Some remarks on the dynamics of polymer melts

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Abstract
Considering one long chain (N monomeric units) in a homodisperse melt of chemically identical, but shorter, “solvent” chains (P monomers per chain), we propose some tentative scaling laws for the self‐diffusion constant D(N) and the relaxation time T(N) of the solute chain. We also discuss the viscosity increment δη due to a small volume fraction Φ of the long chains. We find three regimes of behavior, depending on N and P, and on the distance between entanglement points (assumed smaller than N and P): (A) reptation of the N chain; (B) Stokes–Einstein regime; the solute moves like a usual polymer coil in a viscous fluid of P chains; (C) mixed regime, where D(N) is controlled by reptation, while δη is of type B. Contrary to our earlier belief, we find no significant regime where the process of “tube renewal” could be dominant.