We discuss the application of the direct Monte Carlo method to the theory of cluster formation. Fractal relationships for the kernels appearing in the Smoluchowski equation are implemented in this method and the scaling behavior of the kernels is investigated using computer simulation. We study the effects of cluster disintegrations and also investigate the effects of ‘‘magic’’ numbers in cluster formation.

1.
W. A.
de Heer
,
Rev. Mod. Phys.
65
,
611
(
1993
).
2.
M.
Brack
,
Rev. Mod. Phys.
65
,
677
(
1993
).
3.
E. Haberland and Hellmut, Clusters of Atoms and Molecules (Springer Verlag, Berlin, 1994).
4.
T. Kodas and M. Hampden Smith, The Chemistry of Metal CVD (VCH, Weinheim, 1994), see p. 488.
5.
G.
Selwyn
,
J.
Singh
, and
R.
Bennett
,
J. Vac. Sci. Technol. A
7
,
2758
(
1989
).
6.
L. Bánjay and S. W. Koch, Semi-conductor Quantum Dots (World Scientific, Singapore, 1993).
7.
J. P. Jellinek, in Metal-Ligand Interactions, Structure and Reactivity, edited by N. Russo (Kluwer, Amsterdam, 1995), in press.
8.
K.
Clemenger
,
Phys. Rev. B
32
,
1359
(
1985
).
9.
K.
Clemenger
,
Phys. Rev. B
44
,
12991
(
1991
).
10.
P. P. Wegener, in Nonequilibrium Flows, edited by P. P. Wegener (Marcel Dekker, New York, 1969).
11.
M.
Fisher
,
Physics
3
,
255
(
1967
).
12.
R.
Becker
and
W.
Döring
,
Ann. Phys.
24
,
719
(
1935
).
13.
M. v.
Smoluchowski
,
Phys. Z.
17
,
585
(
1917
).
14.
I.
Ford
,
J.
Barrett
, and
M.
Lazaridis
,
J. Aerosol. Sci.
24
,
581
(
1993
).
15.
R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics and Chemical Reactivity (Oxford University Press, New York, 1987).
16.
J. L.
Katz
and
M. D.
Donohue
,
Adv. Chem. Phys.
40
,
137
(
1979
).
17.
S. L.
Girshick
and
C.-P.
Chiu
,
J. Chem. Phys.
93
,
1273
(
1990
).
18.
S. L.
Girschick
,
J. Chem. Phys.
94
,
826
(
1991
).
19.
M.
Volmer
and
A.
Weber
,
Z. Phys. Chem.
119
,
277
(
1926
).
20.
J.
Katz
,
H.
Saltsburg
, and
H.
Reiss
,
J. Coll. Interf. Sci.
21
,
560
(
1966
).
21.
Z.
Alexandrowicz
,
J. Phys. A
26
,
L655
(
1993
).
22.
W. K.
Kegel
,
J. Chem. Phys.
102
,
1094
(
1995
).
23.
H. Hettema and J. S. McFeaters, J. Chem. Phys. (to be published).
24.
M. v.
Smoluchowski
,
Z. Phys. Chem.
92
,
129
(
1918
).
25.
M.
Villarica
,
M.
Casey
,
J.
Goodisman
, and
J.
Chaiken
,
J. Chem. Phys.
98
,
4610
(
1993
).
26.
M. E.
Costas
,
M.
Moreau
, and
L.
Vicente
,
J. Phys. A
28
,
2981
(
1995
).
27.
J.
Chaiken
and
J.
Goodisman
,
J. Cluster. Sci.
6
,
319
(
1995
).
28.
R.
Ball
,
D.
Weitz
,
T.
Witten
, and
F.
Leyvraz
,
Phys. Rev. Lett.
58
,
274
(
1987
).
29.
R.
Botet
,
R.
Jullien
, and
M.
Kolb
,
Phys. Rev. A
30
,
2150
(
1984
).
30.
R.
Jullien
,
New J. Chem.
14
,
239
(
1990
).
31.
G.
Bird
,
Annu. Rev. Fluid Mech.
10
,
11
(
1978
).
32.
S. D.
Piersall
and
J. B.
Anderson
,
J. Chem. Phys.
95
,
971
(
1991
).
33.
S. D.
Piersall
and
J. B.
Anderson
,
Chem. Phys. Lett.
189
,
95
(
1992
).
34.
S. M.
Dunn
and
J. B.
Anderson
,
J. Chem. Phys.
102
,
2812
(
1995
).
35.
R.
Venkatesh
,
R.
Lucchese
,
W.
Marlow
, and
J.
Schulte
,
J. Chem. Phys.
102
,
7683
(
1995
).
36.
N.
Rao
and
P.
McMurry
,
Aerosol Sci. Technol.
11
,
120
(
1989
).
37.
P. Meakin, in The Fractal Approach to Heterogeneous Chemistry: Surfaces, Colloids, Polymers, edited by D. Avnir (Wiley, New York, 1989).
38.
C.
Wang
,
R.
Huang
,
Z.
Liu
, and
L.
Zheng
,
Chem. Phys. Lett.
227
,
103
(
1994
).
39.
G. Herdan, Small Particle Statistics (Elsevier, Amsterdam, 1953).
40.
M. Preston and R. Bhaduri, Structure of the Nucleus (Addison Wesley, London, 1975).
41.
E.
Kaxiras
and
K.
Jackson
,
Phys. Rev. Lett.
71
,
727
(
1993
).
42.
S. Friedlander, Fundamentals of Aerosol Behaviour (Cornell University Press, Ithaca, 1953).
43.
H. Hettema and J. S. McFeaters (unpublished).
44.
D. Mintzer, in The Mathematics of Physics and Chemistry, edited by H. Margenau and G. M. Murphy (Van Nostrand Reinhold, New York, 1964), Vol. 2, Chap. 1.
This content is only available via PDF.
You do not currently have access to this content.