Paper Number
SM31 

Session
Polymers Solutions, Melts and Blends

Title
Microscopic theory for the center-of-mass dynamics of ring polymer liquids

Presentation Date and Time
October 11, 2022 (Tuesday) 4:25

Track / Room
Track 2 / Sheraton 3

Authors (Click on name to view author profile)

  1. Mei, Baicheng (University of Illinois at Urbana-Champaign)
  2. Schweizer, Kenneth S. (University of Illinois at Urbana-Champaign)

Author and Affiliation Lines (in printed abstract book)
Baicheng Mei and Kenneth S. Schweizer
University of Illinois at Urbana-Champaign, Urbana, IL 61801

Speaker / Presenter 
Mei, Baicheng

Keywords
theoretical methods; glasses; polymer melts; polymer solutions

Text of Abstract
Based on a 2-fractal-form intramolecular structure factor of unconcatenated rings that includes topological effects, plus inter-ring packing correlations determined from PRISM theory, we have constructed a segment-scale force-level statistical dynamical theory for the center-of-mass (CM) dynamics of ring solutions and melts. Two new dynamical regimes beyond Rouse behavior are predicted: (i) weakly-caged regime (crossover at N=ND) due to the appearance of length-scale-dependent temporal correlation of forces exerted on pairs of tagged segments from surrounding rings, and (ii) activated entropic-barrier-controlled transport regime (crossover at higher N=Non proportional to ND) when the temporal force correlations acquire a transiently arrest component. The strength of inter-ring force correlations enters via the macromolecular packing fraction, Kuhn length, tube diameter of the entangled chain analog, and liquid dimensionless compressibility. A combined variable is identified that collapses the dynamical consequences of these factors. The CM diffusion constant scales as the inverse square of N in the weakly-caged regime, followed by an exponential decay with N in the activated regime. The corresponding predictions for the longest conformational relaxation time are also derived. Non-Fickian intermediate time CM sub-diffusion is predicted based on a Generalized Langevin Equation description which encodes memory effects. Apparent sub-diffusive exponents decrease with increasing N/ND. Quantitative comparisons of weak-caging-regime results with that of simulations for semiflexible rings in concentrated solutions and flexible rings in melts show good agreements. As N/Non becomes sufficiently large, a macromolecular scale kinetic glass transition is predicted. Our results provide a physical framework to qualitatively understand dramatic new experimental (Tu and Schroeder) and simulation (O’Connor and Grest) observations for very high molecular weight ring liquids.