Entanglement in the isotropic-nematic crossover regime: does Edwards’ primitive path picture still apply?

Edwards defined entanglements in polymer melts in terms of contacts between individual chains’ primitive paths (PPs). This picture breaks down in the rigid-rod-like limit: while there are no inter-PP contacts, systems remain entangled in the sense that every chain’s transverse motion remains highly constrained by the other chains. How it breaks down as chains approach this limit is largely unknown. Using molecular dynamics simulations and topological analyses, we characterize how entanglement in polymer melts varies and the Edwards picture breaks down as chain stiffness and nematic order increase. We find that the diffusivity and the entanglement length N_e measured by topological analyses are minimized at two different chain stiffnesses k₁ and k₂ (with k₁ < k₂). Both of these are below the stiffness k₃ at which the isotropic-nematic transition occurs. We relate these phenomena to both the gradual onset of local nematic order and the inherent limitations of Edwards’ PP picture for quantifying entanglement in semiflexible polymer melts.