Resummed thermodynamic perturbation theory for bond cooperativity in associating fluids

We develop a resummed thermodynamic perturbation theory for bond cooperativity in associating fluids by extension of Wertheim's multi-density formalism. We specifically consider the case of an associating hard sphere with two association sites and both pairwise and triplet contributions to the energy, such that the first bond in an associated cluster receives an energy -ε((1)) and each subsequent bond in the cluster receives an energy -ε((2)). To test the theory we perform new Monte Carlo simulations for potentials of this type. Theory and simulation are found to be in excellent agreement. We show that decreasing the energetic benefit of hydrogen bonding can actually result in a decrease in internal energy in the fluid. We also predict that when ε((1)) = 0 and ε((2)) is nonzero there is a transition temperature where the system transitions from a fluid of monomers to a mixture of monomers and very long chains.