Stereochemical activity of lone pairs of electrons and supramolecular aggregation patterns based on secondary interactions involving tellurium in its 1,1-dithiolate structures

A survey of the crystallographic literature of tellurium(II)/(IV) 1,1-dithiolates (dithiocarbamate, xanthate, dithiophosphate, or dithiophosphinate) is presented. Coordination numbers range from a low of three in some organotellurium(II) 1,1-dithiolates to a high of eight in the binary tellurium(IV) dithiocarbamates. The coordination geometries are rich and varied due to the stereochemical influence exerted by up to two lone pairs of electrons and the penchant of tellurium to increase its coordination number by forming secondary Te?X interactions, where X = sulphur, halide, tellurium, oxygen, and, in one case, a π system defined by a four-membered TeS₂C chelate. Stereochemical roles of the lone pairs of electrons are always evident in the tellurium(II) structures. By contrast, a stereochemical position is not always evident for the lone pair of electrons in the tellurium(IV) derivatives, in particular in circumstances where the tellurium centre has a high coordination number. Supramolecular aggregation mediated by Te?X secondary interactions often leads to the formation of dimeric aggregates but sometimes to supramolecular polymers, and rarely three-dimensional networks. Comparisons between closely related structures clearly indicate that the dithiocarbamate ligand is a more effective chelating ligand compared with the other 1,1-dithiolate ligands covered in this survey. This difference in coordinating ability is clearly correlated with the observation that non-dithiocarbamate structures are more likely to form high-dimensional supramolecular architectures.     

Considerations on “Harmonic balancing approach to nonlinear oscillations of a punctual charge in the electric field of charged ring”

In a previous short communication [A. Beléndez, E. Fernández, J.J. Rodes, R. Fuentes, I. Pascual, Phys. Lett. A 373 (2009) 735] the nonlinear oscillations of a punctual charge in the electric field of a charged ring were analyzed. Approximate frequency-amplitude relations and periodic solutions were obtained using the harmonic balance method. Now we clarify an important aspect about of this oscillation charge. Taking into account Earnshaw's theorem, this punctual charge cannot be a free charge and so it must be confined, for example, on a finite conducting wire placed along the axis of the ring. Then, the oscillatory system may consist of a punctual charge on a conducting wire placed along the axis of the uniformly charged ring.     

A singularity-avoiding moving least squares scheme for two-dimensional unstructured meshes

Moving least squares interpolation schemes are in widespread use as a tool for numerical analysis on scattered data. In particular, they are often employed when solving partial differential equations on unstructured meshes, which are typically needed when the geometry defining the domain is complex. It is known that such schemes can be singular if the data points in the stencil happen to be in certain special geometric arrangements, however little research has specifically addressed this issue. In this paper, a moving least squares scheme is presented which is an appropriate tool for use when solving partial differential equations in two dimensions, and the precise conditions under which singularities occur are identified. The theory is used to develop a stencil building algorithm which automatically detects singular stencils and corrects them in an efficient manner, while attempting to maintain stencil symmetry as closely as possible. Finally, the scheme is applied in a convection–diffusion equation solver and an incompressible Navier–Stokes solver, and the results are shown to compare favourably with known analytical solutions and previously published results.     

ZnO nanoparticles embedded in UVM-7-like mesoporous silica materials: Synthesis and characterization

ZnO nanodomains embedded in bimodal mesoporous silica (UVM-7) materials with high Zn content (4≤Si/Zn≤30) have been synthesized by an one-pot surfactant-assisted procedure from a hydro alcoholic medium using a cationic surfactant (CTMABr=cetyltrimethylammonium bromide) as structural directing agent, and starting from molecular atrane complexes of Zn and Si as hydrolytic inorganic precursors. This chemical procedure allows optimizing the dispersion of the ZnO particles in the silica walls. The bimodal mesoporous nature of the final high surface area nano-sized materials is confirmed by XRD, TEM, and N₂ adsorption–desorption isotherms. The small intra-particle mesopore system is due to the supramolecular templating effect of the surfactant, while the large pores have their origin in the packing voids generated by aggregation of the primary nanometric mesoporous particles. A limited pore blocking and a high accessibility to the ZnO active nanoparticles have been achieved. The effects induced by the progressive incorporation of ZnO nanoparticles into the mesostructure have been examined, including a careful optical spectroscopic study (PL and UV–visible).     

CO2 Fixation by Cu2+ and Zn2+ complexes of a terpyridinophane aza receptor. Crystal structures of Cu2+ complexes, pH-metric, spectroscopic, and electrochemical studies

The synthesis of the terpyridinophane-type polyamine 2,6,9,12,16-pentaaza[17]-(5,5' ')-cyclo-(2,2':6',2' ')-terpyridinophane heptahydrobromide tetrahydrate (L.7HBr.4H2O) is described. L presents six protonation constants with values in the range 9.21-3.27 logarithmic units. L interacts with Cu2+ and Zn2+ forming in both cases, neutral, protonated, and hydroxylated mono- and binuclear complexes whose constants have been calculated by potentiometry in 0.15 M NaClO4 at 298.1 K. The crystal structures of the compounds [Cu(HL-carb)(H2O)](ClO4)3.2H2O (1) and [Cu2(H2L)(CO3)]2(ClO4)8.9H2O (2) have been solved by X-ray diffraction. In 1, the metal center presents square pyramidal geometry. The base of the pyramid is formed by the three nitrogen atoms of pyridine and one oxygen atom of a CO2 group which is forming a carbamate bond with the central nitrogen atom of the polyamine chain. The axial position is occupied by a water molecule. In 2, one Cu2+ is bound by the three pyridine nitrogens and the other one by the three central nitrogen atoms of the polyamine chain. The square planar coordination geometry is completed by a carbonate group taken up from the atmosphere that behaves as a bridging mu,mu'-ligand between the two centers. The pH-metric titrations on the ternary Cu2+-L-carbonate and Zn2+-L-carbonate systems show the extensive formation of adduct species which above pH 6 are formed quantitatively in solution. The stoichiometries of the main species formed in solution at pH = 6.8 agree with those found in the crystalline compounds. CO2 uptake by the Zn2+ and Cu2+ 1:1 complexes in aqueous solution has also been followed by recording the variations in the band at ca. 300 nm. The formation of the Zn2+ carbamate moiety has been evidenced by 13C NMR and ESI spectroscopy.     

Carleson Conditions in Bergman–Orlicz Spaces

We give characterizations of (forward and reverse) Carleson conditions in terms of inequalities that involve functions in Bergman–Orlicz spaces.     

A concave–convex problem with a variable operator

We study the following elliptic problem \(-A(u) = \lambda u^q\) with Dirichlet boundary conditions, where \(A(u) (x) = \Delta u (x) \chi _{D_1} (x)+ \Delta _p u(x) \chi _{D_2}(x)\) is the Laplacian in one part of the domain, \(D_1\), and the p-Laplacian (with \(p>2\)) in the rest of the domain, \(D_2 \). We show that this problem exhibits a concave–convex nature for \(1<q<p-1\). In fact, we prove that there exists a positive value \(\lambda ^*\) such that the problem has no positive solution for \(\lambda > \lambda ^*\) and a minimal positive solution for \(0<\lambda < \lambda ^*\). If in addition we assume that p is subcritical, that is, \(p<2N/(N-2)\) then there are at least two positive solutions for almost every \(0<\lambda < \lambda ^*\), the first one (that exists for all \(0<\lambda < \lambda ^*\)) is obtained minimizing a suitable functional and the second one (that is proven to exist for almost every \(0<\lambda < \lambda ^*\)) comes from an appropriate (and delicate) mountain pass argument.     

M?ssbauer study of contaminated soils by industrial activity in Paramonga city, Region Lima Provinces, Peru

In this work we characterize soils from the Paramonga city, Region Lima Provinces in Peru, which are contaminated by residual chemicals (Br, As and Sr) from sugar and paper industry in the city. Four samples were collected, labelled as S1, S2, S3 and S4 and analized by X-ray diffraction (XRD), energy-dispersive X-ray fluorescence (EDXRF) and M?ssbauer spectroscopy. For all the samples, the chemical analysis by EDXRF revealed the presence of Fe, Mn, Cu, Zn, K, Br, Sr. The XRD detected the presence of quartz as principal phase and copper sulfide and potassium magnesium as secondary phases. The M?ssbauer spectra at room temperature (RT) for all the samples exhibit sextets which reveal the presence of an iron oxide or hydroxide. The fitting M?ssbauer for both samples S1 and S4 have three doublets corresponding to iron in paramagnetic phases and a magnetic component of around 35.50?T corresponding to goethite, α-FeOOH. Sample S2 have two magnetic phases with internal fields of 37?T and 34.6?T which correspond to the goethite and other incorporated element in the structure. The sample S3 have three magnetic fields of H1?=?36.8?T, H2?=?33.6?T and H3?=?34.8?T which correspond to hydroxide iron, pyrrhotite and goethite respectively.