Molecular Theory of Weak Polyelectrolyte Gels: The Role of pH and Salt Concentration

We develop a detailed molecular theory that describes the response of weak polyelectrolyte gels to changes in both the pH and salt concentration, c, of the solution. This approach includes specific molecular details and conformational degrees of freedom of the polymeric gel, acid−base equilibrium, and solution entropy as well as electrostatic, van der Waals, and excluded-volume interactions. Here, we study polyacid gels in good solvent. The physical properties of the gel are found to depend on the coupling between charge regulation and the molecular interactions. In particular, the gel’s degree of dissociation is not only determined by the bath pH and ionic strength but also by the polymer’s ability in regulating charge to modify the local environment and in swelling or shrinking that depends on the externally controlled variables. The gel pH can be several units smaller than the bath pH depending on the salt ion concentration. The gel pH does not respond linearly to changes in neither bath pH nor c, and its behavior results from the complex interplay between the conformational degrees of freedom and all of the interactions mentioned above. The gel system swells if pH > pKa and collapses if pH < pKa. The continuous transition between collapsed and swollen regimes occurs in a very narrow range of bath pH around pKa whose width depends on the salt concentration. In this intermediate region the volume fraction of the polyacid can be controlled by both c and pH.