We apply extensive molecular dynamics simulations and analytical considerations in order to study the conformations and the effective interactions between weakly charged, flexible polyelectrolyte chains in salt-free conditions. We focus on charging fractions lying below 20%, for which case there is no Manning condensation of counterions and the latter can be thus partitioned in two states: those that are trapped within the region of the flexible chain and the ones that are free in the solution. We examine the partition of counterions in these two states, the chain sizes and the monomer distributions for various chain lengths, finding that the monomer density follows a Gaussian shape. We calculate the effective interaction between the centers of mass of two interacting chains, under the assumption that the chains can be modeled as two overlapping Gaussian charge profiles. The analytical calculations are compared with measurements from molecular dynamics simulations. Good quantitative agreement is found for charging fractions below 10%, where the chains assume coil-like configurations, whereas deviations develop for charge fraction of 20%, in which case a conformational transition of the chain towards a rodlike configuration starts to take place.

1.
F. Oosawa, Polyelectrolytes (Macel Dekker, New York, 1971).
2.
H. Dautzenberg, W. Jaeger, J. Kötz, B. Philipp, Ch. Seidel, and D. Stscherbina, Polyelectrolytes-Formation, Characterization and Application (Hanser, München, 1994).
3.
J.-L.
Barrat
and
J.-F.
Joanny
,
Adv. Chem. Phys.
XCIV
,
1
(
1995
).
4.
J.-P.
Hansen
and
H.
Löwen
,
Annu. Rev. Phys. Chem.
51
,
209
(
2000
).
5.
M. J.
Stevens
and
K.
Kremer
,
J. Chem. Phys.
103
,
1669
(
1995
).
6.
M. J.
Stevens
and
K.
Kremer
,
Phys. Rev. Lett.
71
,
2228
(
1993
).
7.
V. V.
Vasilevskaya
,
A. R.
Khokhlov
, and
K.
Yoshikawa
,
Macromol. Theory Simul.
9
,
600
(
2000
).
8.
Y.
Kantor
and
M.
Kardar
,
Phys. Rev. Lett.
83
,
745
(
1999
).
9.
M.
Castelnovo
,
P.
Sens
, and
J.-F.
Joanny
,
Eur. Phys. J. E
1
,
115
(
2002
).
10.
C.-Y.
Shew
and
A.
Yethiraj
,
J. Chem. Phys.
110
,
676
(
1999
).
11.
U.
Micka
,
C.
Holm
, and
K.
Kremer
,
Langmuir
15
,
4033
(
1999
).
12.
W.
Essafi
,
F.
Lafuma
, and
C. E.
Williams
,
J. Phys. II
5
,
1269
(
1995
).
13.
G.
Migliorini
,
V. G.
Rostiashvili
, and
T. A.
Vilgis
,
Eur. Phys. J. E
4
,
475
(
2001
).
14.
Q.
Liao
,
A. V.
Dobrynin
, and
M.
Rubinstein
,
Macromolecules
36
,
3386
(
2003
).
15.
G. S.
Manning
,
J. Chem. Phys.
51
,
924
(
1969
).
16.
R. M.
Nyquist
,
B.-Y.
Ha
, and
A. J.
Liu
,
Macromolecules
32
,
3481
(
1999
).
17.
M.
Deserno
,
C.
Holm
, and
S.
May
,
Macromolecules
33
,
199
(
2000
).
18.
J.
Blaul
,
M.
Wittemann
,
M.
Ballauff
, and
M.
Rehahn
,
J. Phys. Chem. B
104
,
7077
(
2000
).
19.
M.
Deserno
,
C.
Holm
,
J.
Blaul
,
M.
Ballauff
, and
M.
Rehahn
,
Eur. Phys. J. E
5
,
97
(
2001
).
20.
R. G.
Winkler
,
M.
Gold
, and
P.
Reineker
,
Phys. Rev. Lett.
80
,
3731
(
1998
).
21.
N. V.
Brillantov
,
D. V.
Kuznetsov
, and
R.
Klein
,
Phys. Rev. Lett.
81
,
1433
(
1998
).
22.
H.
Schiessel
and
P.
Pincus
,
Macromolecules
31
,
7953
(
1998
).
23.
H.
Schiessel
,
Macromolecules
32
,
5673
(
1999
).
24.
R.
Golestanian
,
M.
Kardar
, and
T. B.
Liverpool
,
Phys. Rev. Lett.
82
,
4456
(
1999
).
25.
R. G. Winkler, Soft Matter—Complex Materials on Mesoscopic Scales, 33. IFF-Ferienkurs, Forschungszentrum Jülich (Jülich, 2002), Vol. 10.
26.
A.
Yethiraj
and
C.-Y.
Shew
,
Phys. Rev. Lett.
77
,
3937
(
1996
).
27.
C.-Y.
Shew
and
A.
Yethiraj
,
J. Chem. Phys.
106
,
5706
(
1997
).
28.
C.-Y.
Shew
and
A.
Yethiraj
,
J. Chem. Phys.
109
,
5162
(
1998
).
29.
C.-Y.
Shew
and
A.
Yethiraj
,
J. Chem. Phys.
110
,
11599
(
1999
).
30.
L.
Harnau
and
P.
Reineker
,
J. Chem. Phys.
112
,
437
(
2000
).
31.
K. S.
Schweizer
and
J. G.
Curro
,
Adv. Polym. Sci.
116
,
319
(
1995
).
32.
A.
Yethiraj
,
Phys. Rev. Lett.
78
,
3789
(
1997
).
33.
A.
Yethiraj
,
J. Chem. Phys.
108
,
1184
(
1998
).
34.
C.-Y.
Shew
and
A.
Yethiraj
,
J. Chem. Phys.
110
,
5437
(
1998
).
35.
C.-Y.
Shew
and
A.
Yethiraj
,
J. Chem. Phys.
113
,
8841
(
2000
).
36.
G.
Orkoulas
,
S. K.
Kumar
, and
A. Z.
Panagiotopoulos
,
Phys. Rev. Lett.
90
,
048303
(
2003
).
37.
C. N.
Likos
,
Phys. Rep.
348
,
267
(
2001
).
38.
A. A.
Louis
,
P. G.
Bolhuis
,
J.-P.
Hansen
, and
E. J.
Meijer
,
Phys. Rev. Lett.
85
,
2522
(
2000
).
39.
A. A.
Louis
,
P. G.
Bolhuis
, and
J.-P.
Hansen
,
Phys. Rev. E
62
,
7961
(
2000
).
40.
P. G.
Bolhuis
,
A. A.
Louis
,
J.-P.
Hansen
, and
E. J.
Meijer
,
J. Chem. Phys.
114
,
4296
(
2001
).
41.
G. A.
Carri
and
M.
Muthukumar
,
J. Chem. Phys.
111
,
1765
(
1999
).
42.
M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford, 1987).
43.
D. Frenkel and B. Smit, Understanding Molecular Simulation (Academic, San Diego, 1996).
44.
D. C. Rapaport, The Art of Molecular Dynamics Simulation (Cambridge University Press, Cambridge, 1995).
45.
K.
Kremer
and
G. S.
Grest
,
J. Chem. Phys.
92
,
5057
(
1990
).
46.
T. O.
White
,
G.
Ciccotti
, and
J.-P.
Hansen
,
Mol. Phys.
99
,
2023
(
2001
).
47.
R.
Messina
,
C.
Holm
, and
K.
Kremer
,
J. Chem. Phys.
117
,
2947
(
2002
).
48.
J.
Lekner
,
Physica A
176
,
485
(
1991
).
49.
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1995).
50.
G. S.
Grest
,
K.
Kremer
, and
T. A.
Witten
,
Macromolecules
20
,
1376
(
1987
).
51.
G. S.
Grest
,
Macromolecules
27
,
3493
(
1994
).
52.
J. K.
Wolterink
,
F. A. M.
Leermakers
,
G. J.
Fleer
,
L. K.
Koopal
,
E. B.
Zhulina
, and
O. V.
Borisov
,
Macromolecules
32
,
2365
(
1999
).
53.
A.
Jusufi
,
C. N.
Likos
, and
H.
Löwen
,
Phys. Rev. Lett.
88
,
018301
(
2002
).
54.
A.
Jusufi
,
C. N.
Likos
, and
H.
Löwen
,
J. Chem. Phys.
116
,
11011
(
2002
).
55.
P. G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, 1979).
56.
M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon, Oxford, 1986).
57.
R.
Hariharan
,
C.
Biver
,
J.
Mays
, and
W. B.
Russel
,
Macromolecules
31
,
7506
(
1998
).
58.
P.
Pincus
,
Macromolecules
24
,
2912
(
1991
).
59.
T.
Odijk
and
A. H.
Houwaart
,
J. Polym. Sci., Polym. Phys. Ed.
16
,
627
(
1978
).
60.
M. Doi, Introduction to Polymer Physics (Clarendon, Oxford, 1996).
61.
S.
Liu
and
M.
Muthukumar
,
J. Chem. Phys.
116
,
9975
(
2002
).
62.
A.
Jusufi
,
M.
Watzlawek
, and
H.
Löwen
,
Macromolecules
32
,
4470
(
1999
).
63.
I. O.
Götze
,
H. M.
Harreis
, and
C. N.
Likos
,
J. Chem. Phys.
120
,
7761
(
2004
).
64.
A. J.
Archer
,
C. N.
Likos
, and
R.
Evans
,
J. Phys.: Condens. Matter
14
,
12031
(
2002
).
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