Cooperative polymer dynamics at the crossover between the unentangled and the entangled regimes: theoretical predictions of scattering and linear shear relaxation for polyethylene melts

TL;DR

This paper extends the Cooperative Dynamics Generalized Langevin Equation to model the crossover from unentangled to entangled polymer melt dynamics, accurately predicting scattering and shear relaxation behaviors observed in polyethylene melts.

Contribution

The study introduces an extended CDGLE that incorporates entanglement constraints, providing a unified theoretical framework for polymer dynamics across different regimes.

Findings

Accurately predicts the crossover from unentangled to entangled dynamics.

Describes shear relaxation behavior consistent with experimental data.

Confines cooperative dynamics within entanglement regions.

Abstract

The dynamics of polymer melts at the crossover between unentagled and entangled regimes is formalized here through an extension of the Cooperative Dynamics Generalized Langevin Equation (CDGLE) (\textit{J. Chem. Phys.} 110,7574 (1999)), by including the constraint to the dynamics due to entanglements through an effective inter-monomer potential that confines the motion of the chains. As one polymer chain in a melt interpenetrates with a $\sqrt{N}$ other chains, with $N$ the degree of chain polymerization, their dynamics is coupled through their potential of mean-force, leading to chains' cooperative motion and center-of-mass subdiffusive dynamics. When increasing the degree of polymerization, the extended CDGLE approach describes the dynamical behavior of unentangled to weakly entangled systems undergoing cooperative dynamics. By direct comparison of the CDGLE with data of Neutron Spin Echo (NSE) experiments on polyethylene melts we find that the cooperative dynamics in entangled systems are confined in the region delimited by entanglements. We extend the CDGLE to describe linear dynamical mechanical measurements and use it to calculate shear relaxation for the polyethylene samples investigated by NSE. The effects of cooperative dynamics, local flexibility, and entanglements in the shear relaxation are discussed. It is noteworthy that the theoretical approach describes with accuracy the crossover from unentangled to entangled-global dynamics for polyethylene melts of increasing chain length, covering the regimes of unentangled and weakly entangled (up to $13$ entanglements) dynamics in one approach.