Swelling Behaviors of Hydrogels with Alternating Neutral/Highly Charged Sequences

Polyelectrolyte gels comprising fixed ions exhibit swelling behaviors because of external solution conditions. Such behaviors are usually explained by using the Flory-Rehner model that considers the Donnan equilibrium. However, this model assumes a homogeneous distribution for fixed ions; therefore, its applicability to the case of heterogeneous distributions remains unclear. Here, we successfully designed a hydrogel with alternating neutral/highly charged sequences (i.e., tetrapoly(acrylic acid)-poly(ethylene glycol) gel). The Flory-Rehner model with the Donnan equilibrium was found to predict the swelling ratio only below pH 5.6. The distance between two neighboring fixed ions is larger than the Bjerrum length. The swelling behaviors above pH 5.6, where the fixed ions are more closely located than the Bjerrum length, can be explained by considering additionally the counterion condensation in the poly(acrylic acid) units. These results indicate that the ionic interactions within the length scale of the network strand can determine the counterion condensation and that it is vital to estimate accurately the distance between neighboring fixed ions for predicting the swelling behaviors of polyelectrolyte gels.