Integral equation for the Smith–Nezbeda model of associated fluids

Our recent reformulation of statistical thermodynamics for fluids of molecules interacting by site–site bonding forces is extended to the Smith–Nezbeda (SN) model of associated fluids, where sites bond to the hard core of another molecule. The formal theory of the SN model with one molecular site is similar to the case of site–site bonding with one site, with many formal expressions identical. The difference in physical behavior is attributable to the quite different graph content of the functions that enter. The reformulated theory contains two densities, a number density ρ and a density ρ0 of molecules with site unbonded. An integral equation of Percus–Yevick type is derived and transformed using factorization methods. Accurate numerical solutions are obtained and pressures, internal energies, and concentrations of molecules with site unbonded, bonded, and bonded partaking in a double bond are calculated. No gas–liquid phase transition is found. This is explained by insufficient clustering due to a preference for double bond formation, which is strongest at low ρ and temperature T. The degree of consistency of the virial and compressibility equations of state improves with decreasing T and becomes extraordinarily high over an extended density range at low T. Agreement with the twelve Monte Carlo simulation states of SN is excellent for the internal energy and the pair distribution function near contact. For the pressure the agreement is not quite as good, with no clear trend visible in the discrepancy between integral equation and simulation.