Microscopic equations-of-state for hydrocarbon fluids: effect of attractions and comparison with polyethylene experiments

Abstract

Microscopic equations-of-state are developed for n-alkanes and polyethylene based on the polymer reference interaction site model (PRISM) integral equation theory and a generalized Flory approach. The molecules are modeled as a series of overlapping spheres (methylene groups) with constant bond length and bond angles; internal rotations are accounted for by the rotational isomeric state approximation. The interaction between sites on different molecules is taken to be of the Lennard-Jones form. The thermodynamic properties of the fluid are obtained via standard perturbation theory in which the potential is divided into a repulsive reference system and an attractive perturbation. The reference system is approximated by a hard-core repulsion in which the hard-sphere diameter d(T) is estimated for polyethylene from wide-angle X-ray scattering experiments. The PRISM theory is used to calculate the hard-sphere chain contribution to the equation-of-state by three different thermodynamic routes: (1) integrating the compressibility, (2) evaluating the density profile at a hard wall, and (3) using a hard-sphere charging method analogous to the virial approach in monatomic liquids. The generalized Flory dimer (GFD) theory is used to obtain a fourth equation-of-state for the hard-sphere chains. The attractive perturbation is treated with first-order perturbation theory, making use of the radial distributionmore » function g[sub 0](r) of the reference system. The various equations-of-state presented differ in the route to the hard-chain pressure; PRISM is used in all cases to treat the attractions. Excellent agreement for the equation-of-state is found between the hybrid GFD/PRISM calculations and molecular dynamics simulations of n-butane and experimental pressure-volume-temperature (PVT) measurements on polyethylene melts.« less