Sequential Barium‐Catalysed N−H/H−Si Dehydrogenative Cross‐Couplings: Cyclodisilazanes versus Linear Oligosilazanes

Starting from Ph₃SiH, the barium precatalyst Ba[CH(SiMe₃)₂]₂?(THF)₃ was used to produce the disilazane Ph₃SiN(Bn)SiPh₂NHBn ( 4 ) by sequential N?H/H?Si dehydrogenative couplings with BnNH₂ and Ph₂SiH₂. Substrate scope was extended to other amines and hydrosilanes. This smooth protocol gives quantitative yields and full chemoselectivity. Compound 4 and the intermediates Ph₃SiNHBn and Ph₃SiN(Bn)SiHPh₂ were structurally characterised. Further attempts at chain extension by dehydrocoupling of Ph₂SiH₂ with 4 instead resulted in cyclisation of this compound, forming the cyclodisilazane c‐(Ph₂Si‐NBn)₂ ( 5 ) which was crystallographically authenticated. The ring‐closure mechanism leading to 5 upon release of C₆H₆ was determined by complementary experimental and theoretical (DFT) investigations. Ba[CH(SiMe₃)₂]₂?(THF)₃ and 4 react to afford the reactive Ba{N(Bn)SiPh₂N(Bn)SiPh₃}₂, which was characterised in situ by NMR spectroscopy. Next, in a stepwise process, intramolecular nucleophilic attack of the metal‐bound amide on the terminal silicon atom generates a five‐coordinate silicate. It is followed by turnover‐limiting β‐C₆H₅ transfer to barium; this releases 5 and forms a transient [Ba]?Ph species, which undergoes aminolysis to regenerate [Ba]?N(Bn)SiPh₂N(Bn)SiPh₃. DFT computations reveal that the irreversible production of 5 through such a stepwise ring‐closure mechanism is much more kinetically facile (ΔG^≠=26.2 kcal mol^?1) than an alternative σ‐metathesis pathway (ΔG^≠=48.2 kcal mol^?1).     

Distributed forcing of the flow past a blunt-based axisymmetric bluff body

In this paper, we address the influence of a blowing-/suction-type distributed forcing on the flow past a blunt-based axisymmetric bluff body by means of direct numerical simulations. The forcing is applied via consecutive blowing and suction slots azimuthally distributed along the trailing edge of the bluff body. We examine the impact of the forcing wavelength, amplitude and waveform on the drag experienced by the bluff body and on the occurrence of the reflectional symmetry preserving and reflectional symmetry breaking wake modes, for Reynolds numbers 800 and 1,000. We show that forcing the flow at wavelengths inherent to the unforced flow drastically damps drag oscillations associated with the vortex shedding and vorticity bursts, up to their complete suppression. The overall parameter analysis suggests that this damping results from the surplus of streamwise vorticity provided by the forcing that tends to stabilize the ternary vorticity lobes observed at the aft part of the bluff body. In addition, conversely to a blowing-type or suction-type forcing, the blowing-/suction-type forcing involves strong nonlinear interactions between locally decelerated and accelerated regions, severely affecting both the mean drag and the frequencies representative of the vortex shedding and vorticity bursts.     

Origin of the Enantioselectivity in Organocatalytic Michael Additions of β‐Ketoamides to α,β‐Unsaturated Carbonyls: A Combined Experimental,Spectroscopic and Theoretical Study

The organocatalytic enantioselective conjugate addition of secondary β‐ketoamides to α,β‐unsaturated carbonyl compounds is reported. Use of bifunctional Takemoto’s thiourea catalyst allows enantiocontrol of the reaction leading either to simple Michael adducts or spirocyclic aminals in up to 99 % ee. The origin of the enantioselectivity has been rationalised based on combined DFT calculations and kinetic analysis. This study provides a deeper understanding of the reaction mechanism, which involves a predominant role of the secondary amide proton, and clarifies the complex interactions occurring between substrates and the catalyst.     

Analysis of acoustic networks including cavities by means of a linear finite volume method

A procedure allowing for the analysis of complex acoustic networks, including three-dimensional cavities described in terms of zero-dimensional equivalent elements, is presented and validated. The procedure is based on the linearization of the finite volume method often used in gas-dynamics, which is translated into an acoustic network comprising multi-ports accounting for mass exchanges between the finite volumes, and equivalent 2-ports describing momentum exchange across the volume surfaces. The application of the concept to a one-dimensional case shows that it actually converges to the exact analytical solution when a sufficiently large number of volumes are considered. This has allowed the formulation of an objective criterion for the choice of a mesh providing results with a prefixed error up to a certain Helmholtz number, which has been generalized to three-dimensional cases. The procedure is then applied to simple but relevant three-dimensional geometries in the absence of a mean flow, showing good agreement with experimental and other computational results.     

A dissipation-based control method for the multi-scale modelling of quasi-brittle materials

Multi-scale models based on computational homogenisation are nowadays developed for the simulation of complex material behaviour. The use of homogenisation techniques on finite-sized representative volume elements in the presence of quasi-brittle damage may lead to the presence of snap-backs in the macroscopic material response. A methodology to simulate this type of response in the multi-scale technique is proposed, based on the control of the dissipation at the mesoscopic scale. To cite this article: T.J. Massart et al., C. R. Mecanique 333 (2005).