We develop a double mean-field theory for charged macrogels immersed in electrolyte solutions in the spirit of the cell model approach.We first demonstrate that the equilibrium sampling of a single explicit coarse-grained charged polymer in a cell yields accurate predictions of the swelling equilibrium if the geometry is suitably chosen and all pressure contributions have been incorporated accurately. We then replace the explicit flexible chain by a suitably modeled penetrable charged rod that allows to compute all pressure terms within the Poisson-Boltzmann approximation. This model, albeit computationally cheap, yields excellent predictions of swelling equilibria under varying chain length, polymer charge fraction, and external reservoir salt concentrations when compared to coarse-grained molecular dynamics simulations of charged macrogels. We present an extension of the model to the experimentally relevant cases of pH-sensitive gels.
arXiv:1905.04960v1 [cond-mat.soft]Polyelectrolyte gels consist of crosslinked charged polymers (polyelectrolytes) that can be synthesized with various topologies and are produced in sizes ranging from nanometers (nanogels) up to centimeters (macrogels) [1,2]. They show a large, reversible uptake of water that is exploited in numerous dailylife products, such as in superabsorbers, cosmetics, pharmaceuticals [3,4,5], agriculture [6,7], or quite recently water desalination [8,9]. Tailoring polyelectrolyte gels to their applications requires a sufficiently accurate prediction of their swelling capabilities and elastic responses, a task that still goes beyond analytical approaches [10,11,12,13,14,15,16,17,18]. So far only all-atom simulations of short single chains in the bulk (not of whole hydrogels) with explicit water have been performed [19,20,21,22]. On the other hand, coarse-grained polyelectrolyte network models have demonstrated their ability to amend analytical approaches, showing that structural microscopic details can have noticeable effects on the macroscopic properties such as the swelling [23,24,25,26,27,28,29,30,31,32]. Macroscopic gels with monodisperse chain length can be simulated with microscopic detail using molecular dynamics (MD) simulations with periodic boundary conditions (PBCs) (cf. periodic gel model ) where a unit gel section is connected periodically to yield an infinite gel without boundaries. However, even MD simulations of periodic gels remain computationally very expensive due to the many particles and the slow relaxation times of the involved polymers. Thus, the development of computationally efficient mean-field models capable of predicting swelling equilibria have been of scientific interest in the last years [33,15,31,32]. First ideas of using a Poisson-Boltzmann (PB) cell model under tension were put forward by Mann for salt-free gels, with moderate success [33].About sixty years ago Katchalsky and Michaeli [11] suggested a free energy model that has recently been shown to predict swelling equilibria reasonably well [31] when compared to MD simulat...