What is the Entanglement Length in a Polymer Melt ?

TL;DR

This study uses molecular dynamics simulations to analyze the entanglement length in polymer melts, revealing discrepancies in theoretical predictions and experimental measurements, and highlighting the importance of chain length in accurate determination.

Contribution

It provides a detailed simulation-based analysis of entanglement length in polymers and critiques existing experimental methods and theoretical formulas.

Findings

Simulation results agree with the reptation model.

Discrepancy between N_e from G_N and chain segment displacements.

Recent neutron measurements may underestimate N_e due to chain length issues.

Abstract

We present results of molecular dynamics simulations of very long model polymer chains analyzed by various experimentally relevant techniques. The segment motion of the chains is found to be in very good agreement with the repatation model. We also calculated the plateau-modulus G_N. The predicitions of the entanglement length N_e from G_N and from the mean square displacements of the chains segments disagree by a factor of about 2.2(2), indicating an error in the prefactor in the standard formula for G_N. We show that recent neutron spin echo measurements were carried out for chain lengths which are too small for a correct determination of N_e.