Topological Analysis of Linear Polymer Melts:  A Statistical Approach

We introduce an algorithm for the reduction of a computer generated atomistic polymer sample to an entanglement network of primitive paths. These networks are structural representations of the topology underlying a polymer melt. By examining network ensembles of polyethylene and cis-1,4-polybutadiene melts, we provide topological measures and statistical properties of primitive paths. We present the radial distribution function of entanglements and the distribution of the number of monomers between entanglements. A renewal point process that generates entanglement events along the monomer sequence of a chain is found to describe the statistics of detected topological constraints. We discuss chain thickness effects on topological measures and provide a method for detecting persistent chain contacts in melt configurations. A suitable scaling of acquired data leads to a unifying microscopic topological description of the melts studied.