Evidence for N-1/3 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 super sonic expansions. The predicted terminal mean cluster size is compared to t he available data in the case of argon. The agreement between the model and the experimental results requires that the cross-section describing the st icking of an atom on a cluster of size N scales like N-alpha with alpha in the range 0.34-0.44, well below the alpha = 2/3 predicted by the simplest g eometrical 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 N-1/3 for small to mo derate N values and switches to the geometric scaling N-2/3 for very large N values. The crossover between these two scalings occurs when N approximat e to 10(3) for argon, but the mean exponent alpha over the size range 1-10( 4) is 0.46. This N scaling of the sticking cross-section should play an imp ortant role whenever condensation is important as it modifies the kinetics of the early stages.