Simplified hard-sphere and hard-sphere chain equations of state for engineering applications

A simple hard-sphere equation of state is proposed. This hard-sphere equation is a ratio of second-order polynomials that meets the ideal gas and close-packed density limits. It predicts the compressibility of hard-sphere fluids at low and medium densities to within a degree of quality similar to the widely used Carnahan-Starling equation. In addition, the proposed equation performs better at high densities, particularly near the close-packed density. An expression is also derived to relate the site-site correlation function at contact for hard dimers with the site-site correlation function at contact for hard spheres. With this relationship, the thermodynamic perturbation-dimer theory (TPT-D) of hard-sphere chains is simplified. The new theory performs comparably with the TPT-D when the compressibility factors of hard-sphere chain fluids containing up to 201-mer are predicted, however, it has the advantages of both simplicity and accuracy. From a practical perspective, this theory can be used to construct equations of state for polymer solutions or fluid systems containing short- and long-chain molecules.