Thermodynamics of the polymer mean-spherical ideal chain approximation for a fluid of linear chain molecules

Abstract

A mean-spherical approximation (MSA)-like theory is proposed for the site-site molecular fluid represented by hard sphere totally flexible linear chain molecules with a long range site site pair potential of arbitrary type outside the hard core region. The theory is based on the complete association limit of the polymer mean-spherical approximation (PMSA) supplemented by the so-called ideal chain approximation, and belongs to the class of the site-site integral equation theories that are ‘proper’ in the sense of Chandler and coworkers. Both approximations have been used recently in the frame of the multidensity integral equation theory for associating fluids. In the simplest case of chain length 2 the present approach reduces to the Chandler-Silbey-Ladanyi (CSL) equation closed by the corresponding MSA closure conditions. The Hoye-Stell scheme of calculating thermodynamic properties is extended and expressions for the Helmholtz free energy, chemical potential and pressure are derived. The theory is illustrated by its application in the case of charged hard dumbbells, for which an analytical solution of the CSL-MSA is available. Analytical expressions for the Helmholtz free energy, chemical potential and pressure in terms of only one unknown parameter, which satisfies a nonlinear algebraic equation, are derived and used to calculate the liquid-gas phase diagram. Theoretical predictions for the coexistence curve are compared with the corresponding computer simulation predictions for the phase diagrams of the charged hard dumbbell fluid and fluid represented by the restricted primitive model (RPM) of electrolytes. In the latter case the present theory gives more accurate results than those of Zhou, Y., Yeh, S., and Stell, G., 1995, J. chem. Phys., 102, 5785, and are of the same order of accuracy as the version of Fisher-Levin theory which consistently takes into account the hard core contribution (Guillot, B., and Guissani, Y., 1996, Molec. Phys., 87, 37).