Salt-induced effective interactions and phase separation of an ultrasoft model of polyelectrolytes

We use a semi-grand canonical version of mean-field density functional theory to determine the total effective interaction energy of a solution of penetrable polyions characterised by a Gaussian charge distribution, in the presence of added salt. We then apply this effective representation of semi-flexible polyelectrolyte chains to investigate the possibility of a phase separation similar to that predicted earlier for charge-stabilised hard-sphere colloids. Apart from the absence of a hard-core repulsion, the effective pair potential is similar to the familiar Derjaguin-Landau-Verwey-Overbeek (DLVO) potential between charged-stabilised colloids, i.e. of the screened-Coulomb (Yukawa) form, but the effective valence of the polyions differs significantly from that of the DLVO pair potential, especially at high salt concentration. The existence of a well-defined closed-loop spinodal curve predicted by our mean-field calculation points to a phase separation between solutions with high and low polyion concentrations under reasonable physical conditions. The salt concentration at the upper critical point is typically two orders of magnitude larger than in the case of hard-core polyions, indicating that polyion penetrability appears to enhance the tendency towards phase separation.