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Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and
Eleni Panagiotou1, Kenneth C Millett2, Paul J Atzberger3
1Department of Mathematics and SimCenter, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA. eleni-panagiotou@utc.edu.
Polymers
|April 10, 2019
Summary
We developed new topological methods to link polymer chain entanglement to material properties. Our findings reveal linear relationships between polymer topology metrics and viscoelastic responses, enhancing understanding of mechanical behavior.
Area of Science:
- Polymer Physics
- Materials Science
- Topology
Background:
- Polymer chain entanglement significantly influences bulk viscoelastic properties.
- Characterizing these entanglements is crucial for understanding material mechanics.
Purpose of the Study:
- To develop novel topological methods for quantifying polymer chain entanglement.
- To establish relationships between topological characteristics and viscoelastic responses.
- To investigate the rheology of entangled polymer systems with diverse topologies.
Main Methods:
- Introduction of generalized Linking Number and Writhe for open linear chains.
- Non-equilibrium molecular dynamics simulations under sheared Lees⁻Edwards boundary conditions.
- Analysis of polymer rheology across a range of frequencies.
Main Results:
- Topological characteristics effectively capture key features of polymer entanglements.
- A linear relationship was observed between mean absolute Writhe (Wr) and Loss Tangent (tan δ).
- An approximate inverse linear relationship was found between mean absolute Periodic Linking Number (LKP) and Loss Tangent (tan δ).
Conclusions:
- Topological methods provide a powerful tool for characterizing polymer entanglements.
- These methods offer insights into the origins of mechanical responses in polymeric materials.
- The study demonstrates a quantitative link between polymer topology and macroscopic viscoelasticity.
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