A new equation of state for the hard-sphere chain fluids based on the thermodynamic perturbation theory and the multidensity integral equation

Abstract

New equations of state for the freely jointed hard sphere chain fluids are developed. The equations of state are based on Wertheim’s thermodynamic perturbation theory or the statistical associating fluid theory. In developing the new equations of state we use the contact values of the radial distribution functions (RDF) of equimolar mixtures of monomer and dimer fluids as an intermediate reference system. For this purpose two expressions for the contact values of the RDF are adopted from the multidensity Ornstein–Zernike integral equation theory and the Monte Carlo simulation results. The radial distribution functions consist of a monomer term, which is the Carnahan–Starling or the Percus–Yevick type, and a bond contribution term. We compare the radial distribution functions from the theory with the Monte Carlo simulation results for the monomer–dimer mixture, and found that they are in a good agreement with each other. We also compare the equations of state with the simulation results for the compressibility factor of the hard sphere chain fluids. The predicted compressibility factors for hard-sphere chain fluids are in a good agreement with simulation data especially at high densities, and the accuracy of the theories is comparable to the TPT-D theory.