pH-dependent swelling of hydrogels containing highly branched polyamine macromonomers

We examine the pH-dependent swelling of end-linked hydrogels containing high concentrations of amine-functional macromonomers. Gels are formed by end-linking of epoxide-terminated, linear poly(ethylene glycol) (PEG) to either amine-terminated poly(amidoamine) (PAMAM) dendrimers or highly branched poly(ethyleneimine) (PEI). After extraction in neutral water, the hydrogels are swollen in aqueous solutions of HCl or NH₄OH to vary the external pH. Equilibrium volume swelling ratios (Q_s) pass through a maximum value (Q_max) at an external pH denoted as pH^∗ which is approximately 4-5 for the gels studied. The swelling behavior is modeled using Donnan equilibrium theory to describe the ion swelling pressure, with the Flory-Rehner phantom network expression representing the elastic and mixing contributions to the free energy. The model accurately predicts the maximum in swelling near pH = 4-5, but overestimates Q_max for several of the gels due to neglecting the finite extensibility of the short linear PEG chains.