Primitive path identification and entanglement statistics in polymer melts:: Results from direct topological analysis on atomistic polyethylene models

A large number of well-equilibrated atomistic configurations of linear, strictly monodisperse polyethylene (PE) melts of molecular length ranging from C-24 up to C-1000, 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 value (around C-200) is exceeded, the entanglement molecular length for PE at T = 450 K reaches a plateau value, characteristic of the entangled polymeric behavior. We further validate recent analytical predictions [Schieber, J. D. J. Chem. Phys. 2003, 118, 5162] about the shape of the distribution for the number of strands in a chain at equilibrium. At the same time, we show that the number of entanglements obtained by assuming random walk statistics [Everaers, R. et al. Science 2004, 303, 823] deviates significantly from these predictions, which we regard as a clear evidence that by directly counting the entanglements and their distribution functions, as proposed here, offers advantages for a quantitative analysis of the statistical nature of entanglements in polymeric systems.