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Polymers 2019, 11(3), 437; https://doi.org/10.3390/polym11030437

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

1
Department of Mathematics and SimCenter, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
2
Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA 93106-3080, USA
3
Department of Mathematics and Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, CA 93106-3080, USA
*
Authors to whom correspondence should be addressed.
Website: http://atzberger.org/.
Received: 26 January 2019 / Revised: 12 February 2019 / Accepted: 26 February 2019 / Published: 6 March 2019
(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)
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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 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. View Full-Text
Keywords: topology; linking number; writhe; entanglements; knots; viscoelasticity; oscillatory shear topology; linking number; writhe; entanglements; knots; viscoelasticity; oscillatory shear
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Panagiotou, E.; Millett, K.C.; Atzberger, P.J. Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and Viscoelasticity. Polymers 2019, 11, 437.

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