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By combining molecular dynamics simulations and topological analyses withscaling arguments, we obtain analytic expressions that quantitatively predictthe entanglement length $N_e$, the plateau modulus $G$, and the tube diameter$a$ in melts that span the entire range of chain stiffnesses for which systemsremain isotropic. Our expressions resolve conflicts between previous scalingpredictions for the loosely entangled [Lin-Noolandi: $G\ell_K^3/k_\textrm{B}T\sim (\ell_K/p)^3$], semiflexible [Edwards/de Gennes: $G\ell_K^3/k_\textrm{B}T\sim (\ell_K/p)^2$], and tightly-entangled [Morse: $G\ell_K^3/k_\textrm{B}T\sim (\ell_K/p)^{1+\epsilon}$] regimes, where $\ell_K$ and $p$ are respectivelythe Kuhn and packing lengths. We also find that maximal entanglement (minimal$N_e$) coincides with the onset of local nematic order.

Unified analytic expressions for the entanglement length, tube diameter, and plateau modulus of polymer melts