Topological entanglement in polymers

Predicting polymer material properties based on chemical composition, density, crosslinking, or architecture requires bridging the gap between the properties of a single chain and those of a collection of chains. At the core of models of polymer dynamics is entanglement, understanding of which remains elusive. In this talk, we will see how new advances in mathematical topology lead to new tools that can be used to measure topological entanglement in polymers of varying architectures (e.g., ring or linear). We will use Molecular Dynamics simulations of polymer melts to examine how the mathematical topology of polymers varies with molecular weight and stiffness of the chains, and how these can capture refined information about the conformation of the chains. Next we will show that the topological entanglement captured by mathematical methods indeed captures polymer entanglement effects in polymer melts and solutions. We will demonstrate this by using topology to predict a critical lengthscale in entangled polymers, the entanglement length, which is in agreement with experimental estimates. All of these results point to the advantages of topological parameters in analyzing polymers and the emergent topological framework of modeling and prediction of material properties that arises.