Polymer free volume and its connection to the entanglement length and the plateau modulus via polymer mode-coupling theory and equation of state

Abstract

Using a many-chain system of Gaussian chains interacting with each other through the Lennard-Jones (LJ) potential, we demonstrate that there exists a connection between polymer fractional free volume (f) and the entanglement chain length (Ne). Here, f is determined by the generic van der Waals (GvdW) equation of state using the intermolecular radial distribution function [g(r)] of the Gaussian chain generated by the polymer reference interaction sites model while Ne by the polymer mode-coupling theory (PMCT) for strongly coupled macromolecules. The key concept in PMCT is that intermolecular forces experienced by a bead in a chain surrounded by other chains are strongly coupled to the site specific intramolecular radial distribution function. The calculated Gp and η of polyethylene with chain lengths from 500 to 2000 interacting with one another through the LJ potential agree well with experiment and molecular dynamics simulation.