Generalized Flory equations of state for square-well chains

The hard chain Dickman–Hall generalized Flory (GF) and Honnell–Hall generalized Flory-dimer (GF-D) equations of state are extended to square-well chain fluids. The molecules are modeled as a pearl necklace of freely jointed spheres that interact via site–site square-well intermolecular potentials. Equations of state for square-well monomers and square-well dimers (required in the GF-D theory) are obtained from integral equations with a mean spherical approximation (MSA) closure. The theories are compared to Monte Carlo simulation data for the pressure of square-well 4-mers, 8-mers, and 16-mers. The GF-D theory is in excellent agreement with the simulation data; the GF theory overestimates the pressure in all cases. A closed-form equation of state for square-well chains is obtained by employing equations of state for square-well monomers and for square-well dimers using second order perturbation theory. The resulting equation is very accurate when compared to simulations, but not as accurate as when the monomer and dimer equations of state are obtained via the MSA. The effect of intramolecular attractions on the compressibility factor is investigated via Monte Carlo simulation and the GF-D theory. It is found that, for the chain lengths studied, intramolecular attractions have a very small effect on the pressure of the system.