On reptation in polymer melts

Abstract

A rederivation of the basic scaling laws for polymer reptation in a condensed phase yield directly for the coefficient of self-diffusion. Dr∼M−2, where M is proportional to the polymer molecular weight, as the primary relationship, independent of the polymer chain statistics. The derivation is based on a first passage time calculation for a kink to reach the end of a chain. The standard reptation time Tr is shown to be a first passage time for a chain to leave a sphere in which it is initially enclosed with the result Tr ∼M−3. The scaling law for a relaxation time TR, defined for a multichain model, is derived, with the result TR ∼M3+δ, with δ∼0.5, consistent with Dr∼M−2.