Equation of state of polymer melts: Numerical results for athermal freely jointed chain fluids

Abstract

Our microscopic RISM integral equation theory for the virial equation of state of polymer liquids developed in the preceding paper is numerically implemented for athermal melts composed of freely‐jointed chains interacting via hard core site–site potentials. A modified ideal description of the single chain intramolecular correlations is employed which rigorously enforces the nonoverlapping core condition and leads to significant local coil expansion. Comparison of the theoretically computed virial pressure for tangent diatomics and short chains with available Monte Carlo simulation results over a wide range of packing fractions suggests the theory is quite accurate. Significant inconsistencies between the pressure computed via the virial and compressibility routes are found and discussed in light of the known limitations of the RISM method and the importance of self‐consistency corrections for flexible chain molecule liquids. A detailed numerical study of the density and degree of polymerization dependences of the total virial pressure, and its individual two‐ and three‐body components, is presented, along with the limiting infinite chain behavior. The integral equation results are also compared with the predictions of several simple mean field and/or lattice models for both short chains and high polymers. Significant, and in some cases massive, differences are found between the predictions of the various approaches and the integral equation calculations which are attributed to the neglect of polymeric connectivity, intermolecular correlations, and/or the use of a lattice model inherent to the simple theories. In particular, both the density dependence of the pressure and its sensitivity to degree of polymerization are found to be much stronger than the simple theories predict due to self‐screening and correlation hole effects absent in the latter. Finally, model calculations of the intermolecular radial distribution function and static structure factor at fixed pressure are performed for several degrees of polymerization and are found to be very weakly dependent on chain length due to compensating effects associated with a molecular weight dependent packing fraction.