Linear operators in Clifford algebras

We consider the real vector space structure of the algebra of linear endomorphisms of a finite-dimensional real Clifford algebra (2, 4, 5, 6, 7, 8). A basis of that space is constructed in terms of the operators M _{eI, eJ} defined by xe _I · x · e _J , where the e _I are the generators of the Clifford algebra and I is a multi-index (3, 7).In particular, it is shown that the family (M _{eI, eJ} ) is exactly a basis in the even case.     

Efficient Gating of Ion Transport in Three‐Dimensional Metal–Organic Framework Sub‐Nanochannels with Confined Light‐Responsive Azobenzene Molecules

1D nanochannels modified with responsive molecules are fabricated to replicate gating functionalities of biological ion channels, but gating effects are usually weak because small molecular gates cannot efficiently block the large channels in the closed states. Now, 3D metal–organic framework (MOF) sub‐nanochannels (SNCs) confined with azobenzene (AZO) molecules achieve efficient light‐gating functionalities. The 3D MOFSNCs consisting of a MOF UiO66 with ca. 9–12 Å cavities connected by ca. 6 Å triangular windows work as angstrom‐scale ion channels, while confined AZO within the MOF cavities function as light‐driven molecular gates to efficiently regulate the ion flux. The AZO‐MOFSNCs show good cyclic gating performance and high on–off ratios up to 17.8, an order of magnitude higher than ratios observed in conventional 1D AZO‐modified nanochannels (1.3–1.5). This work provides a strategy to develop highly efficient switchable ion channels based on 3D porous MOFs and small responsive molecules.     

Molybdenum (VI)‐functionalized UiO‐66 provides an efficient heterogeneous nanocatalyst in oxidation reactions

A novel heterogeneous nanocatalyst was established by supporting molybdenum (VI) on Zr₆ nodes in the structure of the well‐known UiO‐66 metal–organic framework (MOF). The structure of the UiO‐66 before and after Mo (VI) immobilization was confirmed with XRD, DR‐FTIR and UV–vis spectroscopy, and the presence and amount of Mo (VI) was identified by X‐ray photoelectron spectroscopy and inductively coupled plasma atomic emission spectroscopy. TEM imaging confirmed the absence of Mo clusters on the MOF surface, while SEM confirmed that the appearance of the MOF has not changed upon immobilizing the Mo (VI) catalyst. BET adsorption measurements were used to confirm the porosity of the catalyst. The catalytic activity of this heterogeneous catalyst was investigated in oxidation of sulfides with H₂O₂ in acetonitrile and oxidative desulfurization of dibenzothiophene. Easy work up, convenient and steady reuse and high activity and selectivity are prominent properties of this new hybrid material.     

Gated Channels and Selectivity Tuning of CO2 over N2 Sorption by Post‐Synthetic Modification of a UiO‐66‐Type Metal–Organic Framework

The highly porous and stable metal–organic framework (MOF) UiO‐66 was altered using post‐synthetic modifications (PSMs). Prefunctionalization allowed the introduction of carbon double bonds into the framework through a four‐step synthesis from 2‐bromo‐1,4‐benzenedicarboxylic acid; the organic linker 2‐allyl‐1,4‐benzenedicarboxylic acid was obtained. The corresponding functionalized MOF (UiO‐66‐allyl) served as a platform for further PSMs. From UiO‐66‐allyl, epoxy, dibromide, thioether, diamine, and amino alcohol functionalities were synthesized. The abilities of these compounds to adsorb CO₂ and N₂ were compared, which revealed the structure–selectivity correlations. All synthesized MOFs showed profound thermal stability together with an increased ability for selective CO₂ uptake and molecular gate functionalities at low temperatures.     

Bi2Fe4O9/g-C3N4/UiO-66三元复合材料的协同光催化作用

通过水热法合成具有协同机制的三元复合材料Bi₂Fe₄O₉/g-C₃N₄/UiO-66,研究表明三元复合光催化剂的催化活性要高于二元材料和纯材料。这主要是由于Bi₂Fe₄O₉更易于和g-C₃N₄结合形成稳定的Z-scheme异质结结构,使三元复合材料增强了可见光响应能力,提高了电子-空穴分离能力,增强了空穴和电子的氧化还原能力。     

Optical metal-organic framework sensor for selective discrimination of some toxic metal ions in water

This paper reports the development of a facile and effective approach, based on the use of Zr-based metal-organic frameworks (UiO-66) sensor with micropores geometry, shape and particle morphology for the visual detection and removal of ultra-traces of some toxic metal ions such as Bi(III), Zn(II), Pb(II), Hg(II) and Cd(II). UiO-66 was used as selective carriers for accommodating hydrophobic chromophore probes such as dithizone (DZ) without coupling agent for sensitive and selective discrimination of trace level of toxic analytes. The developed UiO-66 sensor was utilized for the detection of ultra-traces of some toxic metal ions with the naked eye. The new sensor displays high sensitivity and selectivity of a wide range of detectable metals analytes up to 10⁻¹⁰ mol dm⁻³ in solution, in a rapid analyte uptake response (seconds). The developed sensor is stable, cost effective, easy to prepare, and would be useful for rapid detection and removal of ultra-traces of toxic metal ions in water samples.     

UiO-66 and hcp UiO-66 Catalysts Synthesized from Ionic Liquids as Linker Precursors

Using ionic liquids (ILs) as linker precursors, the well-known metal-organic framework (MOF) UiO-66 (Universitetet i Oslo) and the recently reported MOF hcp UiO-66 (hexagonal closed packed) have been successfully synthesized and characterized. The advantage of the applied novel synthesis approach is an economically and environmentally benign work-up procedure, due to the better solubility of the IL. Additionally, the reactivity of the terephthalate anions is increased compared to terephthalic acid, resulting in faster MOF formation with an increased amount of defects in the MOF structure. In order to explore to the influence of defects on the catalytic performance, the cyclisation of citronellal to isopulegol was employed as test reaction. The activity of hcp UiO-66 and fcc UiO-66 (face centered cubic) is improved compared to other MOF or zeolite based catalysts, while the selectivity is similar.     

Zr-MOF空心纳米球固载离子液体对CO2环加成反应的催化性能

通过后合成修饰方法(PSM)构筑了空心纳米球(Void@UiO-66-Ⅰ)和实心块(UiO-66-Ⅰ) 2种形貌的季铵盐功能化UiO-66-NH₂(Zr), 得到兼具酸碱活性位点和氢键给体的新型功能化金属-有机框架材料. 通过一系列表征证明2种催化剂的成功合成, 并将它们用于催化转化CO₂和氧化苯乙烯的环加成反应. 由于Void@UiO-66-Ⅰ催化剂的季铵盐部分含有大量的羟基和卤素阴离子, 可以通过氢键和亲核攻击与环氧化合物连接, 诱导环氧化合物开环, 促使反应顺利进行, 且催化剂的中空结构有利于物质进出催化剂, 起到加快反应速率的作用, 使得该催化剂在CO₂与氧化苯乙烯环加成反应中表现出比实心块UiO-66-Ⅰ催化剂更好的催化性能. Void@UiO-66-Ⅰ催化剂在120 ℃, CO₂压力为1.2 MPa, 反应时间为6 h, 无溶剂和助催化剂的反应条件下, 碳酸苯乙烯酯的收率和选择性分别为85.5%和95%.     

In-situ thermal crosslinked PA66/β-cyclodextrin/PA66 nanofibrous membranes with high mechanical strength for removal of heavy metal ions by flow through adsorption

β-cyclodextrin (β-CD) based materials have been studied widely as adsorbents and filter membranes for removing pollutants in air or water applications. The present study aimed to develop a sandwich structure of eletrospun nanofibrous membrane based on β-cyclodextrin and PA66 to achieve the high mechanical strength and flow-through adsorption of heavy metal ions in water. The surface and cross section morphology of PA66/β-cyclodextrin/PA66 nanofibrous membranes (PA66/β-CD/PA66 NMs) were examined using scanning electron microscopy (SEM). The physicochemical and mechanical properties of PA66/β-CD/PA66 NMs were analyzed by differential scanning calorimetry (DSC), thermogravimetric (TG) analysis and universal testing machine. The diameter of β-CD and PA66 electrospun fibers are 300–400 nm and 20–40 nm respectively. PA66/β-CD/PA66 NMs show a loosely arranged fibers and layer by layer structure. The tensile strength increases remarkably for PA66/β-CD/PA66 NMs, from 1.33 MPa of β-CD NMs to 23.17 MPa and the Young's modulus increases from 34.8 MPa to 253.3 MPa. The mechanical behavior of PA66/β-CD/PA66 NMs is a typical brittle fracture, and its microcosmic fracture diagrams are also involved. TGA/DSC results confirm the thermal crosslinking reaction is effective and complete. On the basis of SEM, DSC, TG and mechanical behavior analysis results, the molecular mechanism of in situ thermal crosslinking reaction is discussed. Fe³⁺、Ni²⁺ were used to confirm the ability to absorb heavy metal ions of PA66/β-CD/PA66 NMs. In conclusion, PA66/β-CD/PA66 NMs could be a promising solution for removal of metal ions by flow-through adsorption.     

Liquid-Phase Quasi-Epitaxial Growth of Highly Stable,Monolithic UiO-66-NH2 MOF thin Films on Solid Substrates

High quality, monolithic UiO-66-NH₂ thin films on diverse solid substrates have been prepared via a low temperature liquid phase epitaxy method. The achievement of continuous films with low defect densities and great stability against high temperatures and hot water is proven, clearly outperforming other reported types of MOF thin films.