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Minimal Surfaces on Unconcatenated Polymer Rings in Melt.

Jan Smrek1, Alexander Y Grosberg1

  • 1Center for Soft Matter Research and Department of Physics, New York University, New York, New York 10003, United States.

ACS Macro Letters
|May 26, 2022
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Summary
This summary is machine-generated.

Mutual threading significantly impacts polymer ring dynamics in melts. Minimal surface analysis reveals threading is common but often involves short loops, explaining why some theories neglecting this phenomenon are surprisingly effective.

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Area of Science:

  • Polymer Physics
  • Computational Chemistry
  • Materials Science

Background:

  • Understanding polymer ring conformations and dynamics is crucial in polymer physics.
  • Mutual threading between polymer rings can influence their topological and dynamic properties.
  • Previous theoretical models have often simplified or neglected the effects of ring threading.

Purpose of the Study:

  • To computationally quantify the effect of mutual threading on the conformations and dynamics of unconcatenated and unknotted polymer rings in a melt.
  • To develop an algorithmic definition of mutual threading using minimal surfaces.
  • To investigate the relationship between ring length, surface area, and threading frequency.

Main Methods:

  • Computational examination of minimal surfaces for polymer rings in a melt.
  • Development of an algorithmic definition for mutual threading based on minimal surface analysis.
  • Analysis of threading dynamics and identification of a relevant order parameter.

Main Results:

  • A linear scaling relationship was found between the surface area of minimal surfaces and ring length.
  • Mutual threading between rings is frequent, but predominantly involves short loops.
  • An order parameter reflecting ring diffusivity was identified through threading dynamics analysis.

Conclusions:

  • The prevalence of short-loop threading explains the success of approximate theories that ignore this effect.
  • Minimal surfaces provide a robust method for defining and quantifying mutual threading in polymer melts.
  • The identified order parameter offers insights into the dynamics and diffusion of threaded polymer rings.