Salt effects over the swelling of ionized mesoscopic gels

In this work, the effects of salt concentration over the swelling of ionic mesoscopic gels will be studied theoretically and verified with experiments. We will restrict ourselves to the weak screening limit where the Debye screening length is larger than the mesh size of the gel. Under this condition, direct electrostatic interactions are negligible and the swelling is driven by the osmotic pressure of the ions. The swelling response of a mesoscopic gel is strongly dependent on the ionization degree of the gel. In particular, a maximum in the size–salt concentration curve appears for a partially ionized gel, when the salt concentration equals the network charge concentration. This maximum is removed for a totally ionized polymer network. Despite these facts, a charge independent asymptotic behavior between size and salt concentration becomes apparent, at sufficiently high values of the latter. The Flory–Huggins mean-field approach together with the Donnan relations describe the observed swelling adequately, thus accounting for the essential physics of the problem. As a final remark, an experimental method for determining gel charge will be inferred from the results.