The resulting form for the excess free energy due to the third-order f -bond contributions in Equation is similar to the terms seen in Equation , and can be interpreted as a series of independent 'states' that can exist along the chain of N * P + sites. The first term in the parenthesis (for each natural log term) is analogous to the vacant monomer site, the second term is related to pairing with the small molecule ions, and then the subsequent terms are related to polymer-polymer correlations between chains that are singly-, doubly-, triply-, and quadruply-bound in a manner analogous to the above schematic. However, this picture is complicated by the different number of monomer sites involved in the multiply-bound states, and fewer of these can 'fit' on a chain with N P + monomer sites. There is thus a longer chain of N * P + states that is described by keeping the assumption of independence. We would prefer to, instead, choose only the number of states needed to accumulate N P + monomer sites along the chain backbone.