Topological analysis of polymeric melts: Chain length effects and fast-converging estimators for entanglement length

TL;DR

This paper analyzes polymer entanglements using primitive path methods, identifies systematic errors in existing estimators, and proposes new, faster-converging estimators that improve accuracy in determining entanglement length.

Contribution

The paper introduces new estimators that eliminate systematic errors in entanglement length calculations, improving accuracy and convergence speed in polymer melt analyses.

Findings

Existing estimators have systematic O(1/N) errors.

New estimators effectively remove these errors.

Formulas based on direct enumeration converge faster.

Abstract

Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_e which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive and test new estimators which eliminate these systematic errors using information obtainable from the variation of entanglement characteristics with chain length. The new estimators produce accurate results for N_e from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.