To derive this using the cluster expansion approach, we must re-define what we mean by z * α (i) and e α,γ (i, j) (or similarly f α,γ (i, j)); instead of considering all of the monomers as independent particles, we now use the RISM formalism that treats the monomers as 'sites' on polymers that are instead considered the particle units. This requires essentially no change to Equation , except for several re-definitions; first, the products over particles go to e.g. n α rather than n α N α , because the entire polymer chain (and not the monomer) is represented by a single 'particle'. Second, the quantity z * α (i) = exp β(µ α -Nα s=1 φ α (r(s))) for polymeric species now sums over the Boltzmann factors of each monomer of species α in the external field φ α . Finally, the quantity f α,γ (1, 2) is now dependent on contributions all of the sites s on the polymer chain(s). For two polymer chains of length N α , we can write: 120