Computer simulation of the dynamics of highly entangled polymers. Part 2.—Static properties of the primitive chain

Abstract

In this paper we examine the static properties of the primitive chain developed by Doi and Edwards to model the viscoelastic properties of polymer melts. An analytical calculation is presented to show that the primitive chain segment length, a, depends on the density of monomers, ρ, as a∝ρ–1/2. A computer simulation is described which models the primitive path. Verification is found for the above result. Also, it is found that the number of segments on the primitive chain, Npp is proportional to N, the number of segments on the original chain. The probability distribution for the number of segments between entanglements is given by P(n)∝ exp (–n/Ne) where Ne is the average number of segments between entanglements.