Nonexistence of nontrivial global solutions for nonlocal in time differential inequalities

In this paper, some nonlocal in time differential inequalities of Sobolev type are considered. Using the nonlinear capacity method, sufficient conditions for the nonexistence of nontrivial global classical solutions are provided.     

Optimal time delays in a class of reaction-diffusion equations

ABSTRACT

A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equation to the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays.     

QbD approached comparison of reaction mechanism in microwave synthesized gold nanoparticles and their superior catalytic role against hazardous nirto‐dye

Microwave irradiation (MI) process characteristically enables extremely rapid “in‐core” heating of dipoles and ions, in comparison to conventional thermal (conductance) process of heat transfer. During the process of nanoparticles synthesis, MI both modulates functionality behaviors as well as dynamic of reaction in favorable direction. So, MI providing a facile, favorable and alternative approach during nanoparticles synthesis nanoparticles with enhanced catalytic performances. Although, conventionally used reducing and capping reagents of synthetic origin, are usually environmentally hazardous and toxic for living organism. But, in absence of suitable capping agent; stability, shelf life and catalytic activity of metallic nanoparticles adversely affected. However, polymeric templates which emerged as suitable choice of agent for both reducing and capping purposes; bearing additional advantages in terms of catalyst free one step green synthesis process with high degree of biosafety and efficiency. Another aspect of current works was to understand role of process variables in growth mechanism and catalytic performances of microwave processed metallic nanoparticles, as well as comparison of these parameters with conventional heating method. However, due to poor prediction ability with previously published architect OFAT (One factor at a time) design with these nanoparticles as well as random selection of process variables with their different levels, such comparison couldn't be possible. Hence, using gum Ghatti (Anogeissus latifolia) as a model bio‐template and under simulated reaction conditions; architect of QbD design systems were integrated in microwave processed nanoparticles to establish mechanistic role these variables. Furthermore, in comparison to conventional heating; we reported well validated mathematical modeling of process variables on characteristic of nanoparticles as well as synthesized gold nanoparticles of desired and identical dimensions, in both thermal and microwave‐based processes. Interestingly, despite of identical dimension, MI processed gold nanoparticles bearing higher efficiency (kinetic rate) against remediation of hazardous nitro dye (4‐nitrophenol), into safer amino (4‐aminophenol) analogues.     

Finely dispersed palladium on silk‐fibroin as an efficient and ligand‐free catalyst for Heck cross‐coupling reaction

A palladium–fibroin complex (Pd/Fib.) was prepared by the addition of sonicated fibroin fiber in water to palladium acetate solution. Pd (OAc)₂ was absorbed by fibroin and reduced with NaBH₄ at room temperature to the Pd(0) nanoparticles. Powder‐X‐ray diffraction, scanning electron microscopy–energy‐dispersive X‐ray spectroscopy, Fourier transform‐infrared, CHN elemental analysis and inductively coupled plasma‐atomic emission spectroscopy were carried out to characterize the Pd/Fib. catalyst. Catalytic activity of this finely dispersed palladium was examined in the Heck coupling reaction. The catalytic coupling of aryl halides (‐Cl, ‐Br, ‐I) and olefins led to the formation of the corresponding coupled products in moderate to high yields under air atmosphere. A variety of substrates, including electron‐rich and electron‐poor aryl halides, were converted smoothly to the targeted products in simple procedure. Heterogeneous supported Pd catalyst can be recycled and reused several times.     

An unexpected Pummerer rearrangement in the synthetic route to ethyl (2′-hydroxy-4′,5′-methylenedioxyphenyl)acetate: An alternative approach to 2,3-dimethylthio benzofurans

The synthesis of ethyl (2′-hydroxy-4′,5′-methylendioxophenyl)acetate, a fragment of the antihyperglycemic natural coumarin subcoriacin, is reported. We found an expeditious route to the title compound in five steps. Final metal catalyzed acid ethanolysis of the vinylic 1,1-methylthio methylsulfoxide derivative afforded the required aryl acetic ester, but in the absence of metal catalyst, an unexpected Pummerer rearrangement produced the 2,3-dimethylthiofuran derivative as the major product. This last result provides an alternative entry to 2,3-dimethlythiobenzofurans.     

Synthesis of α-fluoro-α,β-unsaturated esters monitored by 1D and 2D benchtop NMR spectroscopy

For optimization and control of pharmaceutically and industrially important reactions, chemical information is required in real time. Instrument size, handling, and operation costs are important criteria to be considered when choosing a suitable analytical method apart from sensitivity and resolution. This present study explores the use of a robust and compact nuclear magnetic resonance (NMR) spectrometer to monitor the stereo-selective formation of α-fluoro-α,β-unsaturated esters from α-fluoro-β-keto esters via deprotonation and deacylation in real time. These compounds are precursors of various pharmaceutically active substances. The real-time study revealed the deprotonation and deacylation steps of the reaction. The reaction was studied at temperatures ranging from 293 to 333 K by interleaved one-dimensional ¹H and ¹⁹F and two-dimensional ¹H–¹H COSY experiments. The kinetic rate constants were evaluated using a pseudo first-order kinetic model. The activation energies for the deprotonation and deacylation steps were determined to 28 ± 2 and 63.5 ± 8 kJ/mol, respectively. This showed that the deprotonation step is fast compared with the deacylation step and that the deacylation step determines the rate of the overall reaction. The reaction was repeated three times at 293 K to monitor the repeatability and stability of the system. The compact NMR spectrometer provided detailed information on the mechanism and kinetics of the reaction, which is essential for optimizing the synthetic routes for stepwise syntheses of pharmaceutically active substances.     

Screening of Three Transition Metal‐Mediated Reactions Compatible with DNA‐Encoded Chemical Libraries

The construction of DNA‐encoded chemical libraries (DECLs) crucially relies on the availability of chemical reactions, which are DNA‐compatible and which exhibit high conversion rates for a large number of diverse substrates. In this work, we present our optimization and validation procedures for three copper and palladium‐catalyzed reactions (Suzuki cross‐coupling, Sonogashira cross‐coupling, and copper(I)‐catalyzed alkyne‐azide cycloaddition (CuAAC)), which have been successfully used by our group for the construction of large encoded libraries.     

Reversible Activation of Water by an Air- and Moisture-Stable Frustrated Rhodium Nitrogen Lewis Pair

[Cp*Rh(κ³N,N′,P- L )][SbF₆] (Cp*=C₅Me₅), bearing a guanidine-derived phosphano ligand L , behaves as a “dormant” frustrated Lewis pair and activates H₂ and H₂O in a reversible manner. When D₂O is employed, a facile H/D exchange at the Cp* ring takes place through sequential C(sp³)−H bond activation.     

High-Throughput Synthesis and Characterization of Aryl Silicones by Using the Piers–Rubinsztajn Reaction

Arylsilicones are widely exploited for their thermal and optical properties. The creation of phenylsilicone elastomers with specific physical properties is typically done by a “one-off” formulation and test process. Herein, it is demonstrated that high-throughput synthesis methods can be used to rapidly prepare a series of arylsilicone elastomers and then the relative impact of different aryl groups on their physical properties is assessed. Aromatic groups were incorporated into polydimethylsiloxane (PDMS) elastomers by exploiting the relative reactivity of different functional groups in the Piers–Rubinsztajn reaction. To analyze trends in the silicone mechanical properties as a function of increasing aryl concentration—structure/property relationships—libraries of elastomers were both quickly synthesized and characterized by using high-throughput suites starting from low viscosity silicone oils/monomers in 96-well plates. Liquid handling parameters were optimized to effectively work with the silicones. Incorporating aryl instead of alkyl crosslinkers into the PDMS backbone increased the silicone elastomer modulus by approximately 50 % (at a crosslink density of 6 %); elastomers prepared with an aromatic crosslinker with three contact points led to much higher moduli compared with those with one contact point at the same crosslink density. When located at precise rather than random points on the silicone chains, diphenylsilicones had lower moduli than analogous monophenylsilicones.     

Porous Molybdenum Carbide Nanostructures Synthesized on Carbon Cloth by CVD for Efficient Hydrogen Production

Molybdenum carbide (Mo₂C) is a promising noble-metal-free electrocatalyst for the hydrogen evolution reaction (HER), due to its structural and electronic merits, such as high conductivity, metallic band states and wide pH applicability. Here, a simple CVD process was developed for synthesis of a Mo₂C on carbon cloth (Mo₂C@CC) electrode with carbon cloth as carbon source and MoO₃ as the Mo precursor. XRD, Raman, XPS and SEM results of Mo₂C@CC with different amounts of MoO₃ and growth temperatures suggested a two-step synthetic mechanism, and porous Mo₂C nanostructures were obtained on carbon cloth with 50 mg MoO₃ at 850 °C (Mo₂C-850(50)). With the merits of unique porous nanostructures, a low overpotential of 72 mV at current density of 10 mA cm⁻² and a small Tafel slope of 52.8 mV dec⁻¹ was achieved for Mo₂C-850(50) in 1.0 m KOH. The dual role of carbon cloth as electrode and carbon source resulted into intimate adhesion of Mo₂C on carbon cloth, offering fast electron transfer at the interface. Cyclic voltammetry measurements for 5000 cycles revealed that Mo₂C@CC had excellent electrochemical stability. This work provides a novel strategy for synthesizing Mo₂C and other efficient carbide electrocatalysts for HER and other applications, such as supercapacitors and lithium-ion batteries.