Dynamical Entanglement and Cooperative Dynamics in Entangled Solutions of Ring and Linear Polymers

Abstract

Understanding how entanglements affect the behaviour of polymeric complex fluids is an open challenge in many fields. To elucidate the nature and consequence of entanglements in dense polymer solutions, we propose a novel method: a "dynamical entanglement analysis" (DEA) to extract spatio-temporal entanglement structures from the pair-wise displacement correlation of entangled chains. By applying this method to large-scale Molecular Dynamics simulations of linear and unknotted, nonconcatenated ring polymers, we find a strong and unexpected cooperative dynamics: the footprint of mutual entrainment between entangled chains. We show that DEA is a powerful and sensitive probe that reveals previously unnoticed, and architecture-dependent, spatio-temporal structures of dynamical entanglement in polymeric solutions. We also propose a mean-field approximation of our analysis which provides previously underappreciated physical insights into the dynamics of generic entangled polymers. We envisage DEA will be useful to analyse the dynamical evolution of entanglements in generic polymeric systems such as blends and composites.

Composite entanglement topology and extensional rheology of symmetric ring-linear polymer blends

“…The idea of linear chain "threadings" has a long history [19,36,33] and has grown more common in the recent literature. [25,24,61,26] Regardless, in a molecular simulation study like this one, there is no reason for us to require a reader to take this view for granted. Not when we can characterize it directly.…”

“…Blending rings with linear chains produces even more intriguing viscoelastic behaviors due to the interplay of arXiv:2107.01491v1 [cond-mat.soft] 3 Jul 2021 their distinct topologies. The closed-loop structure of rings enables them to be threaded by other chains [19,20,21,22,23,24,25,26,27], which can significantly alter chain conformations [28,29,30], segmental dynamics [19,12,31,32], and blend viscosity [33,34,21,35]. Roovers showed for ring-linear blends of polybutadiene with approximately 15.3 entanglements per chain that there was a maximum in zero-shear viscosity for a ring fraction φ R ∼ 0.4 [36].…”