We used computer simulations to study the equilibrium swelling of weak (pH-responsive) polyelectrolyte hydrogels as a function of pH and salt concentration in a supernatant solution. Our simulations were 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 applied the recently developed Grand-Reaction Monte-Carlo method. We showed that the ionization of these gels as a function of the pH significantly deviates from the ideal Henderson-Hasselbalch equation due to two main contributions: (1) electrostatic interactions and (2) Donnan partitioning of small ions. The first contribution dominates in the gels composed of alternating neutral and acidic blocks, contrasting with our previous observations that both contributions are comparably strong in hydrogels composed of homogeneously distributed weak acid groups. We also critically examined the counterion condensation argument, previously invoked to explain why the experimentally observed swelling was lower than predicted by theory. Thus, a detailed analysis of the simulations allowed us to understand which of the above effects dominates in different systems and why, 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 experimental measurements but also for designing polyelectrolyte gels tailored to exhibit specific swelling response to pH and salt concentration.
A revised version of the manuscript addressing reviewer comments.