Structural preferences of single-walled silica nanostructures: nanospheres and chemically stable nanotubes

Structural preferences of single-walled and coordinatively saturated spherical and tubular nanostructures of silica have been determined by ab initio calculations. Two families of spherical (SiO2)n clusters derived from Platonic solids and Archimedean polyhedra are depicted, with n ranging from 4-120. The analogue of a truncated icosidodecahedron, Ih-symmetric Si120O240, is favored in energy, closely followed by the Ih-symmetric Si60O120-truncated icosahedron. The silica nanotubes derived from spherical clusters are capped by Si2O2 rings, whereas the tubular section consists of single oxygen bridges. Periodic studies performed with open-ended silica nanotubes and the alpha-quartz polymorph of silica, along with a comparisons to fullerenes and carbon nanotubes, suggest that tubes with diameters of approximately 1 nm should be chemically stable.     

Reactions of 2,4-hexadiyne-1,6-diol with [H2Os3(CO)9(PR3)] clusters. Cyclization of the diyne and reversible exchange of the phosphine ligands between different positions of the "Os3C3" framework

Reactions between unsaturated [H(2)Os(3)(CO)(9)(PR(3))] clusters (PR(3)= PPh(3), P(4-CF(3)-C(6)H(4))(3), PEt(3)) and 2,4-hexadiyne-1,6-diol have been studied. It was found that the diyne ligand easily reacts with all these complexes to give [HOs(3)(CO)8(PR3)-[mu3, eta1:eta3:eta1)-(CH(3)-C-C=CH-CH=C-O)]] complexes (V, VI and VII, respectively) containing the "Os3C3" pentagonal pyramid cluster framework. This structural pattern is formed through the diyne cyclization, dissociation of a CO ligand and eventual coordination of the cyclized organic moiety to the osmium triangle in the [mu3, eta1:eta3:eta1) manner. In the case of the PEt(3) substituted cluster the second hydride transfer onto the organic fragment occurs to afford the nonhydride [Os(3)(CO)(8)(PR3)[mu3), eta1:eta2:eta1)-(CH(3)-CH-C=CH-CH=C-O)]] cluster, VIII, containing distorted pentagonal pyramid framework with a broken Os-C bond. Heating V, VI of VII and in hexane solutions results in formation of the regioisomers (Va, VIa and VIIa) with the phosphine ligand located at adjacent osmium atoms across the Os-Os bond bridged by the coordinated organic fragment. The most probable mechanism of the isomerization includes reversible phosphine migration between these metal centres. Solid-state structure of V, Va, VI, VIIa and VIII have been established by single crystal X-ray diffraction. A general mechanistic scheme for the diyne ligand cyclization and cluster framework transformations is suggested and discussed.     

Canonical Finite Diagrams and Quantifier Elimination

We revisit the theory of amalgamation classes but we do not insist on staying within elementary classes.     

Theoretical studies of aluminoxane chains, rings, cages, and nanostructures

Alumina nanostructures and three families of aluminoxanes, linear, cyclic, and cagelike structures, have structures that resemble their isovalent electronic hydrocarbon analogues. Specific examples of each family are the counterparts of fullerene, allene, benzene, and cubane, respectively. The aluminoxanes and alumina nanostructures are related to each other; the latter can be regarded as a hydrogen- or alkyl-free form of aluminoxane. By exploiting this relationship, the relative stabilities of the three families of aluminoxanes, alumina nanostructures, and alumina crystal lattices have been estimated. According to ab initio calculations, aluminoxane cages, which take the form of a truncated octahedron and related polyhedra, are favored. The stability of the preferred cage, T-symmetric Al28O28H28, is practically equal to that of the alpha-alumina crystal lattice.     

On potential isomorphism and non-structure

We show in the paper that for any non-classifiable countable theory T there are non-isomorphic models and that can be forced to be isomorphic without adding subsets of small cardinality. By making suitable cardinal arithmetic assumptions we can often preserve stationary sets as well. We also study non-structure theorems relative to the Ehrenfeucht-Fraïssé game. The research of the first and second author was partially supported by Academy of Finland grant 40734 Mathematics Subject Classification (2000): 03C55, 03C45     

Influence of mesh deformation on the quality of large eddy simulations

The influence of mesh motion on the quality of large eddy simulation (LES) was studied in the present article. A three‐dimensional, turbulent pipe flow (Re_τ=360) was considered as a test case. Simulations with both stretching and static meshes were carried out in order to understand how mesh motion affects the turbulence statistics. The spatial filtering of static and moving mesh direct numerical simulation (DNS) data showed how an ideal LES would perform, while the comparison of DNS cases with static and moving meshes revealed that no significant numerical errors arise from the mesh motion when the simulation is fully resolved. The comparison of the filtered fields of the DNS with a moving mesh with the corresponding LES fields revealed different responses to mesh motion from different numerical approaches. A straightforward test was applied in order to verify that the moving mesh works consistently in LES: when the mesh is stretched in the streamwise direction, the moving mesh results should be in between the two extremal resolutions between which the mesh is stretched. Numerical investigations using four different LES approaches were carried out. In addition to the Smagorinsky model, three implicit LES approaches were used: linear interpolation (non‐dissipative), the Gamma limiter (dissipative), and the scale‐selective discretisation (slightly dissipative). The results indicate that while the Smagorinsky and the scale‐selective discretisation approaches produce results consistent with the resolution of the non‐static mesh, the implicit LES with linear interpolation or the Gamma scheme do not. Copyright © 2016 John Wiley & Sons, Ltd.     

On the stability of \varphi -uniform domains

We study two metrics, the quasihyperbolic metric and the distance ratio metric of a subdomain $G \subset {\mathbb R}^n$ . In the sequel, we investigate a class of domains, so called $\varphi $ -uniform domains, defined by the property that these two metrics are comparable with respect to a homeomorphism $\varphi $ from $[0,\infty )$ to itself. Finally, we discuss a number of stability properties of $\varphi $ -uniform domains. In particular, we show that the class of $\varphi $ -uniform domains is stable in the sense that removal of a geometric sequence of points from a $\varphi $ -uniform domain yields a $\varphi _1$ -uniform domain.     

Thermooxidative degradation of LDPE nanocomposites: Effect of surface treatments of fumed silica and boehmite alumina

Fumed silica (FS) and synthetic boehmite alumina (BA) nanofillers with and without surface treatments were incorporated in 5 wt. % in low density polyethylene (LDPE) through melt blending. FS was treated using hexadecyl silane, whereas BA using octyl silane and alkylbenzene sulfonic acid. The related nanocomposites were subjected to pyrolysis gas chromatography-mass spectrometry (Py-GC-MS) and thermogravimetric analysis (TGA) under isothermal and dynamic conditions, respectively. Py-GC-MS results proved that the thermal degradation mechanism did not change in the presence of the nanofillers. The latter suppressed the formation of high molecular weight hydrocarbons and affected the relative amounts of diene/alkene/alkane fragments for each hydrocarbon fraction.