Chelate polymers: II. Some novel transition metals complexes with azomethine‐containing siloxanes and their polyesters

New Schiff bases of 2,4‐dihydroxybenzaldehyde with siloxane‐α,ω‐diamines having different numbers of siloxane units in the chain have been synthesized and characterized by spectroscopy, elemental and thermal analyses. These azomethines were found to form complexes readily with copper(II), nickel(II), cobalt(II), cadmium(II) and zinc(II). From IR and UV–Vis studies, the phenolic oxygen and imine nitrogen of the ligand were found to be the coordination sites. Thermogravimetric analysis (TGA) data indicate the chelates to be more stable than the corresponding ligands. The melting points increase with shortening of the siloxane segment from azomethine, as well as the result of complexation. The chelates obtained were covalently inserted in polymeric linear structures by polycondensation through the OH‐difunctionalized ligand with 1,3‐bis(carboxypropyl)tetramethyldisiloxane. Direct polycondensation, assisted either by acetic anhydride or N,N′‐dicyclohexylcarbodiimide as dehydrating agent and the complex 4‐(dimethylamino)pyridinium 4‐toluenesulfonate as catalyst, was used for the synthesis of these compound types. The structures of the polymers obtained were confirmed by IR, UV and ¹H NMR. Characterization was undertaken by TGA, solubility tests and viscosity measurements. Copyright © 2003 John Wiley & Sons, Ltd.     

Maximal triangle-free graphs with restrictions on the degrees

We investigate the problem that at least how many edges must a maximal triangle-free graph on n vertices have if the maximal valency is ≤D. Denote this minimum value by F(n, D). For large enough n, we determine the exact value of F(n, D) if D ≥ (n ? 2)/2 and we prove that lim F(n, cn)/n = K(c) exists for all 0 < c with the possible exception of a sequence c_k → 0. The determination of K(c) is a finite problem on all intervals [γ, ∞). For D = cn^?, 1/2 < ? < 1, we give upper and lower bounds for F(n, D) differing only in a constant factor. (Clearly, D < (n - 1)^1/2 is impossible in a maximal triangle-free graph.)     

On the resolving power of high-contrast saturated absorption spectroscopy

Recently Svanberg et al. [Optics Lett. 11 (1986) 138; J. Opt. Soc. Am. B 4 (1987) 462] obtained saturated absorption resonances with subnatural linewidth by working in the regime of high pumping intensities and optically thick atomic samples. We analyze here this new spectroscopic regime, within the formalism of Maxwell-Bloch-type equations, in the case of a Doppler broadened medium having two nearly degenerate but uncoupled resonances. We show that even in this most favourable case it is not possible to resolve spectral features that lie within the natural linewidth.     

Competitive influence of atactic polystyrene and supercritical carbon dioxide on the conformation of syndiotactic polystyrene

The crystallization behavior of miscible syndiotactic polystyrene (sPS) and atactic polystyrene (aPS) blends with different sPS/aPS weight ratios was investigated in supercritical CO₂ by using Fourier‐transform infrared spectroscopy, differential scanning calorimetry, and wide‐angle X‐ray diffraction. Supercritical CO₂ and aPS exhibited different effects on the conformational change of sPS and competed with each other. Increasing the content of amorphous aPS in the blends made its effect on the conformational change of sPS gradually surpass that of supercritical CO₂. Supercritical CO₂ favored the formation of the helical conformation of sPS in lower temperature range and the all trans planar conformation in higher temperature range, instead of forming the latter one only in higher temperature range in ambient atmosphere. However, increasing aPS content in the blends pushed the range for forming the helical conformation to lower temperature and made the all trans planar conformation dominant in aPS/sPS 25/75 blend after treating in supercritical CO₂ above 60 °C. The all trans planar zigzag conformation was more favorable than the helical conformation after mixing aPS in sPS in supercritical CO₂. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1755–1764, 2007     

Highly edge‐connected detachments of graphs and digraphs

Let G = (V,E) be a graph or digraph and r : V → Z₊. An r‐detachment of G is a graph H obtained by ‘splitting’ each vertex ν ∈ V into r(ν) vertices. The vertices ν₁,…,ν_r(ν) obtained by splitting ν are called the pieces of ν in H. Every edge uν ∈ E corresponds to an edge of H connecting some piece of u to some piece of ν. Crispin Nash‐Williams 9 gave necessary and sufficient conditions for a graph to have a k‐edge‐connected r‐detachment. He also solved the version where the degrees of all the pieces are specified. In this paper, we solve the same problems for directed graphs. We also give a simple and self‐contained new proof for the undirected result. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 67–77, 2003     

Accuracy of the chemical data evaluated from one-atom-at-a-time experiments

Studies of chemistry of the transactinoid elements, which are available only as single atoms, by gas (thermo)chromatographic techniques can provide the adsorption enthalpies of the atoms or molecules. These values serve the ultimate goal—to characterize bulk volatility of the species in terms like sublimation enthalpies. The paper attempts an in-depth discussion of the statistical significance of the adsorption enthalpies derived in such experiments. Usually, the counting statistics are very poor and one faces nonstandard problems in evaluating the confidence intervals for the values of parameters. Here, a most efficient way seems to be the Bayesian approach, realized, when necessary, by Monte Carlo simulations of the counting results. Necessarily, the adsorption enthalpy is not evaluated based on the second law of thermodynamics but through accepting an a priori value of the adsorption entropy. More additional assumptions about the mechanisms and parameters involved are needed. This may produce systematic errors in the quantitative conclusions; the analysis of some recent works with elements 106 and 108 corroborates this concern. Despite such problems, it is possible to reveal qualitative differences in the adsorption behavior of a transactinoid and its expected known congeners as well as to use chemistry for an independent assignment of the atomic numbers of transactinoid nuclides.     

Influence of the loading path on the strength of fiber-reinforced composites subjected to transverse compression and shear

The influence of the loading path on the failure locus of a composite lamina subjected to transverse compression and out-of-plane shear is analyzed through computational micromechanics. This is carried out using the finite element simulation of a representative volume element of the microstructure, which takes into account explicitly fiber and matrix spatial distribution within the lamina. In addition, the actual failure mechanisms (plastic deformation of the matrix and interface decohesion) are included in the simulations through the corresponding constitutive models. Two different interface strength values were chosen to explore the limiting cases of composites with strong or weak interfaces. It was found that failure locus was independent of the loading path for the three cases analyzed (pseudo-radial, compression followed by shear and shear followed by compression) in the composites with strong and weak interfaces. This result was attributed to the fact that the dominant failure mechanism in each material was the same in transverse compression and in shear. Failure is also controlled by the same mechanisms under a combination of both stresses and the failure locus depended mainly on the magnitude of the stresses that trigger fracture rather than in the loading path to reach the critical condition.     

Vertical migration of 85Sr, 137Cs and 131I in various arable and undisturbed soils

The vertical migration of ⁸⁵Sr, ¹³⁷Cs and ¹³¹I in some arable and undisturbed single-contaminated soils was studied by gamma-spectrometry measurements under lysimetric laboratory conditions during irrigation of the soil profiles with wet atmospheric precipitation for about one year, except ¹³¹I. A new simple exponential compartment (box) model was derived, which makes it possible to calculate the migration rate constants and migration rates in the individual soil layers (vertical sections) as well as the total vertical migration rate constants and total vertical migration rates of radionuclides in the bulk soil horizon. The relaxation times of radionuclides in respective soil horizons can also be evaluated.     

Local chain‐configuration dependence of the mechanisms of the chemical reaction of poly(vinyl chloride). IX. Novel results on stereoselectivity of chlorination reaction

A poly(vinyl chloride) (PVC) sample was chlorinated in solution in the presence of 2,2′‐azobisisobutyronitrile and by the fluid‐bed method. The aim was to evaluate the scope of the stereoselectivity of the chlorination reaction. The quantitative microstructural analysis of the residual PVC with a degree of chlorination was followed by ¹³C NMR spectroscopy. From the evolution of the content of isotactic (mm), heterotactic (mr), and syndiotactic (rr) triads and of mmmm, mmmr, and rmmr isotactic pentads in the unchlorinated parts of the polymer, it was unambiguously inferred that the chlorination reaction proceeds by a stereoselective mechanism in that the mr heterotactic triads are the most reactive structures followed by the isotactic triad at mmmr and rmmr pentads. This conclusion was confirmed on the basis of the Fourier transform infrared results. The results provide valuable information regarding the effect of tacticity and related local conformations in the chemical reactions of PVC. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 508–519, 2003