Polyelectrolyte/Ionomer behavior in polymer gel collapse

The theory of collapse of weakly charged polyelectrolyte gels is generalized by taking into account the possibility of counter ion trapping with the formation of ion pairs, which becomes progressively important as the gel shrinks and the dielectric constant of the gel medium decreases. A phenomenon well known in the theory of ionomers, namely the aggregation of ion pairs due to dipole-dipole interactions with the formation of multiplets, is also taken into account. These multiplets act as additional physical cross-links. It is shown that accounting for the two effects mentioned above generally leads to an increase of the region of stability of the collapsed phase and to an increase of the jump in volume at the transition point. The most important, qualitatively new effect is the possibility of existence of a new supercollapsed state of a polymer gel which is very close to the densely packed dry gel. The reason for the thermodynamic stability of the supercollapsed state is a loop of positive feedback: the decrease of the volume of the gel leads to a decrease of the dielectric constant and hence to progressive formation of ion pairs, thus the concentration of mobile counter ions and the corresponding osmotic pressure decrease, the gel shrinks further etc. It is possible to realize the phase transitions between all three states of a polymer gel: swollen, ordinary collapsed and supercollapsed.