Synthesis and structural characterization of acetatobis(triphenylphosphine)dicarbonylrhenium(I). new car☐ylato derivatives of rhenium(I)

Acetatobis(triphenylphosphine)dicarbonylrhenium (I), (PPh₃)₂(CO)₂Re(O₂CCH₃), has been prepared in a novel way by treating (PPh₃)₂(CO)₂Re(NHCOR) (R = C₆H₅, p-MeC₆H₄) with triethylamine and water in the presence of air. Oxidation of the ethyl group of the tertiary amine is presumably involved in the formation of the acetate ligand. Three-dimensional single-crystal X-ray diffraction analysis shows that the complex is octahedral with the phosphines in trans positions and the acetate ion acting as a chelating ligand. The complex crystallizes in theP2₁/c space group with cell dimensions a = 17.63(2), b = 9.72(1), c = 20.95(2)Å, β = 104°38'(6'), Z = 4. The mean values of bond lengths observed are Re-P 2.415, Re-O 2.21 and Re-(CO) 1.85Å. The same acetate derivative and a series of car?ylato complexes (PPh₃)₂(CO)₂Re(O₂CR') have been obtained from reactions of Re(CO)₂(PPh₃)₃H with car?ylic acids R'COOH (R' = H, CH₃, CH₂Cl, CH₂CH₃, C₆H₅). When trifluoroacetic acid is used, a product of formula (PPh₃)₂(CO)₃Re(OC(O)CF₃) is isolated. The action of neutral ligands L on some of these products gave rise to derivatives of formula (PPh₃)₂(CO)₂(L)Re(OC(O)R') (L = CO, R' = H, CH₃, C₆H₅; L = pMeC₆H₄NC, R' = CH₃), having monodentate car?ylato moieties.     

Some catalytic properties of Rh(diphos)(η-BPh4)

The covalent complex Rh(diphos)(η-BPh₄) (I) reacts with CO in polar solvents to afford the cationic dicarbonyl cis-[Rh(diphos)(CO)₂](BPh₄). I is an effective catalyst for methylacetylene oligomerization and allene polymerization. In the presence of CO₂ and methylacetylene, I affords 4,6-dimethyl-2-pyrone.     

A finite-size dynamic-scaling approach for the diffusion front of particles

The scaling behavior of the diffusion front, originated by the random motion of particles under a concentration gradient, is studied by means of the Monte Carlo method and solving the diffusion equation. Simulations are performed on the square lattice using confined geometries of size MxL, where the gradient is established along the M direction while periodic boundary conditions are set along the L direction. A dynamic scaling Ansatz is proposed such as the width of the front [w(M,t)] scales as w(M,t) approximately M(alpha)f(t/M(alpha/beta)), where alpha and beta are the roughness and growing exponents, respectively. This proposal is based on the fact that the development of w is constrained by the gradient, that decays as M(-1), in contrast to the standard Family-Vicsek scaling Ansatz where correlations are constrained by the lateral dimension of the sample. It is found that the roughness exponent exhibits a systematic dependence on the sample size that can be rationalized in terms of a finite-size correction. Extrapolation to the thermodynamic limit gives alpha=4/7, in excellent agreement with theoretical predictions linking the diffusion system to the percolation problem. The evaluation of the growing exponent gives beta=0.30+/-0.02, leading us to the conjecture beta=2/7 for the exact value.     

Non-equilibrium wetting transition in a magnetic Eden model

Magnetic Eden clusters (Ausloos et al., Europhys. Lett. 24, 629 (1993)) with ferromagnetic interaction between nearest-neighbor spins are grown in a confined 2d-geometry with short range magnetic fields acting on the surfaces. The change of the growing interface curvature driven by the field and the temperature is identified as a non-equilibrium wetting transition and the corresponding phase diagram is evaluated. Received 27 March 2000     

A cellular automata model for social-learning processes in a classroom context

A model for teaching-learning processes that take place in the classroom is proposed and simulated numerically. Recent ideas taken from the fields of sociology, educational psychology, statistical physics and computational science are key ingredients of the model. Results of simulations are consistent with well-established empirical results obtained in classrooms by means of different evaluation tools. It is shown that students engaged in collaborative groupwork reach higher achievements than those attending traditional lectures only. However, in many cases, this difference is subtle and consequently very difficult to be detected using tests. The influence of the number of students forming the collaborative groups on the average knowledge achieved is also studied and discussed. Received 22 October 2001     

Some properties of semiconcave functions with general modulus

The class of semiconcave functions represents a useful generalization of the one of concave functions. Such an extension can be achieved requiring that a function satisfies a suitable one-sided estimate. In this paper, the structure of the set of points at which a semiconcave function fails to be differentiable—the singular set—is studied. First, we prove some results on the existence of arcs contained on the singular set. Then, we show how these abstract results apply to semiconcave solutions of Hamilton-Jacobi equations.     

Thermal Stability Evaluation of PA6/LLDPE/SEBS-g-DEM Blends

Summary: The thermal stability of a polyamide-6/low linear density polyethylene blend (PA6/LLDPE) was studied using thermal analysis techniques. The thermogravimetric studies carried out showed that when a diethyl maleate grafted styrene- ethylene/butadiene-styrene terpolymer (SEBS-g-DEM) is added to the PA6/LLDPE blend there is an actual enhancement of the thermal stability due to the increase in the interfacial area within the blend. The Invariant Kinetic Parameter method (IKP) proved to be a qualitative technique unfolding the type of degradation mechanisms taking place in the material vicinity. Nucleation and phase boundary reactions are the kinetic models of thermal decomposition with the most significant probability of occurring.     

On the regularity near the boundary of viscosity solutions of eikonal equations

Abstract We consider a non-characteristic boundary value problem for equations of eikonal type and we show that, near the boundary, the viscosity solution inherits the regularity of the data. As a consequence, we slightly improve the results in [1] on the structure of the cut-locus of a class of distance functions. Keywords: Viscosity solutions, Eikonal equation, Cut-locus, Analytic regularity