Discovery of an Organic Trefoil Knot

We investigate the sedimentation of knotted polymers by means of stochastic rotation dynamics, a molecular dynamics algorithm that takes hydrodynamics fully into account. We show that the sedimentation coefficient s, related to the terminal velocity of the knotted polymers, increases linearly with the average crossing number nc of the corresponding ideal knot. To the best of our knowledge, this provides the first direct computational confirmation of this relation, postulated on the basis of experiments in Ref.[1], for the case of sedimentation. Such a relation was previously shown to hold with simulations for knot electrophoresis. We also show that there is an accurate linear dependence of s on the inverse of the radius of gyration R −1 g , more specifically with the inverse of the Rg component that is perpendicular to the direction along which the polymer sediments. When the polymer sediments in a slab, the walls affect the results appreciably. However, R −1 g remains to a good precision linearly dependent on nc. Therefore, R −1 g is a good measure of a knot's complexity.

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“…Knots are further present in synthetic polymers. Recently an organic trefoil knot was created synthetically by self assembly methods [14].…”

Section: Introductionmentioning

confidence: 99%

Sedimentation of knotted polymers

et al. 2013

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“…It may further provide a route to design novel synthetic molecular knots, if templates of small enough size can be fabricated. This would extend the current range of synthetic molecular topologies which, notwithstanding recent major technical advancements [23][24][25][26][27][28] , is still presently limited.…”

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confidence: 99%

Self-assembling knots of controlled topology by designing the geometry of patchy templates

et al. 2015

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The self-assembly of objects with a set of desired properties is a major goal of material science and physics. A particularly challenging problem is that of self-assembling structures with a target topology. Here we show by computer simulation that one may design the geometry of string-like rigid patchy templates to promote their efficient and reproducible self-assembly into a selected repertoire of non-planar closed folds including several knots. In particular, by controlling the template geometry, we can direct the assembly process so as to strongly favour the formation of constructs tied in trefoil or pentafoil, or even of more exotic torus knots. Polydisperse and racemic mixtures of helical fragments of variable composition add further tunability in the topological self-assembly we discovered. Our results should be relevant to the design of new ways to synthesize molecular knots, which may prove, for instance, to be efficient cargo-carriers due to their mechanical stability.

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“…Der Kleeblattknoten 27 wurde von Sanders und Mitarbeiter in einer DCL aus trimeren elektronenarmen p-Systemen entdeckt (Schema 9). [87] Die DCL wurde durch Disulfidaustausch gebildet, und da als Lçsungsmittel Wasser verwendet wurde,i st die Tr iebkraft fürd ie Verknotung wahrscheinlich die Minimierung der hydrophoben Oberflä-che.…”

Section: Dynamisch-kombinatorische Bibliothekenunclassified

“…Die hydrophobe Oberfläche wird durch die Verzahnung minimiert, sodass Wechselwirkungen mit dem Lçsungsmittel unterdrückt werden, da ein Teil des Systems in der Kavitätlokalisiert ist. [87] Angewandte Chemie Aufsätze 11332 www.angewandte.de (Schema 10). [88] Die Struktur von 30 im Festkçrper zeigt zwei Br À -Ionen in der Knotenkavität, eins über dem anderen (Schema 10).…”

Section: Dynamisch-kombinatorische Bibliothekenunclassified

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Molekulare Knoten

Fielden¹,

Leigh²,

Woltering³

2017

Angewandte Chemie

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Der erste synthetische Kleeblattknoten wurde in den späten 1980er Jahren hergestellt. Kompliziertere Knotentopologien wurden jedoch erst in den letzten Jahren in molekularer Form erhalten. Die Verknotung molekularer Stränge erzeugt sterische Einschränkungen und kann so wichtige physikalische und chemische Eigenschaften verleihen, unter anderem Chiralität, starkes und selektives Binden von Ionen und katalytische Aktivität. Da die Anzahl und Komplexität molekularer Knoten steigt, wird es für Chemiker immer wichtiger, die Knotennomenklatur anderer Disziplinen zu verwenden. Hier geben wir einen Überblick über die Synthesestrategien für molekulare Knoten und beschreiben die Grundlagen der Knoten‐, Zopf‐ und Tangle‐Theorie in einem für Chemiker und molekulare Strukturen angemessenen Umfang.

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Discovery of an Organic Trefoil Knot

Cited by 305 publications

References 21 publications

Sedimentation of knotted polymers

Sedimentation of knotted polymers

Self-assembling knots of controlled topology by designing the geometry of patchy templates

Molekulare Knoten

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