Topological versus rheological entanglement length in primitive path analysis protocols

TL;DR

This paper compares different primitive path analysis protocols in polymer simulations, revealing that some measure the rheological entanglement length while others measure the topological length, with a factor of two difference in certain systems.

Contribution

It clarifies the distinction between topological and rheological entanglement lengths in primitive path analysis and provides a simple analogy explaining their relationship.

Findings

Standard PPA measures rheological entanglement length.

Codes like Z or CReTA measure topological entanglement length.

A factor of two difference exists between the two measures in certain polymer systems.

Abstract

Primitive path analysis algorithms are now routinely employed to analyze entanglements in computer simulations of polymeric systems, but different analysis protocols result in different estimates of the entanglement length, N_e. Here we argue that standard PPA measures the rheological entanglement length, typically employed by tube models and relevant to quantitative comparisons with experiment, while codes like Z or CReTA also determine the topological entanglement length. For loosely entangled systems, a simple analogy between between phantom networks and the mesh of entangled primitive paths suggests a factor of two between the two numbers. This result is in excellent agreement with reported values for poly-ethylene, poly-butadiene and bead-spring polymer melts.