title: A self-consistent mean-field model for polyelectrolyte gels.
abstract: We present a novel approach to modeling polyelectrolyte gels, exploiting the analogy between star-branched polymers and polymer networks as a computationally inexpensive yet reliable alternative to full-scale simulations. In the numerical mean-field model of a star-like polymer we modify the boundary conditions to represent an infinite network. We validate the predictions of our new model against a coarse-grained simulation model. We also validate it against a phenomenological analytical model which has been previously shown to agree with simulations in a limited range of parameters. The mean-field model explicitly considers local density gradients and agrees with the simulation results in a broad range of parameters, beyond that of the analytical model. Finally, we use the mean-field model for predictions of the swelling behaviour of weak polyelectrolyte gels under different pH conditions. We demonstrate that the local density gradients are important and that the ionization of the weak polyelectrolyte gel is significantly suppressed. Under the studied conditions the effective pKAis about one unit higher than that of the free monomer. This shift in the effective pKAstems from the different pH values inside and outside the gel.
authors.affiliation: Institute of Macromolecular Compounds of Russian Academy of Sciences, 199004, Bolshoy pr. 31, Saint-Petersburg, Russia. helvrud@gmail.com and Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University in Prague, Hlavova 8, 128 00 Praha 2, Czech Republic. peter.kosovan@natur.cuni.cz.
authors.forename: Oleg
authors.initials: O
authors.lastname: Rud
authors.affiliation: Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany.
authors.forename: Tobias
authors.initials: T
authors.lastname: Richter
authors.affiliation: Institute of Macromolecular Compounds of Russian Academy of Sciences, 199004, Bolshoy pr. 31, Saint-Petersburg, Russia. helvrud@gmail.com and Institut des Sciences Analytiques et de Physico-Chimie pour l'Environnement et les Matériaux, UMR 5254 CNRS UPPA, Pau, France and Saint-Petersburg National University of Informational Technologies, Mechanics and Optics, 197101, Kronverkskiy pr., 49 A, Saint-Petersburg, Russia.
authors.forename: Oleg
authors.initials: O
authors.lastname: Borisov
authors.affiliation: Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany.
authors.forename: Christian
authors.initials: C
authors.lastname: Holm
authors.affiliation: Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University in Prague, Hlavova 8, 128 00 Praha 2, Czech Republic. peter.kosovan@natur.cuni.cz.
authors.forename: Peter
authors.identifier: http://orcid.org/0000-0002-6708-3344
authors.initials: P
authors.lastname: Košovan