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 polyeth ylene based on the polymer reference interaction site model (PRISM) in tegral equation theory and a generalized Flory approach. The molecules are modeled as a series of overlapping spheres (methylene groups) wit h constant bond length and bond angles; internal rotations are account ed for by the rotational isomeric state approximation. The interaction between sites on different molecules is taken to be of the Lennard-Jo nes form. The thermodynamic properties of the fluid are obtained via s tandard perturbation theory in which the potential is divided into a r epulsive reference system and an attractive perturbation. The referenc e system is approximated by a hard-core repulsion in which the hard-sp here diameter d(T) is estimated for polyethylene from wide-angle X-ray scattering experiments. The PRISM theory is used to calculate the har d-sphere chain contribution to the equation-of-state by three differen t thermodynamic routes: (1) integrating the compressibility, (2) evalu ating the density profile at a hard wall, and (3) using a hard-sphere 'charging'' method analogous to the virial approach in monatomic liqui ds. The generalized Flory dimer (GFD) theory is used to obtain a fourt h equation-of-state for the hard-sphere chains. The attractive perturb ation is treated with first-order perturbation theory, making use of t he radial distribution function g0(r) of the reference system. The var ious equations-of-state presented differ in the route to the hard-chai n pressure; PRISM is used in all cases to treat the attractions. Excel lent agreement for the equation-of-state is found between the hybrid G FD/PRISM calculations and molecular dynamics simulations of n-butane a nd experimental pressure-volume-temperature (PVT) measurements on poly ethylene melts. The compressibility and charging routes predict pressu res which are too low and too high, respectively, for polyethylene. Th e wall route yields pressures in good agreement at experimental densit ies but predicts a melt which is too compressible.