Microscopic Definition of Polymer Entanglements

The dynamics of polymer melts and concentrated solutions is notoriously slow due to the fact that long polymer chains cannot cross each other and therefore find themselves entangled. This popular belief is very difficult to quantify and convert into a mathematical model because there is still no clear definition of what entanglement really is. In this paper we propose to define entanglement as a persistent contact between mean paths of the chains. In molecular dynamics (MD) simulations of well-entangled linear chains we discovered that such very tight and long-lived contacts exist in significant numbers. Moreover, once such contact is formed, it exists at every time step of the simulation until its destruction, which allows one to define its lifetime. We study several properties of individual entanglements and discover several unexpected features not taken into account in the tube theory or slip-links models. We believe that our simple and versatile definition opens the way to the truly microscopic understanding of polymer dynamics.