Swelling and Nonlinear Deformation of Polyelectrolyte Gels in Salt Solutions

Polyelectrolyte gels (PG) made by crosslinking ion-containing polymers demonstrate unique swelling capabilities with their volumes increasing up to 100 times in salt-free solutions. The swelling of polyelectrolyte gels in salt free solution is promoted by the osmotic pressure of free counterions localized within the gel volume due to the Donnan equilibrium. The presence of salt ions results in an exponential screening of the electrostatic interactions and a significant reduction of the osmotic effect of counterions, suppressing PG swelling ability. To quantify this effect as well as strand nonlinear deformation in PGs, we performed coarse-grained molecular dynamics simulations of the swelling and biaxial deformation of a polyelectrolyte gel film immersed in a salt solution. The simulations were performed at a constant pressure in the normal to deformation plane direction which allowed to maintain the constant salt concentration outside the gel film. The gel mechanical properties were studied as a function of the fraction of ionizable groups on the polymer backbone, degree of polymerization between crosslinks, and salt concentrations in both linear and nonlinear deformation regimes. Our simulations have confirmed that the gel swelling ratio increases with decreasing solutions salt concentration and increasing fraction of ionizable groups on the polymer backbone. Furthermore, the gel deformation in contact with a salt reservoir results in partitioning coefficient of small ions to converge to unity. The results of computer simulations are analyzed in the framework of the Flory-Rehner theory of gel swelling modified to account for nonlinear network deformations.