New lower bounds on the radius of spatial analyticity for the KdV equation

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{?1/4}$ as time t goes to infinity. This improves the works of Selberg and da Silva (2017) [30] and Tesfahun (2017) [34]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the I-method.     

Synthesis of Highly Functionalized N,N-Diarylamides by an Anodic C,N-Coupling Reaction

We report an innovative, sustainable and straightforward protocol for the synthesis of N,N-diarylamides equipped with nonprotected hydroxyl groups by using electrosynthesis. The concept allows the application of various substrates furnishing diarylamides with yields up to 57 % within a single and direct electrolytic protocol. The method is thereby easy to conduct in an undivided cell with constant current conditions offering a versatile and short-cut alternative to conventional pathways.     

Nitroxide‐Mediated Polymerization of Bio‐Based Farnesene with a Functionalized Methacrylate

Farnesene (Far) is a bio‐based terpene monomer that is similar in structure to commercially used dienes like butadiene and isoprene. Nitroxide‐mediated polymerization (NMP) is adept for the polymerization of dienes, but not particularly effective at controlling the polymerization of methacrylates using commercial nitroxides. In this study, Far is statistically copolymerized with a functional methacrylate, glycidyl methacrylate (GMA), by NMP using N‐succinimidyl modified commercial BlocBuilder (NHS‐BB) initiator. Reactivity ratios are determined to be r _Far = 0.54 ± 0.04 and r _GMA = 0.24 ± 0.02. The ability of the poly(Far‐stat‐GMA) chains to reinitiate for chain extension with styrene showed a clear shift in molecular weight and monomodal distribution. Copolymerizations using a new alkoxyamine, Dispolreg 007 (D7), is explored as it is shown to homopolymerize methacrylates, but not yet reported for statistical copolymerizations. Bimodal molecular weight distributions are observed when an equimolar ratio of Far and GMA is copolymerized with D7 due to slow decomposition of the initiator, but chain ends are active as shown by successful chain extension with styrene. Both NHS‐BB and D7 initiators are used to synthesize poly[Far‐b‐(GMA‐stat‐Far)] and poly(Far‐b‐GMA) diblock copolymers. While the NHS‐BB initiated polymer chains have lower dispersity, D7 exhibits more linear polymerization kinetics and maintains more active chain ends.     

Red shifting of absorption maxima of phenothiazine based dyes by incorporating electron-deficient thiadiazole derivatives as π-spacer

This study was carried out to design phenothiazine based dyes by incorporating electron-deficient thiadiazole derivatives as π-spacer. Density functional theory and time-dependent density functional theory calculations of the geometries, electronic structures and absorption spectra of the dyes before and after binding to titanium oxide were carried out. Effects of the electron-deficient units on the spectra and electrochemical properties have been investigated. Compared with the reference compound CS1A, Dyes 1–4 display remarkably enhanced spectral responses in the red portion of the solar spectrum. The newly designed dyes demonstrate desirable energetic and spectroscopic parameters, and may lead to efficient metal-free organic dye sensitizers for DSSCs.     

Kinetics and mechanism of trichloroisocyanuric acid/NaNO2-triggered nitration of aromatic compounds under acid-free and Vilsmeier-Haack conditions

Kinetics and mechanism of nitration of aromatic compounds using trichloroisocyanuric acid (TCCA)/NaNO₂, TCCA-N,N-dimethyl formamide (TCCA-DMF)/NaNO₂, and TCCA-N,N-dimethyl acetamide (TCCA-DMA)/NaNO₂ under acid-free and Vilsmeier-Haack conditions. Reactions followed second-order kinetics with a first-order dependence on [Phenol] and [Nitrating agent] ([TCCA], [(TCCA-DMF)], or [(TCCA-DMA)] >> [NaNO₂]). Reaction rates accelerated with the introduction of electron-donating groups and retarded with electron-withdrawing groups, but did not fit well into the Hammett's theory of linear free energy relationship or its modified forms like Brown-Okamoto or Yukawa-Tsuno equations. Rate data were analyzed by Charton's multiple linear regression analysis. Isokinetic temperature (β) values, obtained from Exner's theory for different protocols, are 403.7 K (TCCA-NaNO₂), 365.8 K (TCCA-DMF)/NaNO₂, and 358 K (TCCA-DMA)/NaNO₂. These values are far above the experimental temperature range (303-323 K), indicating that the enthalpy factors are probably more important in controlling the reaction.     

Stereoselective Cascade Cyclizations with Samarium Diiodide to Tetracyclic Indolines: Precursors of Fluorostrychnines and Brucine

A series of γ-indolylketones with fluorine, cyano or alkoxy substituents at the benzene moiety was prepared and subjected to samarium diiodide-promoted cyclization reactions. The desired dearomatizing ketyl cascade reaction forming two new rings proceeded in all cases with high diastereoselectivity, but with differing product distribution. In most cases, the desired annulated tetracyclic compounds were obtained in moderate to good yields, but as second product tetracyclic spirolactones were isolated in up to 29 % yield. The reaction rate was influenced by the substituents at the benzene moiety of the substrate as expected, with electron-accepting groups accelerating and electron-donating groups decelerating the cyclization process. In case of a difluoro-substituted γ-indolylketone a partial defluorination was observed. The intermediate samarium enolate of the tetracyclic products could be trapped by adding reactive alkylating agents as electrophiles delivering products with quarternary carbons. In the case of a dimethoxy-substituted tetracyclic cyclization product a subsequent reductive amination stereoselectively provided a pentacyclic compound that was subsequently N-protected and subjected to a regioselective elimination. The obtained functionalized pentacyclic product should be convertible into the alkaloid brucine by four well-established steps. Overall, the presented report shows that functionalized tetracyclic compounds with different substituents are rapidly available with the samarium diiodide cascade cyclization as crucial step. Hence, analogues of the landmark alkaloid strychnine, for example, with specific fluorine substitutions, should be easily accessible.     

Room-Temperature,Metal-Free,and One-Pot Preparation of 2H-Indazoles through a Mills Reaction and Cyclization Sequence

The Mills reaction and cyclization of readily available 2-aminobenzyl alcohols and nitrosobenzenes using thionyl bromide provided 2H-indazoles in up to 88 % yields. In the metal-free process, acetic acid played a crucial role for the both Mills reaction and cyclization. A brominated 2H-indazole could also be obtained through the one-pot sequence.     

Pentapnictogen heterocyclic monoanions: Structure,stability, and aromaticity

Inorganic planar ring-shape molecules with 4n + 2 π electrons are always the focus of experimental synthesis and theoretical research due to their potential aromaticity and stability. In this work, the whole series of five-membered heterocycle monoanions X _nY_5-n⁻ (X, Y = group 15 elements; n = 1-4) were thoroughly investigated by means of density functional theory calculations. They all have large formation energies and HOMO-LUMO gap energies, suggesting the potential thermodynamic and kinetic stability. Their aromaticities are comparable to that of typical aromatic hydrocarbons. Their thermal stabilities were firmly established by the ab initio molecular dynamics simulations. As most of them are predicted for the first time, their various spectra were simulated for experimental characterization. Furthermore, we demonstrate that these five-membered cyclic anions can be employed as η⁵-ligand to construct novel all-inorganic metallocenes, which may serve as the building blocks of low-dimensional nanomaterials.     

The Effect of Viscosity on the Diffusion and Termination Reaction of Organic Radical Pairs

The effect of viscosity on the diffusion efficiency (F_dif) of an organic radical pair in a solvent cage and the termination mechanism, that is, the selectivity of disproportionation (Disp) and combination (Comb) of the geminated caged radical pair and the diffused radicals encountered, were investigated quantitatively by following the photolysis of dimethyl 2,2′-azobis(2-methylpropionate) (V-601) in the absence and presence of PhSD. F_dif and Disp/Comb selectivity outside the cage [Disp_(dif)/Comb_(dif)] are highly sensitive to the viscosity. In contrast, the Disp/Comb selectivity inside the cage [Disp_(cage)/Comb_(cage)] is rather insensitive. The difference in viscosity dependence between Disp_(cage)/Comb_(cage) and Disp_(dif)/Comb_(dif) is explained by the spin state of the radical pair inside and outside the cage and the spin state dependent configurational changes of the radical pair upon their collision. Given that the configurational change of the radicals associates the displacement and reorganization of solvents around the radicals, the termination outside the cage, which requires larger change than that inside the cage, is highly viscosity dependent. Furthermore, while the bulk viscosity of each solvent shows good correlation with F_dif and Disp/Comb selectivity, microviscosity is the better parameter predicting F_dif and Disp_(dif)/Comb_(dif) selectivity regardless of the solvents.     

Effective permittivity of liquid crystal nanodispersions and composites with different pore structure

The volume filling fraction dependence of the effective permittivity of the nematic liquid crystal 4-n-pentyl-4’-cyanobiphenyl embedded in different porous membranes and dispersed with aerosil nanoparticles was determined using broadband dielectric spectroscopy in the frequency range from 10⁶ to 10⁹ Hz. The experimental data were analyzed and compared with some existing theories based on the effective medium approximation and their modifications. The obtained effective permittivities as a function of the volume filling fraction lie between the lower limits of the Wiener and Hashin–Shtrikman bounds. The observed shift of the experimental points reflects the changes in the structure of the investigated composites.