Finite element modeling applied to analyze experimentally determined hydrogel swelling data provides quantitative description of the hydrogel in the aqueous solutions with well-defined ionic content and environmental parameters. In the present study, we expand this strategy to analysis of swelling of hydrogels over an extended concentration of salt where the Donnan contribution and specific ion effects are dominating at different regimes. Dynamics and equilibrium swelling were determined for acrylamide and cationic acrylamide-based hydrogels by high-resolution interferometry technique for step-wise increase in NaCl and NaBr concentration up to 2 M. Although increased hydrogel swelling volume with increasing salt concentration was the dominant trend for the uncharged hydrogel, the weakly charged cationic hydrogel was observed to shrink for increasing salt concentration up to 0.1 M, followed by swelling at higher salt concentrations. The initial shrinking is due to the ionic equilibration accounted for by a Donnan term. Comparison of the swelling responses at high NaCl and NaBr concentrations between the uncharged and the cationic hydrogel showed similar specific ion effects. This indicates that the ion non-specific Donnan contribution and specific ion effects are additive in the case where they are occurring in well separated ranges of salt concentration. We develop a novel finite element model including both these mechanisms to account for the observed swelling in aqueous salt solution. In particular, a salt-specific, concentration-dependent Flory–Huggins parameter was introduced for the specific ion effects. This is the first report on finite element modeling of hydrogels including specific ionic effects and underpins improvement of the mechanistic insight of hydrogel swelling that can be used to predict its response to environmental change.
Finite Element Modeling for a Morphometric and Mechanical Characterization of Trabecular Bone from High Resolution Magnetic Resonance Imaging