The pH inside a swollen polyelectrolyte gel: poly(N-vinylimidazole)

The pH inside a dissolved polyelectrolyte coil or a swollen ionic polymer network is not accessible to direct measurement. It is here calculated through a simple model, based on Donnan equilibrium, counterion condensation (for charge density exceeding the critical value), and balance of mobile ions, without any assumption on the pKa of the ionizable groups. The data needed for the calculation with this model are polymer concentration, pH value in the initial solution, and pH value in the bath at equilibrium. All three can be determined experimentally by a batch method where the polymer is immersed in a different pot for each starting pH. The model is applied to a sample system, namely, chemically cross-linked poly(N-vinylimidazole) immersed in acidic baths of different pH values. The imidazole units are basic and become protonated by the acid, thus changing the pH of the initial bath. The model shows how the pH developed inside the swollen gel is several units higher than the pH of the bath at equilibrium, both with or without the correction for counterion condensation. Consequently, when the pKa of the polyelectrolyte is determined in the usual way (with the pH measured in the external bath), it gives an apparent value that is several units below the pKa determined from the actual pH inside the swollen gel at equilibrium. The inclusion of the counterion condensation decreases very slightly the polymer basicity. Surface effects and intramolecular association between protonated and unprotonated imidazole rings are discussed to explain the pKa behavior in the limit of low degree of ionization.