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Abstract Knots in open strands such as ropes, fibers, and polymers, cannot typically be described in the language of knot theory, which characterizes only closed curves in space. Simulations of open knotted polymer chains, often parameterized to DNA, typically perform a closure operation and calculate the Alexander polynomial to assign a knot topology. This is limited in scenarios where the topology is less well-defined, for example when the chain is in the process of untying or is strongly confined. Here, we use a discretized version of the Second Vassiliev Invariant for open chains to analyze Langevin Dynamics simulations of untying and strongly confined polymer chains. We demonstrate that the Vassiliev parameter can accurately and efficiently characterize the knotted state of polymers, providing additional information not captured by a single-closure Alexander calculation. We discuss its relative strengths and weaknesses compared to standard techniques, and argue that it is a useful and powerful tool for analyzing polymer knot simulations.
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This content will become publicly available on December 1, 2025
Precision Design of Sequence‐Defined Polyurethanes: Exploring Controlled Folding Through Computational Design
Abstract This study presents the exploration of sequence‐defined polyurethanes (PUs) as a new class of heteropolymers capable of precise conformational control. Utilizing molecular dynamics simulations, the folding behavior of polyurethane chains is investigated of varying lengths (11, 20, and 50 monomers) in both vacuum and aqueous environments. The simulations reveal that the heterogeneous chains systematically refold to approach the designed target structures better than non‐designed chains or chains with artificially disrupted hydrogen‐bond networks. The subsequent synthesis of an optimized 11‐mer sequence (P1) is achieved through solid‐phase chemistry, with thorough characterization via NMR, MS, and SEC confirming the accuracy of the predicted sequence and its controlled chain length. Solubility tests showed favorable results across multiple solvents, highlighting the versatility of the designed polymer. This research underscores the potential of sequence‐defined polyurethanes to emulate the structural and functional attributes of biological macromolecules, opening new pathways for their application in catalysis, drug delivery, and advanced material design. The findings illustrate a promising direction for the development of synthetic polymers with tailored properties, emphasizing the transformative impact of sequence control in polymer chemistry.
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- Award ID(s):
- 2019745
- PAR ID:
- 10597737
- Publisher / Repository:
- Wiley-VCH GmbH
- Date Published:
- Journal Name:
- Macromolecular Chemistry and Physics
- Volume:
- 225
- Issue:
- 23
- ISSN:
- 1022-1352
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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