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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
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Can Polymer Helicity Affect Topological Chirality of Polymer Knots?
Yani Zhao1, Jan Rothörl2, Pol Besenius3
1Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
ACS Macro Letters
|January 27, 2023
Summary
Polymer helicity influences knot chirality, breaking mirror symmetry. Specific helical senses favor particular knot handednesses, revealing a link between polymer structure and topological properties.
Area of Science:
- Polymer Physics
- Computational Chemistry
- Materials Science
Background:
- Chirality in polymers is crucial for their topological properties.
- Understanding how intrinsic polymer helicity affects knot formation is key.
Purpose of the Study:
- To investigate the impact of polymer helicity on the topological chirality of knots.
- To explore the relationship between helical sense and knot handedness.
Main Methods:
- Computer simulations using generic worm-like chains (WLC) model.
- Monte Carlo algorithm to sample polymer conformations.
- Analysis of chiral order and knot statistics.
Main Results:
- The coil-helix transition is a crossover, not a phase transition.
- Polymer helicity breaks topological mirror symmetry in knots.
- Specific helical senses preferentially form certain knot handednesses (e.g., positive helicity favors positive handedness for 3_1 and 5_1 knots).
- An inverse trend was observed for 5_2 knots.
Conclusions:
- Helicity in polymers directly influences the handedness of the knots they form.
- A generic mechanism involving interwoven sections ('braids') explains the coupling between helicity and topological chirality.
- This finding has implications for understanding polymer self-assembly and topological states.
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