Interactions solutés-solvants en milleu eau-alcool tert-butylique: Partie II. Enthalpies de transfert de quelques acides carboxyliques

Solution enthalpies of acetic, propionic and isobutyric acid in water and in mixtures of water and t-butylalcohol are drawn from calorimetric measurements. For those three acids, enthalpies of transfer from water to the hydroorganic solvents exhibit a maximum for a particular composition of the solvents. These results are discussed in terms of structure of the hydroalcoholic media and of structure-breaking and -making abilities of the solutes.     

Etude par Résonance Magnétique Nucléaire de dérivés phosphores. Etude de dithiaphospholanes-1,3,2

The proton NMR spectral analysis of eight different 1,3,2-dithiaphospholanes with various groups attached to the phosphorus atom has been performed. The AA′BB′X (X phosphorus atom) system shows that the two ³J(P? S? C? H) coupling constants have a small magnitude and opposite signs. Using the ³J(HH) values, the torsion about the C₄—C₅ bond has been evaluated. The conformational requirements in the two isomers of the 2 phenyl-4-methyl-1,3,2-dithiaphospholane are also discussed.     

Tight Frames of Polynomials and the Truncated Trigonometric Moment Problem

A simple parametrization is given for the set of positive measures with finite support on the circle group T that are solutions of the truncated trigonometric moment problem: where the parameters are, up to nonzero multiplicative constants, the polynomials whose roots all have a modulus less than one. This result is then used to characterize, on a certain natural Hilbert space of polynomials associated with the problem, all finite "weighted" tight frames of evaluation polynomials. Finally, a new and simple way of parametrizing the whole set of positive Borel measures on T, solutions of the given moment problem is deduced, via a limiting argument.     

On the Brownian motion of a massive sphere suspended in a hard-sphere fluid. II. Molecular dynamics estimates of the friction coefficient

The friction coefficient exerted by a hard-sphere fluid on an infinitely massive Brownian sphere is calculated for several size ratios , where and are the diameters of the Brownian and fluid spheres, respectively. The exact microscopic expression derived in part I of this work from kinetic theory is transformed and shown to be proportional to the time integral of the autocorrelation function of the momentum transferred from the fluid to the Brownian sphere during instantaneous collisions. Three different methods are described to extract the friction coefficient from molecular dynamics simulations carried out onfinite systems. The three independent methods lead to estimates of which agree within statisticalerrors (typically 5%). The results are compared to the predictions of Enskog theory and of the hydrodynamic Stokes law. The former breaks down as the size ratio and/or the packing fraction of the fluid increase. Somewhat surprisingly, Stokes' law is found to hold withstick boundary conditions, in the range 1/4.5 explored in the present simulations, with a hydrodynamic diameterd=. The analysis of the moleuclar dynamics data on the basis of Stokes' law withslip boundary conditions is less conclusive, although the right trend is found as / increases.     

Spectral duality for planar billiards

For a bounded open domain with connected complement inR ² and piecewise smooth boundary, we consider the Dirichlet Laplacian- on and the S-matrix on the complement ^c . We show that the on-shell S-matricesS _k have eigenvalues converging to 1 askk ₀ exactly when-- has an eigenvalue at energyk ₀ ² . This includes multiplicities, and proves a weak form of transparency atk=k ₀. We also show that stronger forms of transparency, such asS _{k 0} having an eigenvalue 1 are not expected to hold in general.     

Infrared study of complexes between iron,salicylaldehyde benzoyl hydrazone and seven analogous derivatives

Summary An i.r. study of Fe complexes prepared from salicylaldehyde benzoyl hydrazone and seven similar chelating agents allowed the assignment of some iron-ligand bands. The amide I and —O band shifts indicate that the ligand O atoms are directly linked to Fe. The analogy between Fe^II and Fe^III complexes in the mid-i.r. range and the chiefly identical frequencies in the far-i.r. range provide evidence that oxidation of Fe^IIhas occurred. The bands directly involved in complexation are shifted compared to the free hydrazones, and all are medium or weak.     

Dynamics and growth of particles undergoing ballistic coalescence

The irreversible evolution of a model for ballistic coalescence of spherical particles, whereby colliding particles merge into a single, larger sphere with conservation of mass and momentum, is analyzed on the basis of scaling assumptions, mean-field theory, and kinetic theory for arbitrary dimensionality and size-mass relation. The asymptotic growth regime is characterized by scaling laws associated with the instantaneous mean mass and kinetic energy of the particles. A hyperscaling relation between the mass and energy exponents is derived. The predictions of the theoretical analysis are tested by extensive simulations of the two-dimensional version of the model. Due to multiple coalescence events, the exponents are found to be nonuniversal (i.e., density dependent) and to differ significantly from the mean-field predictions. The distribution of masses turns out to be universal and exponential. Particle energies follow a Boltzmann distribution, with a time-dependent temperature, or relax toward such a distribution, even when the initial distribution is highly non-Maxwellian. In the case where the particles are swollen [i.e., the size-mass relation involves the Flory exponentv=3/(d+2)], an asymptotic scaling regime is observed only for sufficiently low initial packing fractions. At higher densities, the irreversible evolution terminates in a catastrophic coalescence event involving all remaining particles.     

Les dithiaphospho(III)lanes-1,3,2, noveaux precurseurs de derives du phosphore penta- et dicoordine

The synthesis of new spirodithiaphospholans is described. Lability of these compounds allows to obtain by an orginally way dicoordinated phosphorus derivatives.     

A fast-moving [2]rotaxane whose stoppers are remote from the copper complex core

[reaction: see text] A new copper-complexed rotaxane is described. It consists of a two-coordination site ring threaded by a sterically non-hindering 2,2'-bipyridine derivative. An electrochemical signal (oxidation or reduction of the copper center, Cu(I) or Cu(II)) induces rearrangement of the system. By using long and flexible linkers between the stoppers and the central complex, ligand exchange is fast, which leads to short response times (on the millisecond time scale and even below).     

Preparation and structural properties of macrocyclic phosphonamides. Structural characterization of a potassium complex

A novel class of organophosphorus macrocycles containing one phosphonamide or one thiophosphonamide group was obtained by condensation of bis(dimethylamino)methyl-phosphine with the appropriate oligoether-bisprimary amine, followed by the oxidation of the P(III) species. The structures of two macrocyclic phosphonamide ligands (3 and4) which differ in the length of the oligoether chain, and that of the potassium thiocyanate complex of4, were studied by Xray diffraction. The crystals of3 and4 containe two crystallographically independent molecules. A cavity appears in the centre of each uncomplexed molecule, but the oxygen atoms of the longer oligoether chain are better oriented towards the centre of this cavity. An important rearrangement of the molecular conformation of4 occurs upon complexation as shown in the crystal structure analysis of the complex4· KSCN. The phosphoryl O atom of one molecule binds to the metal ion of another complexed molecule, leading to the self assembly of4· KSCN complexes. Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP. 82161 (27 pages).Research fellow (1986–1989), Université J. Fourier, Grenoble (France)