Abstract
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 N α 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 N 1/3 for small to moderate 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 ≈ 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.
Similar content being viewed by others
References
O.F. Hagena, W. Obert, J. Chem. Phys. 56, 1793 (1972).
J. Farges, B. Raoult, G. Torchet, J. Chem. Phys. 59, 3454 (1973).
J. Farges, M.-F. de Feraudy, B. Raoult, G. Torchet, J. Chem. Phys. 84, 3491 (1986).
A. Lallement, Ph.D. thesis, Orsay University, 1993.
U. Buck, R. Krohne, J. Chem. Phys. 105, 5408 (1996).
M.Y. Benslimane, Ph.D. thesis, École Polytechnique, 1995.
A. De Martino, M. Benslimane, M. Châtelet, C. Crozes, F. Pradrère, H. Vach, Z. Phys. D 27, 185 (1993).
O.F. Hagena, Z. Phys. D 4, 291 (1987).
O.F. Hagena, G. Knop, R. Fromknecht, G. Linkes, J. Vac. Sci. Technol. A 12, 282 (1994).
J. Gspann, H. Vollmar, in Rarefied Gas Dynamics, 8th Symposium, edited by K. Karamcheti (Academic Press, New York, 1974), p. 261.
J. Gspann, H. Vollmar, in Rarefied Gas Dynamics, 11th Symposium, edited by R. Campargue (CEA, Paris, 1979), Vol. II, p. 1193.
O.F. Hagena, Phys. Fluids 17, 894 (1974).
C.E. Klots, Nature 327, 222 (1987).
F. Calvo (unpublished results).
H. Ashkenas, F.S. Sherman, in Rarefied Gas Dynamics, 4th Symposium, edited by J.H. de Leeuw (Academic Press, New york, 1968), Vol. II, p. 84.
D.R. Miller, in Atomic and Molecular Beam Methods, edited by G. Scoles (Oxford University Press, New York, 1988), Vol. I, p. 14.
E. Fort, F. Pradère, A. De Martino, H. Vach, M. Châtelet, Eur. Phys. J. D 1, 79 (1998).
T.L. Hill, J. Chem. Phys. 16, 181 (1948).
F. Calvo, F. Spiegelmann, Phys. Rev. B 54, 10949 (1996).
F. Calvo, Chem. Phys. Lett. 291, 393 (1998).
S. Weerasinghe, F.G. Amar, J. Chem. Phys. 98, 4967 (1993).
D.J. Wales, J.P.K. Doye, J. Phys. Chem. A 101, 5111 (1997).
Handbook of Chemistry and Physics, edited by R.C. Weast, M.J. Astle, 63rd edn. (CRC Press, 1982–1983).
A. Dalgarno, Adv. Chem. Phys. 12, 143 (1967).
J.M. Mestdagh, M.A. Gaveau, C. Gée, O. Sublemontier, J.P. Visticot, Int. Rev. Phys. Chem. 16, 215 (1997).
M.J. Vasile, F.A. Stevie, J. Chem. Phys. 75, 2399 (1981).
Author information
Authors and Affiliations
Corresponding author
Additional information
UMR 5589 du CNRS
Rights and permissions
About this article
Cite this article
Vigué, J., Labastie, P. & Calvo, F. Evidence for N1/3 dependence of the sticking cross-section of atoms on small and medium-size van der Waals clusters. Eur. Phys. J. D 8, 265–272 (2000). https://doi.org/10.1007/s100530050035
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s100530050035