Insights into the structure–photoreactivity relationships in well-defined perovskite ferroelectric KNbO3 nanowires

Structure–function correlations are a central theme in heterogeneous (photo)catalysis. In this study, the geometric and electronic structure of perovskite ferroelectric KNbO₃ nanowires with respective orthorhombic and monoclinic polymorphs have been systematically addressed. By virtue of aberration-corrected scanning transmission electron microscopy, we directly visualize surface photocatalytic active sites, measure local atomic displacements at an accuracy of several picometers, and quantify ferroelectric polarization combined with first-principles calculations. The photoreactivity of the as-prepared KNbO₃ nanowires is assessed toward aqueous rhodamine B degradation under UV light. A synergy between the ferroelectric polarization and electronic structure in photoreactivity enhancement is uncovered, which accounts for the prominent reactivity order: orthorhombic > monoclinic. Additionally, by identifying new photocatalytic products, rhodamine B degradation pathways involving N-deethylation and conjugated structure cleavage are proposed. Our findings not only provide new insights into the structure–photoreactivity relationships in perovskite ferroelectric photocatalysts, but also have broad implications in perovskite-based water splitting and photovoltaics, among others.     

A three‐dimensional coordination polymer based on the Zn4(μ3‐OH)2 unit: poly[[(μ4‐benzene‐1,4‐dicarboxylato)bis(μ3‐benzene‐1,4‐dicarboxylato)bis(μ3‐hydroxido)bis(1,10‐phenanthroline‐5,6‐dione)tetrazinc] dihydrate]

The title compound, {[Zn₄(C₈H₄O₄)₃(OH)₂(C₁₂H₆N₂O₂)₂]·2H₂O}_n, has been prepared hydrothermally by the reaction of Zn(NO₃)₂·6H₂O with benzene‐1,4‐dicarboxylic acid (H₂bdc) and 1,10‐phenanthroline‐5,6‐dione (pdon) in H₂O. In the crystal structure, a tetranuclear Zn₄(OH)₂ fragment is located on a crystallographic inversion centre which relates two subunits, each containing a [ZnN₂O₄] octahedron and a [ZnO₄] tetrahedron bridged by a μ₃‐OH group. The pdon ligand chelates to zinc through its two N atoms to form part of the [ZnN₂O₄] octahedron. The two crystallographically independent bdc²⁻ ligands are fully deprotonated and adopt μ₃‐κO:κO′:κO′′ and μ₄‐κO:κO′:κO′′:κO′′′ coordination modes, bridging three or four Zn^II cations, respectively, from two Zn₄(OH)₂ units. The Zn₄(OH)₂ fragment connects six neighbouring tetranuclear units through four μ₃‐bdc²⁻ and two μ₄‐bdc²⁻ ligands, forming a three‐dimensional framework with uninodal 6‐connected α‐Po topology, in which the tetranuclear Zn₄(OH)₂ units are considered as 6‐connected nodes and the bdc²⁻ ligands act as linkers. The uncoordinated water molecules are located on opposite sides of the Zn₄(OH)₂ unit and are connected to it through hydrogen‐bonding interactions involving hydroxide and carboxylate groups. The structure is further stabilized by extensive π–π interactions between the pdon and μ₄‐bdc²⁻ ligands.     

A three‐dimensional cadmium(II) coordination polymer with unequal homochiral double‐stranded concentric helical chains

A homochiral helical three‐dimensional coordination polymer, poly[[(μ₂‐acetato‐κ³O,O′:O)(hydroxido‐κO)(μ₄‐5‐nicotinamido‐1H‐1,2,3,4‐tetrazol‐1‐ido‐κ⁵N¹,O:N²:N⁴:N⁵)(μ₃‐5‐nicotinamido‐1H‐1,2,3,4‐tetrazol‐1‐ido‐κ⁴N¹,O:N²:N⁴:N⁵)dicadmium(II)] 0.75‐hydrate], {[Cd₂(C₇H₅N₆O)₂(CH₃COO)(OH)]·0.75H₂O}_n, was synthesized by the reaction of cadmium acetate, N‐(1H‐tetrazol‐5‐yl)isonicotinamide (H‐NTIA), ethanol and H₂O under hydrothermal conditions. The asymmetric unit contains two crystallographically independent Cd^II cations, two deprotonated 5‐nicotinamido‐1H‐1,2,3,4‐tetrazol‐1‐ide (NTIA⁻) ligands, one acetate anion, one hydroxide anion and three independent partially occupied water sites. The two Cd^II cations, with six‐coordinated octahedral and seven‐coordinated pentagonal bipyramidal geometries are located on general sites. The tetrazole group of one symmetry‐independent NTIA⁻ ligand links one of the independent Cd^II cations into 6₁ helical chains, while the other NTIA⁻ ligand links the other independent Cd^II cations into similar but unequal 6₁ helical chains. These chains, with a pitch of 24.937 (5) Å, intertwine into a double‐stranded helix. Each of the double‐stranded 6₁ helices is further connected to six adjacent helical chains through an acetate μ₂‐O atom and the tetrazole group of the NTIA⁻ ligand into a three‐dimensional framework. The helical channel is occupied by the isonicotinamide groups of NTIA⁻ ligands and two helices are connected to each other through the pyridine N and carbonyl O atoms of isonicotinamide groups. In addition, N—H...O and O—H...N hydrogen bonds exist in the complex.     

On the Global Solution of a 3‐D MHD System with Initial Data near Equilibrium

In this paper, we prove the global existence of smooth solutions to the three‐dimensional incompressible magnetohydrodynamical system with initial data close enough to the equilibrium state, (e₃,0). Compared with previous works by Lin, Xu, and Zhang and by Xu and Zhang, here we present a new Lagrangian formulation of the system, which is a damped wave equation and which is nondegenerate only in the direction of the initial magnetic field. Furthermore, we remove the admissible condition on the initial magnetic field, which was required in the earlier works. By using the Frobenius theorem and anisotropic Littlewood‐Paley theory for the Lagrangian formulation of the system, we achieve the global L¹‐in‐time Lipschitz estimate of the velocity field, which allows us to conclude the global existence of solutions to this system. In the case when the initial magnetic field is a constant vector, the large‐time decay rate of the solution is also obtained.© 2016 Wiley Periodicals, Inc.     

One-step synthesis of nitrogen-doped porous carbon for supercapacitors utilizing KNO<Subscript>3</Subscript> as an electrolyte

Nitrogen-doped porous carbons were prepared using a facile method, with low-biotechnology fulvic acid potassium salts as a precursor. The prepared carbons had a high surface area (1623 m² g^?1) and good electrochemical properties, making them suitable electrode materials for supercapacitors. Nitrogen-doped porous carbons were tested as an electrode in both 6 M KOH aqueous solution and different concentrations KNO₃ aqueous solution. The nitrogen-doped porous carbons with unique microstructure and nitrogen functionalities exhibited a capacitance of 235 F g^?1 in a 6 M KOH aqueous solution. Electrochemical investigation showed that the nitrogen-doped porous carbons exhibited a broad potential operational window in a 2.5 M KNO₃ aqueous solution. Furthermore, a high capacitance retention of 88.1 % was achieved even after 5000 cycles at 1.7 V. Potassium nitrate solutions in a wide range of concentrations were also proven to be promising electrolytes for electrochemical capacitors because they are cheap, noncorrosive, electrochemically stable, and compatible to diverse current collectors.     

用指数型整函数的最佳限制逼近

我们研究了由仅有实零点的代数多项式导出的微分算子确定的广义Sobolev类利用指数型整函数作为逼近工具的最佳限制逼近问题.利用Fourier变换和周期化等方法,得到在L_2(R)范数下的广义Sobolev光滑函数类的相对平均宽度和最佳限制逼近的精确常数,以及当0是这个代数多项式的一个至多2重的零点时,得到最佳限制逼近在L_1(R)范数和一致范数下的广义Sobolev类的精确到阶的结果.     

两类五阶解非线性方程组的迭代算法

本文首先根据Runge-Kutta方法的思想,结合Newton迭代法,提出了一类带参数的解非线性方程组F(x)=0的迭代算法,然后基于解非线性方程f(x)=0的King算法,给出第二类解非线性方程组的迭代算法,收敛性分析表明这两类算法都是五阶收敛的.其次给出了本文两类算法的效率指数,以及一些已知算法的效率指数,并且将本文算法的效率指数与其它方法进行详细的比较,通过效率比率R_(i,j)可知本文算法具有较高的计算效率.最后给出了四个数值实例,将本文两类算法与现有的几种算法进行比较,实验结果说明本文算法收敛速度快,迭代次数少,有明显的优势.     

Some results on linear codes over the ring $$\mathbb {Z}_4+u\mathbb {Z}_4+v\mathbb {Z}_4+uv\mathbb {Z}_4$$

In this paper, we mainly study the theory of linear codes over the ring \(R =\mathbb {Z}_4+u\mathbb {Z}_4+v\mathbb {Z}_4+uv\mathbb {Z}_4\). By using the Chinese Remainder Theorem, we prove that R is isomorphic to a direct sum of four rings. We define a Gray map \(\Phi \) from \(R^{n}\) to \(\mathbb {Z}_4^{4n}\), which is a distance preserving map. The Gray image of a cyclic code over R is a linear code over \(\mathbb {Z}_4\). We also discuss some properties of MDS codes over R. Furthermore, we study the MacWilliams identities of linear codes over R and give the generator polynomials of cyclic codes over R.     

New algebraic structures from Hermitian one-matrix model

Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field Theory (CFT) method. From multi-loop equations of the one-matrix model, we get a more general constraint. It can be expressed in terms of the operator algebras, which is the Virasoro subalgebra with extra parameters. In this sense, we named as generalized Virasoro constraint. We enlarge this algebra with central extension, this is a new kind of algebra, and the usual Virasoro algebra is its subalgebra. And we give a bosonic realization of its subalgebra.     

锰离子氧化沉淀法实现锂离子电池LiNi0.8Co0.05Mn0.15O2材料的回收和利用

以浓盐酸为浸出剂,以NaOH和NH₄HCO₃为沉淀剂,利用Mn²⁺在碱性条件下的氧化反应改变离子的沉淀次序进而分步回收的方案,探究了浓盐酸酸浸处理三元正极材料LiNi_0.8Co_0.05Mn_0.15O₂的最佳条件。在分步沉淀过程中,Mn²⁺被氧化为不溶于非还原性酸的MnO （OH）₂,并在酸性条件下回收。Ni、Co则在碱性条件下利用NaOH回收,而Li则利用NH₄HCO₃回收。该方法中Mn的回收率达到85.1%,产品纯度达到98.6%; Li的回收率达到95.0%,产品纯度达到99.3%。由回收材料重新合成的三元正极组装的软包电池的首圈放电比容量达到了175 mAh·g^-1,可以以超过99.5%的库仑效率稳定循环50圈。