Homogeneous nucleation with magic numbers: Aluminum

Abstract

Homogeneous nucleation of clusters that exhibit magic numbers is studied numerically, using as an example aluminum at 2000 K, based on recent calculations of free energies [Li et al., J. Phys. Chem. C 111, 16227 (2007)] and condensation rate constants [Li and Truhlar, J. Phys. Chem. C 112, 11109 (2008)] that provide a database for Al(i) up to i=60. The nucleation behavior for saturation ratios greater than about 4.5 is found to be dominated by a peak in the free energy change associated with the reaction iAl-->Al(i) at i=55, making it the critical size over a wide range of saturation ratios. Calculated steady-state nucleation rates are many orders of magnitude lower than predicted by classical nucleation theory (CNT). The onset of nucleation is predicted to occur at a saturation ratio of about 13.3, compared to about 5.1 in CNT, while for saturation ratios greater than about 25 the abundance of magic-numbered clusters becomes high enough to invalidate the assumption that cluster growth occurs solely by monomer addition. Transient nucleation is also predicted to be substantially different than predicted by CNT, with a much longer time required to reach steady state: about 10(-4) s at a saturation ratio of 20, compared to about 10(-7) s from CNT. Magic numbers are seen to play an important role in transient nucleation, as the nucleation currents for clusters of adjacent sizes become equal to each other in temporally successive groups, where the largest cluster in each group is the magic-numbered one.

Atmospheric Cluster Dynamics Code: a flexible method for solution of the birth-death equations

“…Even without using the modified collision rate coefficients (i.e., using Eq. (2) above), ACDC provides results in very close agreement with what is seen by Girshick et al (2009) This is perhaps unsurprising, since Girshick et al (2009) use CNT as a basis for their dynamics calculations, which ACDC has already been validated against through the second test in this section, but it illustrates the flexibility of ACDC; the change from test two to test three required minor changes to the input file and the cluster free energies.…”

“…Li et al (2007) have determined very accurate monomer addition free energies using Monte Carlo simulation of the equilibrium constants and several high level corrections for the aluminum dimer through the 60-mer. Girshick et al (2009) explored the kinetics of this system by using these addition free energies and modified collision rate coefficients (Li and Truhlar, 2008) to predict the nucleation rate and steady-state concentrations of the vapor-liquid nucleation of aluminum. Even without using the modified collision rate coefficients (i.e., using Eq.…”

Ion-pair evaporation from ionic liquid clusters

“…Evidently, the common characteristic between such stable liquid phase prenucleation clusters and gas-phase magic number clusters (which are not stable at the vanishing monomer concentration investigated here) is their singular stability against dissolution or evaporation, enabling them to exist as permanent entities at monomer concentrations at which larger or smaller clusters (except the monomer) are unstable. High magic number cluster abundances have been recently linked also with homogeneous nucleation [17].…”

Modeling of carbon dioxide condensation in the high pressure flows using the statistical BGK approach

“…The studies concentrated on predicting the steady state and transient nucleation rates of aluminum with a generic emphasis on homogeneous nucleation behavior of magic numbered substances such as aluminum, in which a particular size cluster is found with an especially high probability. 3 Finally, in the last few decades, the scope of condensation has broadened to many other disciplines such as biomedical research and nanofabrication. Recently an interesting study was carried out on nucleation of cholesterol aggregates.…”