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We derive several extensions of a previously given first-order perturbation theory (TPT 1) for fluids in which chain and ring polymers can be formed, due to the presence of two singly bondable molecular attraction sites. We retain graphs which contain a single chain of attraction bonds, and evaluate second-order perturbation theory (TPT 2) within this framework. The previous formulation with sites fixed in the molecule is generalized to allow movable sites, thus permitting calculations for flexible bead polymers. The TPT 1 result for the equation of state of an equilibrium mixture of chain lengths is in good agreement with simulations of flexible bead polymers of fixed bead number N, when the mean number ν of beads is equated to the fixed N of the simulations. TPT 2 differs from TPT 1 by a rather small term, with improved agreement. If the distribution of movable sites includes configurations such that bonding of one site blocks bonding of the other, then graph resummation must be used. Resummed TPT yield physically reasonable results over the entire range of conditions. For total blockage, where only dimers can be formed, resummed TPT reduces to a successful version of TPT given earlier for dimerizing systems. The equation of state appears in the form of two parametric equations. The first one gives the excess pressure over the reference system in terms of ν and the number density ρ̄ of beads. In TPT 1 this equation is universal for hard spheres with or without dimerization or chain polymerization. The second equation is nonuniversal and contains the dependence of ν on ρ̄, the strength of the bonding attraction, the number of sites, and the amount of blockage in the case of two sites. An additional simulational test of TPT 2 is suggested.
M. S. Wertheim (Tue,) studied this question.