We study the adsorption of flexible polymer macromolecules on a percolation cluster, formed by a regular two-dimensional disordered lattice at critical concentration pc of attractive sites. The percolation cluster is characterized by a fractal dimension $d_s^{p_c}=91/49$. The conformational properties of polymer chains grafted to such a fractal substrate are studied by means of the pruned-enriched Rosenbluth method. We find estimates for the surface crossover exponent governing the scaling of the adsorption energy in the vicinity of transition point, $\phi _s^{p_c}=0.425\pm 0.009$, and for adsorption transition temperature, $T_A^{p_c}=2.64\pm 0.02$. As expected, the adsorption is diminished when the fractal dimension of the substrate is smaller than that of a plain Euclidean surface. The universal size and shape characteristics of a typical spatial conformation which attains a polymer chain in the adsorbed state are analyzed as well.
REFERENCES
1.
A. K.
Dolan
and S. F.
Edwards
, Proc. R. Soc. London
337
, 509
(1974
);G. J.
Fleer
, J. M.
Scheutjens
, and M. A.
Cohen Stuart
, Colloids Surf.
31
, 1
(1988
).2.
A. F.
Xie
and S.
Granick
, Nature Mater.
1
, 129
(2002
).3.
B.
Maier
and J. O.
Rädler
, Phys. Rev. Lett.
82
, 1911
(1999
).4.
E.
Eisenriegler
, Polymers near Surfaces
(World Scientific
, Singapore
, 1993
).5.
H. W.
Diehl
and S.
Dietrich
, Phys. Rev. B
24
, 2878
(1981
).6.
E.
Eisenriegler
, K.
Kremer
, and K.
Binder
, J. Chem. Phys.
77
, 6296
(1982
).7.
P. G.
de Gennes
, Macromolecules
14
, 1637
(1981
);P. G.
de Gennes
and P.
Pincus
, J. Phys. (Paris), Lett.
44
, L241
(1983
).8.
H. W.
Diehl
and M.
Shpot
, Nucl. Phys. B
528
, 595
(1998
).9.
Z.
Usatenko
, J. Stat. Mech.
2006
, P03009
.10.
H.
Meirovitch
and S.
Livne
, J. Chem. Phys.
88
, 4507
(1988
).11.
R.
Hegger
and P.
Grassberger
, J. Phys. A
27
, 4069
(1994
).12.
R.
Descas
, J.-U.
Sommer
, and A.
Blumen
, J. Chem. Phys.
120
, 8831
(2004
).13.
P.
Grassberger
, J. Phys. A
38
, 323
(2005
).14.
M.
Bachmann
and W.
Janke
, Phys. Rev. E
73
, 041802
(2006
).15.
M.
Möddel
, M.
Bachmann
, and W.
Janke
, Macromolecules
44
, 9013
(2011
).16.
A.
Baumgärtner
and M.
Muthukumar
, J. Chem. Phys.
94
, 4062
(1991
).17.
M.
Kawaguchi
and T.
Arai
, Macromolecules
24
, 889
(1991
).18.
A. C.
Balasz
, K.
Huang
, and P.
McElwain
, Macromolecules
24
, 714
(1991
).19.
A.
Baumgärtner
and M.
Muthukumar
, J. Chem. Phys.
94
, 4062
(1991
).20.
G.
Huber
and T. A.
Vilgis
, Eur. Phys. J. B
3
, 217
(1998
).21.
K.
Sumithra
and A.
Baumgaertner
, J. Chem. Phys.
109
, 1540
(1998
).22.
M. S.
Moghaddam
and S. G.
Whittington
, J. Phys. A
35
, 33
(2002
);M. S.
Moghaddam
, J. Phys. A
36
, 939
(2003
).23.
Z.
Usatenko
and A.
Ciach
, Phys. Rev. E
70
, 051801
(2004
);Z.
Usatenko
and J.-U.
Sommer
, J. Stat. Mech.: Theory Exp.
2007
, P10006
.24.
J.
Zierbarth
, Y.
Wang
, A.
Polotsky
, and M.
Luo
, Macromolecules
40
, 3498
(2007
).25.
Y.
Kim
, J. Phys. A
20
, 1293
(1987
).26.
S. B.
Lee
, H.
Nakanishi
, and Y.
Kim
, Phys. Rev. B
39
, 9561
(1989
);H.
Nakanishi
and J.
Moon
, Physica A
191
, 309
(1992
).27.
R. M.
Ziff
, Phys. Rev. Lett.
72
, 1942
(1994
).28.
D.
Avnir
, D.
Farin
, and P.
Pfeifer
, Nature (London)
308
, 261
(1984
);D.
Avnir
, D.
Farin
, and P.
Pfeifer
, J. Chem. Phys.
79
, 3566
(1983
).29.
E.
Bouchaud
and J.
Vannimenus
, J. Phys. (France)
50
, 2931
(1989
).30.
D.
MacDonald
, D. L.
Hunter
, K.
Kelly
, and J.
Naeem
, J. Phys. A
33
, 5973
(2006
).31.
S.
Elesović-Hadžić
, I.
Živiž
, and S.
Milošević
, J. Phys. A
36
, 1213
(2003
).32.
V.
Bubanja
, M.
Kneževic
, and J.
Vannimenus
, J. Stat. Phys.
71
, 7
(1993
).33.
S.
Kumar
, Y.
Singh
, and D.
Dhar
, J. Phys. A
26
, 4835
(1993
).34.
V.
Miljković
, S.
Milošević
, and I.
Živić
, Phys. Rev. E
52
, 6314
(1995
).35.
T.
Auth
and G.
Gompper
, Phys. Rev. E
68
, 051801
(2003
);T.
Auth
and G.
Gompper
, Phys. Rev. E
72
, 031904
(2005
).36.
S.
Karalus
, W.
Janke
, and M.
Bachmann
, Phys. Rev. E
84
, 031803
(2011
).37.
S.
Havlin
and D.
Ben Abraham
, Adv. Phys.
36
, 155
(1987
).38.
J.
Hoshen
and R.
Kopelman
, Phys. Rev. B
14
, 3438
(1976
).39.
F.
Family
, J. Phys. A
15
, L583
(1982
).40.
P.
Grassberger
, Phys. Rev. E
56
, 3682
(1997
).41.
H.-P.
Hsu
, V.
Mehra
, W.
Nadler
, and P.
Grassberger
, J. Chem. Phys.
118
, 444
(2007
).42.
43.
B.
Nienhuis
, Phys. Rev. Lett.
49
, 1062
(1982
).44.
V.
Blavatska
and W.
Janke
, Europhys. Lett.
82
, 66006
(2008
);V.
Blavatska
and W.
Janke
, J. Phys. A
42
, 015001
(2009
).45.
K.
Solc
and W. H.
Stockmayer
, J. Chem. Phys.
54
, 2756
(1971
);K.
Solc
, J. Chem. Phys.
55
, 335
(1971
).46.
J.
Rudnick
and G.
Gaspari
, J. Phys. A
19
, L191
(1986
);G.
Gaspari
, J.
Rudnick
, and A.
Beldjenna
, J. Phys. A
20
, 3393
(1987
).47.
J. A.
Aronovitz
and D. R.
Nelson
, J. Phys. (France)
47
, 1445
(1986
).48.
M.
Bishop
and C. J.
Saltiel
, J. Chem. Phys.
88
, 6594
(1988
).49.
O.
Jagodzinski
, E.
Eisenriegler
, and K.
Kremer
, J. Phys. I France
2
, 2243
(1992
).50.
S.
Caracciolo
, A. J.
Guttmann
, I.
Jensen
, A.
Pelissetto
, A. N.
Rogers
, and A.
Sokal
, J. Stat. Phys.
120
, 1037
(2005
).51.
V.
Blavatska
and W.
Janke
, J. Chem. Phys.
133
, 184903
(2010
).© 2012 American Institute of Physics.
2012
American Institute of Physics
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