Primitive Path Identification and Entanglement Statistics in Polymer Melts: Results from Direct Topological Analysis on Atomistic Polyethylene Models

Abstract

A large number of well-equilibrated atomistic configurations of linear, strictly monodisperse polyethylene (PE) melts of molecular length ranging from C24 up to C1000, obtained through extensive Monte Carlo simulations based on chain connectivity altering algorithms, have been subjected to a detailed topological analysis. Primitive paths are geometrically constructed connecting the two ends of a polymer chain (which in all cases are considered as fixed in space) under the constraint of no chain crossability, such that the multiple disconnected (coarse-grained) path has minimum contour length. When applied to a given, dense polymer configuration in 3-D space, the algorithm returns the primitive path (PP) and the related number and positions of entanglements (kinks) for all chains in the simulation box, thus providing extremely useful information for the topological structure (the primitive path network) hidden in bulk PE. In particular, our analysis demonstrates that once a characteristic chain length valu...