Associating polyelectrolytes: Finite size cluster stabilization versus physical gel formation

The theory of phase equilibria in the solutions of associating polyelectrolyte telechelic chains proposed earlier is generalized to take into account the possibility of existence in the solutions of finite size thermodynamically stable clusters in addition to the formation of macroscopic physical gel. It is shown that in some region of polymer concentrations and energies of attraction between the end groups of the chain (stickers) the size distribution of chain clusters has a maximum, i.e., the solution is dominated by the clusters of optimum size. The stabilization of such a cluster is due to the interplay between the energy of attraction of stickers, on the one hand, and the Coulomb interaction together with the contribution from the translational entropy of counter ions, on the other hand. For small enough optimum clusters direct Coulomb interactions are more important, while for large optimum clusters the main reason for stabilization is connected with the translational entropy. This type of stabilization mechanism should be quite general for any polyelectrolyte system with attraction.