Halogen‐bonded adduct of 1,2‐dibromo‐1,1,2,2‐tetrafluoroethane and 1,4‐diazabicyclo[2.2.2]octane

Halogen bonding is an intermolecular interaction capable of being used to direct extended structures. Typical halogen‐bonding systems involve a noncovalent interaction between a Lewis base, such as an amine, as an acceptor and a halogen atom of a halofluorocarbon as a donor. Vapour‐phase diffusion of 1,4‐diazabicyclo[2.2.2]octane (DABCO) with 1,2‐dibromotetrafluoroethane results in crystals of the 1:1 adduct, C₂Br₂F₄·C₆H₁₂N₂, which crystallizes as an infinite one‐dimensional polymeric structure linked by intermolecular N...Br halogen bonds [2.829 (3) Å], which are 0.57 Å shorter than the sum of the van der Waals radii.     

The structures of the isomorphous potassium and rubidium salts of 4‐nitrobenzoic acid and an overview of the metal complex stereochemistries of the alkali metal salt series with this ligand

4‐Nitrobenzoic acid (PNBA) has proved to be a useful ligand for the preparation of metal complexes but the known structures of the alkali metal salts of PNBA do not include the rubidium salt. The structures of the isomorphous potassium and rubidium polymeric coordination complexes with PNBA, namely poly[μ₂‐aqua‐aqua‐μ₃‐(4‐nitrobenzoato)‐potassium], [K(C₇H₄N₂O₂)(H₂O)₂]_n, (I), and poly[μ₃‐aqua‐aqua‐μ₅‐(4‐nitrobenzoato)‐rubidium], [Rb(C₇H₄N₂O₂)(H₂O)₂]_n, (II), have been determined. In (I), the very distorted KO₆ coordination sphere about the K⁺ centres in the repeat unit comprise two bridging nitro O‐atom donors, a single bridging carboxylate O‐atom donor and two water molecules, one of which is bridging. In Rb complex (II), the same basic MO₆ coordination is found in the repeat unit, but it is expanded to RbO₉ through a slight increase in the accepted Rb—O bond‐length range and includes an additional Rb—O_carboxylate bond, completing a bidentate O,O′‐chelate interaction, and additional bridging Rb—O_nitro and Rb—O_water bonds. The comparative K—O and Rb—O bond‐length ranges are 2.7352 (14)–3.0051 (14) and 2.884 (2)–3.182 (2) Å, respectively. The structure of (II) is also isomorphous, as well as isostructural, with the known structure of the nine‐coordinate caesium 4‐nitrobenzoate analogue, (III), in which the Cs—O bond‐length range is 3.047 (4)–3.338 (4) Å. In all three complexes, common basic polymeric extensions are found, including two different centrosymmetric bridging interactions through both water and nitro groups, as well as extensions along c through the para‐related carboxylate group, giving a two‐dimensional structure in (I). In (II) and (III), three‐dimensional structures are generated through additional bridges involving the nitro and water O atoms. In all three structures, the two water molecules are involved in similar intra‐polymer O—H...O hydrogen‐bonding interactions to both carboxylate and water O‐atom acceptors. A comparison of the varied coordination behaviour of the full set of Li–Cs salts with 4‐nitrobenzoic acid is also made.     

New hydrophobic L‐amino acid salts: maleates of L‐leucine,L‐isoleucine and L‐norvaline

Crystals of maleates of three amino acids with hydrophobic side chains [L‐leucenium hydrogen maleate, C₆H₁₄NO₂⁺·C₄H₃O₄⁻, (I), L‐isoleucenium hydrogen maleate hemihydrate, C₆H₁₄NO₂⁺·C₄H₃O₄⁻·0.5H₂O, (II), and L‐norvalinium hydrogen maleate–L‐norvaline (1/1), C₅H₁₁NO₂⁺·C₄H₃O₄⁻·C₅H₁₂NO₂, (III)], were obtained. The new structures contain C₂²(12) chains, or variants thereof, that are a common feature in the crystal structures of amino acid maleates. The L‐leucenium salt is remarkable due to a large number of symmetrically non‐equivalent units (Z′ = 3). The L‐isoleucenium salt is a hydrate despite the fact that L‐isoleucine is a nonpolar hydrophobic amino acid (previously known amino acid maleates formed hydrates only with lysine and histidine, which are polar and hydrophilic). The L‐norvalinium salt provides the first example where the dimeric cation L‐Nva...L‐NvaH⁺ was observed. All three compounds have layered noncentrosymmetric structures. Preliminary tests have shown the presence of the second harmonic generation (SGH) effect for all three compounds.     

Malliavin calculus for regularity structures: The case of gPAM

Malliavin calculus is implemented in the context of Hairer (2014) [16]. This involves some constructions of independent interest, notably an extension of the structure which accommodates a robust, and purely deterministic, translation operator, in $L^2$-directions, between “models”. In the concrete context of the generalized parabolic Anderson model in 2D – one of the singular SPDEs discussed in the afore-mentioned article – we establish existence of a density at positive times.     

A coradiant based scalarization to characterize approximate solutions of vector optimization problems with variable ordering structures

This paper investigates some properties of approximate efficiency in variable ordering structures where the variable ordering structure is given by a special set valued map. We characterize $\epsilon$-minimal and $\epsilon$- nondominated elements as approximate solutions of a multiobjective optimization problem with a variable ordering structure and give necessary and sufficient conditions for these solutions, via scalarization.     

Optimal control problem in a domain with branched structure and homogenization

We consider a linear parabolic problem in a thick junction domain which is the union of a fixed domain and a collection of periodic branched trees of height of order 1 and small width connected on a part of the boundary. We consider a three‐branched structure, but the analysis can be extended to n‐branched structures. We use unfolding operator to study the asymptotic behavior of the solution of the problem. In the limit problem, we get a multi‐sheeted function in which each sheet is the limit of restriction of the solution to various branches of the domain. Homogenization of an optimal control problem posed on the above setting is also investigated. One of the novelty of the paper is the characterization of the optimal control via the appropriately defined unfolding operators. Finally, we obtain the limit of the optimal control problem. Copyright © 2016 John Wiley & Sons, Ltd.     

Controlled Synthesis of Hollow PbS‐TiO2 Hybrid Structures through an Ion Adsorption–Heating Process and their Photocatalytic Activity

Hollow hybrid nanostructures have received significant attention because of their unique structural features. This study reports a facile ion adsorption–heating method to fabricate hollow PbS‐TiO₂ hybrid particles. In this method, the TiO₂ spheres used as a substrate material to grow PbS are aggregates of many small amorphous TiO₂ particles, and each small particle is covered with thioglycolic acid ligands through Ti⁴⁺–carboxyl coordination. When Pb²⁺ ions are added to a colloidal solution of these TiO₂ spheres, these ions are adsorbed by sulfhydryl (‐SH) groups to form metal thiolates, and the C−S bond is dissociated by heating to release S²⁻. The S²⁻ ions react with Pb²⁺ ions to form PbS without additive sulfur sources. Additionally, the amorphous TiO₂ spheres are transformed into the anatase phase during the heating process. As a result, the crystallization of TiO₂ spheres along with the formation of PbS is simultaneously carried out by heating. During the heating process, owing to the Kirkendall effect of S²⁻ diffusion and the Ostwald ripening effect of the crystallization of amorphous TiO₂ spheres, PbS‐TiO₂ hollow hybrid structures can be obtained. The XRD and XPS characterizations proved the formation of anatase TiO₂ and PbS. The TEM characterization confirmed the formation of hollow structures in the PbS‐TiO₂ hybrid sample. The photocatalytic activity of the hollow PbS‐TiO₂ hybrid spheres have been investigated for the degradation of Cr⁶⁺ under visible light. The results show that hollow PbS‐TiO₂ hybrid spheres exhibited the highest photocatalytic activity, in which almost all the Cr⁶⁺ was degraded after 140 min.     

Nitrogen‐Doped Mesoporous Carbon‐Encapsulated MoO2 Nanobelts as a High‐Capacity and Stable Host for Lithium‐Ion Storage

N‐doped mesoporous carbon‐capped MoO₂ nanobelts (designated as MoO₂@NC) were synthesized and applied to lithium‐ion storage. Owing to the stable core–shell structural framework and conductive mesoporous carbon matrix, the as‐prepared MoO₂@NC shows a high specific capacity of around 700 mA h g⁻¹ at a current of 0.5 A g⁻¹, excellent cycling stability up to 100 cycles, and superior rate performance. The N‐doped mesoporous carbon can greatly improve the conductivity and provide uninhibited conducting pathways for fast charge transfer and transport. Moreover, the core–shell structure improved the structural integrity, leading to a high stability during the cycling process. All of these merits make the MoO₂@NC to be a suitable and promising material for lithium ion battery.     

Magneto‐Adaptive Surfactants Showing Anti‐Curie Behavior and Tunable Surface Tension as Porogens for Mesoporous Particles with 12‐Fold Symmetry

Gaining external control over self‐organization is of vital importance for future smart materials. Surfactants are extremely valuable for the synthesis of diverse nanomaterials. Their self‐assembly is dictated by microphase separation, the hydrophobic effect, and head‐group repulsion. It is desirable to supplement surfactants with an added mode of long‐range and directional interaction. Magnetic forces are ideal, as they are not shielded in water. We report on surfactants with heads containing tightly bound transition‐metal centers. The magnetic moment of the head was varied systematically while keeping shape and charge constant. Changes in the magnetic moment of the head led to notable differences in surface tension, aggregate size, and contact angle, which could also be altered by an external magnetic field. The most astonishing result was that the use of magnetic surfactants as structure‐directing agents enabled the formation of porous solids with 12‐fold rotational symmetry.     

Multi‐shelled Hollow Metal–Organic Frameworks

Hollow metal–organic frameworks (MOFs) are promising materials with sophisticated structures, such as multiple shells, that cannot only enhance the properties of MOFs but also endow them with new functions. Herein, we show a rational strategy to fabricate multi‐shelled hollow chromium (III) terephthalate MOFs (MIL‐101) with single‐crystalline shells through step‐by‐step crystal growth and subsequent etching processes. This strategy relies on the creation of inhomogeneous MOF crystals in which the outer layer is chemically more robust than the inner layer and can be selectively etched by acetic acid. The regulation of MOF nucleation and crystallization allows the tailoring of the cavity size and shell thickness of each layer. The resultant multi‐shelled hollow MIL‐101 crystals show significantly enhanced catalytic activity during styrene oxidation. The insight gained from this systematic study will aid in the rational design and synthesis of other multi‐shelled hollow structures and the further expansion of their applications.