Elastic modulus and equilibrium swelling of polyelectrolyte gels

We present a scaling theory for the modulus G of polyelectrolyte gels as a function of strand length between cross-links, monomer concentration c, salt concentration c(s), and preparation conditions (monomer concentration c(0) and salt concentration c(s)(0)). The theory assumes affine displacement of the junction points when the concentration is changed. With no added salt (c(s) = c(s)(o) = 0), we predict a new concentration dependence of the modulus G similar to c(5/6). In the high-salt limit, we predict the usual concentration dependence for uncharged polymers but a novel dependence on salt concentration, G similar to c(7/12)c(s)(1/4). We also predict the modulus to decrease as charge is added to the gel strands. The predicted effects of added salt and charge on modulus have recently been observed by Candau and co-workers. At low concentrations, we discuss the strong stretching of network strands and its effect on modulus and equilibrium swelling.