Twist renormalization in molecular crystals driven by geometric frustration

Asaf Haddad; Hillel Aharoni; Eran Sharon; Alexander G. Shtukenberg; Bart Kahr; Efi Efrati

doi:10.1039/C8SM01290C

Twist renormalization in molecular crystals driven by geometric frustration

Asaf Haddad, Hillel Aharoni, Eran Sharon, Alexander G. Shtukenberg, Bart Kahr, Efi Efrati^*

^*Corresponding author for this work

Racah Institute of Physics

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

Symmetry considerations preclude the possibility of twist or continuous helical symmetry in bulk crystalline structures. However, as has been shown nearly a century ago, twisted molecular crystals are ubiquitous and can be formed by about 1/4 of organic substances. Despite its ubiquity, this phenomenon has so far not been satisfactorily explained. In this work we study twisted molecular crystals as geometrically frustrated assemblies. We model the molecular constituents as uniaxially twisted cubes and examine their crystalline assembly. We exploit a renormalization group (RG) approach to follow the growth of the rod-like twisted crystals these constituents produce, inquiring in every step into the evolution of their morphology, response functions and residual energy. The gradual untwisting of the rod-like frustrated crystals predicted by the RG approach is verified experimentally using silicone rubber models of similar geometry. Our theory provides a mechanism for the conveyance of twist across length-scales observed experimentally and reconciles the apparent paradox of a twisted single crystal as a finite size effect.

Original language	American English
Pages (from-to)	116-126
Number of pages	11
Journal	Soft Matter
Volume	15
Issue number	1
DOIs	https://doi.org/10.1039/C8SM01290C
State	Published - 2019

Bibliographical note

Funding Information:
This work was supported by the National Science Foundation under Award DMR-1608374. It was supported partially by the Materials Research Science and Engineering Center (MRSEC) program of the National Science Foundation (NSF) under Award DMR-1420073. H. A. was supported by NSF grant no. DMR-1262047. E. E. is the incumbent of the Ernst and Kaethe Ascher career development chair and thanks the Ascher foundation for their support, and also acknowledges the support by the Alon fellowship. This work was funded by NSF/DMR-BSF grant 2015670, the Minerva foundation grant number 712273, and by the ISF grant number 1479/16.

Publisher Copyright:
© The Royal Society of Chemistry.

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title = "Twist renormalization in molecular crystals driven by geometric frustration",

abstract = "Symmetry considerations preclude the possibility of twist or continuous helical symmetry in bulk crystalline structures. However, as has been shown nearly a century ago, twisted molecular crystals are ubiquitous and can be formed by about 1/4 of organic substances. Despite its ubiquity, this phenomenon has so far not been satisfactorily explained. In this work we study twisted molecular crystals as geometrically frustrated assemblies. We model the molecular constituents as uniaxially twisted cubes and examine their crystalline assembly. We exploit a renormalization group (RG) approach to follow the growth of the rod-like twisted crystals these constituents produce, inquiring in every step into the evolution of their morphology, response functions and residual energy. The gradual untwisting of the rod-like frustrated crystals predicted by the RG approach is verified experimentally using silicone rubber models of similar geometry. Our theory provides a mechanism for the conveyance of twist across length-scales observed experimentally and reconciles the apparent paradox of a twisted single crystal as a finite size effect.",

author = "Asaf Haddad and Hillel Aharoni and Eran Sharon and Shtukenberg, {Alexander G.} and Bart Kahr and Efi Efrati",

note = "Funding Information: This work was supported by the National Science Foundation under Award DMR-1608374. It was supported partially by the Materials Research Science and Engineering Center (MRSEC) program of the National Science Foundation (NSF) under Award DMR-1420073. H. A. was supported by NSF grant no. DMR-1262047. E. E. is the incumbent of the Ernst and Kaethe Ascher career development chair and thanks the Ascher foundation for their support, and also acknowledges the support by the Alon fellowship. This work was funded by NSF/DMR-BSF grant 2015670, the Minerva foundation grant number 712273, and by the ISF grant number 1479/16. Publisher Copyright: {\textcopyright} The Royal Society of Chemistry.",

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AU - Sharon, Eran

AU - Shtukenberg, Alexander G.

AU - Kahr, Bart

AU - Efrati, Efi

N1 - Funding Information: This work was supported by the National Science Foundation under Award DMR-1608374. It was supported partially by the Materials Research Science and Engineering Center (MRSEC) program of the National Science Foundation (NSF) under Award DMR-1420073. H. A. was supported by NSF grant no. DMR-1262047. E. E. is the incumbent of the Ernst and Kaethe Ascher career development chair and thanks the Ascher foundation for their support, and also acknowledges the support by the Alon fellowship. This work was funded by NSF/DMR-BSF grant 2015670, the Minerva foundation grant number 712273, and by the ISF grant number 1479/16. Publisher Copyright: © The Royal Society of Chemistry.

PY - 2019

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N2 - Symmetry considerations preclude the possibility of twist or continuous helical symmetry in bulk crystalline structures. However, as has been shown nearly a century ago, twisted molecular crystals are ubiquitous and can be formed by about 1/4 of organic substances. Despite its ubiquity, this phenomenon has so far not been satisfactorily explained. In this work we study twisted molecular crystals as geometrically frustrated assemblies. We model the molecular constituents as uniaxially twisted cubes and examine their crystalline assembly. We exploit a renormalization group (RG) approach to follow the growth of the rod-like twisted crystals these constituents produce, inquiring in every step into the evolution of their morphology, response functions and residual energy. The gradual untwisting of the rod-like frustrated crystals predicted by the RG approach is verified experimentally using silicone rubber models of similar geometry. Our theory provides a mechanism for the conveyance of twist across length-scales observed experimentally and reconciles the apparent paradox of a twisted single crystal as a finite size effect.

AB - Symmetry considerations preclude the possibility of twist or continuous helical symmetry in bulk crystalline structures. However, as has been shown nearly a century ago, twisted molecular crystals are ubiquitous and can be formed by about 1/4 of organic substances. Despite its ubiquity, this phenomenon has so far not been satisfactorily explained. In this work we study twisted molecular crystals as geometrically frustrated assemblies. We model the molecular constituents as uniaxially twisted cubes and examine their crystalline assembly. We exploit a renormalization group (RG) approach to follow the growth of the rod-like twisted crystals these constituents produce, inquiring in every step into the evolution of their morphology, response functions and residual energy. The gradual untwisting of the rod-like frustrated crystals predicted by the RG approach is verified experimentally using silicone rubber models of similar geometry. Our theory provides a mechanism for the conveyance of twist across length-scales observed experimentally and reconciles the apparent paradox of a twisted single crystal as a finite size effect.

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Twist renormalization in molecular crystals driven by geometric frustration

Abstract

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