Energy Scaling of Compressed Elastic Films –Three-Dimensional Elasticity¶and Reduced Theories

We derive an optimal scaling law for the energy of thin elastic films under isotropic compression, starting from three-dimensional nonlinear elasticity. As a consequence we show that any deformation with optimal energy scaling must exhibit fine-scale oscillations along the boundary, which coarsen in the interior. This agrees with experimental observations of folds which refine as they approach the boundary. We show that both for three-dimensional elasticity and for the geometrically nonlinear Föppl-von Kármán plate theory the energy of a compressed film scales quadratically in the film thickness. This is intermediate between the linear scaling of membrane theories which describe film stretching, and the cubic scaling of bending theories which describe unstretched plates, and indicates that the regime we are probing is characterized by the interplay of stretching and bending energies. Blistering of compressed thin films has previously been analyzed using the Föppl-von Kármán theory of plates linearized in the in-plane displacements, or with the scalar eikonal functional where in-plane displacements are completely neglected. The predictions of the linearized plate theory agree with our result, but the scalar approximation yields a different scaling.     

Synthese De (1,2a)Benzimidazolo-1,3,5,2-triazaphosphorine-2-oxides

The reaction of hexamethylphosphotriamide or methylphosphonic bis(dimethylamide) compounds with amidines derived from N-Benzimidazoyl imidates 1 leads to (1,2a)benzimidazolo-1,3,5,2-tiazaphosphorine-2-oxides 4 in good yields. If the condensation is realized at room temperature, N-phosphonic amidines 3 can be isolated as intermediates. The isolated compounds 2 , 3 , and 4 are identified by spectroscopic methods: IR, 1 H, 13 C, 31 P, NMR, and M.S.     

Uniqueness for an ill-posed parabolic system

The purpose is the uniqueness for an ill-posed parabolic system. This result enables us to state the identifiability for the problem of detecting pointwise organic pollution sources in surface waters.     

Spectral element discretization of the Maxwell equations

We consider a variational problem which is equivalent to the electromagnetism system with absorbing conditions on a part of the boundary, and we prove that it is well-posed. Next we propose a discretization relying on a finite difference scheme for the time variable and on spectral elements for the space variables, and we derive error estimates between the exact and discrete solutions. RESUME. On considère un problème variationnel équivalent aux équations de l'électromagnétisme avec conditions aux limites absorbantes sur une partie de la frontière, qu'on prouve être bien posé. Puis on propose une discrétisation de ce problème par schéma aux différences finies en temps et éléments spectraux en espace, et on établit des estimations d'erreur entre solutions exacte et approchée.

     

REACTION DES O,O-DIETHYL OXO-1 ALKANEPHOSPHONATES AVEC LES DERIVES DE L'HYDRAZINE: UNE VOIE DE SYNTHESE DES HYDRAZONES α-PHOSPHONATEES ET DES HYDRAZIDES

Abstract

Under the normal conditions, the reaction of hydrazine and methylhydrazine with OO-diethyl 1 oxoalkane phosphonates 1 proceeds by cleavage of the phosphorus-carbon bond and leads to the formation of diethylphosphite 2 and N-acylhydrazide 3 . A procedure has been developed for the synthesis of new primary hydrazone of OO-diethyl 1-oxoalkane phosphonates 4 . A mechanism is proposed. The structure of those compounds 4 was confirmed by NMR and IR spectroscopy.     

Hydrolysis-Condensation Kinetics of Different Silane Coupling Agents

Abstract

The hydrolysis kinetics of 14 alkoxy silane coupling agents were carried out in an ethanol:water 80:20 (w/w) solution under acidic conditions and were monitored by ¹H, ¹³C, and ²⁹Si NMR spectroscopy. Acidic conditions were selected in order to enhance the silanol formation and to slow down the self-condensation between the resulting hydrolysed silanol groups. In situ ²⁹Si NMR spectroscopy allowed the determination of the intermediate species as a function of the reaction time. Thus, the following silane coupling agents were studied: 3-methacryloxypropyl trimethoxy silane (MPMS), 3-mercaptopropyl trimethoxy silane (MRPMS), 3-cyanopropyl triethoxy silane (CPES), triethoxy vinyl silane (VES), trimethoxy (2-phenylethyl) silane (PEMS), octyl triethoxy silane (OES), trimethoxy (7-octen-1-yl) silane (OEMS), 3-aminopropyl triethoxy silane (APES), 3-aminopropyl trimethoxy silane (APMS), 3-(2-aminoethylamino)propyl trimethoxy silane, (DAMS), 3-[2-(2-aminoethylamino)-ethylamino]propyl trimethoxy silane (TAMS), 4-amino-3,3-dibutyl trimethoxy silane (ADBMS), trimethoxy [3-(phenylamino)propyl] silane (PAPMS), and triethoxy-3-(2-imidazolin-1-yl) propyl silane (IZPES). A parameter quantifying the grafting potentiality of each silane coupling agent towards OH-rich solid substrates (such as cellulose) was established as a function of the nature of the alkoxy groups (methoxy or ethoxy), as well as that of the fourth substituent (vinyl, aminopropyl, etc.) of the silane studied.

GRAPHICAL ABSTRACT     

Design, synthesis and photo-cross-linking of a new photosensitive macromonomer from tetra-branched poly(ethylene oxide)s

A general procedure to increase the amount of photoreactive chromophore groups per oligoether chain is presented. In this work, a photoreactive macromonomer with four functionalities was synthesized by a four-step synthetic pathway with high yield. The photochemical behavior of this compound was studied with a view to obtaining polymeric networks. The significant advantage in this strategy is that the preparation of this material has as last operation, the obtaining and processing of polymer as thin film. In this way, the synthetic strategy based on assembling: (i) the polyether chains, (ii) a film forming backbone, and (iii) a photoactive moiety to be used for cross-linking, seems a viable solution to the problem of the continuous processing of materials.