“…Such an LS theory has been applied to study the phase behaviors of concentration-asymmetric mixtures of polycation and polyanion solutions, and has revealed a wealth of interesting and complex phase separation scenarios [ 57 ]. Classical density functional theories (cDFT) for charged polymers have been developed based on a similar framework, and have found wide application in many polyelectrolyte systems [ 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 ]. A complete theoretical understanding of the solution phase behaviors of charged polymers, however, remains challenging, both because of the multi-component nature of the system (which, in the simplest case of a salt-free solution of fully charged polymers, consists of solvent, counterions, and charged polymers) and because of the delicate interplay among various factors, including the translational entropy of each component, excluded volume interactions, chain connectivity, and more importantly, the long-range electrostatic interactions.…”