This model builds on the RPA result by including a fraction of bound pairs, given by ζ ± , between polyelectrolytes and the oppositely-charges salt ion. These pairs contribute a free energy of binding ∆G P ±,∓ to the overall free energy, which serves as an empirical parameter in the third line of the above equation, as well as a combinatoric entropy on the second line. This version of the model neglects polyanion-polycation pairing, which is a straightforward extension of this model that the authors used in some of their papers. This approach was originally developed to account for chemical bonding between the polyelectrolytes and their counterions, such that the free energy of binding ∆G P ±,∓ is interpreted as a free energy of reaction and careful accounting of the number of counterions is included in the mixing entropy terms. 100 However, this model could alternatively be interpreted as reflecting concepts such as ion pairing and counterion condensation that are expected to emerge for polymers with high linear charge density, and are challenging to include explicitly in polymer field theory calculations. This is probably the simplest of the class of models that we will call 'ion pairing' models (the other being the transfer matrix model discussed in the next section), 102 and has had success in reproducing several experimental phase diagrams due to the flexibility in defining the effective binding free energies. However, this also poses a challenge; there is no prescriptive way of choosing what is or is not included in this binding free energy ∆G P ±,± , in the absence of an actual chemical reaction.