Benzenoid ring contractions in the thermal automerization of acenaphthylene

Acenaphthylene-1-¹³C (1) rearranges at high temperatures in a flow system to give acenaphthylene-5-¹³C (2) and acenaphthylene-4-¹³C (3) in a 1:1 ratio as the primary products. This apparent migration of a labeled carbon atom from the bridge to the most remote sites in the molecule can be understood in terms of a benzenoid ring contraction mechanism.     

New Applications of Ph 3 P=N--Li in Organic Synthesis and Heteroatom Chemistry

The lithium triphenylaminophosphonium azayldiide 1 proved again to be a very good tool in organic synthesis, allowing further synthesis of various compounds such as vinyl nitriles, aromatic or heteroaromatic nitriles, and mono-, bis-, and trisphosphinimines.     

Vacuum-assisted headspace solid phase microextraction: Improved extraction of semivolatiles by non-equilibrium headspace sampling under reduced pressure conditions

A new headspace solid-phase microextraction (HSSPME) procedure carried out under vacuum conditions is proposed here where sample volumes commonly used in HSSPME (9 mL) were introduced into pre-evacuated commercially available large sampling chambers (1000 mL) prior to HSSPME sampling. The proposed procedure ensured reproducible conditions for HSSPME and excluded the possibility of analyte losses. A theoretical model was formulated demonstrating for the first time the pressure dependence of HSSPME sampling procedure under non equilibrium conditions. Although reduced pressure conditions during HSSPME sampling are not expected to increase the amount of analytes extracted at equilibrium, they greatly increase extraction rates compared to HSSPME under atmospheric pressure due to the enhancement of evaporation rates in the presence of an air-evacuated headspace. The effect is larger for semivolatiles whose evaporation rates are controlled by mass transfer resistance in the thin gas film adjacent to the sample/headspace interface. Parameters that affect HSSPME extraction were investigated under both vacuum and atmospheric conditions and the experimental data obtained were used to discuss and verify the theory. The use of an excessively large headspace volume was also considered. The applicability of Vac-HSSPME was assessed using chlorophenols as model compounds yielding linearities better than 0.9915 and detection limits in the low-ppt level. The repeatability was found to vary from 3.1 to 8.6%.     

An approach to control the spurious currents in a multiphase lattice Boltzmann method and to improve the implementation of initial condition

Multiphase lattice Boltzmann methods are known to generate spurious or parasitic currents at the fluid–fluid interfaces. This nonphysical phenomenon has to be avoided, or at least controlled, in order to achieve reliable solutions. In this article, a method to control these fictitious velocities via lattice refinement is proposed, which is based on interface thickness control for which both the spurious currents and the physical fluid–fluid interface thickness vanishes as the spatial resolution increases. It has been found that a proper interface thickness adjustment is required as the lattice refinement is applied, or an increase in spurious currents, instead of a reduction, can occur. By combining the new method with an appropriate multiphase flow initialization, the overall stability for high density O(1000) and viscosity O(100) ratios is greatly improved. Although this research has been conducted with a Rothman and Keller type lattice Boltzmann model, it is believed that other types of multiphase lattice Boltzmann models could benefit from the basic ideas underlying this research. Copyright © 2015 John Wiley & Sons, Ltd.     

Experimental and Computational Studies of Anti‐Bredt Amidinium Salts

Experimental and computational investigations of anti‐Bredt amidinium salts are presented. Calculations show that the pyramidalization of an amino group can significantly destabilize the formal carbocation center of amidiniums, due to the decreased π donation. In some cases, the unfavorable ‐I effect of nitrogen surpasses its beneficial +M effect, and amidiniums become less stable than iminiums. It is shown that although 1‐aza‐3‐azonia[3.3.1]bicyclo‐non‐2‐enes can be isolated, they feature a nonclassical reactivity, which is more typical for iminium than amidinium salts, such as pronounced electrophilicity and azomethineylide instead of carbene formation.     

Perfectly matched layers for the heat and advection–diffusion equations

We design a perfectly matched layer for the advection–diffusion equation. We show that the reflection coefficient is exponentially small with respect to the damping parameter and the width of the PML and independently of the advection and of the viscosity parameters. Numerical tests assess the efficiency of the approach.     

On Roussel–Rubio-type lemmas and their consequences

Roussel and Rubio proved a lemma which is essential in the proof of the Strong Perfect Graph Theorem. We give a new short proof of the main case of this lemma. In this note, we also give a short proof of Hayward’s decomposition theorem for weakly chordal graphs, relying on a Roussel–Rubio-type lemma. We recall how Roussel–Rubio-type lemmas yield very short proofs of the existence of even pairs in weakly chordal graphs and Meyniel graphs.     

A minimal amount of acrylonitrile turns the nitroxide‐mediated polymerization of methyl methacrylate into an almost ideal controlled/living system

Nitroxide‐mediated controlled/living free‐radical polymerization of methyl methacrylate initiated by the SG1‐based alkoxyamine BlocBuilder was successfully performed in bulk at 80–99 °C with the help of a very small amount of acrylonitrile (AN, 2.2–8.8 mol %) as a comonomer. Well‐defined PMMA‐rich P(MMA‐co‐AN) copolymers were prepared with the number‐average molar mass, M_n, in the 6.1–32 kg mol^?1 range and polydispersity indexes as low as 1.24. Incorporation of AN in the copolymers was demonstrated by ¹H and ¹³C NMR spectroscopy, and its effect on the chain thermal properties was evaluated by DSC and TGA analyses. Investigation of chain‐end functionalization by an alkoxyamine group was performed by means of ³¹P NMR spectroscopy and chain extensions from a P(MMA‐co‐AN)‐SG1 macroinitiator. It demonstrated the very high proportion of SG1‐terminated polymer chains, which opened the door to block copolymer synthesis with a high quality of control. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 34–47, 2010     

Azoalkanes—novel flame retardants and their structure–property relationship

A number of symmetrical and unsymmetrical azoalkanes of the general formula R′?N = N?R and related azoxy, hydrazone as well as azine derivatives have been synthesized in order to assess their potential as novel flame retardants for polypropylene alone or in combination with commercially available flame retardants such as alumina trihydrate (ATH), decabromodiphenyl ether (DecaBDE) and tris(3‐bromo‐2,2‐bis(bromomethyl)‐propyl)phosphate (TBBPP). The experimental results show that in the series of different sized azocycloalkanes the flame retardant efficacy decreased in the following order: R = cyclohexyl > cyclopentyl > cyclobutyl > cyclooctanyl >> cyclododecanyl. Whereas in the series of aliphatic azoalkanes compounds the efficacy decreased in the following order: R = n‐alkyl > tert‐butyl > tert‐octyl. In addition, also some of the prepared azoxy, azine, and hydrazone derivatives provide flame retardancy to polypropylene films at already very low concentrations (0.25–1 wt%). Noteworthy is that in contrast to other halogen‐free radical generators, the azoalkanes are also very effective as flame retardants in polypropylene thick moldings. Interestingly, it was found that 4,4′‐bis(cyclohexylazocyclohexyl)‐methane) shows a strong synergistic effect with ATH. Thus, in the presence of 0.5 wt% of azoalkane the ATH loading could be reduced from 60 to 25 wt% and still UL94 V‐2 rating could be reached. Furthermore, the fire testing data reveal that azoalkanes show a synergistic effect with DecaBDE and when used in conjunction with very low loadings of TBBPP. Copyright © 2010 John Wiley & Sons, Ltd.     

On the geometric interpretation of the nonnegative rank

The nonnegative rank of a nonnegative matrix is the minimum number of nonnegative rank-one factors needed to reconstruct it exactly. The problem of determining this rank and computing the corresponding nonnegative factors is difficult; however it has many potential applications, e.g., in data mining and graph theory. In particular, it can be used to characterize the minimal size of any extended reformulation of a given polytope. In this paper, we introduce and study a related quantity, called the restricted nonnegative rank. We show that computing this quantity is equivalent to a problem in computational geometry, and fully characterize its computational complexity. This in turn sheds new light on the nonnegative rank problem, and in particular allows us to provide new improved lower bounds based on its geometric interpretation. We apply these results to slack matrices and linear Euclidean distance matrices and obtain counter-examples to two conjectures of Beasley and Laffey, namely we show that the nonnegative rank of linear Euclidean distance matrices is not necessarily equal to their dimension, and that the rank of a matrix is not always greater than the nonnegative rank of its square.