Polyelectrolytes in the presence of multivalent ions: gelation versus segregation.

We analyze solutions of strongly charged chains bridged by linkers such as multivalent ions. The gelation induced by the strong short range electrostatic attractions is dramatically suppressed by the long range electrostatic correlations due to the charge along the non-cross-linked monomers and ions. A modified Debye-Hückel approach of cross-linked clusters of charged chains is used to determine the mean field gelation transition self-consistently. Highly dilute polyelectrolyte solutions tend to segregate macroscopically. Semidilute solutions can form gels if the Bjerrum length l(B) and the distance between neighboring charged monomers along the chain b are both greater than the ion size a.