A New Regularity Criterion for the 3D Navier-Stokes Equations via Two Entries of the Velocity Gradient Tensor

We consider the Cauchy problem for the incompressible Navier-Stokes equations in R ³, and provide a new regularity criterion involving only two entries of the Jacobian matrix of the velocity field.     

Aggregation-induced emission of siloles

Aggregation-induced emission (AIE) is a unique and significant photophysical phenomenon that differs greatly from the commonly acknowledged aggregation-caused emission quenching observed for many π-conjugated planar chromophores. The mechanistic decipherment of the AIE phenomenon is of high importance for the advance of new AIE systems and exploitation of their potential applications. Propeller-like 2,3,4,5-tetraphenylsiloles are archetypal AIE-active luminogens, and have been adopted as a core part in the design of numerous luminescent materials with diverse functionalities. In this review article, we elucidate the impacts of substituents on the AIE activity and shed light on the structure–property relationship of siloles, with the aim of promoting the judicious design of AIE-active functional materials in the future. Recent representative advances of new silole-based functional materials and their potential applications are reviewed as well.     

Tetraphenylpyrazine-based AIEgens: facile preparation and tunable light emission

Research on aggregation-induced emission (AIE) has been a hot topic. Due to enthusiastic efforts by many researchers, hundreds of AIE luminogens (AIEgens) have been generated which were mainly based on archetypal silole, tetraphenylethene, distyrylanthracene, triphenylethene, and tetraphenyl-1,4-butadiene, etc. To enlarge the family of AIEgens and to enrich their functions, new AIEgens are in high demand. In this work, we report a new kind of AIEgen based on tetraphenylpyrazine (TPP), which could be readily prepared under mild reaction conditions. Furthermore, we show that the TPP derivatives possess a good thermal stability and their emission could be fine-tuned by varying the substituents on their phenyl rings. It is anticipated that TPP derivatives could serve as a new type of widely utilized AIEgen, based on their facile preparation, good thermo-, photo- and chemostabilities, and efficient emission.     

Remarks on the regularity criteria for generalized MHD equations

We study the Cauchy problem for the generalized MHD equations, and prove some regularity criteria involving the integrability of ∇u in the Morrey, multiplier spaces.     

Homochiral nickel coordination polymers based on salen(Ni) metalloligands: synthesis, structure, and catalytic alkene epoxidation

One-dimensional (1D) homochiral nickel coordination polymers [Ni(3)(bpdc)(RR-L)(2)·(DMF)](n) (2R, RR-L = (R,R)-(-)-1,2-cyclohexanediamino-N,N'-bis(3-tert-butyl-5-(4-pyridyl)salicylidene), bpdc = 4,4'-biphenyldicarboxylic acid) and [Ni(3)(bpdc)(SS-L)(2)·(DMF)](n) (2S, SS-L = (S,S)-(-)-1,2-cyclohexanediamino-N,N'-bis(3-tert-butyl-5-(4-pyridyl)salicylidene) based on enantiopure pyridyl-functionalized salen(Ni) metalloligand units NiL ((1,2-cyclohexanediamino-N,N'-bis(3-tert-butyl-5-(4-pyridyl)salicylidene))Ni(II)) have been synthesized and characterized by microanalysis, IR spectroscopy, solid-state UV-vis spectroscopy, thermogravimetric analysis (TGA), circular dichroism (CD) spectroscopy, cyclic voltammetric measurement, and powder and single crystal X-ray diffraction. Each NiL as unbridging pendant metalloligand uses one terminal pyridyl group to coordinate achiral unit (nickel and bpdc(2-)) building a helical chain, while the other pyridyl group remains uncoordinated. Both 2R and 2S contain left- and right-handed helical chains made of the achiral building blocks, while the NiL as remote external chiral source is perpendicular to the backbone of the helices. The nickel coordination polymers 2R and 2S containing unsaturated active nickel center in metalloligand NiL can be used as self-supported heterogeneous catalysts. They show catalytic activity comparable with their homogeneous counterpart in alkene epoxidation and exhibit great potential as recyclable catalysts.     

Electrochemical survey: the effect of the cage size and structure on the electronic structures of a series of ytterbium metallofullerenes

The electrochemical properties of a series of metallofullerenes with different cages, namely, Yb@C74(II), Yb@C76(I, II), Yb@C78, Yb@C80, Yb@C82(I, II, III), and Yb@C84(II, III, IV), have been systematically investigated by cyclic and differential pulse voltammetry experiments for the first time. This article discusses the electronic structures of these metallofullerenes based on the results from these experiments. From previous electrochemical work and the above discussion, it is concluded that the nondegenerate LUMO is a common characteristic of the electronic structures of the higher fullerenes and monometallofullerenes. In addition, the effect of the cage on the electronic structure and properties of the metallofullerene is estimated from the plot of the reduction potential versus the carbon number of the metallofullerene. This estimation shows that usually the electronic structure and properties of the metallofullerene vary with cage size and structure. The cage structure is of particular importance for determining the electronic structure and properties. Moreover, an explanation concerning the abundance and stability of C82-based trivalent monometallofullerenes is given from an electronic structural standpoint.     

Remarks on the a priori bound for the vorticity of the axisymmetric Navier-Stokes equations

Applications of Mathematics - We study the axisymmetric Navier-Stokes equations. In 2010, Loftus-Zhang used a refined test function and re-scaling scheme, and showed that $$\left| {{\omega...     

Self-healing hyperbranched polytriazoles prepared by metal-free click polymerization of propiolate and azide monomers

The last decade has witnessed the quick develop of self-healing materials. As a newborn strategy, the alternative of irreversible covalent bond formation is, however, to be further developed. In this paper, self-healing hyperbranched poly(aroxycarbonyltriazole) based on such mechanism were prepared by our developed metal-free click polymerization of simplified dipropiolate and triazide. Thanks to their excellent processability and film-forming ability, high quality homogeneous films free from defects were obtained by casting. The cut films could be healed by stacking or pressing the halves together at room temperature and elevated temperature. Thus, this design concept for self-healing materials should be generally applicable to other hyperbranched polymers with reactive groups on their peripheries.     

Electrosynthesis and characterization of 1,2-dibenzyl C60: a revisit

A reinvestigation of the reaction between C60(2-) and benzyl bromide in benzonitrile containing 0.1 M tetra-n-butylammonium perchlorate (TBAP) has shown that there are more reaction products than previously reported. Use of a silica rather than a "Buckyclutcher I" column for HPLC purification led to isolation of two previously unattained products in the reaction mixture, one of which was identified as 1,2-(PhCH2)2C60 by UV-vis and NMR . The earlier incorrectly assigned 1,2-(PhCH2)2C60 was identified as the methanofullerene C61HPh by X-ray single-crystal diffraction. The electrochemistry of genuine 1,2-(PhCH2)2C60 shows that its first reduction potential in PhCN containing 0.1 M TBAP is cathodically shifted by 100 mV with respect to E1/2 for reduction of 1,4-(PhCH2)2C60, indicating that the addition pattern significantly affects the electrochemistry of derivatized C60. Visible and near-IR spectra of the monoanion and dianion of 1,2-(PhCH2)2C60 are also reported.     

Aggregation-induced delayed fluorescence luminogens: the innovation of purely organic emitters for aqueous electrochemiluminescence

Due to overcoming the limitation of aggregation caused quenching (ACQ) of solid-state emitters, aggregation-induced emission (AIE) organic luminogens have become a promising candidate in aqueous electrochemiluminescence (ECL). However, restricted by the physical nature of fluorescence, current organic AIE luminogen-based ECL (AIECL) faces the bottleneck of low ECL efficiency. Here, we propose to construct de novo aqueous ECL based on aggregation-induced delayed fluorescence (AIDF) luminogens, called AIDF-ECL. Compared with the previous organic AIE luminogens, purely organic AIDF luminogens integrate the superiorities of both AIE and the utilization of dark triplets via thermal-activated spin up-conversion properties, thereby possessing the capability of close-to-unity exciton utilization for ECL. The results show that the ECL characteristics using AIDF luminogens are directly related to their AIDF properties. Compared with an AIECL control sample based on a tetraphenylethylene AIE moiety, the ECL efficiency of our AIDF-ECL model system is improved by 5.4 times, confirming the excellent effectiveness of this innovative strategy.

Electrochemiluminescence (ECL) using an aggregation-induced delayed fluorescence (AIDF) organic luminogen, i.e. AIDF-ECL, was reported for the first time, featuring “lighting” dark triplets (ca. 75% in total) for all-exciton-harvesting ECL applications.