On Isolated Submodules

Let R be a ring with identity and let M be a unital left R-module. A proper submodule L of M is radical if L is an intersection of prime submodules of M. Moreover, a submodule L of M is isolated if, for each proper submodule N of L, there exists a prime submodule K of M such that N ? K but L ? K. It is proved that every proper submodule of M is radical (and hence every submodule of M is isolated) if and only if N ∩ IM = IN for every submodule N of M and every (left primitive) ideal I of R. In case, R/P is an Artinian ring for every left primitive ideal P of R it is proved that a finitely generated submodule N of a nonzero left R-module M is isolated if and only if PN = N ∩ PM for every left primitive ideal P of R. If R is a commutative ring, then a finitely generated submodule N of a projective R-module M is isolated if and only if N is a direct summand of M.     

On Dedekind Modules

In this article the authors give the relation between a finitely-generated torsionfree Dedekind module M over a domain R and prime submodules of the 𝒪(M)-module M and the ring 𝒪(M). They also prove that M is a finitely-generated torsionfree Dedekind module over a domain R if and only if every semi-maximal submodule of R-module M is invertible.     

Sources of sensitivity losses in ultrafast 2D NMR

Recent ultrafast techniques make it possible to obtain nD NMR spectra in a single scan. However, an important sensitivity decrease is observed when the excitation duration is increased, which is necessary to improve resolution. A detailed, theoretical and experimental study of sensitivity losses in ultrafast experiments is carried out on the example of J-resolved spectroscopy. The importance of molecular diffusion effects during both encoding and acquisition phases is shown by numerical simulations and experimental results. Other possible sources of signal-to-noise decrease are also considered, such as transverse relaxation, homonuclear J-couplings or chemical shift effects.     

Pattern formation in the ferrocyanide-iodate-sulfite reaction: the control of space scale separation

We revisit the conditions for the development of reaction-diffusion patterns in the ferrocyanide-iodate-sulfite bistable and oscillatory reaction. This hydrogen ion autoactivated reaction is the only example known to produce sustained stationary lamellar patterns and a wealth of other spatio-temporal phenomena including self-replication and localized oscillatory domain of spots, due to repulsive front interactions and to a parity-breaking front bifurcation (nonequilibrium Ising-Bloch bifurcation). We show experimentally that the space scale separation necessary for the observation of stationary patterns is mediated by the presence of low mobility weak acid functional groups. The presence of such groups was overlooked in the original observations made with hydrolyzable polyacrylamide gels. This missing information made the original observations difficult to reproduce and frustrated further experimental exploitation of the fantastic potentialities of this system. Using one-side-fed spatial reactors filled with agarose gel, we can reproduce all the previous pattern observations, in particular the stationary labyrinthine patterns, by introducing, above a critical concentration, well controlled amounts of polyacrylate chains in the gel network. We use two different geometries of spatial reactors (annular and disk shapes) to provide complementary information on the actual three-dimensional character of spatial patterns. We also reinvestigate the role of other feed parameters and show that the system exhibits both a domain of spatial bistability and of large-amplitude pH oscillations associated in a typical cross-shape diagram. The experimental method presented here can be adapted to produce patterns in the large number of oscillatory and bistable reactions, since the iodate-sulfite-ferrocynide reaction is a prototype of these systems.     

On the heat of formation of nitromethane

Two experimental values (?19.3 ± 0.3 and ?17.8 ± 0.1 kcal/mol) for the gas phase heat of formation (δ_fH) (298k) of nitromethane have been reported. Although these values differ by only 1.5 kcal/mol, substantially greater differences in theoretical and experimental results occur when these differing values are used to calculate thermodynamic properties. This is especially evident when these two values for the δ_fH of nitromethane are used to calculate thermodynamic properties of polynitro compounds. For example, when density functional theory (DFT) is coupled with the use of isodesmic reactions, the Δ_fH of octanitrocubane is calculated to be 160.6 or 172.6 kcal/mol, depending on which value is used. It should also be appreciated that several computational theories depend upon having access to reliable experimental data for testing and development. We have examined this discrepancy using several computational models and several levels of theory. Our results coupled with a comprehensive review of the literature support the lower (?19.3 ± 0.3 kcal/mol) experimental value. This is problematic because the higher value (?17.8 ± 0.1 kcal/mol) has been used in the development and/or testing of several semiempirical quantum mechanical models as well as ab initio Gaussian theory (G2 and G3). Copyright © 2008 John Wiley & Sons, Ltd.     

The Synthesis of Quinoline‐based Tin Complexes with Pendant Schiff Bases

Whilst pursuing the synthetic utility of quinoline‐based tin complexes, Me₂Sn(Quin‐NO₂)₂ ( 1 ) and Ph₂Sn(Quin‐NO₂)₂ ( 2 ) (Quin‐NO₂ = 5‐nitroquinolino‐8‐oate) were synthesized bearing coordinatively inert nitro groups. Conventional reduction methodologies successfully converted 1 to Me₂Sn(Quin‐NH₂)₂ ( 3 ) and 2 to Ph₂Sn(Quin‐NH₂)₂ ( 4 ) (Quin‐NH₂ = 5‐aminoquinolino‐8‐oate). The synthetically useful amine groups proved difficult to exploit in the presence of the central tin atom, however, a complete Schiff base functionalized Sn complex of the dimethyltin pro‐ligand Me₂Sn(Quin‐py)₂ ( 6 ) was successfully synthesized from 5‐[(pyridin‐2‐ylmethylene)amino]quinolin‐8‐ol (HQuin‐py; 5 ) in good yield via an alternative strategy exploiting the oxophilic tendencies of tin. All species were fully characterized by NMR (including ¹¹⁹Sn NMR spectroscopy), HR‐ESI MS and single‐crystal X‐ray diffraction, and preliminary studies of their supramolecular potential are also discussed.     

Discovery of Elusive K4O6, a Compound Stabilized by Configurational Entropy of Polarons

Synthesis of elusive K₄O₆ has disclosed implications of crucial relevance for new solid materials discovery. K₄O₆ forms in equilibrium from K₂O₂ and KO₂, in an all‐solid state, endothermic reaction at elevated temperature, undergoing back reaction upon cooling to ambient conditions. This tells that the compound is stabilized by entropy alone. Analyzing possible entropic contributions reveals that the configurational entropy of “localized” electrons, i.e., of polaronic quasi‐particles, provides the essential contribution to the stabilization. We corroborate this assumption by measuring the relevant heats of transformation and tracking the origin of entropy of formation computationally. These findings challenge current experimental and computational approaches towards exploring chemical systems for new materials by searching the potential energy landscape: one would fail in detecting candidates that are crucially stabilized by the configurational entropy of localized polarons.     

Potential‐Induced Fine‐Tuning of the Enantioaffinity of Chiral Metal Phases

Concepts leading to single enantiomers of chiral molecules are of crucial importance for many applications, including pharmacology and biotechnology. Recently, mesoporous metal phases encoded with chiral information have been developed. Fine‐tuning of the enantioaffinity of such structures by imposing an electric potential is proposed, which can influence the electrostatic interactions between the chiral metal and the target enantiomer. This allows the binding affinity between the chiral metal and the target enantiomer to be increased, and thus, the discrimination between two enantiomers to be improved. The concept is illustrated by generating chiral encoded metals in a microfluidic channel by reduction of a platinum salt in the presence of a liquid crystal and l ‐tryptophan as a chiral model template. After removal of the template molecules, the modified microchannel retains a pronounced chiral character. The chiral recognition efficiency of the microchannel can be fine‐tuned by applying a suitable potential to the metal phase. This enables the separation of both components of a racemate flowing through the channel. The approach constitutes a promising and complementary strategy in the frame of chiral discrimination technologies.     

Synthesis of Indoles through Domino Reactions of 2‐Fluorotoluenes and Nitriles

Indoles are essential heterocycles in medicinal chemistry, and therefore, novel and efficient approaches to their synthesis are in high demand. Among indoles, 2‐aryl indoles have been described as privileged scaffolds. Advanced herein is a straightforward, practical, and transition‐metal‐free assembly of 2‐aryl indoles. Simply combining readily available 2‐fluorotoluenes, nitriles, LiN(SiMe₃)₂, and CsF enables the generation of a diverse array of indoles (38 examples, 48–92 % yield). A range of substituents can be introduced into each position of the indole backbone (C4 to C7, and aryl groups at C2), providing handles for further elaboration.