Microphase separation in weakly charged annealed gels and associating polyelectrolyte solutions

Association-caused microphase separation in weakly charged polyelectrolytes dissolved in a good solvent is theoretically predicted. To this end, a theoretical treatment of the concentration fluctuations in solutions of homopolymer chains, containing small fractions of both charged groups and reversible stickers (groups A capable of association via thermoreversible reaction A + A ⇆ A2), is presented. Following Lifshitz, thermoreversible cross-linking is considered as an effective interaction leading to the appearance of an additional association-caused term in the expression for the free energy. The density−density correlation functions are calculated and the thermodynamic stability of the spatially homogeneous state toward both micro- and macrophase separation is analyzed within the random phase approximation (RPA). All possible spinodal curves are classified in the limiting case of the annealed gel (solution with fully associated reversible stickers). For partially associated stickers, the interplay of e...