Single-chain simulations of densely branched comb polymers, or “molecular bottle-brushes” with side-chains attached to every (or every second) backbone monomer, were carried out by off-lattice Monte Carlo technique. A coarse-grained model, described by hard spheres connected by harmonic springs, was employed. Backbone lengths of up to 100 units were considered, and compared with the corresponding linear chains. The backbone molecular size was investigated as a function of its length at fixed arm size, and as a function of the arm size at fixed backbone length. The apparent swelling exponents obtained by a power-law fit were found to be larger than those for the corresponding linear polymers, indicative of stiffening of the comb backbone. The probability distribution function for the backbone end-to-end distance was also investigated for different backbone lengths and arm sizes. Analysis of this function yielded the critical exponents, which revealed an increase in the swelling exponent consistent with values found from the molecular size. The apparent persistence length of the backbone was also determined, and was found to increase with increasing branching density. Finally, the static structure factors of the whole bottle-brushes and of their backbones are discussed, which provides another consistent estimate of the swelling exponents.

1.
M.
Wintermantel
,
M.
Gerle
,
K.
Fischer
,
M.
Schmidt
,
I.
Wataoka
,
H.
Urakawa
,
K.
Kajiwara
, and
Y.
Tsukahara
,
Macromolecules
29
,
978
(
1996
).
2.
Y.
Tsukahara
,
K.
Mizuno
,
A.
Segawa
, and
Y.
Yamashita
,
Macromolecules
22
,
1546
(
1989
);
Y.
Tsukahara
,
K.
Tsutsumi
,
Y.
Yamashita
, and
S.
Shimada
,
Macromolecules
23
,
5201
(
1990
).
3.
M.
Wintermantel
,
K.
Fischer
,
M.
Gerle
,
R.
Ries
,
M.
Schmidt
,
K.
Kajiwara
,
H.
Urakawa
, and
I.
Wataoka
,
Angew. Chem., Int. Ed. Engl.
34
,
1472
(
1995
).
4.
P.
Dziezok
,
S. S.
Sheiko
,
K.
Fischer
,
M.
Schmidt
, and
M.
Möller
,
Angew. Chem., Int. Ed. Engl.
36
,
2812
(
1997
).
5.
R.
Djalali
,
S.-Y.
Li
, and
M.
Schmidt
,
Macromolecules
35
,
4282
(
2002
).
6.
M.
Saariaho
,
O.
Ikkala
,
I.
Szleifer
,
I.
Erukhimovich
, and
G.
ten Brinke
,
J. Chem. Phys.
107
,
3267
(
1997
).
7.
M.
Saariaho
,
I.
Szleifer
,
O.
Ikkala
, and
G.
ten Brinke
,
Macromol. Theory Simul.
7
,
211
(
1998
).
8.
R.
Djalali
,
N.
Hugenberg
,
K.
Fischer
, and
M.
Schmidt
,
Macromol. Rapid Commun.
20
,
444
(
1999
).
9.
J.
Ruokolainen
,
G.
ten Brinke
,
O.
Ikkala
,
M.
Torkkeli
, and
R.
Serimaa
,
Macromolecules
29
,
3409
(
1996
).
10.
K.
Shiokawa
,
K.
Itoh
, and
N.
Nemoto
,
J. Chem. Phys.
111
,
8165
(
1999
).
11.
P. G.
Khalatur
,
D. G.
Shirvanyanz
,
N. Yu.
Starovoitova
, and
A. R.
Khokhlov
,
Macromol. Theory Simul.
9
,
141
(
2000
).
12.
M.
Saariaho
,
A.
Subbotin
,
I.
Szleifer
,
O.
Ikkala
, and
G.
ten Brinke
,
Macromolecules
32
,
4439
(
1999
);
M.
Saariaho
,
O.
Ikkala
, and
G.
ten Brinke
,
J. Chem. Phys.
110
,
1180
(
1999
);
M.
Saariaho
,
A.
Subbotin
,
O.
Ikkala
, and
G.
ten Brinke
,
Macromol. Rapid Commun.
21
,
110
(
2000
).
13.
G. H.
Fredrickson
,
Macromolecules
26
,
2825
(
1993
);
A.
Subbotin
,
M.
Saariaho
,
O.
Ikkala
, and
G.
ten Brinke
,
Macromolecules
33
,
3447
(
2000
).
14.
T. M.
Birshtein
,
O. V.
Borisov
,
Y. B.
Zhulina
,
A. R.
Khokhlov
, and
T. A.
Yurasova
,
Polym. Sci. U.S.S.R.
29
,
1293
(
1987
).
15.
F.
Ganazzoli
,
Yu. A.
Kuznetsov
, and
E. G.
Timoshenko
,
Macromol. Theory Simul.
10
,
325
(
2001
).
16.
F.
Ganazzoli
,
R.
La Ferla
, and
G.
Raffaini
,
Macromolecules
34
,
4222
(
2001
);
F.
Ganazzoli
,
R.
La Ferla
, and
G.
Terragni
,
Macromolecules
33
,
6611
(
2000
);
F.
Ganazzoli
,
Condens. Matter Phys.
5
,
37
(
2002
).
17.
E. G.
Timoshenko
,
Yu. A.
Kuznetsov
, and
R.
Connolly
,
J. Chem. Phys.
117
,
9050
(
2002
);
E. G.
Timoshenko
,
Yu. A.
Kuznetsov
, and
R.
Connolly
,
J. Chem. Phys.
116
,
3905
(
2002
).
18.
R.
Connolly
,
E. G.
Timoshenko
, and
Yu. A.
Kuznetsov
,
J. Chem. Phys.
119
,
8736
(
2003
).
19.
M. P. Allen and D. J. Tildeslay, Computer Simulation of Liquids (Oxford University Press, Oxford, 1987).
20.
P. J. Flory, Statistical Mechanics of Chain Molecules (Wiley Interscience, New York, 1969).
21.
R.
Guida
and
J.
Zinn-Justin
,
J. Phys. A
31
,
8103
(
1998
).
22.
C.
Domb
,
J.
Gillis
, and
G.
Wilmers
,
Proc. Phys. Soc. London
85
,
625
(
1965
).
23.
M. E.
Fisher
,
J. Chem. Phys.
44
,
616
(
1966
);
D. S.
McKenzie
and
M. A.
Moore
,
J. Phys. A
4
,
L82
(
1971
).
24.
J.
des Cloizeaux
,
Phys. Rev. A
10
,
1665
(
1974
);
J.
des Cloizeaux
,
J. Phys.
41
,
223
(
1980
).
25.
B.
Duplantier
,
J. Stat. Phys.
54
,
581
(
1989
).
26.
S.
Müller
and
L.
Schäfer
,
Eur. Phys. J.: Appl. Phys.
2
,
351
(
1998
).
27.
L.
Onsager
,
Ann. N.Y. Acad. Sci.
51
,
627
(
1949
).
28.
A.
Khokhlov
and
A. N.
Semenov
,
Physica A
108
,
546
(
1981
).
29.
S.
Lecommandoux
,
F.
Chécot
,
R.
Borsali
,
M.
Schappacher
,
A.
Deffieux
,
A.
Brûlet
, and
J. P.
Cotton
,
Macromolecules
35
,
8878
(
2002
).
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