Slow Dynamics of Ring Polymer Melts by Asymmetric Interaction of Threading Configuration: Monte Carlo Study of a Dynamically Constrained Lattice Model

Abstract

Abnormally slower diffusional processes than its internal structure relaxation have been observed in ring polymeric melt systems recently. A key structural feature in ring polymer melts is topological constraints which allow rings to assume a threading configuration in the melt phase. In this work, we constructed a lattice model under the assumption of asymmetric diffusivity between two threading rings, and investigated a link between the structural correlation and its dynamic behavior via Monte Carlo simulations. We discovered that the hierarchical threading configurations render the whole system to exhibit abnormally slow dynamics. By analyzing statistical distributions of timescales of threading configurations, we found that the decoupling between internal structure relaxation and diffusion is crucial to understand the threading effects on the dynamics of a ring melt. In particular, in the limit of small but threaded rings, scaling exponents of the diffusion coefficient D and timescale 
 
 
 
 τ
 diff
 
 
 
 with respect to the degree of polymerization N agree well with that of the annealed tree model as well as our mean-field analysis. As N increases, however, the ring diffusion abruptly slows down to the glassy behavior, which is supported by a breakdown of the Stokes–Einstein relation.

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.…”

Using Monte Carlo to Simulate Complex Polymer Systems: Recent Progress and Outlook

“…Lee and Jung [103] used lattice Monte Carlo simulations to study the connection between slow diffusional processes in melts of polymer rings and topological constraints associated with threading events between different ring molecules. Monte Carlo simulations on a face-centered-cubic lattice were employed by Suzuki and collaborators in a series of papers [104][105][106][107][108] to study: (a) the size and conformation of non-concatenated polymer rings in the melt state [104], (b) molecular conformations of trivial, 3 1knot, and 5 1 -knot ring polymers at their theta points [105,106], (c) the temperature dependence of the second virial coefficient of ring polymers [107], and (d) the size and conformation of catenated ring polymers in dilute solution, over a wide range of chain lengths [108].…”

The Longitudinal Superdiffusive Motion of Block Copolymer in a Tight Nanopore

“…The transition between ballistic and diffusive motion is highly dependent on the properties and structure of a particular liquid [13]. Unusually long ballistic motions have been reported by research groups studying particles in polymer melts [14][15][16], polymer-grafted gold nanoparticles [17], polymer rings [18], DNA [19], enzymes [20], and even bacteria [21].…”