Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and Viscoelasticity

TL;DR

This paper introduces topological measures to analyze polymer entanglements and their impact on viscoelastic behavior, revealing linear relationships between topological features and mechanical responses.

Contribution

It develops novel topological characteristics applicable to open chains and demonstrates their correlation with viscoelastic properties through molecular simulations.

Findings

Linear relation between mean absolute Writhe and Loss Tangent.

Inverse linear relation between mean absolute Linking Number and Loss Tangent.

Topological methods effectively characterize chain entanglements affecting mechanical responses.

Abstract

We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear chains. We investigate the rheology of polymeric chains entangled into weaves with varying topologies and levels of chain density. To investigate viscoelastic responses, we perform non-equilibrium molecular simulations over a range of frequencies using sheared Lees-Edwards boundary conditions. We show how our topological characteristics can be used to capture key features of the polymer entanglements related to the viscoelastic responses. We find there is a linear relation over a significant range of frequencies between the mean absolute Writhe $Wr$ and the Loss Tangent $\tan(\delta)$. We also find an approximate inverse linear relationship between the mean absolute Periodic Linking Number $LK_P$ and the Loss Tangent $\tan(\delta)$. Our results show some of the ways topological methods can be used to characterize chain entanglements to better understand the origins of mechanical responses in polymeric materials.