New C2-Chiral Bidentate Ligands Bridging the gap between donor phosphine and acceptor carbonyl ligands

Two new C₂ chiral bidentate phosphorous ligands have been prepared in enantiomerically pure form. The two phosphorous centers bear electron-withdrawing groups ((CF₃)₂CH? O, C₆F₅) and are linked by a trans-cyclopentane-1,2-diol-derived bridge. Photolysis of [Cr(η⁶-C₆H₆)(CO)₃] in the presence of these two new ligands and of two previously reported bidentate phosphites, and fluorophosphinites (L) afforded [Cr(η⁶-C₆H₆)(CO)L] complexes. IR Spectral comparison of the complexes shows the new ligands to be intermediate in their bonding properties between alkyl phosphites and CO.     

Fracture and debonding of a thin film on a stiff substrate: analytical and numerical solutions of a one-dimensional variational model

We study multi-fissuration and debonding phenomena of a thin film bonded to a stiff substrate using the variational approach to fracture mechanics. We consider a reduced one-dimensional membrane model where the loading is introduced through uniform inelastic (e.g., thermal) strains in the film or imposed displacements of the substrate. Fracture phenomena are accounted for by adopting a Griffith model for debonding and transverse fracture. On the basis of energy minimization arguments, we recover the key qualitative properties of the experimental evidences, like the periodicity of transverse cracks and the peripheral debonding of each regular segment. Phase diagrams relate the maximum number of transverse cracks that may be created before debonding takes place, as a function of the material properties and the sample’s geometry. The theoretical results are illustrated with numerical simulations obtained through a finite element discretization and a regularized variational formulation of the Ambrosio–Tortorelli type, which is suited to further extensions in two-dimensional settings.     

Development of SPME on-fiber derivatization for the sampling of formaldehyde and other carbonyl compounds in indoor air

Solid-phase microextraction on-fiber derivatization applied to carbonyl compounds is known, but application to indoor air is poorly developed and the methods deserve to be complemented and optimized. In this work, two derivatization reagents, pentafluorophenylhydrazine and o-2,3,4,5,6-(pentaflurobenzyl)hydroxylamine (PFBHA), and three fiber coatings were tested in order to select the best combination. As Carboxen-based coatings were proven to induce the formation of by-products during the thermal desorption step, a polydimethylsiloxane–divinylbenzene fiber in association with PFBHA was finally chosen. The study of the derivatization kinetics showed that the reaction of PFBHA with carbonyl compounds was instantaneous, except for acetone. Analyses were performed by gas chromatography coupled with flame ionization detection and mass spectrometry. For 5 min fiber exposure, the limits of detection are below 0.5 μg m^-3 in selected ion monitoring mode, the reproducibility was 15 % on average, and the linearity of the calibration curves was satisfactory. For on-site application, the influence of air humidity and the conditions in which the impregnated fibers were stored were studied. It is possible to store the fibers for 3 days before and for at least 2 days after sampling. The relative humidity of air was shown to have no influence on solid-phase microextraction sampling in the range from 0 to 70 %. For formaldehyde, the method was compared with sampling on 2,4-dinitrophenylhydrazine cartridges, and the first results showed good agreement. Finally, the method was applied to three different indoor environments to check its feasibility.     

A new reversed-phase liquid chromatographic/tandem mass spectrometric method for analysis of underivatised amino acids: evaluation for the diagnosis and the management of inherited disorders of amino acid metabolism

Seventy-six compounds of biological interest for the diagnosis of inherited disorders of amino acids (AA) metabolism have previously been demonstrated to be detectable in positive mode electrospray ionisation tandem mass spectrometry (ESI-MS/MS), after separation by ion-pairing reversed-phase liquid chromatography (RPLC). The separation method used tridecafluoroheptanoic acid as ion-pairing agent, and a gradient of acetonitrile for the elution of the most retained compounds. This method had previously been demonstrated to be suitable for the qualitative diagnosis of many AA disorders, and for the quantitative measurement of 16 AA in biological fluids, using their stable isotope labelled (SIL) AA as internal standard. For quantification of the other AA, an internal standard was chosen among the available SIL-AA, as close as possible to the analyte to be measured, in terms of structural analogy, and of retention time in the chromatographic system. The performances of the quantitative analysis of the other AA to be measured are reported here. They show validated results for several AA, allowing their accurate quantification, with another SIL-AA as internal standard. For some other AA, quantitative results were not accurate, allowing only semi-quantitative or qualitative determination for these parameters.     

A continuous/discrete fractional Noether’s theorem

We prove a fractional Noether’s theorem for fractional Lagrangian systems invariant under a symmetry group both in the continuous and discrete cases. This provides an explicit conservation law (first integral) given by a closed formula which can be algorithmically implemented. In the discrete case, the conservation law is moreover computable in a finite number of steps.     

Determination of the Kinetic and Thermodynamic Parameters of Adsorption Processes by a Volume Step Thermal Method

A volume step method measuring the pressure and the adsorbent temperature of an adsorbent-adsorbate system has been developped. It is shown that this method allows the determination of all the relevant parameters of an adsorption process, kinetic as well as thermodynamic in case of Linear Driving Force mass transfer. The method for determining the parameters can be extended to the case of diffusive mass transfer if the mass transfer kinetics is faster than the heat transfer kinetics. An example is given, showing the determination of the diffusion coefficient of carbon dioxide in NaX zeolite pellets and the change of the diffusion coefficient and of the isosteric heat of adsorption when the adsorbent is not fully dehydrated.     

Legendre’s Necessary Condition for Fractional Bolza Functionals with Mixed Initial/Final Constraints

Journal of Optimization Theory and Applications - The present work was primarily motivated by our findings in the literature of some flaws within the proof of the second-order Legendre necessary...     

Time-Resolved Digital Image Correlation in the Scanning Electron Microscope for Analysis of Time-Dependent Mechanisms

Experimental Mechanics - Background: Advancements in the Digitial Image Correlation (DIC) technique over the past decade have greatly improved spatial resolution. However, many processes, such as...     

Helmholtz's inverse problem of the discrete calculus of variations

We derive the discrete version of the classical Helmholtz's condition. Precisely, we state a theorem characterizing second-order finite difference equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide the class of all possible Lagrangian formulations.