Primitive Chain Network Simulation of Elongational Flows of Entangled Linear Chains: Stretch/Orientation-induced Reduction of Monomeric Friction

Abstract

Well-entangled monodisperse linear polystyrene melts exhibit monotonic thinning of the steady state elongational viscosity with increasing the strain rate ε̇ even beyond the Rouse relaxation frequency, τR-1. This behavior is quite different from the thinning followed by hardening at ε̇ > τR-1 observed for entangled semidilute solutions. We attempt to elucidate the molecular origin of this difference by focusing on the concept of stretch/orientation-dependent monomeric friction ζ recently proposed by Ianniruberto and co-workers. Specifically, literature data of the stress relaxation after cessation of transient elongational flow, reported for both PS melts and solutions, are analyzed to evaluate the stretch/orientation-dependent decrease of ζ. In our working hypothesis, ζ is expressed as a function of the factor Fso = λ̃2S̅, where λ̃ is the normalized stretch ratio of entangled subchains defined with respect to the fully stretched state, and S̅ is an average orientational anisotropy of the components (polymer plus solvent if any) in the system. The factor Fso was estimated from the stress decay data after flow cessation. The resulting functional form of ζ(Fso) was then used in the primitive chain network (PCN) simulation including finite extensible nonlinear elasticity (FENE) to examine the elongational behavior of melts and solutions. For melts the simulation indicates that ζ decreases significantly under fast elongation because the entangled subchains are short and approach the fully stretched (and fully oriented) limit rather easily. Hence, the steady elongational viscosity ηE follows this decrease of ζ to exhibit the monotonic thinning even at ε̇ > τR-1. In contrast, for solutions, the simulated ηE exhibits thickening at ε̇ > τR-1 because the average anisotropy S̅ is governed by the solvent and remains small, thus overwhelming the increase of the subchain stretch λ̃. The simulated results proved to be in satisfactory agreement with the experiments.