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.
Bibliographical noteFunding 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.
© The Royal Society of Chemistry.