Mapping of theoretical equations of state for molecular fluids on a biquadratic equation

Abstract

A biquadratic equation of state for the attractive hard sphere chain fluid with dipolar interactions is developed. The background of the development is the mapping of molecular model equations onto a simplified mathematical form. In course of this mapping procedure known properties such as virial coefficients and physical limits are accounted for. For the hard sphere reference model a simple theoretical equation is developed, which is almost as accurate as the Carnahan–Starling (CS) equation and includes the nearly correct high density limit. The perturbation of this reference model due to chain formation and dipolar forces is accounted for by variations of the coefficients in the reference model. These coefficients are constant values for the hard sphere reference fluid and become dependent on the chain length parameter or the reduced dipole moment for the chain fluid or the dipolar fluid, respectively. By simple mathematical manipulations one can recover the usual equation of state form which consists of a sum of additive terms for each molecular property.