Abstract
The Smoluchowski equations describe the coalescence of clusters to form larger clusters. If the kernels or rate constants in these equations are homogeneous, meaning thatK λj, λk =λ 2ω K jk (wherej andk are cluster sizes), it can be shown that the populationsn k approachAk a e -bk for largek and large time, where the constantsa andb depend on the homogeneity parameterω. Deviations of observed populations from this formula may be ascribed to magic-number and/or evaporation effects on the kernels. By integrating the Smoluchowski equations numerically for various choices of the kernels, we derive population distributions and show the effects of magic-number clusters and evaporation on the population distribution. Various methods are used to extract the value ofω, in order to determine the best way to extract the underlying value ofω from experimental data. Experimental populations for sodium metal clusters are then analyzed according to the same procedure, to extract the homogeneity parameter and explain the patterns in the population distribution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Kappes and S. Leutwyler (1988). In G. Scoles (ed.),Atomic and Molecular Beam Methods, Vol. 1, Chap. 15 (Oxford University Press, New York, 1988).
D. Rooney, T. Byassee, D. Macero, B. Vastag, and J. Chaiken (1990).J. Electrochem. Soc. 137, 1162–1166; J. U. S. Chaiken (1990). Patent 4.971,853.
J. Chaiken, M. J. Casey, and M. Villarica (1992)J. Phys. Chem. 96, 3183.
M. J. Casey, J. M. Osman, and J. Chaiken (1992).Proc. SPIE 1626, 317.
M. Villarica, M. J. Casey, J. Goodisman, and J. Chaiken (1993).J. Chem. Phys. 98, 1.
R. Jullien (1990).New Journal Chem. 14, 239.
R. Botet and R. Jullien (1984).J. Phys. A 17, 2517.
M. V. Smoluchowski (1917).Phys. Zeits. 17, 557.
J. Goodisman and J. Chaiken (1994).J. Photosci. Photobiol. A: Chem. 80, 53–59.
D. Siano (1972).J. Chem. Ed. 49, 755: G. Herdan and M. L. Smith. Small Particle Statistics (Elsevier, New York, 1953).
W. D. Knight, K. Clemenger, W. A. de Heer, W. Saunders, M. Y. Chou, and M. L. Cohen (1984).Phys. Rev. Lett. 52, 2141.
T. D. Klots, B. J. Winter, E. Parts, and S. J. Riley (1990).J. Chem. Phys. 92, 2110.
H. W. Kroto, J. R. Heath, S. C. O'Brien, R. F. Curl, and S. E. Smalley (1985).Nature (London) 318. 162.
K. Suslick (1991).Nature (London) 353, 414.
D. J. Auerbach, in G. Scoles (ed.).Atomic and Molecular Beam Methods, Vol. 1, Chap. I (Oxford University Press, New York, 1988).
G. Zumofen, A. Blumen, and J. Klafter (1990).New J. Chem. 14, 189–196, and references therein.
M. Tence, J. P. Chevaier, and R. Jullien (1986).J. Physique 47. 1989.
R. Pool (1990).Science 248, 186–1188, and references therein.
T. P. Martin, T. Bergmann, H. Gohlich, and T. Lange (1991).J. Phys. Chem.95. 5421.
W. H. Stockmayer (1943).J. Chem. Pins. 11, 45.
J. W. Brady. J. Doll, and D. L. Thompson (1979).J. Chem. Phys. 71, 2467.
C. Brchignac, P. Cahuzac, and J. Leygnier (1989).J. Crem. Phys. 90, 1493.
K. J. Laidler.Chemical Kinetics (Harpher and Row. New York, 1987), p. 157.
A. V. Dem'yanenko and A. A. Puretzky (1990).Spectrochimica Acta A 46, 509.
A. A. Puretzky, in J. Chaiken (ed.).Laser Chemistry of Organometallics, ACS Symposium Series, Vol. 503 (American Chemical Society. Washington, D.C. 1993).
S. H. Bauer (1977).J. Phys. Chem. 81, 1479.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chaiken, J., Goodisman, J. Interpreting magic-number and evaporation effects in cluster size distributions. J Clust Sci 6, 319–342 (1995). https://doi.org/10.1007/BF01169699
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01169699