Identification of Topological Constraints in Entangled Polymer Melts Using the Bond-Fluctuation Model

Abstract

We propose an algorithm to locate individual entanglements along chains, equilibrated using the bond-fluctuation lattice model. The algorithm identifies entanglements as local deviations of the primitive path from the shortest possible path between beads on a chain that are on lattice sites. For well-entangled chains (number of beads, N ≥ 125), the average number of entanglements enumerated using the proposed method is in excellent agreement with the number of entanglements per chain inferred using the ensemble-averaged primitive path length 〈Lpp〉 and mean-squared end-to-end distance 〈R2〉 of the chains, namely Z = 〈Lpp〉2/〈R2〉. As an application of this method, we show that the elimination of an entanglement releases, approximately, one additional entanglement. This implies a value of α = 1.03 ± 0.02 for the “dilution exponent” relating entanglement density ρent to polymer concentration c via ρent ∝ c1+α and is consistent with the description of entanglements as binary contacts