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

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.

• The paper demonstrates that strong pairwise interactions primarily confine polyethylene chains, supporting refined slip-link model mapping in both network and melt systems.
• The paper introduces a novel atomistic simulation framework that quantifies entanglement density and distinguishes local (pairwise) from collective topological constraints.
• The paper suggests that these insights can refine theoretical models and improve computational predictions for polymer dynamics and material behavior.

Microscopic Description of Entanglements in Polyethylene Networks and Melts

The paper discusses atomistic molecular dynamics simulations to investigate the nature of entanglements in polyethylene networks and melts, focusing particularly on the characteristics of topological constraints (TCs). Understanding these entanglements is crucial as they significantly influence dynamic, flow, and deformation properties of polymer melts and networks. The paper seeks to clarify whether these constraints are best modeled as collective entanglement effects, as in tube model theories, or as pairwise uncrossability interactions, as presented in slip-link models.

The authors examine polyethylene systems where entanglements are constrained, consisting of a perfect network and a melt with grafted chain ends. They have developed a novel methodological framework that allows for the analysis of entanglement in terms of local, pairwise interactions, similar to slip-links. The simulations reveal variations in confinement strengths across the spectrum, categorized as strong and weak interactions.

Several quantitative metrics and constructs emerge from these simulations, most notably the pairwise parameter, which helps in distinguishing the character of the entanglement environment between pairwise (local) interactions and collective (mean-field type) effects. Findings suggest that, within the network and melt systems studied, entanglements possess a primarily pairwise character, although they remain inherently collective due to the abundance of interactions involved.

Key conclusions drawn from the investigation include:

1. Entanglement Density and Strength: The study identifies a broad range of entanglement strengths, with strong pairwise interactions primarily responsible for confining the polymer chains. Weak interactions, on the other hand, make negligible contributions to mechanical properties like the plateau modulus of a melt or the low-frequency modulus of an elastomer.
2. Mapping to Slip-Link Models: The methodology allows a mapping from sophisticated atomistic simulations to mesoscopic slip-link models. It acknowledges that slip links, representing entanglements, act as the most significant pairwise interactions within a network of collective entanglements. Such mappings enable a bridged understanding between atomistic details and polymer physics models.
3. Pairwise Parameter: The pairwise parameter offers a novel perspective, indicating a dominant pairwise nature of the mean-field interactions traditionally utilized in slip-link models. This measure appears robust to variations in chain length and entanglement density, presenting a reliable factor for predicting and modeling polymer behavior.

The implications of these findings are significant, as they provide a unified framework to understand and simulate polymer networks and melts, thus serving both theoretical explorations and practical applications in material science. The study further speculates that this methodological advancement could refine existing polymer dynamic models and aid in the development of new computational methods for understanding polymer behavior under various conditions.

Future research could extend this framework to more complex polymer systems and explore its utility in diverse contexts such as nonlinear deformation and polymer-glass transitions. Moreover, the integration of these findings may enhance our predictive capabilities for designing new materials with tailored mechanical properties and improve computational efficiencies in polymer physics simulations.