We use hybrid molecular dynamics/Monte Carlo simulations and coarse-grained polymer models to study the swelling of polyelectrolyte gels in salt solutions. Besides existing industrial applications, such gels have been recently proposed as a promising agent for water desalination. We employ the semi-grand canonical ensemble to investigate partitioning of the salt between the bulk solution and the gel and the salt-induced deswelling of the gels under free swelling equilibrium and under compression. We compare our findings to the analytic model of Katchalsky and Michaeli which explicitly accounts for electrostatic effects. The partitioning of small ions predicted by the model well captures the deviations from the simple Donnan approximation observed in the simulation data. In contrast, the original model highly overestimates the gel swelling, predicting even chain stretching beyond contour length. With a modified model, where we replace the Gaussian elasticity with the Langevin function for finite extensibility, we obtain nearly quantitative agreement between theory and simulations both for the swelling ratio and for the partitioning of salt, across the whole range of studied gel parameters and salt concentrations. The modified model thus provides a very good description of swelling of polyelectrolyte gels in salt solutions and can be used for theoretical predictions of water desalination using hydrogels. These predictions are much less computationally demanding than the simulations which we used to validate the model. ■ INTRODUCTIONPolyelectrolytes are polymers composed of monomers that dissociate upon dissolution in water, releasing small counterions (e.g., Na + ) into the solution. Polyelectrolyte hydrogels are a network of cross-linked polyelectrolytes. Their prominent feature is a huge swelling capacity in aqueous solution up to 10 3 times their dry volume. Because of their ability to absorb water, they are widely used as superabsorbers for hygiene products 1 as well as biomedical 2−9 and agricultural 10−12 applications. In contrast to bulk materials, polyelectrolyte micro-and nanogels are being investigated as nanoreactors 13−15 or as carriers for controlled drug release. 16−20 Recently, polyelectrolyte hydrogels were proposed to desalinate saline water. 21,22 The swelling of polyelectrolyte hydrogels is determined by the balance of several factors. On one hand, there is the electrostatic repulsion among the fixed charges of the polymer and the osmotic pressure of its counterions. Both the above contributions promote gel swelling. This is counteracted by the elasticity of the polymer chains, which balances out the other two contributions at a particular volume of the swollen gel. Electrostatic interactions may be screened by the addition of salt, which results in deswelling of the gels as compared to the salt-free case. The salt content in the gel, however, is different from that in the bulk, which is the key observation for the proposed use of hydrogels for desalination. 22 Deswelling of the gels can be induc...

This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels.

No abstract

The target of this work is to study conformational properties of starlike polyelectrolytes with pH-sensitive (annealed) dissociation in salt-free solutions. We confront hybrid Monte Carlo (HMC) simulations with computationally less expensive approximate numerical self-consistent field (SCF) calculations and with analytical theories. We demonstrate when the mean-field results are reliable and their advantage over MC in terms of efficiency can be exploited and when not. In the interior of the star, where inter-arm interactions dominate over intra-arm ones, the mean-field approximation works well and SCF agrees with the MC results. Intra-arm interactions dominate at star periphery, and their role is underestimated by the mean field. Here, conformations and dissociation resemble those of linear polyelectrolytes. Consequently, the dissociation profile along the chain contour is qualitatively different between MC and SCF. Comparison of the two methods and a distinction between intra-arm and inter-arm contributions to interactions enables us to understand the transition in behavior from linear to starlike chain topology.