The mechanics of trefoil knots in both closed and open configurations

2020 ◽  
Author(s):  
Paul Johanns
Keyword(s):  
Trefoil Knots

Same knot, longer rope: altering ligand geometry provides control over nuclearity in self-assembled trefoil knots

2021 ◽  
Vol 57 (76) ◽  
pp. 9772-9775
Author(s):  
Qi-Li-Sha Wang ◽  
Yue-Jian Lin ◽  
Guo-Xin Jin
Keyword(s):  
Self Assembled ◽  
Trefoil Knots

Selective constructions of Cp*Rh(iii)-based hexanuclear and octanuclear trefoil knots are realized using two ester bipyridyl ligands bearing minor differences in geometry.

Design of and Stability Studies on Trefoil Knots Featuring RhCp* Building Blocks

2019 ◽  
Vol 25 (41) ◽  
pp. 9721-9727 ◽  
Author(s):  
Bei‐Bei Guo ◽  
Yue‐Jian Lin ◽  
Guo‐Xin Jin
Keyword(s):  
Building Blocks ◽  
Stability Studies ◽  
Trefoil Knots

Template‐Free Self‐Assembly of Molecular Trefoil Knots and Double Trefoil Knots Featuring Cp*Rh Building Blocks

2020 ◽  
Vol 26 (22) ◽  
pp. 5093-5099 ◽  
Author(s):  
Wei‐Long Shan ◽  
Xiang Gao ◽  
Yue‐Jian Lin ◽  
Guo‐Xin Jin
Keyword(s):  
Self Assembly ◽  
Building Blocks ◽  
Template Free ◽  
Trefoil Knots

scholarly journals Design and synthesis of a bis-macrocyclic host and guests as building blocks for small molecular knots

2020 ◽  
Vol 16 ◽  
pp. 2314-2321
Author(s):  
Elizabeth A Margolis ◽  
Rebecca J Keyes ◽  
Stephen D Lockey ◽  
Edward E Fenlon
Keyword(s):  
Molecular Weight ◽  
Electrostatic Interactions ◽  
Second Generation ◽  
Building Blocks ◽  
Design And Synthesis ◽  
Host Compound ◽  
Novel Method ◽  
Trefoil Knots

The thread–link–cut (TLC) approach has previously shown promise as a novel method to synthesize molecular knots. The modular second-generation approach to small trefoil knots described herein involves electrostatic interactions between an electron-rich bis-macrocyclic host compound and electron-deficient guests in the threading step. The bis-macrocyclic host was synthesized in eight steps and 6.6% overall yield. Ammonium and pyridinium guests were synthesized in 4–5 steps. The TLC knot-forming sequence was carried out and produced a product with the expected molecular weight, but, unfortunately, further characterization did not produce conclusive results regarding the topology of the product.

Spontaneous Knotting — From Oligoamide Threads to Trefoil Knots.

ChemInform ◽  
2007 ◽  
Vol 38 (11) ◽  
Author(s):  
Jens Brueggemann ◽  
Stephan Bitter ◽  
Sonja Mueller ◽  
Walter M. Mueller ◽  
Ute Mueller ◽  
...  
Keyword(s):  
Trefoil Knots

scholarly journals Non-commutative trigonometry and the A-polynomial of the trefoil knot

2002 ◽  
Vol 133 (2) ◽  
pp. 311-323 ◽  
Author(s):  
RĂZVAN GELCA
Keyword(s):  
Character Variety ◽  
Skein Modules ◽  
Skein Module ◽  
Kauffman Bracket ◽  
Trefoil Knot ◽  
Sum Formula ◽  
Left And Right ◽  
Trefoil Knots ◽  
The Relationship ◽  
The Ideal

The non-commutative generalization of the A-polynomial of a knot of Cooper, Culler, Gillet, Long and Shalen [4] was introduced in [6]. This generalization consists of a finitely generated left ideal of polynomials in the quantum plane, the non- commutative A-ideal, and was defined based on Kauffman bracket skein modules, by deforming the ideal generated by the A-polynomial with respect to a parameter. The deformation was possible because of the relationship between the skein module with the variable t of the Kauffman bracket evaluated at −1 and the SL(2, C)-character variety of the fundamental group, which was explained in [2]. The purpose of the present paper is to compute the non-commutative A-ideal for the left- and right- handed trefoil knots. As will be seen below, this reduces to trigonometric operations in the non-commutative torus, the main device used being the product-to-sum formula for non-commutative cosines.

Construction of organometallic trefoil knots and one-dimensional chains featuring half-sandwich Cp*Rh corner units and an abnormal zwitterion ligand

2021 ◽  
Author(s):  
Xiang Gao ◽  
Zheng Cui ◽  
Yue-Jian Lin ◽  
Guo-Xin Jin
Keyword(s):  
Self Assembly ◽  
One Dimensional ◽  
Trefoil Knots ◽  
Half Sandwich ◽  
1D Chains ◽  
Self Adaptive

An abnormal flexible O-coordinated zwitterion ligand L shows self-adaptive conformation behaviour in chemical self-assembly. Two trefoil knots were obtained with C-shaped ligand L and two novel 1D chains were obtained with Z-shaped ligand L.

ChemInform Abstract: Molecular Knots: Template Synthesis of Dicopper(I) Trefoil Knots of Various Size.

ChemInform ◽  
2010 ◽  
Vol 23 (50) ◽  
pp. no-no
Author(s):  
C. O. DIETRICH-BUCHECKER ◽  
J.-F. NIERENGARTEN ◽  
J.-P. SAUVAGE
Keyword(s):  
Template Synthesis ◽  
Trefoil Knots

A template-free strategy for the synthesis of highly stable trefoil knots

2020 ◽  
Vol 912 ◽  
pp. 121172
Author(s):  
Xiang Gao ◽  
Bei-bei Guo ◽  
Li-long Dang ◽  
Guo-Xin Jin
Keyword(s):  
Template Free ◽  
Trefoil Knots
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