Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

TL;DR

This study uses atomistic simulations to analyze the microscopic nature of entanglements in polyethylene, revealing that they are predominantly pairwise interactions with a spectrum of strengths, and introduces a novel methodology to connect atomistic details with mesoscopic models.

Contribution

The paper develops a new method to decompose entanglements into pairwise interactions and demonstrates that these are mainly strong links, bridging atomistic simulations with slip link models.

Findings

Entanglements are more pairwise than collective in polyethylene systems.

Strong links dominate the confinement of polymer chains.

Weak interactions do not significantly affect the elastic properties.

Abstract

We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, or as certain pairwise uncrossability interactions, as in slip-link models. A pairwise parameter, which varies between these limiting cases, shows that, for the systems studied, the character of the entanglement environment is more pairwise than collective. We employ a novel methodology, which analyzes entanglement constraints into a complete set of pairwise interactions, similar to slip links. Entanglement confinement is assembled by a plethora of links, with a spectrum of confinement strengths, from strong to weak. The strength of interactions is quantified through a link `persistence', which is the fraction of time for which the links are active. By weighting links according to their strength, we show that confinement is imposed mainly by the strong ones, and that the weak, trapped, uncrossability interactions cannot contribute to the low frequency modulus of an elastomer, or the plateau modulus of a melt. A self-consistent scheme for mapping topological constraints to specific, strong binary links, according to a given entanglement density, is proposed and validated. Our results demonstrate that slip links can be viewed as the strongest pairwise interactions of a collective entanglement environment. The methodology developed provides a basis for bridging the gap between atomistic simulations and mesoscopic slip link models.