  Dilute solutions of strongly charged polymer electrolytes undergo, upon
addition of multivaltent salt to the solutions, a phase transition from
extended conformations to collapsed or bundled ones. Upon further addition of
salt they experience a second transition, a redissolution back into extended
conformations. This paper presents a theoretical study of the structure and
properties of the phase diagram of these solutions. On the basis of simple
phenomenological observations a schematic phase diagram is constructed that
allows a simple and explicit determination of the direction of the tie lines
within the coexistence region. The actual shape of the coexistence boundary is
determined by means of a model mean free energy functional that explicitly
includes the possibility of association of both counterions and coions to the
electrolyte. It is found that it is possible to redissolve the electrolytes
into conformations where the bare charge of the electrolyte is overcompensated
by the counterions but, due to the associated coions, can have either sign of
total effective charge. When coion association is possible, the redissolution
approximately coincides with the reassociation of the coions and counterions in
the bulk of the solution.
