Relationship of Fractional Free Volumes Derived from the Equations of State (EOS) and the Doolittle Equation

Abstract

This research investigates the relationships of the pressure–volume–temperature (PVT) and the zero-shear viscosity of polymer melts through their correlations with the fractional free volume. Polystyrene (PS) has been used as a case example in this study. First, the fractional free volume is determined from the Simha–Somcynsky (SS) equation of state (EOS) or the Sanchez–Lacombe (SL) EOS using the PVT data of a polymer melt. Then the fractional free volume is also determined from the Doolittle equation (with respect to the occupied volume) using the zero-shear viscosity and PVT data. These two fractional free volumes are compared to check if the EOS and the Doolittle equation consistently describe the PVT behaviors and the zero-shear viscosity through the fractional free volume. Before comparison, the fractional free volume based on the Doolittle equation is recalculated with respect to the total volume to be consistent with other fractional free volumes defined with respect to the total volume.