The first four terms on the left hand side are simply the mixing entropy contribution, and the last term is a phenomenological term to account for charge packing. The interactions are accounted for in the fifth and sixth terms, which are the free energies of a test polyelectrolyte interacting with its surrounding, oppositely-charged species. These oppositelycharged species are modeled as 'adsorbing' to monomer 'sites' along the one-dimensional polyelectrolyte chain, such that each monomer can be in one of four states: paired with a salt ion (S), paired with a polymer charge (P' or P), or unpaired (0). The difference between states P' and P account for whether the polymer charge is the first in a run of interacting monomers (P') or one of the subsequent pairs in this run (P). With these states defined, we write a grand canonical partition function Ξ P ± = ψ i M ij,± ψ j that accounts for these interactions using a 'transfer matrix' M ij,± that includes the Boltzmann factors associated with pairs of monomers in different adsorption states: 102