Functionalization of Intramolecular Frustrated Lewis Pairs by 1,1‐Carboboration with Conjugated Enynes

The vicinal P/B frustrated Lewis pair (FLP) Mes₂PCH₂CH₂B(C₆F₅)₂ undergoes 1,1‐carboboration reactions with the Me₃Si‐substituted enynes to give ring‐enlarged functionalized C₃‐bridged P/B FLPs. These serve as active FLPs in the activation of dihydrogen to give the respective zwitterionic [P]H⁺/[B]H^? products. One such product shows activity as a metal‐free catalyst for the hydrogenation of enamines or a bulky imine. The ring‐enlarged FLPs contain dienylborane functionalities that undergo “bora‐Nazarov”‐type ring‐closing rearrangements upon photolysis. A DFT study had shown that the dienylborane cyclization of such systems itself is endothermic, but a subsequent C₆F₅ migration is very favorable. Furthermore, substituted 2,5‐dihydroborole products are derived from cyclization and C₆F₅ migration from the photolysis reaction. In the case of the six‐membered annulation product, a subsequent stereoisomerization reaction takes place and the resultant compound undergoes a P/B FLP 1,2‐addition reaction with a terminal alkyne with rearrangement.     

An inequality concerning the growth bound of an evolution family and the norm of a convolution operator

Let \(\mathcal {U}=\{U(t,s)\}_{t\ge s\ge 0}\) be a strongly continuous and exponentially bounded evolution family acting on a complex Banach space X and let \(\mathcal {X}\) be a certain Banach function space of X-valued functions. We prove that the growth bound of the family \(\mathcal {U}\) is less than or equal to \(-\frac{1}{c(\mathcal {U}, \mathcal {X})}\) provided that the convolution operator \(f\mapsto \mathcal {U}*f\) acts on \(\mathcal {X}.\) It is well known that under the latter assumption, the convolution operator is bounded and then \(c(\mathcal {U}, \mathcal {X})\) denotes (ad-hoc) its norm in \(\mathcal {L}(\mathcal {X}).\) As a consequence, we prove that if \(\sup \nolimits _{s\ge 0}\int \nolimits _{s}^\infty \Vert U(t,s)\Vert dt=u_1(\mathcal {U})<\infty ,\) then \(\omega _0(\mathcal {U})u_1(\mathcal {U})\le -1.\) Finally, we give an example showing that the accuracy of the estimates may be quite accurate.     

Dispersion de Taylor généralisée à un fluide à propriétés physiques variablesGeneralized Taylor dispersion for heterogeneous fluid

The investigation of non-reactive miscible solute dispersion in a vertical Hele–Shaw cell is considered. An asymptotic method is used to extend Taylor model to the case of the fluid density, the dynamic viscosity and the molecular diffusion coefficient are solute concentration-dependent. It is demonstrated that the averaged variables over the gap are governed by a convection–dispersion equation in which the dispersion tensor is concentration-dependent. To cite this article: C. Felder et al., C. R. Mecanique 332 (2004).     

Large-Eddy Simulations of Spray a Flames Using Explicit Coupling of the Energy Equation with the FGM Database

This paper provides a numerical study on n-dodecane flames using Large-Eddy Simulations (LES) along with the Flamelet Generated Manifold (FGM) method for combustion modeling. The computational setup follows the Engine Combustion Network Spray A operating condition, which consists of a single-hole spray injection into a constant volume vessel. Herein we propose a novel approach for the coupling of the energy equation with the FGM database for spray combustion simulations. Namely, the energy equation is solved in terms of the sensible enthalpy, while the heat of combustion is calculated from the FGM database. This approach decreases the computational cost of the simulation because it does not require a precise computation of the entire composition of the mixture. The flamelet database is generated by simulating a series of counterflow diffusion flames with two popular chemical kinetics mechanisms for n-dodecane. Further, the secondary breakup of the droplet is taken into account by a recently developed modified version of the Taylor Analogy Breakup model. The numerical results show that the proposed methodology captures accurately the main characteristics of the reacting spray, such as mixture formation, ignition delay time, and flame lift-off. Additionally, it captures the “cool flame" between the flame lift-off and the injection nozzle. Overall, the simulations show differences between the two kinetics mechanisms regarding the ignition characteristics, while similar flame structures are observed once the flame is stabilised at the lift-off distance.

     

A fluorescence anisotropy method for measuring protein concentration in complex cell culture media

The rapid, quantitative analysis of the complex cell culture media used in biopharmaceutical manufacturing is of critical importance. Requirements for cell culture media composition profiling, or changes in specific analyte concentrations (e.g. amino acids in the media or product protein in the bioprocess broth) often necessitate the use of complicated analytical methods and extensive sample handling. Rapid spectroscopic methods like multi-dimensional fluorescence (MDF) spectroscopy have been successfully applied for the routine determination of compositional changes in cell culture media and bioprocess broths. Quantifying macromolecules in cell culture media is a specific challenge as there is a need to implement measurements rapidly on the prepared media. However, the use of standard fluorescence spectroscopy is complicated by the emission overlap from many media components. Here, we demonstrate how combining anisotropy measurements with standard total synchronous fluorescence spectroscopy (TSFS) provides a rapid, accurate quantitation method for cell culture media. Anisotropy provides emission resolution between large and small fluorophores while TSFS provides a robust measurement space. Model cell culture media was prepared using yeastolate (2.5 mg mL^–1) spiked with bovine serum albumin (0 to 5 mg mL^–1). Using this method, protein emission is clearly discriminated from background yeastolate emission, allowing for accurate bovine serum albumin (BSA) quantification over a 0.1 to 4.0 mg mL^–1range with a limit of detection (LOD) of 13.8 μg mL^–1.     

Structural Diversity of Metallosupramolecular Assemblies from Cu(phen)2+ (phen = 1,10‐Phenanthroline) Building Blocks and 4,4′‐Bipyridine

Attempts to crystal engineer metallosupramolecularcomplexes from Cu(phen)²⁺ building blocks and the prototypical,rod‐like, exo‐bidentate ligand 4,4′‐bipyridine (4,4′‐bipy) by layering techniques are described. Reactions of Cu(phen)²⁺ (phen = 1,10‐phenanthroline) with 4,4′‐bipy in the presence of NO₃^– counterions yielded two distinct, discrete, dinuclear, C_i symmetric, dumbbell‐typecomplexes, [{Cu(NO₃)₂(phen)}₂(4,4′‐bipy)] ( 1 ) and [{Cu(NO₃)(phen)(H₂O)}₂(4,4′‐bipy)](NO₃)₂ ( 2 ), depending upon the mixture of solvents used for crystallization. In compound 1 , a mono‐ and a bidentate nitrato group coordinate to Cu²⁺, whereas in 2 the monodentate nitrato groups are replaced by aqua ligands, which introduce additional hydrogen‐bond donor functionality to the molecule. The crystal structure of 1 was determined by single‐crystal X‐ray analysis at 296 and 110 K. Upon cooling, a disorder‐order transition occurs, with retention of the space group symmetry. The crystal structure of 2 at room temperature was reported previously [Z.‐X. Du, J.‐X. Li, Acta Cryst. 2007 , E63, m2282]. We have redetermined the crystal structure of 2 at 100 K. A phase transition is not observed for 2 , but the low temperature single‐crystal structure determination is of significantly higher precision than the room temperature study. Both 1 and 2 are obtained phase‐pure, as proven by powder X‐ray diffraction of the bulk materials. Crystals of [Cu(phen)(CF₃SO₃)₂(4,4′‐bipy) · 0.5H₂O]_n ( 3 ), a one‐dimensional coordination polymer, were obtained from [Cu(CF₃SO₃)₂(phen)(H₂O)₂] and 4,4′‐bipy. In 3 , Cu(phen)²⁺ corner units are joined by 4,4′‐bipy via the two vacant cis sites to form polymeric zig‐zag chains, which are tightly packed in the crystal. Compounds 1 – 3 were further studied by infrared spectroscopy.     

The use of 1,2-dipiperidinoacetylene for the preparation of monometallic diaminoacetylene and homo- or heterobimetallic diaminodicarbene ruthenium(II) complexes

The reaction of the ynediamine 1,2-dipiperidinoacetylene (1) with [(η(2)-COE)Cr(CO)(5)], [(THF)W(CO)(5)] and [RuCl(2)(η(6)-cymene)](2) afforded homobimetallic complexes 2a, 2b and 3, in which the diaminoacetylene 1 acts as a bis(aminocarbene) ligand by bridging two complex fragments Cr(CO)(5) (in 2a), W(CO)(5) (in 2b) and RuCl(2)(η(6)-cymene) (in 3). The reaction of 1 with [RuCl(2)(PPh(3))(3)] gave trans-[(1)RuCl(PPh(3))(2)]Cl, [4]Cl, in which the alkyne 1 coordinates as a 4-electron donor ligand. The cation 4 represents a rare example of a square-planar Ru(II) complex with a low-spin ground state (S = 0), and its stability can be ascribed to the strong alkyne-metal π-interaction as confirmed by DFT calculations. Treatment with one or two equivalents of NaBPh(4) in acetonitrile gave [4]BPh(4) and the dicationic [(1)Ru(PPh(3))(2)(CH(3)CN)(2)](BPh(4))(2), [5](BPh(4))(2). [4]Cl can be used for the preparation of heterobimetallic Ru-Pd bis(aminocarbene) complexes by reaction with [(MeCN)(2)PdCl(2)], resulting in the formation of bimetallic 6 and tetrametallic 7.