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

By postulating that the contributions to the dimensionless plateau modulus from flexible-, semiflexible-, and stiff-chain entanglement mechanisms combine additively (in parallel), and testing this postulate with molecular dynamics simulations and topological analyses of Kremer-Grest bead-spring polymer melts, we obtain analytic expressions that quantitatively predict the plateau modulus G, the entanglement length N_e, and the tube diameter a in melts that span three orders of magnitude in l_K/p, where l_K and p are respectively the Kuhn and packing lengths. Our expressions resolve conflicts between previous scaling predictions for the loosely entangled [Lin-Noolandi: Gl_K³/k_BT ~ (l_K/p)³] and tightly-entangled [Morse: Gl_K³/k_BT ~ (l_K/p)^7/5] regimes.