Decoding chirality in circuit topology of a self entangled chain through braiding
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Decoding chirality in circuit topology of a self entangled chain through braiding. / Berx, Jonas; Mashaghi, Alireza.
In: Soft Matter, Vol. 19, No. 31, 21.07.2023, p. 5888-5895.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Decoding chirality in circuit topology of a self entangled chain through braiding
AU - Berx, Jonas
AU - Mashaghi, Alireza
N1 - Publisher Copyright: © 2023 The Royal Society of Chemistry.
PY - 2023/7/21
Y1 - 2023/7/21
N2 - Circuit topology employs fundamental units of entanglement, known as soft contacts, for constructing knots from the bottom up, utilizing circuit topology relations, namely parallel, series, cross, and concerted relations. In this article, we further develop this approach to facilitate the analysis of chirality, which is a significant quantity in polymer chemistry. To achieve this, we translate the circuit topology approach to knot engineering into a braid-theoretic framework. This enables us to calculate the Jones polynomial for all possible binary combinations of contacts in cross or concerted relations and to show that, for series and parallel relations, the polynomial factorises. Our results demonstrate that the Jones polynomial provides a powerful tool for analysing the chirality of molecular knots constructed using circuit topology. The framework presented here can be used to design and engineer a wide range of entangled chain with desired chiral properties, with potential applications in fields such as materials science and nanotechnology.
AB - Circuit topology employs fundamental units of entanglement, known as soft contacts, for constructing knots from the bottom up, utilizing circuit topology relations, namely parallel, series, cross, and concerted relations. In this article, we further develop this approach to facilitate the analysis of chirality, which is a significant quantity in polymer chemistry. To achieve this, we translate the circuit topology approach to knot engineering into a braid-theoretic framework. This enables us to calculate the Jones polynomial for all possible binary combinations of contacts in cross or concerted relations and to show that, for series and parallel relations, the polynomial factorises. Our results demonstrate that the Jones polynomial provides a powerful tool for analysing the chirality of molecular knots constructed using circuit topology. The framework presented here can be used to design and engineer a wide range of entangled chain with desired chiral properties, with potential applications in fields such as materials science and nanotechnology.
U2 - 10.1039/d3sm00390f
DO - 10.1039/d3sm00390f
M3 - Journal article
C2 - 37477235
AN - SCOPUS:85167338484
VL - 19
SP - 5888
EP - 5895
JO - Soft Matter
JF - Soft Matter
SN - 1744-683X
IS - 31
ER -
ID: 371847362