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

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 entangl...

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Bibliographic Details
Published in:Polymers 2019-03, Vol.11 (3), p.437
Main Authors: Panagiotou, Eleni, Millett, Kenneth C, Atzberger, Paul J
Format: Article
Language:English
Subjects:
Boundary conditions
Chain entanglement
Chains (polymeric)
Entanglement
entanglements
Equilibrium
Investigations
knots
linking number
MATERIALS SCIENCE
MATHEMATICS AND COMPUTING
oscillatory shear
Polymer melts
Polymer Science
Polymers
Rheological properties
Rheology
Topology
Viscoelasticity
writhe
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Summary: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 W r and the Loss Tangent tan ( δ ) . We also find an approximate inverse linear relationship between the mean absolute Periodic Linking Number L K P and the Loss Tangent tan ( δ ) . 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.
ISSN:2073-4360
2073-4360
DOI:10.3390/polym11030437