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 (Qs) pass through a maximum value (Qmax) 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 Qmax for several of the gels due to neglecting the finite extensibility of the short linear PEG chains.