Dynamic model of monovalent-divalent cation exchange in polyelectrolyte gels.

A multicomponent model that imposes conservation laws and constitutive relations for polymer chains, water, and ions was investigated by determining the transient changes in a negatively charged gel exposed to a solution containing both mono- and divalent cations. Association of ion exchange with gel volume is achieved by imposing a linear relation between the polymer-solvent interaction parameter and concentration of divalent cations adsorbed onto the polymer chains. Semiquantitative agreement with measurements made on sodium polyacrylate gels is demonstrated in three aspects: (1) dynamics of gel swelling and deswelling, (2) ion partitioning coefficient, and (3) effect of cross-link density. These results imply that the multicomponent coarse-grained continuum modeling approach can be useful for quantitative predictions over macroscopic length and timescales including the description of volume transitions exhibited by these systems.