Modeling of Polyelectrolyte Gels in Equilibrium with Salt Solutions

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

Sequestration of Small Ions and Weak Acids and Bases by a Polyelectrolyte Complex Studied by Simulation and Experiment

Mixing of oppositely charged polyelectrolytes can result in phase separation into a polymer-poor supernatant and a polymer-rich polyelectrolyte complex (PEC). We present a new coarse-grained model for the Grand-reaction method that enables us to determine the composition of the coexisting phases in a broad range of pH and salt concentrations. We validate the model by comparing it to recent simulations and experimental studies, as well as our own experiments on poly(acrylic acid)/poly(allylamine hydrochloride) complexes. The simulations using our model predict that monovalent ions partition approximately equally between both phases, whereas divalent ones accumulate in the PEC phase. On a semiquantitative level, these results agree with our own experiments, as well as with other experiments and simulations in the literature. In the sequel, we use the model to study the partitioning of a weak diprotic acid at various pH values of the supernatant. Our results show that the ionization of the acid is enhanced in the PEC phase, resulting in its preferential accumulation in this phase, which monotonically increases with the pH. Currently, this effect is still waiting to be confirmed experimentally. We explore how the model parameters (particle size, charge density, permittivity, and solvent quality) affect the measured partition coefficients, showing that fine-tuning of these parameters can make the agreement with the experiments almost quantitative. Nevertheless, our results show that charge regulation in multivalent solutes can potentially be exploited in engineering the partitioning of charged molecules in PEC-based systems at various pH values

Dynamics in Stimuli-Responsive Poly(<i>N</i>‑isopropylacrylamide) Hydrogel Layers As Revealed by Fluorescence Correlation Spectroscopy

We employ fluorescence correlation spectroscopy (FCS) to study the translational mobility of molecular tracers in stimuli-responsive grafted poly­(<i>N</i>-isopropylacrylamide) (PNiPAAm) hydrogels, under variable solvency conditions. Tracer–matrix interactions were tuned by selecting three different molecular tracers. In contrast to a noninteracting tracer (Alexa 647), the mobility of a weakly (Alexa 488) and a strongly interacting (Rhodamine 6G) tracer deviates from a simple single Fickian diffusion. In addition to pure crowding effects, the mobility of both Alexa488 and Rhodamine 6G is influenced by tracer–polymer interactions. We interpret the observed trends in tracer mobility in terms of the interplay between Coulombic repulsions and short-range attractions. Although tracer dynamics and hydrogel swelling ratio are interdependent properties, their relation turns out to be nontrivial and does not allow predictions of tracer dynamics on the basis of polymer structural information. Hence, a universal scaling behavior is not possible, due to tracer–polymer interactions

Modeling of Ionization and Conformations of Starlike Weak Polyelectrolytes

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