A study of the entanglement in systems with periodic boundary conditions

TL;DR

This paper introduces the local periodic linking number (LK) as a measure of entanglement in systems with periodic boundary conditions and applies it to analyze polyethylene chains before and after the CReTA algorithm.

Contribution

It defines a new measure of entanglement, LK, suitable for periodic systems, and demonstrates its effectiveness in polymer melt analysis.

Findings

LK is an appropriate entanglement measure for periodic systems

CReTA algorithm does not alter the entanglement statistics of polyethylene chains

Numerical results confirm the stability of entanglement measures before and after CReTA

Abstract

We define the local periodic linking number, LK, between two oriented closed or open chains in a system with three-dimensional periodic boundary conditions. The properties of LK indicate that it is an appropriate measure of entanglement between a collection of chains in a periodic system. Using this measure of linking to assess the extent of entanglement in a polymer melt we study the effect of CReTA algorithm on the entanglement of polyethylene chains. Our numerical results show that the statistics of the local periodic linking number observed for polymer melts before and after the application of CReTA are the same.