Threading of Unconcatenated Ring Polymers at High Concentrations: Double-Folded vs Time-Equilibrated Structures

Area of Science:

• Polymer Physics
• Soft Matter Physics
• Materials Science

Background:

• Unconcatenated ring polymers in concentrated solutions and melts are often modeled as double-folded conformations on branched primitive trees.
• Recent evidence suggests extensive intermingling and long-lived topological constraints (threadings) between nearby rings.

Purpose of the Study:

• To quantify the extent of threading in double-folded ring polymers compared to rings in equilibrated molecular dynamics simulations.
• To investigate the dynamics of threading formation in polymer solutions.

Main Methods:

• Utilized the concept of ring minimal surface to analyze topological constraints.
• Employed molecular dynamics simulations of polymer solutions.
• Calculated universal, model-independent observables like average fraction of threaded length and total penetrations between rings.

Main Results:

• Double-folded ring polymers exhibit significantly less threading than their counterparts at equilibrium.
• Threading formation is a slow process, with a characteristic timescale similar to ring diffusion.
• Findings are robust and based on universal observables.

Conclusions:

• The double-folded conformation model may underestimate the degree of topological entanglement in ring polymer solutions.
• Understanding threading dynamics is crucial for predicting the rheological and physical properties of entangled ring polymers.