Volume phase transition of polyelectrolyte gels: effects of ionic size

Although the volume transition of the polyelectrolyte gel has been studied for decades, less study on the finite size effects of the mobile ions has been conducted. In the present paper, Tanaka's classical theory of polyelectrolyte gel is extended to the cases of mobile ions of finite volume. In the salt free limit, the theoretical results show that the discontinuous volume transition of the polyelectrolyte gel will become a continuous one for counterionic size larger than a critical value. When a significant amount of salt is added, the critical value for the volume transition increases as a result of electrostatic screening. An increase in salt concentration can also make the polyelectrolyte gel in poor solvent collapse. Poorer solvent is needed to trigger the salt-induced collapse in polyelectrolyte gel with larger mobile ions than that with smaller ones. The effects of ionic size on the critical points and phase diagram of the volume transition are also discussed. The theoretical results suggest that the swelling behavior of polyelectrolyte gel might be tuned with salt of different volumes.