Topological entanglement of polymers and viscoelasticity*

Polymer entanglement is closely related to polymeric material viscoelastic response. However, the notion of entanglement in polymers remains elusive. In this talk we will see how rigorous measures of topological complexity from Knot Theory can be applied to quantify polymer entanglement. In particular, we use the Gauss linking integral, the periodic linking number [1] and the Jones polynomial [2] to mathematically characterize polymer entanglement of linear chains. Next, we use Molecular Dynamics Simulations to examine how these mathematical measures of complexity capture entanglement effects related to material properties [3,4]. Our results confirm that mathematical entanglement complexity reflects material properties. If time permits, we will also see a new topology user package for physicists and engineers [5].


[1] Panagiotou E. 2015, J. Comp. Phys. 300 533-573
[2] Panagiotou E. and Kauffman L. H., 2020, Proc. R. Soc. A 47620200124
[3] Panagiotou E., Millett K. C. and Atzberger P., 2019, Polymers ,11(3), 437.
[4] Panagiotou E., Kr\"oger M and Millett K. C., 2013, Phys. Rev. E 88 062604.
[5] Herschberg, T. and Panagiotou, E., Topology User Package