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Both authors contributed equally to this work. State Key Laboratory of Luminescent Materials and Devices Institute for Organic Chemistry, University of Kiel School of Materials Science and Engineering, Hubei University The Hong Kong University of Science and TechnologyĬlear Water Bay, Kowloon, Hong Kong (China) Institute of Molecular Functional Materials
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State Key Laboratory of Molecular Neuroscience Tangĭepartment of Chemistry, Division of Life Science This strategy, the first triply Mçbius dehydroannulene (Lk = 3) Rzepa and Herges proposed to apply this feature to construct annulenes with higher Mçbius topologies. Of Lk tends to release its strain by projecting twist into writhe. Generally, a closed ribbon with a higher order Of Lk denote non-orientable and one-sided ribbons, such as The linking number Lk is an integer, with even numbers of Lk describing orientable and two-sided ribbons, whereas odd numbers The three parameters are connected by the Călugăreanu theorem as: Lk = Wr + Tw. (Lk), twist (Tw), and writhe (Wr), are applied to define the geometry of a closed twisted ribbon. In topological analysis, three parameters, linking number More difficult owing to increased strain. Consequently, the synthesis of multiply twisted Mçbius macrocycles should be even The difficulty in the synthesis of Mçbius-type molecules is mainly due Mçbius hydrocarbon was prepared by Herges et al. ContinuousĮfforts devoted to the synthesis of Mçbius-type molecules notwithstanding, it was not until 2003 that the first stable Rotaxanes, and knots, non-orientable Mçbius bands haveĪroused wide interest from synthetic chemists. Just like other molecular topologies, such as catenanes, South Area, Hi-tech Park Nanshan, Shenzhen 518057 (China)Į-mail: as well as the challenges involved in their synthesis.
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Of scientists because of their (theoretically predicted) unusual Molecules with intriguing topologies stimulate the imagination Theoretical studies including topological and electronicĬalculations reveal the energetically favorable interconversion process between triply and singly twisted topologies. The macrocycle adjusts its conformations so as to accommodate different guest molecules in its crystals.
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Twisted and flexible nature of the tetraphenylethene units, Macrocycle (TPE-ET) and investigate its analogous triplyĪnd singly twisted Mçbius topologies. Here, we report the facile synthesis of an aggregation-induced-emission (AIE)-active However, synthetic difficulties and the lack ofįunctionality impede their fundamental understandingĪnd practical applications. Such as organic chemistry, inorganic chemistry, and material science. Williams, Xuhui Huang, Rainer Herges,*Ībstract: Molecules with Mçbius topology have drawn increasing attention from scientists in a variety of fields, These models are also used to explore possible generalizations of the underlying splitting paradigm and to realize configurations that could not easily be carved from stone.Aggregation-Induced-Emission-Active Macrocycle ExhibitingĪnalogous Triply and Singly Twisted Mçbius TopologiesĮrjing Wang, Zikai He, Engui Zhao, Luming Meng, Christian Schìtt, The basic concepts related to these shapes are clarified and explained with computer-generated renderings and through stylized plastic maquettes built on a rapid prototyping machine. Keizo's split loop sculptures are reviewed and classified by the topological and geometrical rules that govern how toroidal structures can be split in a regular way. In the case of a torus with a 360-degree rotation of the cut, he obtains two twisted, tangled loops, which can be re-arranged in an ingenious way to form a dramatic figure-of-eight configuration. Starting with a simple circular torus or with more elaborate twisting bands, he drills a large number of closely spaced holes to form two strands, which may or may not be connected, depending on the overall rotation of the cutting void. Keizo Ushio is a leading international stone sculptor whose work has introduced split tori and Möbius bands to the world on a grand scale.
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