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

Abstract

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.

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

“…To determine the composition of the coexisting phases, we expand on the approach used in our previous simulations of polyelectrolyte gels. ,, First, we select a supernatant phase of a given composition and then try to identify whether there could be an PEC phase in equilibrium with this supernatant. For such an PEC phase, at least two conditions have to be met: (i) chemical potentials of exchanged ions and solutes are equal in both of the phases, and (ii) pressures of both of the phases are equal.…”

“…Arguably, the charge regulation can become a nontrivial actor, especially if the polyanion-polycation mixing ratio is not unity, due to the emerging Donnan potential between the phases. In principle, the Monte Carlo in the Grand-reaction ensemble (G-RxMC) method used here is able to quantitatively capture these effects, as repeatedly proven in simulations of gels and peptide solutions. − Herein, we focus only on the charge regulation of a small solute in the presence of an PEC. The effects of charge regulation and pH on the formation of PECs will be addressed in detail in our follow-up publication.…”

Polyelectrolyte Gels: Swelling and Deswelling upon Nonlinear Deformations

“…The developed framework to study polyelectrolyte gel swelling and deformation is different from the currently adopted approach. Instead of using hybrid of molecular dynamics simulations and Monte Carlo simulations for ion exchange between a gel and a salt reservoir, ,− we performed simulations of the gel film surrounded by salt solution. This setup has an advantage since it does not suffer from simulation slow down due to the rejection of insertion steps at large densities of salt ions and monomers in a gel.…”

“…17,20,38,59 Our approach can be extended to examine the effects of gel deformation on the dissociation equilibrium of ionizable groups in gels of weak polyelectrolytes. 50,52,59,60 Such a study could illuminate the interplay between solution pH and nonlinear gel elasticity. We hope that this work will prompt further studies in this area.…”

Charge Regulation of Polyelectrolyte Gels: Swelling Transition

“…The theoretical analysis of the PE gel swelling was originally centered on the concept of Donnan equilibrium and gel elasticity. , Later, it was extended , to include a more detailed description of electrostatic interactions based either on the linear Debye–Hückel theory , or on the full nonlinear Poisson–Boltzmann (PB) theory, combined with Flory–Huggins theory for polymer mixtures and gel elasticity. − In addition, there are extensive works done using particle-based models. − …”