Influence of oxophilic behavior of UiO-66(Ce) metal–organic framework with superior catalytic performance in Friedel-Crafts alkylation reaction

In recent years, one of the analogous metal organic frameworks (MOFs) with UiO-66(Zr) topology receiving wider attention is UiO-66(Ce), which exhibits interesting properties and high thermal and chemical stability. Hence, in the present work, UiO-66(Ce) is synthesized by adopting an earlier procedure and characterized by series of spectroscopic techniques like UV-visible (UV-Vis), Fourier transform infrared (FT-IR), Raman and scanning electron microscope (SEM) to confirm its structural features and crystallinity using powder X-ray diffraction (XRD) and these results are in close agreement with other reports. The catalytic performance of UiO-66(Ce) was evaluated in the Friedel–Crafts alkylation reaction between β-nitrostyrene and indole to obtain heterocyclic compounds with biological activity. A series of control experiments indicate that Ce⁴⁺ located within the framework plays an important role in promoting this reaction and its activity is found to be much superior to that of UiO-66(Zr). This enhanced activity with Ce⁴⁺ compared to Zr⁴⁺ is attributed due to the higher oxophilicity of Ce⁴⁺, which can readily bind with an oxygen-containing substrate such as β-nitrostyrene. The leaching test confirms the heterogeneity of the reaction and the catalyst can be reused three times with identical activity to the fresh solid. UiO-66(Ce) shows wide substrate scope with high yields of the desired product. A proposed mechanism is also discussed.     

Faber polynomials, Cayley-Hamilton equation and Newton symmetric functions

We give an explicit formula for the Faber polynomials and for generalized Faber polynomials introduced by H. Airault and J. Ren in [H. Airault, J. Ren, An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math. 126 (5) (2002) 343-367]. We introduce a new family of polynomials related to the Faber polynomials of the second kind. This allows us to give a generalized Cayley-Hamilton equation.     

核壳结构NH2-UiO-66@TiO2的制备及其可见光下的甲苯降解性能研究

Metal-organic frameworks (MOFs) are of significant interest for photocatalysis using visible light, but they are typically limited by the instability and high recombination ratio of photoexcited pairs. Integrating MOFs into an inorganic semiconductor is one of the most widespread methods to promote their activity. In this study, a core-shell structured MOF@TiO₂ (NH₂-UiO-66@TiO₂) was synthesized as an efficient photocatalyst for the degradation of toluene. Pristine NH₂-UiO-66 was synthesized by a hydrothermal method as the core, which was then coated with an amorphous TiO₂ shell. Compared with pristine NH₂-UiO-66 and other samples prepared by the direct mixing of NH₂-UiO-66 and TiO₂, NH₂-UiO-66@TiO₂ exhibited a higher degradation rate of toluene. Using NH₂-UiO-66@TiO₂ as a catalyst, the degradation efficiency of toluene reached 76.7% within 3 h, which is 1.48 times higher than that of NH₂-UiO-66. The degradation performance was also stable in four repeated reuse experiments, and the slight deactivation was reactivated after washing with ethanol. A series of characterization methods were used to determine the physicochemical properties of NH₂-UiO-66@TiO₂, including X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). Using the measured physicochemical properties, the photocatalytic mechanism of NH₂-UiO-66@TiO₂ was explored. NH₂-UiO-66 is an ideal photocatalyst, with visible-light response and a huge specific surface area (914.9 m²·g^-1), which is favorable for the utilization of sunlight as well as the absorption of pollutants in indoor air. In addition, a new interface formed between the two components (NH₂-UiO-66 and TiO₂), which efficiently broaden the light absorption area and enhanced the utilization of photogenerated species. The photogenerated holes and electrons could transfer through the interlayer as soon as they were formed. It is speculated that holes would transfer to the HOMO of NH₂-UiO-66, and then combine with H₂O molecules to form hydroxyl radicals (·OH). At the same time, more electrons tended to combine with oxygen molecules in the conduction band of TiO₂ rather than recombine with holes. Consequently, the recombination rate of electrons and holes decreased, while the quantity of oxygen radicals and hydroxyl radicals increased. Toluene was efficiently oxidized by these two types of radicals. Owing to the outstanding properties mentioned above, the strategy of constructing NH₂-UiO-66@TiO₂ is considered to be an effective approach. This work may provide new insights into the design of core-shell structured MOF@photocatalysts for the photocatalytic degradation of indoor air pollutants.      

Factorization of staircase class operators in Hilbert space

A class of linear bounded staircase operators (H, G spaces) defined by (1) with two infinite sequences of orthogonal decompositions ofH and chain property (2) is considered. Necessary and sufficient conditions for the factorizationZ=XY are obtained, whereX, Y are block-diagonal, bounded, andY has a bounded inverse. All the pairs (X, Y) are explicitly constructed. These conditions are specialized for finite and infinite dimensions of the blocks ofX, Y and for differentX, Y. A direct application to bitriangular and biquasitriangular operators is indicated.     

去除内毒素的柱亲和介质与膜亲和介质的制备和特征

以琼脂糖和尼龙６６微孔滤膜为原料，发展了两种用于去 内毒素的不同类型的亲和介质。在对原料进行化学改性后，键合了含六个碳原子的间隔臂和组氨酸亲和配基。它们对内毒素的亲和容量分别为２．０ｍｇ／ｇ和０．２ｍｇ／ｇ，内毒素和介质之间的表观解离常数分别为８．１＊１０＾－１０ｍｏｌ／Ｌ和３．０＊１０＾－８ｍｏｌ／Ｌ。     

Reactions of CH-acids with α,β-unsaturated aldehydes in ionic liquids

Metal carbonate-catalyzed reactions of CH-acids (diethyl malonate, ethyl acetoacetate, ethyl cyanoacetate, and ethyl 2-acetyl- and 2-ethoxycarbonyl-5,9-dimethyldeca-4,8-dienoates) with ,-unsaturated aldehydes (acrolein, crotonaldehyde, citral) were studied in an ionic liquid, 1-butyl-3-methylimidazolium hexafluorophosphate [bmim][PF₆], and in a 1-butyl-3-methylimidazolium bromide ([bmim][Br]) — benzene system. The reactions with acrolein and crotonaldehyde afforded Michael addition products, those with citral resulted in Knoevenagel addition products. Sonication increased the yields of the Michael adducts. The ionic liquid [bmim][PF₆] can be recovered and repeatedly used in the reactions.     

Catalytic synthesis of cyclic carbonates from epoxides and carbon dioxide by magnetic UiO‐66 under mild conditions

The catalytic activity of UiO‐66@Fe₃O₄@SiO₂ catalyst was investigated in the fixation of carbon dioxide with epoxides under mild conditions. In this manner, a facile magnetization of UiO‐66 was achieved simultaneously by simply mixing this metal–organic framework and silica‐coated Fe₃O₄ nanoparticles in solution under sonication. The prepared catalyst was characterized using Fourier transform infrared and UV–visible spectroscopies, X‐ray diffraction, transmission and field emission scanning electron microscopies, N₂ adsorption and inductively coupled plasma atomic emission spectroscopy. This new heterogeneous catalyst was applied as a highly efficient catalyst in the coupling of carbon dioxide with epoxides at mild temperatures and pressures. Furthermore, it could be easily recovered with the assistance of an external magnetic field and reused three consecutive times without significant loss of activity and mass.     

The Chemistry of Nucleation: In Situ Pair Distribution Function Analysis of Secondary Building Units During UiO-66 MOF Formation

The concept of secondary building units (SBUs) is central to all science on metal-organic frameworks (MOFs), and they are widely used to design new MOF materials. However, the presence of SBUs during MOF formation remains controversial, and the formation mechanism of MOFs remains unclear, due to limited information about the evolution of prenucleation cluster structures. Here in situ pair distribution function (PDF) analysis was used to probe UiO-66 formation under solvothermal conditions. The expected SBU—a hexanuclear zirconium cluster—is present in the metal salt precursor solution. Addition of organic ligands results in a disordered structure with correlations up to 23 Å, resembling crystalline UiO-66. Heating leads to fast cluster aggregation, and further growth and ordering results in the crystalline product. Thus, SBUs are present already at room temperature and act as building blocks for MOF formation. The proposed formation steps provide insight for further development of MOF synthesis.     

Impact of the Nature of the Organic Spacer on the Crystallization Kinetics of UiO‐66(Zr)‐Type MOFs

The influence of the constitutive dicarboxylate linkers (size, functional group) over the crystallization kinetics of a series of porous Zr metal–organic frameworks with the UiO‐66 topology has been investigated by in situ time‐resolved energy dispersive X‐ray diffraction (EDXRD). Both large aromatic spacers (2,6‐naphthalene‐, 4,4′‐biphenyl‐ and 3,3′‐dichloro‐4,4′‐azobenzene‐dicarboxylates) and a series of X‐functionalized terephthalates (X=NH₂, NO₂, Br, CH₃) were investigated in dimethylformamide (DMF) at different temperatures and compared with the parent UiO‐66. Using different crystallization models, rate constants and further kinetic parameters (such as activation energy) have been extracted. Finally, the impact of the replacement of the toxic DMF by water on the crystallization kinetics was studied through the synthesis of the functionalized UiO‐66‐NO₂ solid.     

Representations of the Lie algebra of vector fields on a sphere

For an affine algebraic variety X we study a category of modules that admit compatible actions of both the algebra A of functions on X and the Lie algebra of vector fields on X. In particular, for the case when X is the sphere ${\mathbb{S}}^2$, we construct a set of simple modules that are finitely generated over A. In addition, we prove that the monoidal category that these modules generate is equivalent to the category of finite-dimensional rational ${\mathrm{GL}}_2$-modules.