Semiflexible polymers in lyotropic solution confined inside spherical nanoscopic “containers” with repulsive walls are studied by molecular dynamics simulations and density functional theory, as a first step to model confinement effects on stiff polymers inside of miniemulsions, vesicles, and cells. It is shown that the depletion effects caused by the monomer-wall repulsion depend distinctly on the radius R of the sphere. Further, nontrivial orientational effects occur when R, the persistence length p, and the contour length L of the polymers are of similar magnitude. At intermediate densities, a “shell” of wall-attached chains is forming, such that the monomers belonging to those chains are in a layer at about the distance of one monomer from the container wall. At the same time, the density of the centers of mass of these chains is peaked somewhat further inside, but still near the wall. However, the arrangement of chains is such that the total monomer density is almost uniform in the sphere, apart from a small layering peak at the wall. It is shown that excluded volume effects among the monomers are crucial to account for this behavior, although they are negligible for comparable isolated single semiflexible chains of the same length.

1.
A. Y.
Grosberg
and
A. R.
Khokhlov
,
Statistical Physics of Macromolecules
(
AIP Press
,
Woodbury
,
1994
).
2.
M.
Rubinstein
and
R. H.
Colby
,
Polymer Physics
(
Oxford University Press
,
Oxford
,
2003
).
3.
A. Y.
Grosberg
and
A. R.
Khokhlov
,
Adv. Polym. Sci.
41
,
53
(
1981
).
4.
T.
Odijk
,
Macromolecules
19
,
2313
(
1986
).
5.
T.
Sato
and
A.
Teramoto
,
Adv. Polym. Sci.
126
,
85
(
1996
).
6.
R.
Holyst
and
P.
Oswald
,
Macromol. Theory Simul.
10
,
1
(
2001
).
7.
A.
Ciferri
,
Liquid Crystallinity in Polymers: Principles and Fundamental Properties
(
VCH Publishers
,
New York
,
1991
).
8.
A. M.
Donald
,
A. H.
Windle
, and
S.
Hanna
,
Liquid Crystalline Polymers
(
Cambridge University Press
,
Cambridge
,
2006
).
9.
M. R.
Mofrad
and
R.
Kamm
,
Cytoskeletal Mechanics
(
Cambridge University Press
,
Cambridge
,
2006
).
10.
B.
Alberts
,
A.
Johnson
,
J.
Lewis
,
M.
Raff
,
K.
Roberts
, and
P.
Walker
,
Molecular Biology of the Cell
(
Garland Science
,
New York
,
2007
).
11.
Q.
Wen
and
P. A.
Janmey
,
Curr. Opin. Solid State Mater. Sci.
15
,
177
(
2011
).
12.
H. N.
Yow
and
A. F.
Routh
,
Soft Matter
2
,
940
(
2006
).
13.
A. P.
Esser-Kahn
,
S. A.
Odom
,
N. R.
Sottos
,
S. R.
White
, and
J. S.
Moore
,
Macromolecules
44
,
5539
(
2011
).
14.
S. P.
Friedman
and
Y.
Mualem
,
Fert. Res.
39
,
19
(
1994
).
15.
X. Y.
Shi
and
T. W.
Tan
,
Biomaterials
23
,
4469
(
2002
).
16.
W.
Qi
,
X. H.
Yan
,
J. B.
Fei
,
A. H.
Wang
,
Y.
Cui
, and
J. B.
Li
,
Biomterials
30
,
2799
(
2009
).
17.
T.
Sakaue
,
Macromolecules
40
,
5206
(
2007
).
18.
G.
Morrison
and
D.
Thirumalai
,
Phys. Rev. E
79
,
011924
(
2009
).
19.
K.
Ostermeir
,
K.
Alim
, and
E.
Frey
,
Soft Matter
6
,
3467
(
2010
).
20.
K.
Ostermeir
,
K.
Alim
, and
E.
Frey
,
Phys. Rev. E
81
,
061802
(
2010
).
21.
D.
Reith
and
P.
Virnau
,
Comput. Phys. Commun.
181
,
800
(
2010
).
22.
P.
Cifra
and
T.
Bleha
,
Macromol. Symp.
296
,
336
(
2010
).
23.
D.
Marenduzzo
,
C.
Micheletti
, and
E.
Orlandini
,
J. Phys.: Condens. Matter
22
,
283102
(
2010
).
24.
C.
Micheletti
,
D.
Marenduzzo
, and
E.
Orlandini
,
Phys. Rep.
504
,
1
(
2011
).
25.
Y.
Higuchi
,
K.
Yoshikawa
, and
T.
Iwaki
,
Phys. Rev. E
84
,
021924
(
2011
).
26.
P.
Cifra
and
T.
Bleha
,
Macromol. Theory Simul.
21
,
15
(
2012
).
27.
D.
Reith
,
P.
Cifra
,
A.
Stasiak
, and
P.
Virnau
,
Nucleic Acids Res.
40
,
5129
(
2012
).
28.
D.
Marenduzzo
,
C.
Micheletti
,
E.
Orlandini
, and
D.
Sumners
,
Proc. Natl. Acad. Sci. U. S. A.
110
,
20081
(
2013
).
29.
M.
Fosnaric
,
A.
Iglic
,
D. M.
Kroll
, and
S.
May
,
Soft Matter
9
,
3976
(
2013
).
30.
J.
Gao
,
P.
Tang
,
Y.
Yang
, and
J. Z. Y.
Chen
,
Soft Matter
10
,
4674
(
2014
).
31.
J.
Skolnick
,
J. Chem. Phys.
145
,
100901
(
2016
).
32.
K.
Nakaya
,
M.
Imai
,
S.
Komura
,
T.
Kawakatsu
, and
N.
Urakami
,
Europhys. Lett.
71
,
494
(
2005
).
33.
H.-P.
Hsu
and
K.
Binder
,
Macromolecules
46
,
2496
(
2013
).
34.
M.
Hase
and
K.
Yoshikawa
,
J. Chem. Phys.
124
,
104903
(
2006
).
35.
A.
Kato
,
E.
Shindo
,
T.
Sakaue
,
A.
Tsuji
, and
K.
Yoshikawa
,
Biophys. J.
97
,
1678
(
2009
).
36.
M.
Negishi
,
T.
Sakaue
,
K.
Takiguchi
, and
K.
Yoshikawa
,
Phys. Rev. E
81
,
051921
(
2010
).
37.
D. A. D.
Parry
and
E. N.
Baker
,
Rep. Prog. Phys.
47
,
1133
(
1984
).
38.
W.
Reisner
,
J. N.
Pedersen
, and
R. H.
Austin
,
Rep. Prog. Phys.
75
,
106601
(
2012
).
39.
G. A.
Voth
,
Coarse-Graining of Condensed Phase and Biomolecular Systems
(
CRC Press
,
Boca Raton
,
2009
).
40.
G. S.
Grest
and
K.
Kremer
,
Phys. Rev. A
33
,
3628
(
1986
).
41.
K.
Kremer
and
G. S.
Grest
,
J. Chem. Phys.
92
,
5057
(
1990
).
42.
S. A.
Egorov
,
A.
Milchev
, and
K.
Binder
,
Phys. Rev. Lett.
116
,
187801
(
2016
).
43.
S. A.
Egorov
,
A.
Milchev
,
P.
Virnau
, and
K.
Binder
,
Soft Matter
12
,
4944
(
2016
).
44.
S. A.
Egorov
,
A.
Milchev
, and
K.
Binder
,
Polymers
8
,
296
(
2016
).
45.
M. R.
Wilson
and
M. P.
Allen
,
Mol. Phys.
80
,
277
(
1993
).
46.
H.
Fynewever
and
A.
Yethiraj
,
J. Chem. Phys.
108
,
1636
(
1998
).
47.
S. A.
Egorov
,
J. Chem. Phys.
129
,
064901
(
2008
).
48.
M.
Dijkstra
and
D.
Frenkel
,
Phys. Rev. E
51
,
5891
(
1995
).
49.
F. A.
Escobedo
and
J. J.
dePablo
,
J. Chem. Phys.
106
,
9858
(
1997
).
50.
R. D.
Kamien
and
G. S.
Grest
,
Phys. Rev. E
55
,
1197
(
1997
).
51.
C.
Junghans
,
M.
Bachmann
, and
W.
Janke
,
Europhys. Lett.
87
,
40002
(
2009
).
52.
T.
van Westen
,
B.
Oyarzun
,
T. J. H.
Vlugt
, and
J.
Gross
,
J. Chem. Phys.
139
,
034505
(
2013
).
53.
D.
Panja
,
G. T.
Barkema
, and
J. M. J.
van Leeuwen
,
Phys. Rev. E
92
,
032603
(
2015
).
54.
D. A.
Luzhbin
and
Y.-L.
Chen
,
Macromolecules
49
,
6139
(
2016
).
55.
S. A.
Egorov
,
A.
Milchev
,
P.
Virnau
, and
K.
Binder
,
J. Chem. Phys.
144
,
174902
(
2016
).
56.
S. A.
Egorov
,
A.
Milchev
, and
K.
Binder
,
Macromol. Theory Simul.
25
,
1600036
(
2016
).
57.
J. D.
Weeks
,
D.
Chandler
, and
H. C.
Andersen
,
J. Chem. Phys.
54
,
5237
(
1971
).
58.
M. P.
Allen
and
D. J.
Tildesley
,
Computer Simulation of Liquids
(
Clarendon
,
Oxford
,
1989
).
59.
D. C.
Rapaport
,
The Art of Molecular Dynamics Simulation
, 2nd ed. (
Cambridge University Press
,
Cambridge
,
2004
).
60.
J.
Anderson
,
C.
Lorenz
, and
A.
Travesset
,
J. Comput. Phys.
227
,
5342
(
2008
).
61.
J.
Glaser
,
T. D.
Nguyen
,
J. A.
Anderson
,
P.
Liu
,
F.
Spiga
,
J. A.
Millan
,
D. C.
Morse
, and
S. C.
Glotzer
,
Comput. Phys. Commun.
192
,
97
(
2015
).
62.
Y.
Trukhina
and
T.
Schilling
,
Phys. Rev. E
77
,
011701
(
2008
).
63.
D.
Meng
,
R. P.
Hjelm
,
J. M.
Hu
, and
J. Z.
Wu
,
Biophys. J.
101
,
2476
(
2011
).
64.
Z. H.
Jin
and
J. Z.
Wu
,
J. Chem. Phys.
137
,
044905
(
2012
).
65.
T. L.
Hill
,
Thermodynamics of Small Systems
(
W. A. Benjamin, Inc.
,
New York
,
1963
).
66.
A.
Winkler
,
A.
Statt
,
P.
Virnau
, and
K.
Binder
,
Phys. Rev. E
87
,
032307
(
2013
).
67.
K.
Binder
and
D. W.
Heermann
,
Monte Carlo Simulation in Statistical Physics—An Introduction
, 5th ed. (
Springer
,
Berlin
,
2010
).
68.
E.
Torino
,
R.
Aruta
,
T.
Sibillano
,
C.
Giannini
, and
P. A.
Netti
,
Sci. Rep.
6
,
32727
(
2016
).
69.
B.
Groh
and
S.
Dietrich
,
Phys. Rev. E
59
,
4216
(
1999
).
70.
L.
Onsager
,
Ann. N. Y. Acad. Sci.
51
,
627
(
1949
).
71.
R. C.
Tolman
,
J. Chem. Phys.
17
,
333
(
1949
).
72.
W.
Helfrich
,
Z. Naturforsch. C
28
,
693
(
1973
).
73.
J. S.
Rowlinson
and
B.
Widom
,
Molecular Theory of Capillarity
(
Clarendon
,
Oxford
,
1982
).
74.
H.-P.
Hsu
,
W.
Paul
, and
K.
Binder
,
Europhys. Lett.
95
,
68004
(
2011
).
75.
O.
Kratky
and
G.
Porod
,
Recl. Trav. Chim. Pays-Bas
68
,
1106
(
1949
).
77.
H.-P.
Hsu
,
W.
Paul
, and
K.
Binder
,
Europhys. Lett.
92
,
28003
(
2010
).
78.
P. G.
de Gennes
and
J.
Prost
,
The Physics of Liquid Crystals
, 2nd ed. (
Clarendon
,
Oxford
,
1992
).
79.
A.
Nikoubashman
,
D. A.
Vega
,
K.
Binder
, and
A.
Milchev
, “
Semiflexible polymers in spherical confinement: bipolar orientational order versus tennis-ball states
,”
Phys. Rev. Lett.
(in press); available at https://journals.aps.org/prl/accepted/19074Ya1P7e11d67700846e18bcaf1f444ca2f7c6.
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