Kinetics and mechanism of acrylonitrile polymerization by p-toluenesulfinic acid. III. Initiation through disproportionation

A mechanism for radical formation from aromatic sulfinic acids through the disproportionation reaction is suggested. It is postulated that two parallel steps, one a bimolecular reaction and the other involving a trimer of sulfinic acid, yield sulfenyl sulfonate. This labile compound decomposes into free radicals or reacts with another molecule of sulfinic acid producing thiol sulfonate and sulfonic acid. This mechanism explains the variety and unusually high orders encountered in polymerization initiated by sulfinic acid initiators. The proposed kinetic scheme is in agreement with the proton dependence found for both the initiation as well as the disproportionation reactions.     

A note on regular Ramsey graphs

We prove that there is an absolute constant C>0 so that for every natural n there exists a triangle‐free regular graph with no independent set of size at least \({{C}}\sqrt{{{n}}\log{{n}}}\). © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 244–249, 2010     

Emission characteristics of a glow discharge plasma based on a mixture of helium with chlorine molecules

We present the results of a study of the emission characteristics of a longitudinal glow discharge based on a mixture of helium and chlorine. Study of the emission characteristics of the discharge showed that it emits most efficiently in the bands of the chlorine molecule with maxima at 200 nm and 258 nm in an He-Cl₂ mixture (P = 0.2–0.3 kPa). We present the optimization of the average emission power of a UV emitter as a function of the glow discharge parameters, the pressure, and the composition of the working gas mixture. Based on solution of the Boltzmann equation for the electron energy distribution function in a discharge based on the optimal mixture (according to experimental data), we calculated the power losses per unit pressure going toward elementary processes, the electron transport characteristics, the ionization and attachment coefficients as a function of the parameter E/P. The calculated parameters of the plasma for the UV emitter allowed us to provide a basis for the qualitative pattern of physicochemical processes in the studied plasma. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 1, pp. 121–124, January–February, 2008.     

Macroscopic Polarization Change of Mononuclear Valence Tautomeric Cobalt Complexes Through the Use of Enantiopure Ligand

The crystallization of a complex having electron transfer properties in a polar space group can induce the polarization switching of a crystal in a specific direction, which is attractive for the development of sensors, memory devices, and capacitors. Unfortunately, the probability of crystallization in a polar space group is usually low. Noticing that enantiopure compounds crystallize in Sohncke space groups, this paper reports a strategy for the molecular design of non-ferroelectric polarization switching crystals based on the use of intramolecular electron transfer and chirality. In addition, this paper describes the synthesis of a mononuclear valence tautomeric (VT) cobalt complex bearing an enantiopure ligand. The introduction of enantiomer enables the crystallization of the complex in the polar space group (P2₁). The polarization of the crystals along the b-axis direction is not canceled out and the VT transition is accompanied by a change in the macroscopic polarization of the polar crystal. Polarization switching via electron transfer is realized at around room temperature.     

Dense Free Sets

Let κ = 2 ^ω , and assume \(f:\mathbb {R}\rightarrow \mathcal {P}(\mathbb {R})\) satisfies the intersection properties C(ω,κ) and C(κ,ω). We prove that if \(\mathfrak {r}<\text {cf}(\kappa )\) then there exists a dense free set for f.     

Selective bromination of perylene diimides under mild conditions

A novel method for the bromination of perylene diimides, PDI (1), under mild conditions is reported. Variation of the reaction conditions allows mono- and dibromination of PDIs to afford 2 and 3 (these can be separated through standard procedures) or exclusive dibromination to afford 3. Pure 1,7 regioisomers are obtained through repetitive crystallization. The structure of 1,7-3b was elucidated by a single-crystal X-ray analysis. The facility of the bromination reaction, which decreases in the order 1a > 1b > 1c, depends on PDI aggregation propensities. Monobrominated PDIs were utilized for the syntheses of novel unsymmetrical piperidinyl (4a and 4b) and trimethylsilylethynyl derivatives (5a and 5b). Computational studies (DFT) on imide substituent rotation in PDIs reveal that in the case of bulky groups there is a restricted rotation leading to isomers, in agreement with our experimental results. An aromatic core twist in PDIs bearing one and two bromine substituents was also investigated by DFT.     

Emission spectra of working mixtures of a HgBr/HgCl excimer lamp

A study of emission spectra of a gas-discharge plasma produced in a HgBr/HgCl excimer lamp, which is filled with multicomponent working mixtures at atmospheric pressure (HgBr₂ and HgCl₂ with additions of molecular nitrogen and xenon), are reported. A gas-discharge plasma was produced by high-frequency (pulses ～100 ns long with a repetition rate of up to 2000 Hz) barrier and surface discharges, which took place simultaneously. Emission of HgBr* and HgCl* excimer molecules, the second positive system of molecular oxygen, and helium and xenon lines in the UV, visible, and IR spectral regions was observed. The strongest emission of HgBr* and HgCl* molecules (the emission intensities were in the ratio 10:1) was observed in the HgBr₂: HgCl₂: N₂: He mixture. Regularities in spectral and integrated characteristics of gas-discharge plasma emission are discussed.     

Why does PMLG proton decoupling work at 65 kHz MAS?

Schemes such as phase-modulated Lee–Goldburg (PMLG) for homonuclear dipolar decoupling have been shown to yield high-resolution ¹H spectra at high magic-angle spinning (MAS) frequencies of 50–70 kHz. This is at variance to the commonly held notion that these methods require MAS frequencies not comparable to the cycle frequencies of the pulse schemes. Here, a theoretical argument, based on bimodal Floquet theory, is presented to explain this aspect together with conditions where PMLG type of schemes may be successful at high MAS frequencies.     

On the problem of vacuum energy in brane theories

We point out that modern brane theories suffer from a severe vacuum energy problem. To be specific, the Casimir energy associated with the matter fields confined to the brane, is stemming from the one and the same localization mechanism which forms the brane itself, and is thus generically unavoidable. Possible practical solutions are discussed, including in particular spontaneously broken supersymmetry, and quantum mechanically induced brane tension.