Bi-Lipschitz geometry of complex surface singularities

We discuss the bi-Lipschitz geometry of an isolated singular point of a complex surface with particular emphasis on when it is metrically conical.      

Local Lipschitz geometry of real weighted homogeneous surfaces

We compute Hölder Complexes, i.e. the complete bi-Lipschitz invariants, for germs of real weighed homogeneous algebraic or semialgebraic surfaces.     

Ruthenium hydride catalyzed silylvinylation of terminal alkynes under ethylene atmosphere at 80 psi

The development of methods for the stereoselective synthesis of polysubstituted 1,3-dienes is a challenge to synthetic chemistry. Herein is reported a selective approach for the synthesis of polysubstituted 1,3-dienes using the ruthenium hydride catalyzed intramolecular silylvinylation of alkynes under 80 psi of ethylene gas. This strategy affords a single diene isomer, is applicable to substrates with aryl and alkyl substitution at the propargyl and homopropargyl positions, and has been utilized in the synthesis of 5- and 6-membered oxasilacycles.     

Structuration de la convection mixte en milieu poreux confiné latéralement et chauffé par le bas : effets d''inertiePattern formation of mixed convection in a porous medium confined laterally and heated from below: effect of inertia

We consider the onset of convection in a porous medium heated from below and subjected to a horizontal mean flow. The effect of porous inertia is studied, and the transverse aspect ratio a of the medium is taken into accout. We find that the dominant modes are longitudinal rolls (L.R) if a is an integer or transverse traveling rolls (T.R) if a is below a_c with a_c<1. When a is not an integer with a>a_c, the setting on patterns are oscillatory three-dimensional structures (3D) for a>1 or T.R for a_c<a<1 provided that the Reynolds number remains below a critical value Re_K^*. We show that these structures are replaced by L.R if Re_K>Re_K^*. To cite this article: A. Delache et al., C. R. Mecanique 330 (2002) 885–891.     

Correlation between superhydrophobicity and the power spectral density of randomly rough surfaces

We show experimentally and analytically that for single-valued, isotropic, homogeneous, randomly rough surfaces consisting of bumps randomly protruding over a continuous background, superhydrophobicity is related to the power spectral density of the surface height, which can be derived from microscopy measurements. More precisely, superhydrophobicity correlates with the third moment of the power spectral density, which is directly related to the notion of Wenzel roughness (i.e., the ratio between the real area of the surface and its projected area). In addition, we explain why randomly rough surfaces with identical root-mean-square roughness values may behave differently with respect to water repellence and why roughness components with wavelength larger than 10 μm are not likely to be of importance or, stated otherwise, why superhydrophobicity often requires a contribution from submicrometer-scale components such as nanoparticles. The analysis developed here also shows that the simple thermodynamic arguments relating superhydrophobicity to an increase in the sample area are valid for this type of surface, and we hope that it will help researchers to fabricate efficient superhydrophobic surfaces based on the rational design of their power spectral density.     

DFT, ab initio, NMR, and NBO analyses of N-substituted hydrazino acetamides: Experimental vs theoretical values

We studied the DFT (B3LYP) and HF at 6-31+G/6-31+G^∗∗ levels of theory in order to throw light on the conformation, structure, intramolecular hydrogen bond network, as well as proton and nitrogen NMR (GIAO method) of a series of model primary amides in the gas phase and/or in solution (chloroform, methanol, water, dimethyl sulfoxide, and heptane). In this manner, it was possible to show that the amidic group of these model compounds acts as the H-bond donor and interacts with two different H-bond acceptors, thus stabilizing the C₈ pseudocycle. The study was conducted to gain a better understanding of the conformation (both experimentally and theoretically) adopted by hydrazino acetamides (model compounds for aza-β³-peptides). In the light of this, we were able to explain why aza-β³-peptides develop a different H-bond network in comparison to their isosteric β³-peptide analogues (an extension of the β-peptide concept).     

Facially coordinating triamine ligands with a cyclic backbone: some structure-stability correlations

Metal complex formation of the two cyclic triamines 6-methyl-1,4-diazepan-6-amine (MeL(a)) and all-cis-2,4,6-trimethylcyclohexane-1,3,5-triamine (Me(3)tach) was studied. The structure of the free ligands (H(x)MeL(a))(x+) and H(x)Me(3)tach(x+) (0 ≤ x ≤ 3) was investigated by pH-dependent NMR spectroscopy and X-ray diffraction experiments. The crystal structure of (H(2)Me(3)tach)(p-O(3)S-C(6)H(4)-CH(3))(2) showed a chair conformation with axial nitrogen atoms for the doubly protonated species. In contrast to a previous report, Me(3)tach was found to be a stronger base than the parent cis-cyclohexane-1,3,5-triamine (tach); pK(a)-values of H(3)Me(3)tach(3+) (25 °C, 0.1 M KCl): 5.2, 7.4, 11.2. The crystal structures of (H(3)MeL(a))(BiCl(6))·2H(2)O and (H(3)MeL(a))(ClO(4))Cl(2) exhibited two distinct twisted chair conformations of the seven membered diazepane ring. [Co(MeL(a))(2)](3+) (cis: 1(3+), trans: 2(3+)), trans-[Fe(MeL(a))(2)](3+) (3(3+)), [(MeL(a))ClCd(μ(2)-Cl)](2) (4), trans-[Cu(MeL(a))(2)](2+) (5(2+)), and [Cu(HMeL(a))Br(3)] (6) were characterized by single crystal X-ray analysis of 1(ClO(4))(3)·H(2)O, 2Br(3)·H(2)O, 3(ClO(4))(3)·0.8MeCN·0.2MeOH, 4, 5Br(2)·0.5MeOH, and 6·H(2)O. Formation constants and redox potentials of MeL(a) complexes were determined by potentiometric, spectrophotometric, and cyclovoltammetric measurements. The stability of [M(II)(MeL(a))](2+)-complexes is low. In comparison to the parent 1,4-diazepan-6-amine (L(a)), it is only slightly enhanced. In analogy to L(a), MeL(a) exhibited a pronounced tendency for forming protonated species such as [M(II)(HMeL(a))](3+) or [M(II)(MeL(a))(HMeL(a))](3+) (see 6 as an example). In contrast to MeL(a), Me(3)tach forms [M(II)L](2+) complexes (M = Cu, Zn) of very high stability, and the coordination behavior corresponds mainly to an "all-or-nothing" process. Molecular mechanics calculations showed that the low stability of L(a) and MeL(a) complexes is mainly due to a large amount of torsional strain within the pure chair conformation of the diazepane ring, required for tridentate coordination. This behavior is quite contrary to Me(3)tach and tacn (tacn =1,4,7-triazacyclononane), where the main portion of strain is already preformed in the free ligand, and the amount, generated upon complex formation, is comparably low.     

A general approach to indole-7-yl derivatives of isoxazole, oxadiazole, thiadiazole and pyrazole

Isosteric replacement of the α,β-unsaturated amide at the C-7 position of indoles with a diverse set of five-membered amino-heterocycles including isoxazole, oxadiazole, thiadiazole and pyrazole followed by subsequent derivatization of the heterocyclic amino group to yield amides, sulfonamides and phosphoramides is described. Distinctive features of these procedures include the versatility and robust nature of the synthetic steps along with the high yields of the targeted molecules.     

New cyclic phosphonium salts derived from the reaction of phosphine-aldehydes with acid

Various cyclic phosphonium structures are formed in high yield by the deprotection of unstable phosphine-aldehydes in acidic solution. When there is a methylene spacer between the phosphine and the aldehyde, a phosphonium ion [PHR₂CH₂CH(OEt)₂]Br₂, R=iPrOH, Et is obtained. Reaction of these phosphonium salts with water produces the dimers [-PR₂CH₂CH(OH)-]₂[Br]₂ R = iPr, Et. When there is an ethylene spacer as in PPh₂CH₂CH₂CH(OCH₂CH₂O), a remarkable tetramer with a 16-membered ring [-PPh₂CH₂CH₂CH (OH)-]₄[Cl]₄ forms as one diastereomer in hydrochloric acid solution. Reaction of HCl with the protected phosphine-aldehyde with a propylene spacer (PPh₂CH₂CH₂CH₂CH(OCH₂CH₂O)) results in the formation of the monomeric phosphonium salt [-PPh₂ CH₂CH₂CH₂CH(OH)-]Cl with a 5-membered ring. Solid state structures of different ring types were determined using X-ray diffraction experiment.