Electrostatic contribution to polymer gels

We evaluate an approximate free energy for polyelectrolyte gels, including entropic effects due to flexibility of chains and electrostatic effects due to net charge of chains. The electrostatic terms depend on the binding fraction of ions m to the network and on the degree of swelling α of the chains. One term describes the interaction of the chains with the ionic solution and the other comes from the internal partition function of the macromolecules of the gel. The equilibrium values of m, α and the mixing parameter χ are obtained. This is also done for some experimental values of gel strength and volume fractions. The critical point for volume phase transitions is evaluated, and we find that the critical temperature increases as the charge on the chains increases, while the critical volume fraction of polymer decreases.