Towards an Explanation of the 3.4-Power Dependence of the Viscosity on Molecular Weight

A numerical simulation of a concentrated polymer system is presented. The dynamics used are those of the primitive chain model of Doi and Edwards with excluded volume, known as "reptation dynamics." It is found that the time-dependent correlation functions with excluded volume relax more slowly than in the case of no excluded volume. From the power-law dependence of these correlation functions on time, an estimate of the relaxation time for this system is obtained as a function of molecular weight $M$. This implies that the viscosity should be proportional to $M^{3.25\pm 0.1}$.