In one and two component polar solvents, we calculate the counterion distribution around an ionizable rod treating the degree of ionization as an annealed variable dependent on its local environment. In the two component case, we take into account the preferential solvation of the charged particles and the short-range interaction between the rod and the solvent. It follows a composition-dependent mass action law. The composition becomes heterogeneous around a charged rod on a mesoscopic scale, strongly affecting the counterion distribution. We predict a first order phase transition of weak-to-strong ionization for hydrophobic chains. This transition line starts from a point on the solvent coexistence curve and ends at an ionization critical point. The composition heterogeneity is long-ranged near the solvent critical point.
REFERENCES
1.
G. S.
Manning
, J. Chem. Phys.
51
, 924
(1969
);2.
3.
J. L.
Barrat
and J. F.
Joanny
, Adv. Chem. Phys.
94
, 1
(1996
).4.
Y.
Levin
, Rep. Prog. Phys.
65
, 1577
(2002
).5.
N.
Volk
, D.
Vollmer
, M.
Schmidt
, W.
Oppermann
, and K.
Huber
, Adv. Polym. Sci.
166
, 29
(2004
).6.
C.
Holm
, J. F.
Joanny
, K.
Kremer
, R. R.
Netz
, P.
Reineker
, C.
Seidel
, T. A.
Vilgis
, and R. G.
Winkler
, Adv. Polym. Sci.
166
, 67
(2004
).7.
A. V.
Dobrynin
and M.
Rubinstein
, Prog. Polym. Sci.
30
, 1049
(2005
).8.
W.
Essafi
, F.
Lafuma
, D.
Baigl
, and C. E.
Williams
, Europhys. Lett.
71
, 938
(2005
).9.
D.
Andelman
, Proceeding of the Nato ASI and SUSSP on Soft Condensed Matter in Molecular and Cell Biology
, edited by by W.
Poon
and D.
Andelman
, 2005
(Taylor and Francis
, New York
, 2006
), pp. 97
–122
.10.
A.
Naji
and R. R.
Netz
, Phys. Rev. E
73
, 056105
(2006
).11.
R.
Messina
, J. Phys.: Condens. Matter
21
, 113102
(2009
).12.
E.
Raphael
and J. F.
Joanny
, Europhys. Lett.
13
, 623
(1990
).13.
I.
Borukhov
, D.
Andelman
, and H.
Orland
, Europhys. Lett.
32
, 499
(1995
).14.
I.
Borukhov
, D.
Andelman
, R.
Borrega
, M.
Cloitre
, L.
Leibler
, and H.
Orland
, J. Phys. Chem. B
104
, 11027
(2000
).15.
M.
Muthukumar
, J. Chem. Phys.
120
, 9343
(2004
).16.
Y.
Burak
and R. R.
Netz
, J. Phys. Chem. B
108
, 4840
(2004
) (This paper shows that the electrostatic interaction among the charged monomers gives rise to correlated ionization.).17.
A.
Onuki
and R.
Okamoto
, J. Phys. Chem. B
113
, 3988
(2009
).18.
C. B.
Post
and B. H.
Zimm
, Biopolymers
21
, 2139
(1982
).19.
P. G.
Arscott
, C.
Ma
, J. R.
Wenner
, and V. A.
Bloomfield
, Biopolymers
36
, 345
(1995
).20.
A.
Hultgren
and D. C.
Rau
, Biochemistry
43
, 8272
(2004
).21.
C.
Stanley
and D. C.
Rauy
, Biophys. J.
91
, 912
(2006
).22.
S.
Flock
, R.
Labarbe
, and C.
Houssier
, Biophys. J.
70
, 1456
(1996
).23.
D.
Baigl
and K.
Yoshikawa
, Biophys. J.
88
, 3486
(2005
).24.
S. M.
Mel’nikov
, V. G.
Sergeyev
, and K.
Yoshikawa
, J. Am. Chem. Soc.
117
, 2401
(1995
).25.
D.
Ben-Yaakov
, D.
Andelman
, D.
Harries
, and R.
Podgornik
, J. Phys. Chem. B
113
, 6001
(2009
).26.
27.
A.
Onuki
and H.
Kitamura
, J. Chem. Phys.
121
, 3143
(2004
).28.
A.
Onuki
, Phys. Rev. E
73
, 021506
(2006
).29.
A.
Onuki
, J. Chem. Phys.
128
, 224704
(2008
).30.
Y.
Tsori
and L.
Leibler
, Proc. Natl. Acad. Sci. U.S.A.
104
, 7348
(2007
).31.
J.
Zwanikken
, J.
de Graaf
, M.
Bier
, and R.
van Roij
, J. Phys.: Condens. Matter
20
, 494238
(2008
).32.
A.
Onuki
, Europhys. Lett.
82
, 58002
(2008
).33.
J. W.
Cahn
, J. Chem. Phys.
66
, 3667
(1977
).34.
C.
Ebner
and W. F.
Saam
, Phys. Rev. Lett.
38
, 1486
(1977
).35.
P.
Tarazona
and R.
Evans
, Mol. Phys.
48
, 799
(1983
).36.
A.
Onuki
, Phase Transition Dynamics
(Cambridge University Press
, Cambridge
, 2002
).37.
R. M.
Fuoss
, A.
Katchalsky
, and S.
Lifson
, Proc. Natl. Acad. Sci. U.S.A.
37
, 579
(1951
).38.
For ideal gases the entropic free energy is of the form with , where is the Planck constant and is the particle mass. This term is larger than that in Eq. (7) by , where is a constant shift in the chemical potential of the ions.
39.
T.
Osakai
and K.
Ebina
, J. Phys. Chem. B
102
, 5691
(1998
). In water-nitrobenzene (Nr) in two phase coexistence, they measured the number of hydrating water molecules around ions in a Nr-rich region at room temperatures. The water number per ion in the Nr-rich phase was estimated to be 4 for , 6 for , and 15 for , while it was nearly zero for hydrophobic ions. Their experiment demonstrates strong binding of water molecules to hydrophilic ions even at small water contents.40.
A.
Hamnett
, C. H.
Hamann
, and W.
Vielstich
, Electrochemistry
(Wiley-VCH
, Weinheim
, 1998
).41.
P.
Debye
and K.
Kleboth
, J. Chem. Phys.
42
, 3155
(1965
).42.
H.
Ohtaki
, Bull. Chem. Soc. Jpn.
42
, 1573
(1969
).43.
D.
Bonn
, D.
Ross
, S.
Hachem
, S.
Gridel
, and J.
Meunier
, Europhys. Lett.
58
, 74
(2002
).44.
45.
L. Q.
Hung
, J. Electroanal. Chem.
115
, 159
(1980
).46.
G.
Marcus
, S.
Samin
, and Y.
Tsori
, J. Chem. Phys.
129
, 061101
(2008
). These authors assumed the homogeneity of , where the counterions are absent and the gradient term is neglected. Compare their and our in Eq. (42). In their theory, ( for rods) plays the role of an inhomogeneous ordering field.47.
H.
Kitamura
and A.
Onuki
, J. Chem. Phys.
123
, 124513
(2005
).48.
P. G.
de Gennes
, J. Phys. (Paris)
37
, 59
(1976
). Polymers can interact with two solvent components asymmetrically. There arises a pairwise attractive interaction among the monomers mediated by the critical fluctuations. Similar attractive interactions were derived among ions in mixture solvents by one of the present authors (Ref. 28).49.
A.
Dondos
and Y.
Izumi
, Makromol. Chem.
181
, 701
(1980
);50.
T.
Sumi
, K.
Kobayashi
, and H.
Sekino
, J. Chem. Phys.
127
, 164904
(2007
).51.
A. F.
Kostko
, M. A.
Anisimov
, and J. V.
Sengers
, Phys. Rev. E
70
, 026118
(2004
).52.
H.
Matsuoka
, D.
Schwahn
, and N.
Ise
, Macromolecules
24
, 4227
(1991
).53.
J. J.
Tanahatoe
and M. E.
Kuil
, J. Phys. Chem. B
101
, 5905
(1997
).54.
B. D.
Ermi
and E. J.
Amis
, Macromolecules
31
, 7378
(1998
).55.
K.
Sadakane
, H.
Seto
, H.
Endo
, and M.
Shibayama
, J. Phys. Soc. Jpn.
76
, 113602
(2007
);56.
K.
Shirahama
, K.
Takashima
, and N.
Takisawa
, Bull. Chem. Soc. Jpn.
60
, 43
(1987
).57.
K.
Tanaka
and Y.
Okahata
, J. Am. Chem. Soc.
118
, 10679
(1996
).58.
P. S.
Kuhn
, Y.
Levin
, and M. C.
Barbosa
, Chem. Phys. Lett.
298
, 51
(1998
).© 2009 American Institute of Physics.
2009
American Institute of Physics
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