Organometallic–inorganic charge transfer salts containing a cationic iron mixed sandwich and polyoxomolybdate anions: Syntheses,X-ray molecular structures and spectroscopic properties

Two new organometallic–inorganic charge transfer salts formulated as [(η⁵-Cp)Fe(η⁶-MeO-p-C₆H₄–NHNH₂)]₂[Mo₆O₁₉], 1, and [(η⁵-Cp)Fe(η⁶-MeO-p-C₆H₄–NHNH₂)]₄[β-Mo₈O₂₆], 2, were prepared through a metathesis reaction between the organometallic hydrazine precursor [(η⁵-Cp)Fe(η⁶-MeO-p-C₆H₄–NHNH₂)]⁺PF₆^? and either [n-Bu₄N]₂[Mo₆O₁₉] or [n-Bu₄N]₄[α-Mo₈O₂₆] in acetonitrile. In the second case, the [α-Mo₈O₂₆]^4? anion transforms into the [β-Mo₈O₂₆]^4? isomer. These organometallic–inorganic hybrids were characterized by spectroscopic techniques (IR, ¹H NMR and UV–vis). In addition, the UV–vis diffuse reflectance spectra of 1 and 2 in solid state exhibit a band at λ_max = 475 and 470 nm, respectively, not observed in DMSO solution, which have been attributed to a charge transfer transition. On the other hand, the solid state structure of 2, solved by X-ray diffraction analysis shows the formation of hydrogen bonds between the protons of the –NHNH₂ and C–H groups with the terminal oxo groups of the β-octamolybdate anions [β-Mo₈O₂₆]^4?. Finally, hybrid 3, formulated as [(η⁵-Cp)Fe(η⁶-C₆H₅OMe)]₄[β-Mo₈O₂₆] was prepared in EtOH under solvothermal conditions. The single crystal X-ray structure shows the elimination of the –NHNH₂ group from the organometallic mixed sandwich reducing its associative ability toward the oxo groups of the counterion only to the electrostatic interactions and to the very weak CH?O hydrogen bonds.     

Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction–diffusion problem

A semilinear reaction–diffusion two-point boundary value problem, whose second-order derivative is multiplied by a small positive parameter e²{\varepsilon^2} , is considered. It can have multiple solutions. The numerical computation of solutions having interior transition layers is analysed. It is demonstrated that the accurate computation of such solutions is exceptionally difficult. To address this difficulty, we propose an artificial-diffusion stabilization. For both standard and stabilised finite difference methods on suitable Shishkin meshes, we prove existence and investigate the accuracy of computed solutions by constructing discrete sub- and super-solutions. Convergence results are deduced that depend on the relative sizes of e{\varepsilon} and N, where N is the number of mesh intervals. Numerical experiments are given in support of these theoretical results. Practical issues in using Newton’s method to compute a discrete solution are discussed.     

Attracting cycles for the relaxed Newton’s method

We study the relaxed Newton’s method applied to polynomials. In particular, we give a technique such that for any n≥2, we may construct a polynomial so that when the method is applied to a polynomial, the resulting rational function has an attracting cycle of period n. We show that when we use the method to extract radicals, the set consisting of the points at which the method fails to converge to the roots of the polynomial p(z)=z^m−c (this set includes the Julia set) has zero Lebesgue measure. Consequently, iterate sequences under the relaxed Newton’s method converge to the roots of the preceding polynomial with probability one.     

Electron-deficient and polycenter bonds in the high-pressure γ-B28 phase of boron

The peculiar bonding situation in γ boron is characterized on the basis of an experimental electron-density distribution which is obtained by multipole refinement against low-temperature single-crystal x-ray diffraction data. A topological analysis of the electron-density distribution reveals one-electron-two-center bonds connecting neighboring icosahedral B(12) clusters. A unique polar-covalent two-electron-three-center bond between a pair of atoms of an icosahedral cluster and one atom of the interstitial B(12) dumbbell explains the observed charge separation in this high-pressure high-temperature polymorph of boron.     

A novel method for the synthesis of polystyrene-graft-silica particles using random copolymers based on styrene and triethoxyvinylsilane

In the present research, random copolymers based on triethoxyvinylsilane (TEVS) and styrene (St) are synthesized and structurally characterized. According to the reactivity ratios of the monomers determined by infrared analysis; St tends to form blocks whilst TEVS is expected to be incorporated as isolated units. A sample of poly(styrene-co-triethoxyvinylsilane) synthesized at low conversion using a monomer feeding ratio St:TEVS of 2:3 was used as macrosilane in the synthesis of polystyrene-g-silica particles. The grafting reaction was confirmed by infrared spectroscopy, thermogravimetric analysis and by the evaluation of the morphological characteristics of the hybrid particles.     

Photoinduced protonation and mechanical motion in the cyclodextrin cavity: Synthesis,structure and spectral properties of 4-(2-napthyl)pyridine and their pseudorotaxane complexes

The spontaneous and photoinduced protonation of 4-(2-naphthyl)pyridine (1) in solutions and in complexes with β-cyclodextrin (β-CD) and 2-hydroxypropyl-β-cyclodextrin (HP-β-CD) were studied by absorption and fluorescence spectroscopy. The structure and stability of the complexes (log K = 1.5–2.3) of 1, its protonated form 2, and quaternized derivative, 1-methyl-4-(2-naphthyl)pyridinium perchlorate (3), with β-CD and HP-β-CD were studied by ¹H NMR. It was shown that irrespective of the solution pH, compound 1 resides in the cyclodextrin cavity. HP-β-CD better binds the neutral form of 1 than β-CD, while naphthylpyridinium salts have approximately equal binding affinity to both cyclodextrins. The structures of salt 3 and pseudorotaxane complex 1@β-CD were determined by X-ray diffraction analysis. According to spectral data, pK_a of 1 in water is 5.12, which promotes protonation of nitrogen both in the ground state and in the excited state. As a consequence, the fluorescence spectrum exhibits only the protonated form with a lifetime of 15 ns. The addition of HP-β-CD to a solution of 1 results in inclusion complex 1@HP-β-CD; simultaneously pK_a of 1 decreases to 4.62 and non-protonated form fluorescence (NFF) of 1 with a lifetime of 1.25 ns appears. Thus, the residence of 1 in the HP-β-CD cavity hampers its protonation in the excited state. From comparison of the initial regions of fluorescence of 1 in solution and in the HP-β-CD complex after pulse excitation, a mechanism for appearance of short-lived NFF of 1 was proposed. Quantum chemical simulation of the protonation and complexation of 1 in the presence of water was performed. On the basis of results, reversible photoinduced mechanical motion of 1 in the HP-β-CD cavity was suggested.     

The Universal Multiplicative Envelope of the Free Malcev Superalgebra on One Odd Generator

A base of the universal multiplicative envelope for the free Malcev superalgebra on one odd generator is constructed. Some corollaries for central skew-symmetric elements in free Malcev and free alternative algebras are obtained. In particular, the Malcev Grassmann algebra is constructed.     

Harmonic vibration of prismatic shells in zero approximation of Vekua's hierarchical models

In this article elastic cusped symmetric prismatic shells (i.e., plates of variable thickness with cusped edges) in the zero approximation of I.Vekua's hierarchical models is considered. The well-posedness of the boundary value problems (BVPs) under the reasonable boundary conditions at the cusped edge and given displacements at the non-cusped edge is studied in the case of harmonic vibration. The approach works also for non-symmetric prismatic shells word for word. The classical and weak setting of the BVPs in the case of the zero approximation of hierarchical models is considered. Appropriate weighted functional spaces are introduced. Uniqueness and existence results for the variational problem are proved. The structure of the constructed weighted space is described and its connection with weighted Sobolev spaces is established. Moreover, some sufficient conditions for a linear functional arising in the right-hand side of the variational equation to be bounded are given.     

Exciton–polariton condensation

We review, aiming at an audience of final year undergraduates, the phenomena observed in, and properties of, microcavity exciton–polariton condensates. These are condensates of mixed light and matter, consisting of superpositions of photons in semiconductor microcavities and excitons in quantum wells. Because of the imperfect confinement of the photon component, exciton–polaritons have a finite lifetime, and have to be continuously re-populated. Therefore, exciton–polariton condensates lie somewhere between equilibrium Bose–Einstein condensates and lasers. We review in particular the evidence for condensation, the coherence properties studied experimentally, and the wide variety of spatial structures either observed or predicted to exist in exciton–polariton condensates, including quantised vortices and other coherent structures. We also discuss the question of superfluidity in a non-equilibrium system, reviewing both the experimental attempts to investigate superfluidity to date, and the theoretical suggestions of how it may be further elucidated.     

Equilibrium Problems for Infinite Dimensional Vector Potentials with External Fields

We consider a minimal energy problem with an external field over noncompact classes of infinite dimensional vector measures $(\mu^i)_{i\in I}$ on a locally compact space. The components μ ⁱ are positive measures normalized by $\int g_i\,d\mu^i=a_i$ (where a _i and g _i are given) and supported by closed sets A _i with the sign +?1 or ??1 prescribed such that A _i ?∩?A _j ?=?? whenever ${\rm sign}\,A_i\ne{\rm sign}\,A_j$ , and the law of interaction between μ ⁱ , i?∈?I, is determined by the matrix $\bigl({\rm sign}\,A_i\,{\rm sign}\,A_j\bigr)_{i,j\in I}$ . For positive definite kernels satisfying Fuglede’s condition of consistency, sufficient conditions for the existence of equilibrium measures are established and properties of their uniqueness, vague compactness, and strong and vague continuity are studied. Examples illustrating the sharpness of the sufficient conditions are provided. We also obtain variational inequalities for the weighted equilibrium potentials, single out their characteristic properties, and analyze continuity of the equilibrium constants. The results hold, e.g., for classical kernels in $\mathbb R^n$ , $n\geqslant 2$ , which is important in applications.