A new beryllium-free deep-ultraviolet (DUV) nonlinear optical (NLO) material, beta-Rb2Al2B2O7 (beta-RABO), has been synthesized and characterized. The chiral nonpolar acentric material shows ...second-harmonic generation (SHG) activity at both 1064 and 532nm with efficiencies of 2×KH2PO4 and 0.4×beta-BaB2O4, respectively, and exhibits a short absorption edge below 200nm. beta-Rb2Al2B2O7 has a three-dimensional structure of corner-shared Al(BO3)3O polyhedra. The discovery of beta-RABO shows that through careful synthesis and characterization, replacement of KBe2BO3F2 (KBBF) by a Be-free DUV NLO material is possible.
Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any ...algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.
Metal–organic polyhedra (MOPs) or frameworks (MOFs) based on Cr3+ are notoriously difficult to synthesize, especially as crystals large enough to be suitable for characterization of the structure or ...properties. It is now shown that the co‐existence of In3+ and Cr3+ induces a rapid crystal growth of large single crystals of heterometallic In‐Cr‐MOPs with the M8L12 (M=In/Cr, L=dinegative 4,5‐imidazole‐dicarboxylate) cubane‐like structure. With a high concentration of protons from 12 carboxyl groups decorating every edge of the cube and an extensive H‐bonded network between cubes and surrounding H2O molecules, the newly synthesized In‐Cr‐MOPs exhibit an exceptionally high proton conductivity (up to 5.8×10−2 S cm−1 at 22.5 °C and 98 % relative humidity, single crystal).
In3+ befriending Cr3+: Indium and chromium ions drag each other into unprecedented heterometallic In‐Cr‐MOP (metal–organic polyhedra) crystals. These have a high proton conductivity (5.8×10−2 S cm−1) at 22.5 °C and 98 % relative humidity for a single crystal.
Stimuli‐responsive metal–organic polyhedra (srMOPs) functionalized with azobenzene showed UV‐irradiation‐induced isomerization from the insoluble trans‐srMOP to the soluble cis‐srMOP, whereas ...irradiation with blue light reversed this process. Guest molecules were trapped and released upon cis‐to‐trans and trans‐to‐cis isomerization of the srMOPs, respectively. This study provides a new direction in the ever‐diversifying field of MOPs, while laying the groundwork for a new class of optically responsive materials.
Lock in the guests, later set them free: Stimuli‐responsive metal–organic polyhedra (srMOPs) functionalized with azobenzene showed UV‐light‐induced isomerization from insoluble srMOPs substituted with trans‐azobenzene to soluble srMOPs with cis‐azobenzene units; irradiation with blue light reversed this process (see picture). Guest molecules were trapped upon cis‐to‐trans and released upon trans‐to‐cis isomerization of the azobenzene units.
Rational control of the self-assembly of large structures is one of the key challenges in chemistry, and is believed to become increasingly difficult and ultimately impossible as the number of ...components involved increases. So far, it has not been possible to design a self-assembled discrete molecule made up of more than 100 components. Such molecules-for example, spherical virus capsids-are prevalent in nature, which suggests that the difficulty in designing these very large self-assembled molecules is due to a lack of understanding of the underlying design principles. For example, the targeted assembly of a series of large spherical structures containing up to 30 palladium ions coordinated by up to 60 bent organic ligands was achieved by considering their topologies. Here we report the self-assembly of a spherical structure that also contains 30 palladium ions and 60 bent ligands, but belongs to a shape family that has not previously been observed experimentally. The new structure consists of a combination of 8 triangles and 24 squares, and has the symmetry of a tetravalent Goldberg polyhedron. Platonic and Archimedean solids have previously been prepared through self-assembly, as have trivalent Goldberg polyhedra, which occur naturally in the form of virus capsids and fullerenes. But tetravalent Goldberg polyhedra have not previously been reported at the molecular level, although their topologies have been predicted using graph theory. We use graph theory to predict the self-assembly of even larger tetravalent Goldberg polyhedra, which should be more stable, enabling another member of this polyhedron family to be assembled from 144 components: 48 palladium ions and 96 bent ligands.
Aqueous zinc‐ion batteries (ZIBs) have been considered as prospective alternatives for lithium‐ion batteries, which are able to serve as power sources for next‐generation wearable and flexible ...devices, owing to the merits of abundant zinc resources and high safety of aqueous electrolyte. However, the lack of suitable cathode materials with flexibility for ZIBs hinders their further application. Herein, a novel cathode material i.e., MnO2 nanosheet‐assembled hollow polyhedron anchored on carbon cloth (MnO2/CC) was prepared through a rapid hydrothermal method by using ZIF‐67 as self‐sacrificing template. When tested in an aqueous ZIB, the MnO2/CC delivered a high reversible capacity of 263.9 mAh g−1 at 1.0 A g−1 after 300 cycles, far exceeding those of the commercial MnO2 electrode. More importantly, benefiting from the unique structural advantages, a flexible ZIB assembled based on the MnO2/CC displayed a stable output voltage of 1.53 V and a specific capacity of 91.7 mAh g−1 at 0.1 A g−1 after 30 cycles. It also successfully lit LED bulbs even under different bending angles, showing good flexibility. This research contributes to the development of MnO2‐based cathode materials for high‐performance flexible ZIBs.
Flexing its performance: A high‐performance, flexible aqueous zinc‐ion battery (ZIB) is fabricated with a carbon cloth‐coated MnO2 nanosheet‐assembled hollow polyhedron, which is obtained through a facile and wet‐chemical synthetic approach. The flexible ZIB is able to power a LED under different bending states, demonstrating the utility of this hierarchically structured cathode material.
Three polyoxovanadate-based metal-organic polyhedra (denoted as VMOP-1, -2, and -3), adopting isostructural discrete octahedral cage geometries, were successfully synthesized under solvothermal ...conditions. These structures are all built up from the same pentavanadate {V5O9Cl} cluster connected by linear bidentate ligands (H2L1 = H2BDC, H2L2 = H2BDC-NH2, H2L3 = H2BDC-Br), respectively.
Abstract
The polyhedra with
A
3
,
B
3
/
C
3
,
H
3
reflection symmetry group
G
in the real 3
D
space are considered. The recursive rules for finding orbits with smaller radii, which provide the ...structures of nested polytopes, are demonstrated.
In this study experimental and numerical investigations with the discrete element method (DEM) on the discharge of spheres and polyhedral dices from a hopper are conducted. In DEM the dices are ...approximated by polyhedra and smoothed polyhedra respectively and hence allow examining the influence of sharply-edged and smooth particle geometries on the discharge properties. Simulation results are in good general agreement with the experiments and hence demonstrate the adequacy of DEM as well as polyhedral and smoothed polyhedral approximation schemes to simulate non-spherical particle geometries. Compared to spheres the dices exhibit an increased flow resistance and readiness to form pile-ups at the bottom walls of the hopper. Both phenomena are better approximated using polyhedral approximations of the dices, showcasing the influence of the selected shape approximation scheme on the numerical results.
In this study experimental and numerical investigations with the discrete element method (DEM) on the discharge of spheres and polyhedral dices from a hopper are conducted. In DEM the dices are approximated by polyhedra and smoothed polyhedra respectively. Simulation results are in good general agreement with the experiments and hence demonstrate the adequacy of the DEM to simulate non-spherical particle geometries. Display omitted
► Good agreement between experimental and numerical results of hopper discharge. ► Angular particles increase flow resistance and formation of pile-ups. ► Shape approximation in DEM has a non-negligible influence on simulation results.
In this review, we describe two recently implemented conceptual approaches facilitating the design and deliberate construction of metal-organic frameworks (MOFs), namely supermolecular building block ...(SBB) and supermolecular building layer (SBL) approaches. Our main objective is to offer an appropriate means to assist/aid chemists and material designers alike to rationally construct desired functional MOF materials, made-to-order MOFs. We introduce the concept of
net
-coded building units (
net
-cBUs), where precise embedded geometrical information codes uniquely and matchlessly a selected net, as a compelling route for the rational design of MOFs. This concept is based on employing pre-selected 0-periodic metal-organic polyhedra or 2-periodic metal-organic layers, SBBs or SBLs respectively, as a pathway to access the requisite
net
-cBUs. In this review, inspired by our success with the original
rht
-MOF, we extrapolated our strategy to other known MOFs
via
their deconstruction into more elaborate building units (namely polyhedra or layers) to (i) elucidate the unique relationship between edge-transitive polyhedra or layers and minimal edge-transitive 3-periodic nets, and (ii) illustrate the potential of the SBB and SBL approaches as a rational pathway for the design and construction of 3-periodic MOFs. Using this design strategy, we have also identified several new hypothetical MOFs which are synthetically targetable.
A toolbox for the design of made-to-order MOFs: Pinpointing the rationale and benefits of the Supermolecular Building Block (SBB) and Supermolecular Building Layer (SBL) approaches.
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