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

Abstract

Understanding how entanglements affect the behavior 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 spatiotemporal entanglement structures from the pairwise 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 spatiotemporal structures of dynamical entanglement in polymeric solutions. We also propose a mean-field approximation of our analysis that provides previously under-appreciated physical insights into the dynamics of generic entangled polymers. We envisage DEA will be useful to analyze the dynamical evolution of entanglements in generic polymeric systems such as blends and composites.

Effects of chain length on Rouse modes and non-Gaussianity in linear and ring polymer melts

“…This observation indicates that the dynamics in ring polymers without chain ends becomes spatially homogeneous and the mechanism of the chain motion is essentially different from the reptation model for linear polymers A plausible key feature for topological constraints in ring polymers is an inter-ring threading event. [39][40][41][42][43][44][45][46][47] In particular, Michieletto et al have proposed the "random pinning" procedure, wherein some fractions of rings are frozen, to investigate the role of threadings on the dynamics. 44 They demonstrated that random pinning can enhance the glass-like heterogeneous dynamics in ring polymers.…”

Quantifying the mobility of chromatin during embryogenesis: Nuclear size matters

“…It is evident that the observed MSD is dominated by the correlation ∆r 1 (τ )•∆r 2 (τ ) , which increases almost linearly with time. Note that the origin of measured correlation is not the coherent motion of the chromosomes inside the nucleus [18,19]. Rather, the above observation, in particular the linear scaling of the correlation, indicates that the two tracked loci move together with the nucleus undergoing Brownian motion.…”

“…If the nucleus itself is quiescent, the displacement correlation ∆r 1 (τ ) • ∆r 2 (τ ) between two loci will become negligibly small compared to oMSD [18,19]. In this case, the mean square change in d(t) is reduced to approximately twice the oMSD.…”

Persistence Homology Of Entangled Rings

“…Ring polymers are the simplest class of topologically non-trivial polymers that manifestly depart from the predictions of theoretical cornerstones such as the reptation and tube models [1]. Over the last 3 decades, there have been several theoretical and experimental attempts at understanding the statics and dynamics of rings [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and yet their behaviour in entangled solutions is still poorly understood. Individual ring polymers in the melt or entangled solutions assume compact non-Gaussian conformations, which are distinct from the ones assumed by linear polymers.…”