Simulations explain the Swelling Behavior of Hydrogels with Alternating Neutral and Weakly Acidic Blocks

We use computer simulations to study the swelling behavior of weak (pH-responsive) polyelectrolyte hydrogels, coupled to a solution of small ions, termed the reservoir. The gels consist of a covalent, regular network composed of alternating four-armed neutral and acidic stars. The model designed to represent recently synthesized gels composed of tetrapoly\-(acrylic acid) and tetrapoly(ethylene glycol) stars. To model the ionization equilibrium of the weak acid groups and the exchange of small ions with the reservoir, we apply the recently developed Grand-Reaction Monte-Carlo method (G-RxMC) and determine the free swelling equilibrium of these gels at various pH values and salt concentrations in the reservoir. Our results show that the dependence of the swelling ratio on the pH significantly deviates from the ideal Henderson-Hasselbalch equation, due to electrostatic interactions and Donnan partitioning of small ions. By analyzing the simulation results we are able to separate the Donnan effect from the effect electrostatic interactions, showing that the latter contribution dominates in this particular system. This observation contrasts with our previous observations that both effects are comparably strong in hydrogels composed of homogeneously distributed weak acid groups and that the Donnan effect dominates in polyelectrolyte brushes. Our simulations allow us to understand which of the above effects may dominate in different systems (various types of polyelectrolyte gels and brushes), thereby allowing us to identify the correct physical origin of the deviations from ideal swelling. Such an understanding is important not only for correctly interpreting the experimental measurements but also for designing polyelectrolyte gels tailored to exhibit specific swelling response to pH and salt concentration. Finally, we revisit the Manning argument that was invoked in a theoretical analysis of Tang et al. and demonstrate that it alone does not provide a consistent explanation for the swelling behaviour in terms of an extended Flory-Rehner model.