Computer simulation of the dynamics of highly entangled polymers. Part 1.—Equilibrium dynamics

Abstract

We present a computer simulation of the stochastic motion of a highly entangled polymer chain in three dimensions. Very good agreement is found between the results of these simulations and the predictions of the theory of reptation, first propounded by de Gennes and developed by Doi and Edwards to account for the viscoelastic properties of polymer melts. It is shown that a polymer diffusing through a network of entanglements obeys the laws T_R∝M³; D_R∝N^–2; 〈r²(t)〉∝t^1/4 where D_R is the centre-of-mass diffusion constant, T_R the chain reaction time and 〈r²(t)〉 the mean-square displacement of a monomer at short times (≪T_R).