Non-collapsing in fully non-linear curvature flows

We consider compact, embedded hypersurfaces of Euclidean spaces evolving by fully non-linear flows in which the normal speed of motion is a homogeneous degree one, concave or convex function of the principal curvatures, and prove a non-collapsing estimate: Precisely, the function which gives the curvature of the largest interior ball touching the hypersurface at each point is a subsolution of the linearized flow equation if the speed is concave. If the speed is convex then there is an analogous statement for exterior balls. In particular, if the hypersurface moves with positive speed and the speed is concave in the principal curvatures, the curvature of the largest touching interior ball is bounded by a multiple of the speed as long as the solution exists. The proof uses a maximum principle applied to a function of two points on the evolving hypersurface. We illustrate the techniques required for dealing with such functions in a proof of the known containment principle for flows of hypersurfaces.     

Alkaline hydrolysis of ethiofencarb: Kinetic study and mechanism degradation

The present paper deals with the hydrolysis of ethiofencarb [2‐ethylthiomethyl(phenyl)‐N‐methylcarbamate] in alkaline solution. The reaction kinetics has been investigated using spectrophotometric and liquid chromatographic techniques. The rate constants were determined following a proposed first‐order kinetic model. The positive activation entropy Δ S^≠ = +100.07 J mol^?1 K^?1 and the absence of general basic catalysis indicated an E1cB hydrolytic mechanism, involving the formation of methyl isocyanate. This result was confirmed by the fact that ethiofencarb fits well into Brönsted and Hammett lines, obtained for a series of substituted N‐methylcarbamate whose decomposition in aqueous media was established to follow an E1cB mechanism. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 45: 118–124, 2013     

Taming the Reactivity of Phosphiranium Salts: Site‐Selective C‐Centered Ring Opening for Direct Synthesis of Phosphinoethylamines

Advances in the field of phosphorus chemistry are documented, by revealing the synthetic utility of previously underutilized quaternary phosphiranium salts (QPrS) as three‐chain‐atom electrophilic building blocks. Notably, control of their challenging C‐centered electrophilicity is disclosed with an expedient synthesis of tertiary β‐anilino phosphines as a proof‐of‐concept.     

Ambident electrophilicity of 4-nitrobenzochalcogenadiazoles: Kinetic studies and structure-reactivity relationships

The kinetics of the reactions of 4-nitrobenzofurazane 1a , 4-nitrobenzothiadiazole 1b , and 4-nitrobenzoselenadiazole 1c with a series of 4-Y-substituted phenoxide anions 2a-e (Y = OMe, Me, H, Cl, and CN) in aqueous solution at 20°C were investigated photometrically. The derived second-order rate constants (k₂) have been combined with the nucleophilicity parameters values of these series of anions 2a-e to determine the electrophilicity parameters E of electrophiles 1a-c according to the linear free-energy relationship (log k₂)/s versus N. General reactivity of these electrophiles 1a-c is found to be fairly similar with E values ranging in −10.77 ± 0.61 < E < −7.53 ± 0.29. The comparison with structurally related neutral electron-deficient heteroaromatic and aromatic compounds revealed that 1a - c are more reactive than 1,3,5-trinitrobenzene, as benchmark aromatic electrophile used in nucleophilic addition or substitution processes. The rate constants for the reactions of 4-nitrobenzochalcogenadiazoles 1a-c with some other nucleophiles were measured and found to agree with those calculated from Mayr's equation. Finally, analysis of the rate data in terms of the Brønsted approach reveals that 1a-c exhibits especially low intrinsic reactivity in σ-adducts 3 forming reactions.     

Homopolycyclotrimerization of A4‐type tetrayne: A new approach for the creation of a soluble hyperbranched poly(tetraphenylethene) with multifunctionalities

A tetraphenylethene‐containing A₄‐type tetrayne, named 1,1,2,2‐tetrakis(4‐ethynylphenyl)ethene is synthesized and its TaCl₅‐Ph₄Sn catalyzed homopolycyclotrimerization affords hyperbranched poly(tetraphenylethene) with high molecular weight (M_w = 280,000) in high yield (97%). The polymer shows good solubility and high thermal stability. It is aggregation‐enhanced emission (AEE)‐active and functions as a fluorescent chemosensor for explosive detection with a superamplification effect and large quenching constants up to 758,000 M^?1. The polymer shows high and tunable refractive indices (RI = 1.9288?1.6746) in a wide wavelength region. Porous fluorescent polymer thin film is prepared by breath figure (BF) methods and real‐time monitoring of the elusive BF formation process is realized. Photolithography of the thin films readily generates well‐resolved fluorescent photopattern without and with porous secondary structure. The polymer is metallified and pyrolysed to give magnetic ceramics with high magnetic susceptibilities (M_s = 83 emu/g) and near‐zero coercivity (H_c = 0.08 kOe). © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4752–4764