We analyze the statistics of loops formation in f-branched star polymers in an environment with structural defects, correlated at large distances r according to a power law . Applying the direct polymer renormalization approach, we found the values of the set of universal exponents, governing the scaling of probabilities of various types of loops in macromolecules.
REFERENCES
1.
N.
Hadjichristidis
, H.
Iatrou
, M.
Pitsikalis
, P.
Driva
, G.
Sakellariou
, and M.
Chatzichristidi
, “Polymers with star-related structures: Synthesis, properties, and applications
,” in Polymer Science: A Comprehensive Reference
(Elsevier
, Amsterdam
, 2012
).2.
W.
Zhu
, J.
Ling
, and Z.
Shen
, Macromol. Chem. Phys.
207
, 844
(2006
).3.
X.
Liu
, X.
Jin
, and P. X.
Ma
, Nat. Mater.
10
, 398
(2011
).4.
G. S.
Grest
, L. J.
Fetters
, J. S.
Huang
, and D.
Richter
, Adv. Chem. Phys.
94
, 67
(1996
).5.
C. N.
Likos
, Phys. Rep.
348
, 267
(2001
).6.
B.
Duplantier
, J. Stat. Phys.
54
, 581
(1989
).7.
A.
Chremos
and J. F.
Douglas
, J. Chem. Phys.
143
, 111104
(2015
).8.
Order, Disorder and Criticality
, Advanced Problems of Phase Transition Theory Vol. 1, edited by Y.
Holovatch
(World Scientific
, Singapore
, 2004
).9.
L. J.
Perry
and R.
Wetzel
, Science
226
, 555
(1984
).10.
J. A.
Wells
and D. B.
Powers
, J. Biol. Chem.
261
, 6564
(1986
).11.
C. N.
Pace
, G. R.
Grimsley
, J. A.
Thomson
, and B. J.
Barnett
, J. Biol. Chem.
263
, 11820
(1988
).12.
A. D.
Nagi
and L.
Regan
, Folding Des.
2
, 67
(1997
).13.
R.
Schlief
, Science
240
, 127
(1988
).14.
K.
Rippe
, P. H.
von Hippel
, and J.
Langowski
, Trends Biochem. Sci.
20
, 500
(1995
).15.
K. B.
Towles
, J. F.
Beausang
, H. G.
Garcia
, R.
Phillips
, and P. C.
Nelson
, Phys. Biol.
6
, 025001
(2009
).16.
P.
Fraser
, Curr. Opin. Genet. Dev.
16
, 490
(2006
).17.
M.
Simonis
, P.
Klous
, E.
Splinter
, Y.
Moshkin
, R.
Willemsen
, E.
de Wit
, B.
van Steensel
, and W.
de Laat
, Nat. Genet.
38
, 1348
(2006
).18.
J.
Dorier
and A.
Stasiak
, Nucleic Acids Res.
37
, 6316
(2009
).19.
H.
Jacobson
and W. H.
Stockmayer
, J. Chem. Phys.
18
, 1600
(1950
).20.
H. S.
Chan
and K. A.
Dill
, J. Chem. Phys.
90
, 492
(1989
).21.
S.
Redner
, J. Phys. A: Math. Gen.
13
, 3525
(1980
).22.
H. P.
Hsu
, W.
Nadler
, and P.
Grassberger
, Macromolecules
37
, 4658
(2004
).23.
P. N.
Pusey
and W.
van Megen
, Nature
320
, 340
(1986
).24.
S.
Kumar
and M. S.
Li
, Phys. Rep.
486
, 1
(2010
).25.
A.
Minton
, J. Biol. Chem.
276
, 10577
(2001
).26.
Y.
Kim
, J. Phys. C: Solid State Phys.
16
, 1345
(1983
).27.
K.
Kremer
, Z. Phys. B: Condens. Matter
45
, 149
(1981
).28.
S. B.
Lee
and H.
Nakanishi
, Phys. Rev. Lett.
61
, 2022
(1988
).29.
K. Y.
Woo
and S. B.
Lee
, Phys. Rev. A
44
, 999
(1991
).30.
P.
Grassberger
, J. Phys. A: Math. Gen.
26
, 1023
(1993
).31.
A.
Ordemann
, M.
Porto
, H. E.
Roman
, S.
Havlin
, and A.
Bunde
, Phys. Rev. E
61
, 6858
(2000
).32.
H.-K.
Janssen
and O.
Stenull
, Phys. Rev. E
75
, 020801(R)
(2007
).33.
A. L.
Dullen
, Porous Media: Fluid Transport and Pore Structure
(Academic
, New York
, 1979
).34.
A.
Weinrib
and B. I.
Halperin
, Phys. Rev. B
27
, 413
(1983
).35.
V.
Blavats’ka
, C.
von Ferber
, and Yu.
Holovatch
, J. Mol. Liq.
92
, 77
(2001
);V.
Blavats’ka
, C.
von Ferber
, and Yu.
Holovatch
, Phys. Rev. E
64
, 041102
(2001
).36.
V.
Blavats’ka
, C.
von Ferber
, and Yu.
Holovatch
, Phys. Rev. E
74
, 031801
(2006
);V.
Blavats’ka
, C.
von Ferber
, and Yu.
Holovatch
, Condens. Matter Phys.
15
, 33603
(2012
).37.
K.
Haydukivska
and V.
Blavatska
, J. Chem. Phys.
141
, 094906
(2014
).38.
K.
Haydukivska
and V.
Blavatska
, J. Chem. Phys.
144
, 084901
(2016
).39.
S. F.
Edwards
, Proc. Phys. Soc.
85
, 613
(1965
);S. F.
Edwards
, Proc. Phys. Soc.
88
, 265
(1965
).40.
J.
des Cloizeaux
and G.
Jannink
, Polymers in Solutions: Their Modelling and Structure
(Clarendon Press
, Oxford
, 1990
).41.
A. P.
Prudnikov
, Yu. A.
Brychkov
, and O. I.
Marychev
, Integrals and Series: Special Functions
(Nauka
, Moskow
, 1983
).© 2017 Author(s).
2017
Author(s)
You do not currently have access to this content.
