Polymeric oxidizing reagents based on polyacrylamides: Effect of the nature and extent of crosslinking on reactivity

Acrylamide was copolymerized with N,N′-methylene-bis-acrylamide (NNMBA), tetraethyl-eneglycol diacrylate (TEGDA), and divinyl benzene (DVB) in different proportions to afford crosslinked polyacrylamides with varying nature and extent of crosslinking. These insoluble polymers were functionalized with the N-bromoamide function and the reactivity of the resulting polymeric N-bromoamide was investigated under different conditions. The capacities of the reagents varied from 6.7 mequiv / g for the linear polymeric reagent to 1.1 mequiv / g for the 15% DVB-crosslinked reagent. Oxidation of benzoin to benzil was used as the model reaction. Investigation of the reaction under different conditions of solvent and varying molar excess revealed a significant influence of the nature and extent of crosslinking in deciding the extent of reaction. In the case of NNMBA-crosslinked reagents, the reactivity increased up to 10% crosslinking and then decreased. The reactivity of the reagents increased up to 15% crosslinking in the case of TEGDA-crosslinked ones and for DVB-crosslinked reagents the reactivity decreased with crosslinking. The polarity of the crosslinking agent and its molar percentage on the polymeric reagent (crosslink density) are factors affecting the solvent compatibility, which in turn, is decisive in the facilitation of the reactions.     

Theory of activated rate processes: Coupled modes

The thermally activated escape rate of a classical particle out of a potential well is studied in a simple model which includes coupling between the escape (reactive) coordinate and another coordinate. The main effect of the non-reactive coordinate is to open a new (non-markovian) channel between the reactive coordinate and the thermal bath.     

A Note on τ-Critical Linear Hypergraphs

J.P. Roudneff as well as R. Aharoni and R. Ziv conjectured that every τ-critical hypergraph has at most $\left( {\begin{array}{*{20}{c}} {\tau + 1} \\ 2 \end{array}} \right)$ edges. In this note we prove this conjecture for τ ≤ 5, and obtain a nontrivial upper bound for general τ.     

Ramsey numbers of cubes versus cliques

The cube graph Q _n is the skeleton of the n-dimensional cube. It is an n-regular graph on 2 ⁿ vertices. The Ramsey number r(Q _n ;K _s ) is the minimum N such that every graph of order N contains the cube graph Q _n or an independent set of order s. In 1983, Burr and Erd?s asked whether the simple lower bound r(Q _n ;K _s )≥(s?1)(2 ⁿ ?1)+1 is tight for s fixed and n sufficiently large. We make progress on this problem, obtaining the first upper bound which is within a constant factor of the lower bound.     

Some Remarks on Rainbow Connectivity

An edge (vertex) colored graph is rainbow‐connected if there is a rainbow path between any two vertices, i.e. a path all of whose edges (internal vertices) carry distinct colors. Rainbow edge (vertex) connectivity of a graph G is the smallest number of colors needed for a rainbow edge (vertex) coloring of G. In this article, we propose a very simple approach to studying rainbow connectivity in graphs. Using this idea, we give a unified proof of several known results, as well as some new ones.     

Unavoidable patterns

Let Fk denote the family of 2-edge-colored complete graphs on 2k vertices in which one color forms either a clique of order k or two disjoint cliques of order k. Bollobás conjectured that for every ?>0 and positive integer k there is n(k,?) such that every 2-edge-coloring of the complete graph of order n?n(k,?) which has at least edges in each color contains a member of Fk. This conjecture was proved by Cutler and Montágh, who showed that n(k,?)<⁴k/?. We give a much simpler proof of this conjecture which in addition shows that n(k,?)<?−ck for some constant c. This bound is tight up to the constant factor in the exponent for all k and ?. We also discuss similar results for tournaments and hypergraphs.     

Methods to reduce interference effects in thermal conversion elemental analyzer/continuous flow isotope ratio mass spectrometry delta18O measurements of nitrogen-containing compounds

On-line determination of the oxygen isotopic composition (delta(18)O value) in organic and inorganic samples is commonly performed using a thermal conversion elemental analyzer (TC-EA) linked to a continuous flow isotope ratio mass spectrometry (IRMS) system. Accurate delta(18)O analysis of N-containing compounds (like nitrates) by TC-EA-IRMS may be complicated because of interference of the N(2) peak on the m/z 30 signal of the CO peak. In this study we evaluated the effectiveness of two methods to overcome this interference which do not require any hardware modifications of standard TC-EA-IRMS systems. These methods were (1) reducing the amount of N(2) introduced into the ion source through He dilution of the N(2) peak and (2) an improved background correction on the CO m/z 30 sample peak integration.Our results show that He dilution is as effective as diverting the N(2) peak in order to eliminate this interference. We conclude that the He-dilution technique is a viable method for the delta(18)O analysis of nitrates and other N-containing samples (which are not routinely measured using He dilution) using TC-EA-IRMS, since it can easily be programmed in the standard software of IRMS systems. With the He-dilution technique delta(18)O values of the nitrate isotope standards USGS34, IAEA-N3 and USGS35 were measured using the shortest possible traceability chain to the VSMOW-SLAP scale, and the results were -28.1 +/- 0.1 per thousand, +25.5 +/- 0.1 per thousand and +57.5 +/- 0.2 per thousand, respectively. An improved background correction was also an effective method, but required manual correction of the raw data.     

2,6‐Di­phenylthiapyran‐4‐one

In the title compound, 2,6‐di­phenyl­thia­cyclo­hexan‐4‐one, C₁₇H₁₆OS, mirror site symmetry is retained by the mol­ecule in the solid state in the absence of C—H?X hydrogen bonds. The crystal structure is stabilized by van der Waals interactions, the shortest S?O and C?O contacts being 3.567 (2) and 3.512 (3) Å, respectively.     

Herring‐bone π–π interactions in trans‐2,6‐diphenyl‐2,3,5,6‐tetrahydrothiapyran‐4‐one

The structure of the title compound, C₁₇H₁₆OS, is primarily stabilized by T‐shaped and parallel‐displaced aromatic clusters. The distances between the centroids of the aromatic pairs are in the range 4.34–5.30 Å. In the crystal packing, the mol­ecules dimerize by means of π–π interactions of both face‐to‐face and edge‐to‐face types, and the aromatic rings associate in a cyclic edge‐to‐face tetrameric arrangement of the herring‐bone type. These herring‐bone interactions appear to insulate hydrogen‐bond interactions in the crystal structure.     

Pyrrolidinium-based ionic liquids as electrolytes for lithium batteries: A Computational Study

Electrochemical windows (ECWs) of the cyclic ammonium based ionic liquids formed by the combination of two common pyrrolidinium cations—N,N-butylmethyl pyrrolidinum(P_yr14) and N,N-hexylmethyl pyrrolidinium(P_yr16) and five anions—dicyanamide, trifluoroacetate, fluoromethane sulfonate, bis((trifluoromethylsulfonyl)imide, and bis(fluorosulfonyl)imide were investigated. The ECW of each ionic liquid was obtained from the oxidation and reduction potentials of these ionic liquids with respect to a Li⁺/Li reference electrode by using thermodynamic cycle method. The work reveals that the ECWs of these ionic liquids are solely decided by the HOMO energy of pairing anions. The ECWs were also computed using HOMO-LUMO method employing Møller-Plesset perturbation theory to the second order and M06L methods with a basis set of 6-31 + G(d, p). The ECW computed using M06L functional with an extended basis set of 6-311++G(d, p) showed better agreement with experimental values suggesting accurate computation of ECW is possible at lower computational cost.