Understanding physical properties of hydrocarbon polymers using an equation of state developed from semi soft core potential function

A semi-soft core intermolecular potential function for hydrocarbon molecules has been developed that expands the Boltzmann angle average of the van der Waals type-interaction. The logarithmic form simplifies the many thermodynamic derivatives related to Boltzmann statistics and clarifies the concept of the collision diameter. Second and third virial coefficients were derived as closed expressions and both the additive and non-additive terms were derived, especially for the third virial coefficient. A virial equation of state (EOS) was derived using the newly developed virial coefficients and compared to experimentally observed compressibility factors of natural gases. A perturbation EOS is derived to obtain vapor–liquid equilibrium (VLE) using the present potential function and the method of statistical mechanics. The EOS was employed to explain the VLE of pure hydrocarbon molecules. To expand the applicable range from small molecules to long chain polymers, the perturbation EOS was modified to a polymer EOS by introducing chain terms. Despite the relatively short expressions, each of the developed EOSs developed in this study were comparable in accuracy to well-known EOSs for each field, which demonstrates the advantage of applying these EOSs to multicomponent mixtures and long chain molecules.