MICROSCOPIC EQUATIONS-OF-STATE FOR HYDROCARBON FLUIDS - EFFECT OF ATTRACTIONS AND COMPARISON WITH POLYETHYLENE EXPERIMENTS

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 distribution function g0(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. The compressibility and charging routes predict pressures which are too low and too high, respectively, for polyethylene. The wall route yields pressures in good agreement at experimental densities but predicts a melt which is too compressible.