. When a certain sized Stillinger cluster first appears in the simulation, the cluster tends to have a more ramified structure than Stillinger clusters of that size observed later in the simulation. However, for the latter clusters the ratio of Stillinger and ten Wolde-Frenkel sizes in the vapor is the same as in the equilibrium simulations, implying similar structure of critical and equilibrium clusters.