Macroscopic Modeling of a Single Entanglement at High Deformation Rates of Polymer Melts

Abstract We constructed a macroscopic model illustrating behavior of a single entanglement knot of macromolecules in a melt and examined its behavior at different deformation rates. A model consists of flexible elastic strips, which are tied in a granny knot (modeling not a real geometrical form of entanglements but their behavior at relatively easy sliding). This scheme models the situation when elastic energy exceeds the energy of the Brownian motion. The behavior of a knot chosen for modeling is different at low and high deformation rates. In the previous case knots disentangle as predicted by the “tube” model, elastic strips slip out a knot and this is an illustration of flow. In the latter case, knots tighten up, further extension of strips leads to the increase in stresses up to breakup of a strip. This effect imitates the transition from the flow to the rubbery-like behavior of polymer melts, when flow becomes impossible due to the formation of quasi-permanent entanglements. The general dimensionless correlation for the process under discussion has been proposed.