Hierarchies of Hofstadter butterflies in 2D covalent-organic frameworks

The Hofstadter butterfly is one of the first and most fascinating examples of the fractal and self-similar quantum nature of free electrons in a lattice pierced by a perpendicular magnetic field. However, the direct experimental verification of this effect on single-layer materials is still missing as very strong and inaccessible magnetic fields are necessary. For this reason, its indirect experimental verification has only been realized in artificial periodic 2D systems, like moir\'e lattices. The only recently synthesized 2D covalent-organic frameworks might circumvent this limitation: Due to their large pore structures, magnetic fields needed to detect most features of the Hofstadter butterfly are indeed accessible with today's technology. This work opens the door to making this exotic and theoretical issue from the 70s measurable and might solve the quest for the experimental verification of the Hofstadter butterfly in single-layer materials. Moreover, the intrinsic hierarchy of different pore sizes in a 2D covalent-organic framework adds additional complexity and beauty to the original butterflies and leads to a directly accessible playground for new physical observations

Structural Reinforcement in Mechanically Interlocked Two-Dimensional Polymers by Suppressing Interlayer Sliding

Preserving the superior mechanical properties of monolayer two-dimensional (2D) materials when transitioning to bilayer and layer-stacked structures poses a great challenge, primarily arising from the weak van der Waals (vdW) forces that facilitate interlayer sliding and decoupling. Here, we discover that mechanically interlocked 2D polymers (2DPs) offer a means for structural reinforcement from monolayer to bilayer. Incorporating macrocyclic molecules with one and two cavities into 2DPs backbones enables the precision synthesis of mechanically interlocked monolayer (MI-M2DP) and bilayer (MI-B2DP). Intriguingly, we have observed an exceptionally high effective Young's modulus of 222.4 GPa for MI-B2DP, surpassing those of MI-M2DP (130.1 GPa), vdW-stacked MI-M2DPs (2 MI-M2DP, 8.1 GPa) and other reported multilayer 2DPs. Modeling studies demonstrate the extraordinary effectiveness of mechanically interlocked structures in minimizing interlayer sliding (~0.1 {\AA}) and energy penalty (320 kcal/mol) in MI-B2DP compared to 2 MI-M2DP (~1.2 {\AA}, 550 kcal/mol), thereby suppressing mechanical relaxation and resulting in prominent structural reinforcement

When Tree Rings Go Global: Challenges and Opportunities for Retro- and Prospective Insight

The demand for large-scale and long-term information on tree growth is increasing rapidly as environmental change research strives to quantify and forecast the impacts of continued warming on forest ecosystems. This demand, combined with the now quasi-global availability of tree-ring observations, has inspired researchers to compile large tree-ring networks to address continental or even global-scale research questions. However, these emergent spatial objectives contrast with paleo-oriented research ideas that have guided the development of many existing records. A series of challenges related to how, where, and when samples have been collected is complicating the transition of tree rings from a local to a global resource on the question of tree growth. Herein, we review possibilities to scale tree-ring data (A) from the sample to the whole tree, (B) from the tree to the site, and (C) from the site to larger spatial domains. Representative tree-ring sampling supported by creative statistical approaches is thereby key to robustly capture the heterogeneity of climate-growth responses across forested landscapes. We highlight the benefits of combining the temporal information embedded in tree rings with the spatial information offered by forest inventories and earth observations to quantify tree growth and its drivers. In addition, we show how the continued development of mechanistic tree-ring models can help address some of the non-linearities and feedbacks that complicate making inference from tree-ring data. By embracing scaling issues, the discipline of dendrochronology will greatly increase its contributions to assessing climate impacts on forests and support the development of adaptation strategies