Computer simulation of the dynamics of highly entangled polymers. Part 3.—Dynamics of the primitive chain

Abstract

We combine the results of two earlier papers to examine the validity of the primitive-chain model for the dynamics of highly entangled polymers. It is shown that D_R=c₀D_RO/N_pp and T_R=T_RON_pp/c₀ where D_R and T_R are the diffusion constant and relaxation time of a highly entangled chain, and D_RO and T_RO are the free-chain values. N_pp is the number of primitive-chain segments or, equivalently, number of entanglement points. c₀ is found to be approximately constant. Values are found for certian undetermined parameters in the Doi–Edwards theory of polymer melts, leading to the predictions η∝N³ρ³; G∝N⁰ρ^2.0; T∝N³ρ where η is the steady-state viscosity, G the rigidity modulus, T the terminal relaxation time, ρ the monomer density and N the chain length.