Modeling the effect of ionic strength on swelling of pH-sensitive macro- and nanogels

•Conditions are found for non-monotonic changes in degree of swelling with molar fraction of salt.•The influence of constraints on swelling of macrogels is shown.•The effects are revealed of thickness and surface charges on swelling of nanogels.•Qualitative difference is demonstrated between water uptake by nanogels and polymer brushes.

Some polyelectrolyte gels demonstrate a monotonic decrease in their equilibrium degree of swelling with molar fraction of salt, while the others reveal a non-monotonic dependence of water uptake on concentration of salt. A model is developed for the mechanical behavior of anionic gels which shows that the non-monotonicity arises when concentration of ionizable functional groups becomes relatively high. Material constants in the governing equations are found by fitting observations on poly(acrylic acid) and poly(acrylamide-co-acrylic acid) gels. The model is applied to the analysis of constrained swelling of a gel layer grown on a rigid substrate when (i) thickness of the layer exceeds strongly the Debye length (macrogel), and (ii) these parameters are comparable (nanogel). Simulation reveals that water uptake by a nanogel differs pronouncedly from that of a macrogel or a polymer brush. Under some conditions (the interface between the layer and the substrate is charged positively), the average degree of swelling of a nanogel decays monotonically with ionic strength while that of a macrogel evolves non-monotonically.

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