Self-similar asymptotic behavior for the solutions of a linear coagulation equation

In this paper we consider the long-time asymptotics of a linear version of the Smoluchowski equation which describes the evolution of a tagged particle moving in a random distribution of fixed particles. The volumes v of these particles are independently distributed according to a probability distribution which decays asymptotically as a power law $v^{?\sigma }$. The validity of the equation has been rigorously proved in [22] taking as a starting point a particle model and for values of the exponent $\sigma >3$, but the model can be expected to be valid, on heuristic grounds, for $\sigma >\frac{5}{3}$. The resulting equation is a non-local linear degenerate parabolic equation. The solutions of this equation display a rich structure of different asymptotic behaviors according to the different values of the exponent σ. Here we show that for $\frac{5}{3}<\sigma <2$ the linear Smoluchowski equation is well-posed and that there exists a unique self-similar profile which is asymptotically stable.     

Asymmetric Reactions involving Lewis Base Catalyst Tethered Dearomatized Intermediates

Numerous protocols have been developed for the functionalization of aromatic substances. Among them, the strategy by which aromatic substrates are activated in situ to generate dearomatized intermediates is highly efficient but challenging, especially in the field of asymmetric catalysis. In this Concept article, the application of some well-established chiral Lewis base catalysis, including primary/secondary amines and N-heterocyclic carbenes, that can covalently form catalyst-tethered dearomatized ortho/para-quinodimethane species with diverse heteroaryl and aryl carbonyl substrates is summarized in a number of asymmetric cycloaddition and addition reactions with diverse reagents generally having electrophilic properties. As a result, a variety of enantioenriched aromatic products with higher molecular complexity are constructed effectively through a rearomatization process.     

Imide-Functionalized Polymer Semiconductors

Imide-functionalized π-conjugated polymer semiconductors have received a great deal of interest owing to their unique physicochemical properties and optoelectronic characteristics, including excellent solubility, highly planar backbones, widely tunable band gaps and energy levels of frontier molecular orbitals, and good film morphology. The organic electronics community has witnessed rapid expansion of the materials library and remarkable improvement in device performance recently. This review summarizes the development of imide-functionalized polymer semiconductors as well as their device performance in organic thin-film transistors and polymer solar cells, mainly achieved in the past three years. The materials mainly cover naphthalene diimide, perylene diimide, and bithiophene imide, and other imide-based polymer semiconductors are also discussed. The perspective offers our insights for developing new imide-functionalized building blocks and polymer semiconductors with optimized optoelectronic properties. We hope that this review will generate more research interest in the community to realize further improved device performance by developing new imide-functionalized polymer semiconductors.     

Cytotoxicity of Shear Exfoliated Pnictogen (As,Sb, Bi) Nanosheets

The experimental achievement of phosphorene, which exhibits superior electronic, physical, and optical properties has spurred recent interest in other Group 15 elemental 2D nanomaterials such as arsenene, antimonene, and bismuthene. These unique and superior properties of the pnictogen nanosheets have spurred intensive research efforts and led to the discovery of their diversified potential applications; for instance, optical Kerr material, photonic devices, pnictogen-decorated microfibers, high-speed transistors, and flexible 2D electronics. Previous studies have mainly been dedicated to study the synthesis, properties, and applications of the heavy pnictogens nanosheets; however, the toxicological behaviour of these nanosheets has yet to be established. Herein, the cytotoxicity study of pnictogen nanosheets (As, Sb, and Bi) was conducted over 24 h of incubation with various concentrations of test materials and adenocarcinoma human lung epithelial A549 cells. After the treatment period, the remaining cell viabilities were obtained through absorbance measurements with WST-8 and MTT assays. These findings demonstrate that the toxicity of pnictogen nanosheets decreases down Group 15, whereby arsenic nanosheets are considered to be the most toxic, whereas bismuth nanosheets induce low cytotoxicity. The findings of this study constitute an important initial step towards enhancing our understanding of the toxicological effects of pnictogen nanosheets in light of their prospective commercial applications.     

Construction of Cyclobutanes by Multicomponent Cascade Reactions in Homogeneous Solution through Visible-Light Catalysis

[2+2] Photocycloaddition of two olefins is a general method to assemble the core scaffold, cyclobutane, found in numerous bioactive molecules. A new approach to synthesize cyclobutanes through multicomponent cascade reactions by merging aldol reaction and Witting reaction with visible-light-induced [2+2] cycloaddition is reported. An array of cyclobutanes with high selectivity has been achieved from commercially available aldehydes, ketones (or phosphorus ylide), and olefins with visible-light irradiation of a catalytic amount of (fac-tris(2-phenylpyridinato-C₂,N)iridium) ([Ir(ppy)₃]) at room temperature. Control experiments and spectroscopic studies revealed that the triplet–triplet energy transfer from the excited [Ir(ppy)₃]* to enones, generated in situ from aldehyde and ketone or aldehyde and phosphorus ylide, is responsible for these simple and efficient muticomponent transformations.     

Enantioselective C2-Alkylation of Indoles through a Redox-Relay Heck Reaction of 2-Indole Triflates

A palladium-catalyzed enantioselective redox-relay Heck reaction of 2-indole triflates and disubstituted alkenes is reported. This process combines readily available indole triflates with a variety of alkenes to afford a range of indole derivatives bearing a stereocenter adjacent to C2. Enantioselectivity is achieved through use of a simple pyridine-oxazoline ligand. Tuning the electronics of the indole, through judicious choice of N-protecting group, is required to ensure selective β-hydride elimination away from the indole core. Utility of this method is highlighted in a modular formal synthesis of an S1P₁ agonist precursor developed by Merck.     

Conformational Changes and Redox Properties of Bimetallic Single Helicates of Hexapyrrole-α,ω-dicarbaldehydes

The hexapyrrole-α,ω-dicarbaldehydes 1 a and 1 b were metallated with Cu^II, Ni^II, and Pd^II to give bimetallic complexes where a pair of 3 N+O four-coordinate metal planes are helically distorted and the central 2,2′-bipyrrole subunit adopts a cis or trans conformation. X-ray crystallographic analysis of the bisCu complex revealed a closed form with a cis-2,2′-bipyrrole subunit and an open form with a trans-2,2′-bipyrrole subunit. The bisPd complexes took a closed form both in the solid state and in solution. They are regarded as single helicates of two turns and the energy barrier for the interchange between an M helix and a P helix was remarkably influenced by the bulky 3,3′-substituent of the central 2,2′-bipyrrole subunit. Although the bisNi complexes adopt a closed form in the solid state, they exist as a homohelical open C₂-symmetric form or a heterohelical open C_i-symmetric form in solution. A theoretical study suggested that the closed form of 1 a Pd was stabilized by the Pd–Pd interaction. Compound 1 a Pd was reversibly oxidized by one electron at 0.14 V versus ferrocene/ferrocenium (Fc/Fc⁺) and this oxidized species showed Vis/NIR absorption bands at λ=767 and 1408 nm.     

Excited-State Dynamics of Thienoguanosine,an Isomorphic Highly Fluorescent Analogue of Guanosine

Thienoguanosine (^thG) is an isomorphic analogue of guanosine with promising potentialities as fluorescent DNA label. As a free probe in protic solvents, ^thG exists in two tautomeric forms, identified as the H1, being the only one observed in nonprotic solvents, and H3 keto–amino tautomers. We herein investigate the photophysics of ^thG in solvents of different polarity, from water to dioxane, by combining time-resolved fluorescence with PCM/TD-DFT and CASSCF calculations. Fluorescence lifetimes of 14.5–20.5 and 7–13 ns were observed for the H1 and H3 tautomers, respectively, in the tested solvents. In methanol and ethanol, an additional fluorescent decay lifetime (≈3 ns) at the blue emission side (λ≈430 nm) as well as a 0.5 ns component with negative amplitude at the red edge of the spectrum, typical of an excited-state reaction, were observed. Our computational analysis explains the solvent effects observed on the tautomeric equilibrium. The main radiative and nonradiative deactivation routes have been mapped by PCM/TD-DFT calculations in solution and CASSCF in the gas phase. The most easily accessible conical intersection, involving an out-of plane motion of the sulfur atom in the five-membered ring of ^thG, is separated by a sizeable energy barrier (≥0.4 eV) from the minimum of the spectroscopic state, which explains the large experimental fluorescence quantum yield.     

Hydrogel-Derived Honeycomb Ni3S4/N,P-C as an Efficient Oxygen Evolution Catalyst

The development of high-efficiency electrocatalysts with low costs for the oxygen evolution reaction (OER) is essential, but remains challenging. Herein, a new synthetic process is proposed to prepare Ni₃S₄ particles embedded in N,P-codoped honeycomb porous carbon aerogels (Ni₃S₄/N,P-HPC) through a hydrogel approach. The preparation of Ni₃S₄/N,P-HPC begins with the sol–gel polymerization of tripolyphosphate, chitosan, and guanidine polymer that contains metal-binding sites, allowing for the uniform incorporation of Ni ions into the gel matrix, freeze-drying, and subsequent carbonization under an inert atmosphere. This synthesis resolves difficulties in synthesizing the pure Ni₃S₄ phase caused by the instability of Ni₃S₄ at high temperature, while affording good control of the porous structure and N,P-doping of carbon aerogels. The synergy between the structural advantages of N,P-carbon aerogels (such as easily accessible active sites, high specific surface area, and excellent electron transport) and the intrinsic electrochemical properties of Ni₃S₄ result in the outstanding OER performance of Ni₃S₄/N,P-HPC, with overpotentials as low as 0.37 V at 10 mA cm⁻². The work outlined herein offers a simple and effective method for the development of carbon-based electrocatalysts for renewable energy conversion.     

Directing-Group-Free C7-Alkylations of N-Alkylindoles Mediated by Cationic Zirconium Complexes: Role of Brønsted Acid for Catalytic Manifold

Highly position selective alkylations of N-alkylindoles at C7-positions have been enabled by cationic zirconium complexes. The strategy provides a straightforward access to install alkyl groups at C7-positions of indoles without a complex directing group. Mechanistic studies provided support for the importance of Brønsted acids in the catalytic manifold.