Abstract
A model of a polyelectrolyte solution has been formulated on the basis of the formalism of the thermodynamic perturbation theory. Macromolecules have been described in terms of the model of a flexible chain with an excluded volume and a variable electrical charge. During construction of the thermodynamic perturbation theory, a set of three independent subsystems—polyelectrolyte macromolecules placed in a structureless charge background of counterions, counterions placed in a structureless charge background of macromolecules, and Coulomb gas ions of a low-molecular-mass salt—has been taken as the reference system. In the framework of this model, liquid-liquid phase separation due to strong correlation-induced attraction has been predicted. The behavior of the degree of ionization over a wide monomer concentration range, including the region of phase separation either in a salt-free solution or in the presence of univalent ions of a low-molecular-mass salt in the solution, has been studied. It has been shown that macromolecules in the coexisting phases should have different degrees of ionization. The occurrence of phase separation under normal conditions in the case when dimethylformamide is taken as a solvent and the nonoccurrence of this phase separation in the case of aqueous solutions of flexible-chain polyelectrolytes are predicted.
Similar content being viewed by others
References
G. H. Fredrickson, The Eguilibrium Theory of Inhomogenous Polymers (Clarendon, Oxford, 2005).
A. V. Dobrynin and M. Rubinstein, Prog. Polym. Sci. 30, 1049 (2005).
A. V. Dobrynin, Curr. Opin. Colloid Interface Sci. 13, 376 (2008).
C. Holm, J. F. Joanny, K. Kremer, R. R. Netz, P. Reineker, C. Seidel, T. A. Vilgis, and R. G. Winkler, Adv. Polym. Sci. 66, 67 (2004).
Y. Levin, Rep. Prog. Phys. 65, 1577 (2002).
A. Yu. Grosberg and A. R. Khokhlov, Statistical Physics of Macromolecules (Nauka, Moscow, 1989; AIP, New York, 1994).
P.-G. De Gennes, (Cornell Univ. Press, 1979).
V. Yu. Borue and I. Ya. Erukhimovich, Macromolecules 21, 3240 (1988).
J. F. Joanny and L. J. Leibler, J. Phys. (Paris) 51, 545 (1990).
A. R. Khohlov and I. A. Nyrkova, Macromolecules 25, 1493 (1992).
M. Gottschalk, P. Linse, and L. Piculell, Macromolecules 31, 8407 (1998).
E. Yu. Kramarenko, I. Ya. Erukhimovich, and A. R. Khohlov, Macromol. Theory Simul. 11, 462 (2002).
P. B. J. Warren, J. Phys. (Paris) 7, 343 (1997).
K. A. Mahdi and M. Olvera De la Cruz, Macromolecules 33, 7649 (2000).
G. Orkoulas, S. K. Kumar, and A. J. Panagiotopoulos, Phys. Rev. Lett. 90, 048303-1 (2003).
A. V. Ermoshkin and M. Olvera de la Cruz, Macromolecules 36, 7824 (2003).
N. V. Brilliantov, Contrib. Plasma Phys. 38, 489 (1998).
N. V. Brilliantov, V. V. Malinin, and R. R. Netz, Eur. Phys. J. D 18, 339 (2002).
N. V. Brilliantov, D. V. Kuznetzov, and R. Klein, Phys. Rev. Lett. 81, 1433 (1998).
A. V. Ermoshkin and M. Olvera de la Cruz, Phys. Rev. Lett. 90, 125504-1 (2003).
M. Muthukumar, Macromolecules 35, 9142 (2002).
C.-L. Lee and M. J. Muthukumar, Chem. Phys. 130, 024904 (2009).
J. W. Jiang, L. Blum, O. Bernard, and J. M. Prausnitz, Mol. Phys. 99, 1121 (2001).
J.-L. Barrat and J.-P. Hansen, Basic Concepts for Simple and Complex Fluids (Cambridge Univ. Press, Cambridge, 2003).
J. P. Hansen and I. R. Donald, Theory of Simple Liquids (Academic, London, 1976).
I. R. Yukhnovskii and M. F. Golovko, Statistical Theory of Classical Equilibrium Systems (Naukova Dumka, Kiev, 1980) [in Russian].
S. F. Edwards, Proc. Phys. Soc. 85, 613 (1965).
N. V. Brilliantov, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 48, 4536 (1993).
M. Muthukumar, J. Chem. Phys. 120, 9343 (2004).
J. Hubbard and P. Schofield, Phys. Lett. A 40, 245 (1972).
M. Muthukumar and S. F. Edwards, J. Chem. Phys. 76, 265 (1982).
A. Nikoubashman, J. P. Hansen, and G. J. Kahl, Chem. Phys. 137, 094905 (2012).
W. B. Warren and A. J. Masters, J. Chem. Phys. 138, 074901 (2013).
Yu. A. Budkov, A. I. Frolov, M. G. Kiselev, and N. V. Brilliantov, J. Chem. Phys. 139, 194901 (2013).
R. J. Kubo, J. Phys. Soc. Jpn. 17, 1100 (1962).
J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon, Oxford, 1989).
A. Levy, D. Andelman, and H. Orland, Phys. Rev. Lett. 108, 227801 (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © Yu.A. Budkov, A.L. Kolesnikov, E.A. Nogovitsyn, M.G. Kiselev, 2014, published in Vysokomolekulyarnye Soedineniya. Ser. A, 2014, Vol. 56, No. 5, pp. 559–574.
Rights and permissions
About this article
Cite this article
Budkov, Y.A., Kolesnikov, A.L., Nogovitsyn, E.A. et al. Electrostatic-interaction-induced phase separation in solutions of flexible-chain polyelectrolytes. Polym. Sci. Ser. A 56, 697–711 (2014). https://doi.org/10.1134/S0965545X14050022
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965545X14050022