Complexation of a long flexible polyelectrolyte (PE) molecule with oppositely charged spherical particles such as colloids, micelles, or globular proteins in a salty water solution is studied. PE binds spheres winding around them, while spheres repel each other and form almost periodic necklace. If the total charge of PE in the solution is larger than total charge of spheres, repulsive correlations of PE turns on a sphere lead to inversion of the net charge of each sphere. In the opposite case when the total charge of spheres is larger, we predict another correlation effect; spheres bind to the PE in such a great number that they invert the charge of the PE. The inverted charge by absolute value can be larger than the bare charge of PE even when screening by monovalent salt is weak. At larger concentrations of monovalent salt, the inverted charge can reach giant proportions. Near the isoelectric point where total charges of spheres and PE are equal, necklaces condense into macroscopic bundles. Our theory is in qualitative agreement with recent experiments on micelles–PE systems.

1.
Y.
Wang
,
K.
Kimura
,
Q.
Huang
,
P. L.
Dubin
, and
W.
Jaeger
,
Macromolecules
32
,
7128
(
1999
).
2.
V. A.
Kabanov
,
V. P.
Evdakov
,
M. I.
Mustafaev
, and
A. D.
Antipina
,
Mol. Biol. (Moscow)
11
,
52
(
1976
);
J. Xia and P. L. Dubin, in Macromolecular Complexes in Chemistry and Biology, edited by P. L. Dubin et al. (Springer-Verlag, Berlin, 1994).
3.
E.
Braun
,
Y.
Eichen
,
U.
Sivan
, and
G.
Ben-Yoseph
,
Nature (London)
391
,
775
(
1998
).
4.
T.
Wallin
and
P.
Linse
,
Langmuir
12
,
305
(
1996
).
5.
E. M.
Mateescu
,
C.
Jeppersen
, and
P.
Pincus
,
Europhys. Lett.
46
,
454
(
1999
).
6.
S. Y.
Park
,
R. F.
Bruinsma
, and
W. M.
Gelbart
,
Europhys. Lett.
46
,
493
(
1999
).
7.
R. R.
Netz
and
J. F.
Joanny
,
Macromolecules
32
,
9026
(
1999
).
8.
P.
Sens
and
E.
Gurovitch
,
Phys. Rev. Lett.
82
,
339
(
1999
).
9.
P.
Chodanowski
and
S.
Stoll
,
Macromolecules
34
,
333
(
2001
).
10.
T. T.
Nguyen
and
B. I.
Shklovskii
,
Physica A
293
,
N3–4
,
444
(
2001
).
11.
V. I.
Perel
and
B. I.
Shklovskii
,
Physica A
274
,
446
(
1999
);
B. I.
Shklovskii
,
Phys. Rev. E
60
,
5802
(
1999
).
12.
T. T.
Nguyen
,
A. Yu.
Grosberg
, and
B. I.
Shklovskii
,
Phys. Rev. Lett.
85
,
1568
(
2000
).
13.
T. T.
Nguyen
,
A. Yu.
Grosberg
, and
B. I.
Shklovskii
,
J. Chem. Phys.
113
,
1110
(
2000
).
14.
R. R.
Netz
and
J. F.
Joanny
,
Macromolecules
32
,
9013
(
1999
).
15.
A. V.
Dobrynin
,
A.
Deshkovski
, and
M.
Rubinstein
,
Macromolecules
34
,
8888
(
2001
).
16.
I.
Rouzina
and
V. A.
Bloomfield
,
J. Phys. Chem.
100
,
9977
(
1996
);
N.
Gronbech-Jensen
,
R. J.
Mashl
,
R. F.
Bruinsma
, and
W. M.
Gelbart
,
Phys. Rev. Lett.
78
,
2477
(
1997
);
B. J.
Ha
and
A. J.
Liu
,
Phys. Rev. Lett.
79
,
1289
(
1997
);
R.
Podgornik
and
V. A.
Parsegian
,
Phys. Rev. Lett.
80
,
1560
(
1998
);
J. J.
Arenzon
,
J. F.
Stilck
, and
Y.
Levin
, cond-mat/9806358;
B. I.
Shklovskii
,
Phys. Rev. Lett.
82
,
3268
(
1999
).
17.
T. T.
Nguyen
,
I.
Rouzina
, and
B. I.
Shklovskii
,
J. Chem. Phys.
112
,
2562
(
2000
).
18.
M. Jonsson and P. Linse, J. Chem. Phys. (submitted).
19.
J. O.
Rädler
,
I.
Koltover
,
T.
Salditt
, and
C. R.
Safinya
,
Science
275
,
810
(
1997
).
20.
R. F.
Bruinsma
,
Eur. Phys. J. B
4
,
75
(
1998
).
21.
This idea was suggested to us by A. Yu. Grosberg.
22.
T. A.
Vilgis
,
A.
Johner
, and
J. F.
Joanny
,
Eur. Phys. J. E
2
,
289
(
2000
);
M. N.
Tamashiro
and
H.
Schiessel
,
Macromolecules
33
,
5263
(
2000
).
23.
G. S.
Manning
,
J. Chem. Phys.
51
,
924
(
1969
).
24.
M.
Guerom
and
G.
Weisbuch
,
Biopolymers
19
,
353
(
1980
);
S.
Alexander
,
P. M.
Chaikin
,
P.
Grant
,
G. J.
Morales
,
P.
Pincus
, and
D.
Hone
,
J. Chem. Phys.
80
,
5776
(
1984
);
S. A.
Safran
,
P. A.
Pincus
,
M. E.
Cates
, and
F. C.
MacKintosh
,
J. Phys. (Paris)
51
,
503
(
1990
);
L. Belloni, doctoral thesis, University of Paris IV, 1982;
S. A.
Safran
,
P. A.
Pincus
,
M. E.
Cates
, and
F. C.
MacKintosh
,
Chem. Phys.
99
,
43
(
1985
).
25.
T.
Odijk
,
J. Polym. Sci., Polym. Chem. Ed.
15
,
477
(
1977
);
J.
Skolnick
and
M.
Fixman
,
Macromolecules
10
,
5
(
1977
);
J.
Skolnick
and
M.
Fixman
,
Macromolecules
10
,
944
(
1977
).
26.
H.
Schiessel
,
J.
Rudnick
,
R.
Bruinsma
, and
W. M.
Gelbart
,
Europhys. Lett.
51
,
237
(
2000
).
27.
E.
Raspaud
,
I.
Chaperon
,
A.
Leforestier
, and
F.
Livolant
,
Biophys. J.
77
,
1547
(
1999
).
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