Random packing of spheres inside fractal collectors of dimension 2 < d < 3 is studied numerically using Random Sequential Adsorption (RSA) algorithm. The paper focuses mainly on the measurement of random packing saturation limit. Additionally, scaling properties of density autocorrelations in the obtained packing are analyzed. The RSA kinetics coefficients are also measured. Obtained results allow to test phenomenological relation between random packing saturation density and collector dimension. Additionally, performed simulations together with previously obtained results confirm that, in general, the known dimensional relations are obeyed by systems having non-integer dimension, at least for d < 3.
REFERENCES
1.
J. H.
Conway
and N. J. A.
Sloane
, Sphere Packings, Lattices and Groups
(Springer-Verlag
, New York
, 1998
).2.
3.
T. C.
Hales
and S. P.
Ferguson
, Int. J. Math. Comput. Sci.
36
(1
), 21
(2006
);T. C.
Hales
, Ann. Math.
162
, 1065
(2005
).4.
H.
Cohn
and A.
Kumar
, Ann. Math.
170
, 1003
(2009
).5.
S.
Torquato
and F. H.
Stillinger
, Rev. Mod. Phys.
82
, 2633
(2010
).6.
S.
Torquato
, Random Heterogeneous Materials: Microstructure and Macroscopic Properties
(Springer-Verlag
, New York
, 2002
).7.
Z.
Adamczyk
, Particles at Interfaces: Interactions, Deposition, Structure
(Elsevier
, Amsterdam
, 2006
).8.
9.
S.
Torquato
, O. U.
Uche
, and F. H.
Stillinger
, Phys. Rev. E
74
, 061308
(2006
).10.
A. M. R.
Cadilhe
and V.
Privman
, Mod. Phys. Lett. B
18
, 207
(2004
).11.
Y.
Fan
and J. K.
Percus
, Phys. Rev. Lett.
67
(13
), 1677
(1991
).12.
J.
Feder
, J. Theor. Biol.
87
, 237
(1980
).13.
R. H.
Swendsen
, Phys. Rev. A
24
, 504
(1981
).14.
V.
Privman
, J.-S.
Wang
, and P.
Nielaba
, Phys. Rev. B
43
, 3366
(1991
).15.
S.
Torquato
and F. H.
Stillinger
, J. Phys. Chem. B
106
, 8354
(2002
).16.
M.
Ciesla
and J.
Barbasz
, J. Chem. Phys.
137
, 044706
(2012
).17.
B.
Bonnier
, D.
Boyer
, and P.
Viot
, J. Phys. A
27
, 3671
(1994
).18.
A. H.
Fuchs
and A. K.
Cheetham
, J. Phys. Chem. B
105
(31
), 7375
(2001
).19.
S.
Kinge
, M.
Crego-Calama
, and D. N.
Reinhoudt
, ChemPhysChem
9
(1
), 20
(2008
).20.
P.
Pfeifer
and D.
Avnir
, J. Chem. Phys.
79
, 3558
(1983
).21.
D.
Avnir
, D.
Farin
, and P.
Pfeifer
, J. Chem. Phys.
79
, 3566
(1983
);P.
Pfeifer
, D.
Avnir
, and D.
Farin
, Surf. Sci.
126
, 569
(1983
);D.
Avnir
, D.
Farin
, and P.
Pfeifer
, Nature (London)
308
, 261
(1984
).22.
E.
Basillais
, C. R. Acad. Sci., Ser. III
321
(4
), 295
(1998
).23.
M. M.
Khasanov
and I. I.
Abyzbaev
, J. Eng. Phys. Thermophys.
61
(6
), 1516
(1991
).24.
M. S.
Nazzarro
, A. J. Ramirez
Pastor
, J. L.
Riccardo
, and V.
Pereyra
, J. Phys. A
30
, 1925
(1997
).25.
E. S.
Loscar
, R. A.
Borzi
, and E. V.
Albano
, Phys. Rev. E
68
, 041106
(2003
).26.
M. W.
Cole
and N. S.
Holter
, Phys. Rev. B
33
, 8806
(1986
).27.
P.
Pfeifer
, Y. J.
Wu
, M. W.
Cole
, and J.
Krim
, Phys. Rev. Lett.
62
, 1997
(1989
).28.
N. V.
Brilliantov
, Yu. A.
Andrienko
, P. L.
Krapivsky
, and J.
Kurths
, Phys. Rev. E
58
, 3530
(1998
).29.
M.
Ciesla
and J.
Barbasz
, J. Stat. Mech.: Theory Exp.
2012
, P03015
.30.
Z.
Adamczyk
, J.
Barbasz
, and M.
Ciesla
, Langmuir
26
, 11934
(2010
).31.
Z.
Adamczyk
, J.
Barbasz
, and M.
Ciesla
, Langmuir
27
, 6868
(2011
).32.
M.
Ciesla
, Phys. Rev. E
87
, 052401
(2013
).33.
G.
Tarjus
, P.
Schaaf
, and J.
Talbot
, J. Stat. Phys.
63
, 167
(1991
).34.
K.
Ball
, Int. Math. Res. Notices
1992
, 217
.© 2013 AIP Publishing LLC.
2013
AIP Publishing LLC
You do not currently have access to this content.
