Evidence for N1/3 dependence of the sticking cross-section of atoms on small and medium-size van der Waals clusters

This paper introduces a simple model describing the cluster growth in supersonic expansions. The predicted terminal mean cluster size is compared to the available data in the case of argon. The agreement between the model and the experimental results requires that the cross-section describing the sticking of an atom on a cluster of size N scales like Nα with α in the range 0.34–0.44, well below the α = 2/3 predicted by the simplest geometrical scaling argument. We explain this unexpected result in two steps. First, using Monte Carlo simulations, we check that the potential between an atom and a cluster is accurately represented by the Gspann and Vollmar potential, even at finite temperature. Then, using Langevin’s approximation, we show that the sticking cross-section scales like N1/3 for small to moderate N values and switches to the geometric scaling N2/3 for very large N values. The crossover between these two scalings occurs when N ≈ 103 for argon, but the mean exponent α over the size range 1–104 is 0.46. This N scaling of the sticking cross-section should play an important role whenever condensation is important as it modifies the kinetics of the early stages.