3 that makes these chains semiflexible. The length scale a is the radius of the beads, and is also related to the equilibrium bond distance r eq . Finally, we use periodic boundary conditions to limit the region of space over which we perform the cluster integrals, using a value of L/a = 25 that is far longer range than the cluster integral interactions due to the criteria defined by θ s,s and/or θ s,± . Polymer chains are modeled with a harmonic bonding potential that keeps connected monomers at a distance r eq and with a bending potential that is associated with the bond angle θ. Ion pairing criteria are given by the cutoff radius r c , which is larger than the bead radius a. All parameters associated with these cutoffs and potentials are chosen to be the same as in our previous work, Lytle, et al. To calculate the cluster diagrams, we must integrate over the possible conformations of the polymer chains and particles, and account for the interactions. For the polycation/anion system, as an example, we numerically perform the integral: