Viscoelasticity of Networks Consisting of Crosslinked or Entangled Macromolecules. II. Verification of the Theory for Entanglement Networks

Abstract

The molecular theory of the viscoelasticity of entanglement networks developed in the first part of this series is refined. From an approximate treatment, the relaxation spectra of these networks can be determined analytically. The predictions are in good agreement with the values obtained from more accurate calculations performed on a computer. Equations are obtained and mathematical procedures developed to determine from experimental data the necessary parameters m and δ , where (m — 1) is the average number of entanglements per molecule, and δ is a slip parameter. The results of the theory are tested on data for the mechanical properties of a high molecular weight sample of poly‐n‐octyl methacrylate. Calculations are performed with one set of m and δ and a single molecular weight of 3.36 × 106. With the values of 81 for m and 10−5 for δ the calculations carried out on a computer yield the relaxation spectrum of this sample over nine decades of time. Corrections for molecular rotations are taken into account by assuming that the friction factor f is molecular‐weight dependent. In spite of the lack of knowledge of the molecular‐weight distribution of this sample, it turns out that the agreement between theory and experiment is very good, although some discrepancy is noted. A more precise fit would be expected if the molecular‐weight distribution were known.