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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